Regarding Scientifically Based Research Studies   The purpose of the Content Network's review tables is to organize the review teams' information regarding science research studies. The tables are works in progress; editing is in progress to streamline the data presention, and review teams are analyzing additional studies for inclusion. The table includes links to the teams' original reviews.

NCTM Mathematics Standards   The mathematics research reviews are organized around the mathematics standards from the National Council of Teachers of Mathematics (NCTM). Column 5 of the table identifies the relevant standards and topics applicable to each research review.

Reviewers' Ratings of Research   As explained in the Mathematics Summary page, selection of research for this database has emphasized studies meeting the definition of quality research as outlined in the federal No Child Left Behind legislation. Remember that ratings in column 2 apply to the research design, not to the quality of the intervention studied or how powerful the method, strategy, or approach is in influencing overall student achievement. Rating levels, as illustrated by the Gold Standard pyramid, are further defined on the Definitions page. The review tables below are arranged by column 2, Design Rating, with highest ratings first.

Grades 6 to 8 – Overview of Research

Based on Individual Studies Reviewed by the Iowa Content Network and Prominent Published Reviews of Collections of Research

The traditional U. S. middle grades mathematics curriculum has been limited in depth and breadth and the weakest area in both international and domestic comparisons with respect to mathematics proficiency is middle school students’ performance in geometry (NCTM, 2000). In order to strengthen students’ backgrounds and increase their options in life and career opportunities, it is recommended in the Principles and Standards for School Mathematics that a significant amount of both algebra and geometry need to be integrated in the middle grades curriculum for all students (NCTM, 2000).

A number of studies evaluated the content strands in the grade 6-8 curriculum (algebra, data analysis and probability, geometry, measurement, and number and operations); these studies compared NCTM standards-based to traditional curriculum. In all cases the test scores of students in the standards-based curriculum was comparable or exceeded test scores of students studying the traditional curriculum. (See NCTM Standards-based Summary).

Three studies focused on ability grouping. When comparing homogeneous to heterogeneous groupings, low ability or average students were more likely to make gains in heterogeneous classes. Performances of high ability students were not effected. (Hunt 1996; Linchevski et al. 1998; Leonard [date]). These results are consistent with summaries on the effects of ability grouping including data from international studies that support the assumption that all students can learn mathematics and work within heterogeneously grouped classes (Kilpatrick 2001).

Greater student gains were the result of teaching strategies that included presenting problem solving situations in context using videos, organizing instruction around big ideas, teaching explicit strategies, guiding through scaffolding, and including review that requires students to apply their knowledge (Arthurs et al.1998; Bottge, [date], Grossen 2000). Other factors contributing to student gains included teachers who had acquired a mathematics major; who participated in professional development in developing higher-order thinking strategies, and who implemented teaching strategies such as hands-on learning and higher-order thinking skills (Wenglisky 2002).

The number of studies that involved only algebra, data analysis and probability, geometry, and measurement were limited to nonexistent (although several studies addressed all strands together). There were a larger number of studies that involved evaluation of number and operations.

Algebra
Only one study involved only algebra; no differences in achievement were found between the Saxon Algebra text and conventional textbooks on linear combinations; the control group (conventional textbooks) performed significantly better on one subscale measuring definitions and theory. The experimental group had a significantly more positive attitude in every area except for study habits (Johnson et al. 1987).

Geometry
In addition to the studies reported above, one study (Carroll 1998) reported a growth in students’ geometric reasoning by evaluating van Hiele levels as a result of implementing Everyday Math in contrast to a traditional curriculum. The van Hieles’ theory of levels of geometric reasoning provides a framework for curriculum and teaching and most traditional textbooks do not provide a curriculum that requires students to develop higher levels of geometric reasoning across the grades (Clements 2003).

Number and Operations
Mental computation is not only a practical skill but it also helps students develop number and operation sense; in recent decades this topic has not been included in the U.S. traditional curriculum (Kilpatrick 2001). Mental computation skills were enhanced for groups using the standards-based curriculum, Everyday Math (Carroll 1996). Another study found that mental computation skills improved when representations were presented through a computer environment (Ainsworth et al. 2002).

Research on rational numbers relates student difficulties to weak conceptual understandings of rational numbers and a lack of connecting fractions and decimals. Approaches such as standards-based curriculum that build on students’ informal understandings and incorporate representations and contexts offer more promise than rule-based programs (Kilpatrick 2001). Student achievement on fractions was enhanced when teachers were committed to implementing a reform curriculum in contrast to teachers who had no interest (Stipek et al. 1998). See Summaries on Fractions and Problem-based Instruction.

Another study that focused on student understanding involved proportional reasoning. Students made greater gains in proportional reasoning when studying curriculum where they developed their own concepts and procedures (Ben-Chaim et al. 1998).

With respect to the role of calculators and instruction, the factor in greater achievement in solving problems was learning problem-solving strategies rather than calculator use. Additionally, students who used calculators had more positive attitudes towards math and their computation scores were not significantly different (Szetela et al. 1998).

The research supporting this overview falls into two categories – prominent published reviews of collections of research, and individual studies. These two categories are presented below.

1. Prominent Published Reviews of Collections of Research

These nationally-recognized reviews of substantial bodies of research have been written by experts in the field and reviewed by peers.

• Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell (Eds.) (2001) Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy Press.
• Clements, Douglas H. (2003) “Teaching and Learning Geometry.” In Jeremy Kilpatrick, W. Gary Martin and Deborah Schifter (Eds.) A Research Companion to Principles and Standards for School Mathematics (179-192). Reston, VA: NCTM.
• National Council of Teachers of Mathematics (2000) Principles and Standards for School Mathematics. Reston, VA: NCTM.

2. Individual Studies (Examine the tables of summaries on this page.)

Study:
D. Johnson and B. Smith.

Title: An Evaluation of Saxon's Algebra Text.

Read full review

math_9-12_13

New
Review

4

Strategy: The Saxon Algebra textbook
Subjects: 276 students in twelve sections of Algebra I, (a Saxon, treatment group, 136 students) and (a traditional text, control group, 140 students). Six teachers who were involved in the study each taught one section using the Saxon textbook and one section using a traditional textbook
Results: Results indicate no differences in the treatment or control groups in achievement measures, but a significantly more positive attitude toward mathematics in the experimental group.

Description: The Saxon Algebra I textbook is designed to differ from a traditional textbook in three

areas: (1) the text is organized into lessons to avoid the uneven or abrupt flow of material that can result when topics are organized into chapters, (2) Saxon uses an extensive conversational presentation of the material rather than charts and diagrams, and (3) only a small number of the exercises in each lesson are on the new material, the majority are practice and drill of previously presented concepts and skills.

NCTM Math Standard:
• Algebra

Math Topics: Polynomials, exponents, rational expressions, definitions, theory, linear equations and inequalities, systems of equations, coordinates, radicals, quadratics, and arithmetic word problems.

8th to 10th Grades

Study:
Ridgway, Zawojewski, Hoover & Lambdin.

Student attainment in the Connected Mathematics curriculum.

Read full review

math_6-8_5

Description: A problem-oriented curriculum which provides a broad range of mathematical topics with a focus on concept development and student discussion prior to written work.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

6th to 8th Grades

Study:
Riordan & Noyce.

The impact of two standards-based mathematics curricula on student achievement in Massachusetts ["standards-based" instruction is identified as Connected Math (cmp) and/or Everyday Math (em)].

Read full review

math_6-8_6

Strategy: Connected Math (CMP) and Everyday Math (EM)
Subjects: Standards-Based" Instruction Traditional Instruction Matched
EM1 n=48 schools 4+ years using EM n=51 schools
EM2 n=19 2-3 years using EM n=27
CMP1 n=1 4+ years using CMP n=4
CMP2 n=20 2-3 years using CMP n=30
Results: Massachusetts’ students in the standard-based programs performed significantly better on the 1999 statewide mathematics tests than did Massachusetts’ students in traditional programs attending matched comparison schools.
Effect Size: Late implementation of EM= +0.15
Early implementation of EM and CMP= +0.34

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

4th & 8th Grades

Study:
Hunt.

The effect on mathematics achievement and attitude of homogeneous and heterogeneous grouping of gifted sixth-grade students.

Read full review

math_6-8_11

Strategy: Homogeneous vs. heterogeneous grouping.
Subjects: 208 sixth grade students at a middle school in a suburban Southwestern city.
Racial background of 6th gr. Teams - 46% African American, 28% Hispanic American, 16% White, 10% Asian American
Racial background of gifted group - 29% African American, 29% White, 26% Asian American, 17% Hispanic American
Results:No significant differences in math achievement were found regardless of ability group. There were significantly more activities completed by the gifted and average-ability students when grouped homogeneously. The low-ability students had significantly more activities completed when grouped heterogeneously.

Description: Students were randomly selected for placement in 5 classes of heterogeneously grouped students and 5 classes of homogeneously grouped students. Groups used self-paced mathematics learning guides, three weeks in length involving three levels of activities -- regular, extension, and exploratory.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Computation, problem solving

6th Grade

Study:
Linchevski & Kutscher.

Tell me with whom you're learning, and I'll tell you how much you've learned: Mixed-ability versus same-ability grouping in mathematics.

Read full review

math_6-8_13

Strategy: TAP (Together and APart) Project.
Subjects: 1730 seventh grade students in the 12 Israeli junior high schools that participated in the TAP project
389 8th grade students in 4 of the 12 Israeli junior high schools
Results: The gap between better and weaker students learning together in mixed-ability settings for a certain period of time was not different from the gap that would be expected on the basis of initial differences between the two groups. Placement in heterogeneous classes does significantly increase intermediate and low-ability students’ achievement while not significantly impacting the high-ability student.

Description: TAP’s main principle is to keep students together as one learning unit while responding to the different needs of the students. Teaching was conducted within four major settings: (1) students working in a whole-class setting, (2) students working in small mixed-ability groups, (3) students working in small homogeneous groups, and (4) students working in large homogeneous groups.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Seventh and eighth grade algebra, problem solving, and geometry.

7th & 8th Grades

Study:
Arthurs, DeFranco, and Young.

An examination of the impact of tuning students' attention to information in a mathematics problem on their problem-solving performance.

Read full review

math_6-8_23

Description: Two 6th grade classrooms were shown the videodisc "Rescue at Boone's Meadow." The experimental group was "tuned" to the information in the video by receiving a presentation on bald eagles prior to problem solving. The control group was provided information on inductive reasoning via the software package "The King's Rule." The intervention lasted nine days. Students' problem-solving skills were evaluated.

NCTM math standards:
• Algebra
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Problem solving, data gathering

6th Grades

Study:
Reys, Reys, Lapan and Holliday.

Assessing the impact of standards-based middle grades mathematics curriculum materials on student achievement.

Read full review

math_6-8_24

Strategy: Standards-based middle grades mathematics curriculum. Subjects: Two thousand eighth grade students from six school districts. Students were matched for prior mathematics achievement, SES (free and reduced lunch), the same building configuration, and geographic location.
Results: After two years in a standards-based curriculum, the treatment group equaled or exceeded the comparison group. Students in each of the three districts using standards-based curriculum scored significantly higher in two content strands (algebra, and data analysis and probability).

Description: Eighth grade students used standards-based mathematics curriculum materials (specifically MathThematics and Connected Mathematics) for at least two years.

NCTM Math Standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Number &   Operations

Math Topic(s):
All topics, including discrete mathematics.

6th to 8th grades

Study:
Romberg & Shafer.

Mathematics in context - Preliminary evidence about student outcomes.

Read full review

math_6-8_2

Strategy: Mathematics in Context (MiC)
Subjects: 17 schools from 2 suburban and 2 urban districts
54 teachers in grades 5-8, 80% have used MiC curriculum
2225 students in the program 1,2, or 3 years
Results: The degree of implementation of the Mathematics in Context curriculum varied throughout the four districts. According to data, students in the MiC program outperformed students in the conventional program on Number, Geometry, Algebra, and Statistics/Probability. However, the percentages of correct responses varied among all groups.

Description: Mathematics in Context is a standards-based curriculum for grades 5-8 designed to help students progress from informal to formal mathematical reasoning in number, geometry (and measurement), algebra, statistics, and probability. The curriculum focuses on placing students in realistic situations that they must resolve. During their resolution process, students progress from informal notions toward formal mathematical reasoning and representations to model and solve non-routine problems. Throughout the curriculum, students develop conceptual knowledge first and re-visit it as necessary.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

5th to 8th Grades

Study:
Billstein & Williamson.

Middle grades MATH thematics: The STEM project.

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math_6-8_3

Strategy: MATH Thematics - STEM Project
Subjects: Study 1 treatment group: 115 midwestern MATH Thematics 6th graders in middle-class suburban school.
Study 1 control group: 46 non-MATH Thematics students from another school district.
Study 2: longitudinal; rural western school; 2 groups of 9th graders tested at different times (1993 & 1997 ITEDS). 1993 9th graders had not completed the MATH Thematics curriculum, whereas1997 9th graders had completed MATH Thematics curriculum for grades 6 - 8.
Study 3: Suburban 6th & 8th graders at a MATH Thematics field-test site had used MATH Thematics at the seventh grade level for 4 years.
Results: Study 1: no significant difference
Study 2: 1993 Non MATH-Thematic students ranked 44th percentile on ITEDs; 1997 MATH Thematic students ranked 89th percentile on ITEDs
Study 3: Treatment students scored 12% higher on ITBS
Study 4: After statistical corrections, 14 of 42 CRT objectives favored MATH-Thematic students, 1 of 42 CRT objectives favored control students

Description: A Standards-based curriculum for grades 6, 7, and 8 characterized as problem-oriented with a focus on concept development and student discussion prior to written work. Students are expected to actively do mathematics by investigating, discovering, and applying mathematics to new situations. Students must be able to communicate their ideas effectively through cooperative groups and whole-class discussions.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

6th to 8th Grades

Study:
Bottge.

Effects of contextualized math instruction on problem solving of average and below-average achieving students.

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math_6-8_10

Strategy: Contextualized mathematics instruction on problem solving
Subjects: 66 eighth grade students from a rural school district in the upper Midwest (37 boys and 29 girls; 17 in a remedial class and 49 in pre-algebra classes; 7 were in special education).
Results: The experimental groups outperformed the control groups on contextualized problems and transfer tasks but not on word problem tests or computational tests.

Description: Students in the experimental groups (contextualized group) were taught problem solving strategies over two weeks using two videos that were intended to teach problem solving. The videos presented problems that were not as overtly stated as traditional problem solving. To solve the problems, students had to first discover the pertinent information, come up with a hypothesis, and assess their hypothesis.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Addition and subtraction of rational numbers in fraction and decimal form.

8th Grade

Study:
Leonard.

How group composition influenced the achievement of sixth-grade mathematics students.

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math_6-8_12

Strategy: Comparison of heterogeneous vs. homogeneous grouping.
Subjects: 177 6th grade students, approx. 10% of total school enrollment on free or reduced lunch
suburban elementary school in Maryland
Results: Low achieving and middle achieving students scored significantly better in heterogeneous grouping than homogeneous. High-achieving students’ scores were not significantly different. Follow-up interviews indicate that group cohesiveness may impact achievement more than ability grouping.

Description: Sixth-grade students were grouped heterogeneously and homogeneously to determine how groups differ in mathematics achievement and what influence group composition has on student interactions in heterogeneous and homogeneous small groups. Students were assigned to one of three homerooms. The research was conducted for two consecutive academic years. The first year students were grouped heterogeneously by ability. The second year students were grouped homogeneously.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Number concepts, whole numbers, mixed numbers and fractions, decimals, measurement, data, and problem solving

6th Grade

Study:
Threadgill-Sowder & Julips.

Manipulatives versus symbolic approaches to teaching logical connectives in junior high school: An aptitude x treatment interaction study.

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math_6-8_14

Strategy: Manipulative versus symbolic approaches to teaching logical connectives
Subjects: One-hundred forty-seven seventh-grade students from two junior high schools in Calgary, Alberta, Canada participated in the study. The students included the total seventh-grade population from the two schools, with the exception of absent students or those with severe behavioral problems. The schools were located in Canadian middle-class communities.
Results: Results indicated no significant difference between the treatment groups (use of manipulative materials or symbolic instruction) in the mean scores on the achievement post-test or the test that measured ability to transfer knowledge to more general logical connective statements. However, students with very low scores on the Mathematics Concepts and Mathematics Problem Solving Tests received higher scores on the achievement post-test when instructed with manipulative materials and students with high scores on the Mathematics Concepts and Mathematics Problem Solving Tests found the symbolic instruction more beneficial.

Description: The treatment students were taught logical connectives over the course of three class periods; instruction was either a manipulative or symbolic approach. Control students received no instruction on this topic.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Logical connectives (including conjunction, disjunction, and negation).

7th Grade

Study:
Wenglisky.

How schools matter: The link between teacher classroom practices and student academic performance.

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math_6-8_15

Strategy: This study links teacher classroom practices and achievement on the NAEP eighth grade mathematics assessment.
Subjects: 7,146 8th grade students who took the 1996 NAEP Mathematics Assessment
Results: The study found a positive relationship between student achievement on NAEP and teachers with a major in mathematics, professional development in higher-order thinking skills and diversity, using hands-on learning and higher-order thinking skills in the classroom. The influence of these teacher qualities was greater than the influence of SES as a student characteristic on students taking the NAEP assessment.

Description: Using various classroom practices such as writing about math, solving real world problems, having students work with objects, having students talk about math, working in small groups, etc.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

8th Grade

Study:
Grossen

The BIG Accommodation Model: The direct instruction model for secondary schools.

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math_6-8_25

Strategy: BIG Accommodation Model
Subjects: 518 students in the seventh and eighth grades from "the lowest performing middle school in one of the lowest performing districts in northern California." Ninety-five percent of the students received free or reduced lunch; 56% lived with families that qualified for ADC; about 40% were ELL (English Language Learners); and 91% were various minorities.
Results: Grades 7 and 8 results were combined and reported by the percentages of students at different grade levels. The median-score student increased two grade levels during the first year of the program.

Description: The BIG Accommodation Model, is described as a new generation direct instruction program that is organized around big ideas. It includes: a presentation of big ideas, concepts, and principles that facilitate the most efficient and broad acquisition of knowledge, teaching conspicuous strategies, pre-teaching background knowledge, guiding through scaffolding, reviewing that requires students to apply previously learned knowledge, and blending new and old knowledge to build big ideas.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

7th & 8th Grades

Study:
Senk.

Effects of the UCSMP secondary school curriculum on students' achievement.

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math_9-12_6

Strategy: University of Chicago School Mathematics Project (UCSMP)
Subjects: Study 1: Three districts. Site A, one large urban district magnet school, grades 7-12, (1/3 minority). Sites B and C (affluent suburban areas with largely white populations).
Study 2: Study 2: Three private coed schools, mostly middle to upper income families; six public schools (two in mid-sized cities, two in suburbs, and two magnet schools in urban areas).
Study 3: Study 3: Students (n = 139) from four schools, one in Indiana with an African American majority; two in Oregon with white majorities; and one middle class, suburban school in South Carolina, (25% African American).
Study 4: Study 4: Included four schools. One suburban Atlanta school, predominantly white; one rural school with predominantly white population; one small town Mississippi school, 25% white and 75% African American; and one school in an affluent area of Philadelphia with all white student population.
Results: Study 1: Standardized test results were mixed. At sites A and B, UCSMP students outperformed all but one of their comparison groups at statistically significant levels. At site C, course level comparison group outperformed UCSMP students.
Study 2: PDM students' posttest scores were comparable to a calculus sample and higher than the precalculus sample from the SIMS.
Study 3: Results indicated that classes using UCSMP Geometry outperformed comparison classes on the test assessing reasoning, transformations, and applications not covered on the standardized test.
Study 4: Results indicated that classes using UCSMP Advanced Algebra outperformed comparison classes on the Multiple-Choice Test.

UCSMP is composed of courses called Transitional Mathematics (Algebra; Geometry; Advanced Algebra; Functions, Statistics, and Trigonometry; and Precalculus and Discrete Mathematics). Algebra uses variables to develop linear, exponential, and quadratic patterns. Geometry presents coordinates, transformations, measurement formulas, along with work involving writing proofs. Advanced Algebra studies functions, equations, and inequalities. The Functions, Statistics, and Trigonometry course integrates statistical and algebraic concepts. Precalculus and Discrete Mathematics incorporate many topics required for success in Calculus and Computer Science. The content strands of applied mathematics, prealgebra, and elementary geometry are woven throughout the six courses.

NCTM Math Standards
• Algebra
• Geometry

All Math Topic(s)

7th to 12th grades

Study:
Ridgway, Zawojewski, Hoover & Lambdin.

Student attainment in the Connected Mathematics curriculum.

Read full review

math_6-8_5

Description: A problem-oriented curriculum which provides a broad range of mathematical topics with a focus on concept development and student discussion prior to written work.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

6th to 8th Grades

Study:
Riordan & Noyce.

The impact of two standards-based mathematics curricula on student achievement in Massachusetts ["standards-based" instruction is identified as Connected Math (cmp) and/or Everyday Math (em)].

Read full review

math_6-8_6

Strategy: Connected Math (CMP) and Everyday Math (EM)
Subjects: Standards-Based" Instruction Traditional Instruction Matched
EM1 n=48 schools 4+ years using EM n=51 schools
EM2 n=19 2-3 years using EM n=27
CMP1 n=1 4+ years using CMP n=4
CMP2 n=20 2-3 years using CMP n=30
Results: Massachusetts’ students in the standard-based programs performed significantly better on the 1999 statewide mathematics tests than did Massachusetts’ students in traditional programs attending matched comparison schools.
Effect Size: Late implementation of EM= +0.15
Early implementation of EM and CMP= +0.34

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

4th & 8th Grades

Study:
Hunt.

The effect on mathematics achievement and attitude of homogeneous and heterogeneous grouping of gifted sixth-grade students.

Read full review

math_6-8_11

Strategy: Homogeneous vs. heterogeneous grouping.
Subjects: 208 sixth grade students at a middle school in a suburban Southwestern city.
Racial background of 6th gr. Teams - 46% African American, 28% Hispanic American, 16% White, 10% Asian American
Racial background of gifted group - 29% African American, 29% White, 26% Asian American, 17% Hispanic American
Results:No significant differences in math achievement were found regardless of ability group. There were significantly more activities completed by the gifted and average-ability students when grouped homogeneously. The low-ability students had significantly more activities completed when grouped heterogeneously.

Description: Students were randomly selected for placement in 5 classes of heterogeneously grouped students and 5 classes of homogeneously grouped students. Groups used self-paced mathematics learning guides, three weeks in length involving three levels of activities -- regular, extension, and exploratory.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Computation, problem solving

6th Grade

Study:
Linchevski & Kutscher.

Tell me with whom you're learning, and I'll tell you how much you've learned: Mixed-ability versus same-ability grouping in mathematics.

Read full review

math_6-8_13

Strategy: TAP (Together and APart) Project.
Subjects: 1730 seventh grade students in the 12 Israeli junior high schools that participated in the TAP project
389 8th grade students in 4 of the 12 Israeli junior high schools
Results: The gap between better and weaker students learning together in mixed-ability settings for a certain period of time was not different from the gap that would be expected on the basis of initial differences between the two groups. Placement in heterogeneous classes does significantly increase intermediate and low-ability students’ achievement while not significantly impacting the high-ability student.

Description: TAP’s main principle is to keep students together as one learning unit while responding to the different needs of the students. Teaching was conducted within four major settings: (1) students working in a whole-class setting, (2) students working in small mixed-ability groups, (3) students working in small homogeneous groups, and (4) students working in large homogeneous groups.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Seventh and eighth grade algebra, problem solving, and geometry.

7th & 8th Grades

Study:
Arthurs, DeFranco, and Young.

An examination of the impact of tuning students' attention to information in a mathematics problem on their problem-solving performance.

Read full review

math_6-8_23

Description: Two 6th grade classrooms were shown the videodisc "Rescue at Boone's Meadow." The experimental group was "tuned" to the information in the video by receiving a presentation on bald eagles prior to problem solving. The control group was provided information on inductive reasoning via the software package "The King's Rule." The intervention lasted nine days. Students' problem-solving skills were evaluated.

NCTM math standards:
• Algebra
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Problem solving, data gathering

6th Grades

Study:
Reys, Reys, Lapan and Holliday.

Assessing the impact of standards-based middle grades mathematics curriculum materials on student achievement.

Read full review

math_6-8_24

Strategy: Standards-based middle grades mathematics curriculum. Subjects: Two thousand eighth grade students from six school districts. Students were matched for prior mathematics achievement, SES (free and reduced lunch), the same building configuration, and geographic location.
Results: After two years in a standards-based curriculum, the treatment group equaled or exceeded the comparison group. Students in each of the three districts using standards-based curriculum scored significantly higher in two content strands (algebra, and data analysis and probability).

Description: Eighth grade students used standards-based mathematics curriculum materials (specifically MathThematics and Connected Mathematics) for at least two years.

NCTM Math Standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Number &   Operations

Math Topic(s):
All topics, including discrete mathematics.

6th to 8th grades

Strategy:
Everyday Mathematics (EM)

Subjects:
Longitudinal study (from first grade to fifth grade) started with 496 first-grade students in five school districts.
1,885 third graders from suburban Chicago;
78 fifth grade students in four classes;
246 sixth grade students in six classes;
166 fifth grade students in six districts, 4 in Illinois, 1 each in Pennsylvania and Minnesota (three districts were suburban, two rural and one urban);

Results:
Overall, Everyday Mathematics students had a mean score of 47% correct compared with 24% correct for control group. Everyday Mathematics students' mean score on the Comprehensive Testing Program was at the 94th percentile compared to the control group at the 85th percentile.

Description:
In kindergarten EM the focus is on manipulative activities that form a basis of understanding symbols. In grades 1-3 the concepts learned in previous grades are extended with special attention on mental and symbolic arithmetic, measurement, geometry, data (collection and use), and algebra. A strong emphasis is placed on formulating and solving "number stories" with real world information in science, geography, and other areas. The curriculum for grades 4-6 employs mathematical modeling of everyday events and projects while building on the mathematical strands introduced in previous grades by blending them with science, geography, sports, and architecture.

NCTM math standards:
• Geometry
• Data Analysis &  
  Probability
• Measurement
• Number & Operations

Math Topics:
Basic facts, mental and symbolic arithmetic, collection and use of data, computation, logical thinking

K to 6th Grades

Study:
Romberg & Shafer.

Mathematics in context - preliminary evidence about student outcomes.

Read full review

math_6-8_2

Strategy: Mathematics in Context (MiC)
Subjects: 17 schools from 2 suburban and 2 urban districts
54 teachers in grades 5-8, 80% have used MiC curriculum
2225 students in the program 1,2, or 3 years
Results: The degree of implementation of the Mathematics in Context curriculum varied throughout the four districts. According to data, students in the MiC program outperformed students in the conventional program on Number, Geometry, Algebra, and Statistics/Probability. However, the percentages of correct responses varied among all groups.

Description: Mathematics in Context is a standards-based curriculum for grades 5-8 designed to help students progress from informal to formal mathematical reasoning in number, geometry (and measurement), algebra, statistics, and probability. The curriculum focuses on placing students into realistic situations that they must resolve. During their resolution process, students progress from informal notions toward formal mathematical reasoning and representations to model and solve non-routine problems. Throughout the curriculum, students develop conceptual knowledge first and re-visit it as necessary.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

5th to 8th Grades

Study:
Billstein & Williamson.

Middle grades MATH thematics: The STEM project.

Read full review

math_6-8_3

Strategy: MATH Thematics - STEM Project
Subjects: Study 1 treatment group: 115 midwestern MATH Thematics 6th graders in middle-class suburban school.
Study 1 control group: 46 non-MATH Thematics students from another school district.
Study 2: longitudinal; rural western school; 2 groups of 9th graders tested at different times (1993 & 1997 ITEDS). 1993 9th graders had not completed the MATH Thematics curriculum, whereas1997 9th graders had completed MATH Thematics curriculum for grades 6 - 8.
Study 3: Suburban 6th & 8th graders at a MATH Thematics field-test site had used MATH Thematics at the seventh grade level for 4 years.
Results: Study 1: no significant difference
Study 2: 1993 Non MATH-Thematic students ranked 44th percentile on ITEDs; 1997 MATH Thematic students ranked 89th percentile on ITEDs
Study 3: Treatment students scored 12% higher on ITBS
Study 4: After statistical corrections, 14 of 42 CRT objectives favored MATH-Thematic students, 1 of 42 CRT objectives favored control students

Description: A Standards-based curriculum for grades 6, 7, and 8 characterized as problem-oriented with a focus on concept development and student discussion prior to written work. Students are expected to actively do mathematics by investigating, discovering, and applying mathematics to new situations. Students must be able to communicate their ideas effectively through cooperative groups and whole-class discussions.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

6th to 8th Grades

Study:
Bottge.

Effects of contextualized math instruction on problem solving of average and below-average achieving students.

Read full review

math_6-8_10

Strategy: Contextualized mathematics instruction on problem solving
Subjects: 66 eighth grade students from a rural school district in the upper Midwest (37 boys and 29 girls; 17 in a remedial class and 49 in pre-algebra classes; 7 were in special education).
Results: The experimental groups outperformed the control groups on contextualized problems and transfer tasks but not on word problem tests or computational tests.

Description: Students in the experimental groups (contextualized group) were taught problem solving strategies over two weeks using two videos that were intended to teach problem solving. The videos presented problems that were not as overtly stated as traditional problem solving. To solve the problems, students had to first discover the pertinent information, come up with a hypothesis, and assess their hypothesis.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Addition and subtraction of rational numbers in fraction and decimal form.

8th Grade

Study:
Leonard.

How group composition influenced the achievement of sixth-grade mathematics students.

Read full review

math_6-8_12

Strategy: Comparison of heterogeneous vs. homogeneous grouping.
Subjects: 177 6th grade students, approx. 10% of total school enrollment on free or reduced lunch
suburban elementary school in Maryland
Results: Low achieving and middle achieving students scored significantly better in heterogeneous grouping than homogeneous. High-achieving students’ scores were not significantly different. Follow-up interviews indicate that group cohesiveness may impact achievement more than ability grouping.

Description: Sixth-grade students were grouped heterogeneously and homogeneously to determine how groups differ in mathematics achievement and what influence group composition has on student interactions in heterogeneous and homogeneous small groups. Students were assigned to one of three homerooms. The research was conducted for two consecutive academic years. The first year students were grouped heterogeneously by ability. The second year students were grouped homogeneously.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Number concepts, whole numbers, mixed numbers and fractions, decimals, measurement, data, and problem solving

6th Grade

Study:
Threadgill-Sowder & Julips.

Manipulatives versus symbolic approaches to teaching logical connectives in junior high school: An aptitude x treatment interaction study.

Read full review

math_6-8_14

Strategy: Manipulative versus symbolic approaches to teaching logical connectives
Subjects: One-hundred forty-seven seventh-grade students from two junior high schools in Calgary, Alberta, Canada participated in the study. The students included the total seventh-grade population from the two schools, with the exception of absent students or those with severe behavioral problems. The schools were located in Canadian middle-class communities.
Results: Results indicated no significant difference between the treatment groups (use of manipulative materials or symbolic instruction) in the mean scores on the achievement post-test or the test that measured ability to transfer knowledge to more general logical connective statements. However, students with very low scores on the Mathematics Concepts and Mathematics Problem Solving Tests received higher scores on the achievement post-test when instructed with manipulative materials and students with high scores on the Mathematics Concepts and Mathematics Problem Solving Tests found the symbolic instruction more beneficial.

Description: The treatment students were taught logical connectives over the course of three class periods; instruction was either a manipulative or symbolic approach. Control students received no instruction on this topic.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Logical connectives (including conjunction, disjunction, and negation).

seventh Grade

Study:
Wenglisky.

How schools matter: The link between teacher classroom practices and student academic performance.

Read full review

math_6-8_15

Strategy: This study links teacher classroom practices and achievement on the NAEP eighth grade mathematics assessment.
Subjects: 7,146 8th grade students who took the 1996 NAEP Mathematics Assessment
Results: The study found a positive relationship between student achievement on NAEP and teachers with a major in mathematics, professional development in higher-order thinking skills and diversity, using hands-on learning and higher-order thinking skills in the classroom. The influence of these teacher qualities was greater than the influence of SES as a student characteristic on students taking the NAEP assessment.

Description: Using various classroom practices such as writing about math, solving real world problems, having students work with objects, having students talk about math, working in small groups, etc.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

8th Grade

Study:
Grossen

The BIG Accommodation Model: The direct instruction model for secondary schools.

Read full review

math_6-8_25

Strategy: BIG Accommodation Model
Subjects: 518 students in the seventh and eighth grades from "the lowest performing middle school in one of the lowest performing districts in northern California." Ninety-five percent of the students received free or reduced lunch; 56% lived with families that qualified for ADC; about 40% were ELL (English Language Learners); and 91% were various minorities.
Results: Grades 7 and 8 results were combined and reported by the percentages of students at different grade levels. The median-score student increased two grade levels during the first year of the program.

Description: The BIG Accommodation Model, is described as a new generation direct instruction program that is organized around big ideas. It includes: a presentation of big ideas, concepts, and principles that facilitate the most efficient and broad acquisition of knowledge, teaching conspicuous strategies, pre-teaching background knowledge, guiding through scaffolding, reviewing that requires students to apply previously learned knowledge, and blending new and old knowledge to build big ideas.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

7th & 8th Grades

Strategy: Everyday Math
Subjects: Experiment group: 109 ethnically diverse sixth grade heterogeneously grouped students;
76 ethnically diverse fifth grade heterogeneously grouped students from rural, suburban and urban districts.
Control group: 137 sixth graders matched to experiment group on location, demographics including SES;
91 fifth graders matched to experiment group on location, demographics including SES
Results: On all measures, EveryDay Math students outperformed the traditional curriculum students.
Sixth grade effect Size = +0.64
Fifth grade effect Size = +0.73

NCTM math standards:
• Geometry
• Number & Operations

Math Topic(s):
Geometric reasoning

5th & 6th grades

Study:
Reys, Reys, Lapan and Holliday.

Assessing the impact of standards-based middle grades mathematics curriculum materials on student achievement.

Read full review

math_6-8_24

Strategy: Standards-based middle grades mathematics curriculum. Subjects: Two thousand eighth grade students from six school districts. Students were matched for prior mathematics achievement, SES (free and reduced lunch), the same building configuration, and geographic location.
Results: After two years in a standards-based curriculum, the treatment group equaled or exceeded the comparison group. Students in each of the three districts using standards-based curriculum scored significantly higher in two content strands (algebra, and data analysis and probability).

Description: Eighth grade students used standards-based mathematics curriculum materials (specifically MathThematics and Connected Mathematics) for at least two years.

NCTM Math Standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Number &   Operations

Math Topic(s):
All topics, including discrete mathematics.

6th to 8th grades

Study:
Ridgway, Zawojewski, Hoover & Lambdin.

Student attainment in the Connected Mathematics curriculum.

Read full review

math_6-8_5

Description: A problem-oriented curriculum which provides a broad range of mathematical topics with a focus on concept development and student discussion prior to written work.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

6th to 8th Grades

Study:
Riordan & Noyce.

The impact of two standards-based mathematics curricula on student achievement in Massachusetts ["standards-based" instruction is identified as Connected Math (cmp) and/or Everyday Math (em)].

Read full review

math_6-8_6

Strategy: Connected Math (CMP) and Everyday Math (EM)
Subjects: Standards-Based" Instruction Traditional Instruction Matched
EM1 n=48 schools 4+ years using EM n=51 schools
EM2 n=19 2-3 years using EM n=27
CMP1 n=1 4+ years using CMP n=4
CMP2 n=20 2-3 years using CMP n=30
Results: Massachusetts’ students in the standard-based programs performed significantly better on the 1999 statewide mathematics tests than did Massachusetts’ students in traditional programs attending matched comparison schools.
Effect Size: Late implementation of EM= +0.15
Early implementation of EM and CMP= +0.34

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

4th & 8th Grades

Study:
Hunt.

The effect on mathematics achievement and attitude of homogeneous and heterogeneous grouping of gifted sixth-grade students.

Read full review

math_6-8_11

Strategy: Homogeneous vs. heterogeneous grouping.
Subjects: 208 sixth grade students at a middle school in a suburban Southwestern city.
Racial background of 6th gr. Teams - 46% African American, 28% Hispanic American, 16% White, 10% Asian American
Racial background of gifted group - 29% African American, 29% White, 26% Asian American, 17% Hispanic American
Results:No significant differences in math achievement were found regardless of ability group. There were significantly more activities completed by the gifted and average-ability students when grouped homogeneously. The low-ability students had significantly more activities completed when grouped heterogeneously.

Description: Students were randomly selected for placement in 5 classes of heterogeneously grouped students and 5 classes of homogeneously grouped students. Groups used self-paced mathematics learning guides, three weeks in length involving three levels of activities -- regular, extension, and exploratory.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Computation, problem solving

6th Grade

Study:
Linchevski & Kutscher.

Tell me with whom you're learning, and I'll tell you how much you've learned: Mixed-ability versus same-ability grouping in mathematics.

Read full review

math_6-8_13

Strategy: TAP (Together and APart) Project.
Subjects: 1730 seventh grade students in the 12 Israeli junior high schools that participated in the TAP project
389 8th grade students in 4 of the 12 Israeli junior high schools
Results: The gap between better and weaker students learning together in mixed-ability settings for a certain period of time was not different from the gap that would be expected on the basis of initial differences between the two groups. Placement in heterogeneous classes does significantly increase intermediate and low-ability students’ achievement while not significantly impacting the high-ability student.

Description: TAP’s main principle is to keep students together as one learning unit while responding to the different needs of the students. Teaching was conducted within four major settings: (1) students working in a whole-class setting, (2) students working in small mixed-ability groups, (3) students working in small homogeneous groups, and (4) students working in large homogeneous groups.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Seventh and eighth grade algebra, problem solving, and geometry.

7th & 8th Grades

Study:
Romberg & Shafer.

Mathematics in context - preliminary evidence about student outcomes.

Read full review

math_6-8_2

Strategy: Mathematics in Context (MiC)
Subjects: 17 schools from 2 suburban and 2 urban districts
54 teachers in grades 5-8, 80% have used MiC curriculum
2225 students in the program 1,2, or 3 years
Results: The degree of implementation of the Mathematics in Context curriculum varied throughout the four districts. According to data, students in the MiC program outperformed students in the conventional program on Number, Geometry, Algebra, and Statistics/Probability. However, the percentages of correct responses varied among all groups.

Description: Mathematics in Context is a standards-based curriculum for grades 5-8 designed to help students progress from informal to formal mathematical reasoning in number, geometry (and measurement), algebra, statistics, and probability. The curriculum focuses on placing students into realistic situations that they must resolve. During their resolution process, students progress from informal notions toward formal mathematical reasoning and representations to model and solve non-routine problems. Throughout the curriculum, students develop conceptual knowledge first and re-visit it as necessary.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

5th to 8th Grades

Study:
Billstein & Williamson.

Middle grades MATH thematics: The STEM project.

Read full review

math_6-8_3

Strategy: MATH Thematics - STEM Project
Subjects: Study 1 treatment group: 115 midwestern MATH Thematics 6th graders in middle-class suburban school.
Study 1 control group: 46 non-MATH Thematics students from another school district.
Study 2: longitudinal; rural western school; 2 groups of 9th graders tested at different times (1993 & 1997 ITEDS). 1993 9th graders had not completed the MATH Thematics curriculum, whereas1997 9th graders had completed MATH Thematics curriculum for grades 6 - 8.
Study 3: Suburban 6th & 8th graders at a MATH Thematics field-test site had used MATH Thematics at the seventh grade level for 4 years.
Results: Study 1: no significant difference
Study 2: 1993 Non MATH-Thematic students ranked 44th percentile on ITEDs; 1997 MATH Thematic students ranked 89th percentile on ITEDs
Study 3: Treatment students scored 12% higher on ITBS
Study 4: After statistical corrections, 14 of 42 CRT objectives favored MATH-Thematic students, 1 of 42 CRT objectives favored control students

Description: A Standards-based curriculum for grades 6, 7, and 8 characterized as problem-oriented with a focus on concept development and student discussion prior to written work. Students are expected to actively do mathematics by investigating, discovering, and applying mathematics to new situations. Students must be able to communicate their ideas effectively through cooperative groups and whole-class discussions.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

6th to 8th Grades

Study:
Bottge.

Effects of contextualized math instruction on problem solving of average and below-average achieving students.

Read full review

math_6-8_10

Strategy: Contextualized mathematics instruction on problem solving
Subjects: 66 eighth grade students from a rural school district in the upper Midwest (37 boys and 29 girls; 17 in a remedial class and 49 in pre-algebra classes; 7 were in special education).
Results: The experimental groups outperformed the control groups on contextualized problems and transfer tasks but not on word problem tests or computational tests.

Description: Students in the experimental groups (contextualized group) were taught problem solving strategies over two weeks using two videos that were intended to teach problem solving. The videos presented problems that were not as overtly stated as traditional problem solving. To solve the problems, students had to first discover the pertinent information, come up with a hypothesis, and assess their hypothesis.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Addition and subtraction of rational numbers in fraction and decimal form.

8th Grade

Study:
Leonard.

How group composition influenced the achievement of sixth-grade mathematics students.

Read full review

math_6-8_12

Strategy: Comparison of heterogeneous vs. homogeneous grouping.
Subjects: 177 6th grade students, approx. 10% of total school enrollment on free or reduced lunch
suburban elementary school in Maryland
Results: Low achieving and middle achieving students scored significantly better in heterogeneous grouping than homogeneous. High-achieving students’ scores were not significantly different. Follow-up interviews indicate that group cohesiveness may impact achievement more than ability grouping.

Description: Sixth-grade students were grouped heterogeneously and homogeneously to determine how groups differ in mathematics achievement and what influence group composition has on student interactions in heterogeneous and homogeneous small groups. Students were assigned to one of three homerooms. The research was conducted for two consecutive academic years. The first year students were grouped heterogeneously by ability. The second year students were grouped homogeneously.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Number concepts, whole numbers, mixed numbers and fractions, decimals, measurement, data, and problem solving

6th Grade

Study:
Threadgill-Sowder & Julips.

Manipulatives versus symbolic approaches to teaching logical connectives in junior high school: An aptitude x treatment interaction study.

Read full review

math_6-8_14

Strategy: Manipulative versus symbolic approaches to teaching logical connectives
Subjects: One-hundred forty-seven seventh-grade students from two junior high schools in Calgary, Alberta, Canada participated in the study. The students included the total seventh-grade population from the two schools, with the exception of absent students or those with severe behavioral problems. The schools were located in Canadian middle-class communities.
Results: Results indicated no significant difference between the treatment groups (use of manipulative materials or symbolic instruction) in the mean scores on the achievement post-test or the test that measured ability to transfer knowledge to more general logical connective statements. However, students with very low scores on the Mathematics Concepts and Mathematics Problem Solving Tests received higher scores on the achievement post-test when instructed with manipulative materials and students with high scores on the Mathematics Concepts and Mathematics Problem Solving Tests found the symbolic instruction more beneficial.

Description: The treatment students were taught logical connectives over the course of three class periods; instruction was either a manipulative or symbolic approach. Control students received no instruction on this topic.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Logical connectives (including conjunction, disjunction, and negation).

7th Grade

Study:
Wenglisky.

How schools matter: the link between teacher classroom practices and student academic performance.

Read full review

math_6-8_15

Strategy: This study links teacher classroom practices and achievement on the NAEP eighth grade mathematics assessment.
Subjects: 7,146 8th grade students who took the 1996 NAEP Mathematics Assessment
Results: The study found a positive relationship between student achievement on NAEP and teachers with a major in mathematics, professional development in higher-order thinking skills and diversity, using hands-on learning and higher-order thinking skills in the classroom. The influence of these teacher qualities was greater than the influence of SES as a student characteristic on students taking the NAEP assessment.

Description: Using various classroom practices such as writing about math, solving real world problems, having students work with objects, having students talk about math, working in small groups, etc.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

8th Grade

Study:
Rowell
& Mansfield.

The Teaching of Transformation Geometry in Grade Eight: A Search for Aptitude-Treatment Interactions.

Read full review

math_6-8_20

Description: There were four categories of treatment based on two dimensions of curricular decisions. The classes were either teacher demonstrated, in which the teacher would demonstrate the solutions to the various problems or a student activity in which the materials guided the students to solving a particular problem. The other dimension was whether the class was taught using a deductive approach, in which rules were cited to answer student questions or an inductive approach, in which students or the teacher worked from specific examples and then generalized a rule.

NCTM math standards:
• Geometry

Math topics:
Reflections, rotations, and translations

8th Grade

Study:
Grossen

The BIG Accommodation Model: The direct instruction model for secondary schools.

Read full review

math_6-8_25

Strategy: BIG Accommodation Model
Subjects: 518 students in the seventh and eighth grades from "the lowest performing middle school in one of the lowest performing districts in northern California." Ninety-five percent of the students received free or reduced lunch; 56% lived with families that qualified for ADC; about 40% were ELL (English Language Learners); and 91% were various minorities.
Results: Grades 7 and 8 results were combined and reported by the percentages of students at different grade levels. The median-score student increased two grade levels during the first year of the program.

Description: The BIG Accommodation Model, is described as a new generation direct instruction program that is organized around big ideas. It includes: a presentation of big ideas, concepts, and principles that facilitate the most efficient and broad acquisition of knowledge, teaching conspicuous strategies, pre-teaching background knowledge, guiding through scaffolding, reviewing that requires students to apply previously learned knowledge, and blending new and old knowledge to build big ideas.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

7th & 8th Grades

Study:
Senk.

Effects of the UCSMP secondary school curriculum on students' achievement.

Read full review

math_9-12_6

Strategy: University of Chicago School Mathematics Project (UCSMP)
Subjects: Study 1: Three districts. Site A, one large urban district magnet school, grades 7-12, (1/3 minority). Sites B and C (affluent suburban areas with largely white populations).
Study 2: Study 2: Three private coed schools, mostly middle to upper income families; six public schools (two in mid-sized cities, two in suburbs, and two magnet schools in urban areas).
Study 3: Study 3: Students (n = 139) from four schools, one in Indiana with an African American majority; two in Oregon with white majorities; and one middle class, suburban school in South Carolina, (25% African American).
Study 4: Study 4: Included four schools. One suburban Atlanta school, predominantly white; one rural school with predominantly white population; one small town Mississippi school, 25% white and 75% African American; and one school in an affluent area of Philadelphia with all white student population.
Results: Study 1: Standardized test results were mixed. At sites A and B, UCSMP students outperformed all but one of their comparison groups at statistically significant levels. At site C, course level comparison group outperformed UCSMP students.
Study 2: PDM students' posttest scores were comparable to a calculus sample and higher than the precalculus sample from the SIMS.
Study 3: Results indicated that classes using UCSMP Geometry outperformed comparison classes on the test assessing reasoning, transformations, and applications not covered on the standardized test.
Study 4: Results indicated that classes using UCSMP Advanced Algebra outperformed comparison classes on the Multiple-Choice Test.

UCSMP is composed of courses called Transitional Mathematics (Algebra; Geometry; Advanced Algebra; Functions, Statistics, and Trigonometry; and Precalculus and Discrete Mathematics). Algebra uses variables to develop linear, exponential, and quadratic patterns. Geometry presents coordinates, transformations, measurement formulas, along with work involving writing proofs. Advanced Algebra studies functions, equations, and inequalities. The Functions, Statistics, and Trigonometry course integrates statistical and algebraic concepts. Precalculus and Discrete Mathematics incorporate many topics required for success in Calculus and Computer Science. The content strands of applied mathematics, prealgebra, and elementary geometry are woven throughout the six courses.

NCTM Math Standards
• Algebra
• Geometry

All Math Topic(s)

7th to 12th grades

Study:
Bottge, Heinrichs, Mehta & Hung.

Weighing the benefits of anchored math instruction for students with disabilities in general education classes.

Read full review

math_6-8_27

Strategy: Enhanced Anchored Instruction (EAI)
Subjects: 42 seventh grade students (pre-dominantly white) from a middle school in a rural Midwest school district. Eight students were identified with disabilities.
Results: The results showed that students in the EAI classroom outperformed the other students in contextualized problems and the ability to transfer problem-solving skills at a later date on similar problems. There was no significant gain in achievement for students with learning disabilities.

Description: Students were placed in four small groups of 10 to 11 for instruction. Students in the EAI classroom also spent time, in the technology education classroom, solving related problems. The instruction was divided among math teacher, special education teacher, and a technology education teacher. Students, in the treatment and control groups, solved problems aligned with NCTM standards.

NCTM math standards:
• Measurement
• Number and Operations

Math Topics: Computation, fractions, arithmetic word problems

Grade: seventh Grade

Study:
Ridgway, Zawojewski, Hoover & Lambdin.

Student attainment in the Connected Mathematics curriculum.

Read full review

math_6-8_5

Description: A problem-oriented curriculum which provides a broad range of mathematical topics with a focus on concept development and student discussion prior to written work.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

6th to 8th Grades

Study:
Riordan & Noyce.

The impact of two standards-based mathematics curricula on student achievement in Massachusetts ["standards-based" instruction is identified as Connected Math (cmp) and/or Everyday Math (em)].

Read full review

math_6-8_6

Strategy: Connected Math (CMP) and Everyday Math (EM)
Subjects: Standards-Based" Instruction Traditional Instruction Matched
EM1 n=48 schools 4+ years using EM n=51 schools
EM2 n=19 2-3 years using EM n=27
CMP1 n=1 4+ years using CMP n=4
CMP2 n=20 2-3 years using CMP n=30
Results: Massachusetts’ students in the standard-based programs performed significantly better on the 1999 statewide mathematics tests than did Massachusetts’ students in traditional programs attending matched comparison schools.
Effect Size: Late implementation of EM= +0.15
Early implementation of EM and CMP= +0.34

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

4th & 8th Grades

Study:
Hunt.

The effect on mathematics achievement and attitude of homogeneous and heterogeneous grouping of gifted sixth-grade students.

Read full review

math_6-8_11

Strategy: Homogeneous vs. heterogeneous grouping.
Subjects: 208 sixth grade students at a middle school in a suburban Southwestern city.
Racial background of 6th gr. Teams - 46% African American, 28% Hispanic American, 16% White, 10% Asian American
Racial background of gifted group - 29% African American, 29% White, 26% Asian American, 17% Hispanic American
Results:No significant differences in math achievement were found regardless of ability group. There were significantly more activities completed by the gifted and average-ability students when grouped homogeneously. The low-ability students had significantly more activities completed when grouped heterogeneously.

Description: Students were randomly selected for placement in 5 classes of heterogeneously grouped students and 5 classes of homogeneously grouped students. Groups used self-paced mathematics learning guides, three weeks in length involving three levels of activities -- regular, extension, and exploratory.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Computation, problem solving

6th Grade

Study:
Linchevski & Kutscher.

Tell me with whom you're learning, and I'll tell you how much you've learned: Mixed-ability versus same-ability grouping in mathematics.

Read full review

math_6-8_13

Strategy: TAP (Together and APart) Project.
Subjects: 1730 seventh grade students in the 12 Israeli junior high schools that participated in the TAP project
389 8th grade students in 4 of the 12 Israeli junior high schools
Results: The gap between better and weaker students learning together in mixed-ability settings for a certain period of time was not different from the gap that would be expected on the basis of initial differences between the two groups. Placement in heterogeneous classes does significantly increase intermediate and low-ability students’ achievement while not significantly impacting the high-ability student.

Description: TAP’s main principle is to keep students together as one learning unit while responding to the different needs of the students. Teaching was conducted within four major settings: (1) students working in a whole-class setting, (2) students working in small mixed-ability groups, (3) students working in small homogeneous groups, and (4) students working in large homogeneous groups.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Seventh and eighth grade algebra, problem solving, and geometry.

7th & 8th Grades

Study:
Arthurs, DeFranco, and Young.

An examination of the impact of tuning students' attention to information in a mathematics problem on their problem-solving performance.

Read full review

math_6-8_23

Description: Two 6th grade classrooms were shown the videodisc "Rescue at Boone's Meadow." The experimental group was "tuned" to the information in the video by receiving a presentation on bald eagles prior to problem solving. The control group was provided information on inductive reasoning via the software package "The King's Rule." The intervention lasted nine days. Students' problem-solving skills were evaluated.

NCTM math standards:
• Algebra
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Problem solving, data gathering

6th Grades

Study:
Romberg & Shafer.

Mathematics in Context - Preliminary evidence about student outcomes.

Read full review

math_6-8_2

Strategy: Mathematics in Context (MiC)
Subjects: 17 schools from 2 suburban and 2 urban districts
54 teachers in grades 5-8, 80% have used MiC curriculum
2225 students in the program 1,2, or 3 years
Results: The degree of implementation of the Mathematics in Context curriculum varied throughout the four districts. According to data, students in the MiC program outperformed students in the conventional program on Number, Geometry, Algebra, and Statistics/Probability. However, the percentages of correct responses varied among all groups.

Description: Mathematics in Context is a standards-based curriculum for grades 5-8 designed to help students progress from informal to formal mathematical reasoning in number, geometry (and measurement), algebra, statistics, and probability. The curriculum focuses on placing students in realistic situations that they must resolve. During their resolution process, students progress from informal notions toward formal mathematical reasoning and representations to model and solve non-routine problems. Throughout the curriculum, students develop conceptual knowledge first and re-visit it as necessary.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

5th to 8th Grades

Study:
Billstein & Williamson.

Middle grades MATH thematics: The STEM project.

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math_6-8_3

Strategy: MATH Thematics - STEM Project
Subjects: Study 1 treatment group: 115 midwestern MATH Thematics 6th graders in middle-class suburban school.
Study 1 control group: 46 non-MATH Thematics students from another school district.
Study 2: longitudinal; rural western school; 2 groups of 9th graders tested at different times (1993 & 1997 ITEDS). 1993 9th graders had not completed the MATH Thematics curriculum, whereas1997 9th graders had completed MATH Thematics curriculum for grades 6 - 8.
Study 3: Suburban 6th & 8th graders at a MATH Thematics field-test site had used MATH Thematics at the seventh grade level for 4 years.
Results: Study 1: no significant difference
Study 2: 1993 Non MATH-Thematic students ranked 44th percentile on ITEDs; 1997 MATH Thematic students ranked 89th percentile on ITEDs
Study 3: Treatment students scored 12% higher on ITBS
Study 4: After statistical corrections, 14 of 42 CRT objectives favored MATH-Thematic students, 1 of 42 CRT objectives favored control students

Description: A Standards-based curriculum for grades 6, 7, and 8 characterized as problem-oriented with a focus on concept development and student discussion prior to written work. Students are expected to actively do mathematics by investigating, discovering, and applying mathematics to new situations. Students must be able to communicate their ideas effectively through cooperative groups and whole-class discussions.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

6th to 8th Grades

Study:
Bottge.

Effects of contextualized math instruction on problem solving of average and below-average achieving students.

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math_6-8_10

Strategy: Contextualized mathematics instruction on problem solving
Subjects: 66 eighth grade students from a rural school district in the upper Midwest (37 boys and 29 girls; 17 in a remedial class and 49 in pre-algebra classes; 7 were in special education).
Results: The experimental groups outperformed the control groups on contextualized problems and transfer tasks but not on word problem tests or computational tests.

Description: Students in the experimental groups (contextualized group) were taught problem solving strategies over two weeks using two videos that were intended to teach problem solving. The videos presented problems that were not as overtly stated as traditional problem solving. To solve the problems, students had to first discover the pertinent information, come up with a hypothesis, and assess their hypothesis.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Addition and subtraction of rational numbers in fraction and decimal form.

8th Grade

Study:
Leonard.

How group composition influenced the achievement of sixth-grade mathematics students.

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math_6-8_12

Strategy: Comparison of heterogeneous vs. homogeneous grouping.
Subjects: 177 6th grade students, approx. 10% of total school enrollment on free or reduced lunch
suburban elementary school in Maryland
Results: Low achieving and middle achieving students scored significantly better in heterogeneous grouping than homogeneous. High-achieving students’ scores were not significantly different. Follow-up interviews indicate that group cohesiveness may impact achievement more than ability grouping.

Description: Sixth-grade students were grouped heterogeneously and homogeneously to determine how groups differ in mathematics achievement and what influence group composition has on student interactions in heterogeneous and homogeneous small groups. Students were assigned to one of three homerooms. The research was conducted for two consecutive academic years. The first year students were grouped heterogeneously by ability. The second year students were grouped homogeneously.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Number concepts, whole numbers, mixed numbers and fractions, decimals, measurement, data, and problem solving

6th Grade

Study:
Threadgill-Sowder & Julips.

Manipulatives versus symbolic approaches to teaching logical connectives in junior high school: An aptitude x treatment interaction study.

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math_6-8_14

Strategy: Manipulative versus symbolic approaches to teaching logical connectives
Subjects: One-hundred forty-seven seventh-grade students from two junior high schools in Calgary, Alberta, Canada participated in the study. The students included the total seventh-grade population from the two schools, with the exception of absent students or those with severe behavioral problems. The schools were located in Canadian middle-class communities.
Results: Results indicated no significant difference between the treatment groups (use of manipulative materials or symbolic instruction) in the mean scores on the achievement post-test or the test that measured ability to transfer knowledge to more general logical connective statements. However, students with very low scores on the Mathematics Concepts and Mathematics Problem Solving Tests received higher scores on the achievement post-test when instructed with manipulative materials and students with high scores on the Mathematics Concepts and Mathematics Problem Solving Tests found the symbolic instruction more beneficial.

Description: The treatment students were taught logical connectives over the course of three class periods; instruction was either a manipulative or symbolic approach. Control students received no instruction on this topic.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Logical connectives (including conjunction, disjunction, and negation).

7th Grade

Study:
Wenglisky.

How schools matter: The link between teacher classroom practices and student academic performance.

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math_6-8_15

Strategy: This study links teacher classroom practices and achievement on the NAEP eighth grade mathematics assessment.
Subjects: 7,146 8th grade students who took the 1996 NAEP Mathematics Assessment
Results: The study found a positive relationship between student achievement on NAEP and teachers with a major in mathematics, professional development in higher-order thinking skills and diversity, using hands-on learning and higher-order thinking skills in the classroom. The influence of these teacher qualities was greater than the influence of SES as a student characteristic on students taking the NAEP assessment.

Description: Using various classroom practices such as writing about math, solving real world problems, having students work with objects, having students talk about math, working in small groups, etc.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

8th Grade

Study:
Grossen

The BIG Accommodation Model: The direct instruction model for secondary schools.

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math_6-8_25

Strategy: BIG Accommodation Model
Subjects: 518 students in the seventh and eighth grades from "the lowest performing middle school in one of the lowest performing districts in northern California." Ninety-five percent of the students received free or reduced lunch; 56% lived with families that qualified for ADC; about 40% were ELL (English Language Learners); and 91% were various minorities.
Results: Grades 7 and 8 results were combined and reported by the percentages of students at different grade levels. The median-score student increased two grade levels during the first year of the program.

Description: The BIG Accommodation Model, is described as a new generation direct instruction program that is organized around big ideas. It includes: a presentation of big ideas, concepts, and principles that facilitate the most efficient and broad acquisition of knowledge, teaching conspicuous strategies, pre-teaching background knowledge, guiding through scaffolding, reviewing that requires students to apply previously learned knowledge, and blending new and old knowledge to build big ideas.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

7th & 8th Grades

Study:
Lin.

Effects of computer graphics types and epistemological beliefs on students' learning of mathematics concepts.

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math_6-8_26

Strategy: Computer graphic modes: static, animated, or video clips of a teacher demonstration.
Subjects: Experiment 1: 1240 students in the fourth through sixth grades from an urban elementary school in north Taiwan.
Experiment 2: 167 fourth grade students from an urban elementary school in north Taiwan.
Results: Experiment 1: It was revealed that there were four factors that affected students' epistemological beliefs: (a) First Time Learning (believing in first time learning), (b) Omniscient Authority (don't criticize authority), (c) Quick Learning (learning is done quickly or it will never be learned), and (d) Simple Learning (questions only have one answer).
Experiment 2: Students who use computer graphics programs with animations do significantly better than students who use video clips of teacher demonstrations on computer programs.

Description: Two experiments were conducted to determine the factors involved in students' epistemological beliefs and to investigate the effects of computer graphics types and students' beliefs on achievement and attitude.
Experiment 1: Students were given a questionnaire that asked them to rate statements on a scale of 1 (strongly disagree) to 6 (strongly agree). The questionnaire was adapted from Jacobson and Jehng's Epistemological Belief Questionnaire.
Experiment 2: After taking the epistemological belief questionnaire students were divided into two groups using the mean scores of each factor. Students were classified as having naive or mature epistemological beliefs on the factors. Subjects were randomly assigned to one of three computer graphics groups for a self-paced computer based lesson.

NCTM math standards:
• Measurement

Math topics:
Volume

4th to 6th Grades

Study:
Woodward, Baxter & Robinson.

Rules and reasons: Decimal instruction for academically low achieving students.

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math_6-8_4

Description: Both groups were taught by the same teacher. The treatment (visual/conceptual) group experienced lessons from Mathematics in the Mind's Eye: Modeling Rationals, a program utilizing highly visual representations and encouraging the use of physical manipulatives to develop decimal knowledge. This was followed by some drill and practice. The control (procedural) group watched a daily video program, "Mastering decimals and percents," a highly integrated program emphasizing the application of decimal information. This video program incorporates practice into the daily experience.

NCTM math standards:
• Numbers & Operation

Math Topics:
Decimals and percents

8th and 9th Grades

Study:
Bottge, Heinrichs, Mehta & Hung.

Weighing the benefits of anchored math instruction for students with disabilities in general education classes.

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math_6-8_27

Strategy: Enhanced Anchored Instruction (EAI)
Subjects: 42 seventh grade students (pre-dominantly white) from a middle school in a rural Midwest school district. Eight students were identified with disabilities.
Results: The results showed that students in the EAI classroom outperformed the other students in contextualized problems and the ability to transfer problem-solving skills at a later date on similar problems. There was no significant gain in achievement for students with learning disabilities.

Description: Students were placed in four small groups of 10 to 11 for instruction. Students in the EAI classroom also spent time, in the technology education classroom, solving related problems. The instruction was divided among math teacher, special education teacher, and a technology education teacher. Students, in the treatment and control groups, solved problems aligned with NCTM standards.

NCTM math standards:
• Measurement
• Number and Operations

Math Topics: Computation, fractions, arithmetic word problems

7th Grade

Strategy: Everyday Math
Subjects: Experiment group: 109 ethnically diverse sixth grade heterogeneously grouped students
76 ethnically diverse fifth grade heterogeneously grouped students from rural, suburban and urban districts
Control group: 137 sixth graders matched to experiment group on location, demographics including SES
91 fifth graders matched to experiment group on location, demographics including SES
Results: On all measures, EveryDay Math students outperformed the traditional curriculum students.
Sixth grade effect Size = +0.64
Fifth grade effect Size = +0.73

NCTM math standards:
• Geometry
• Number & Operations

Math Topic(s):
Geometric reasoning

5th & 6th grades

Study:
Ridgway, Zawojewski, Hoover & Lambdin.

Student attainment in the Connected Mathematics curriculum.

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math_6-8_5

Description: A problem-oriented curriculum which provides a broad range of mathematical topics with a focus on concept development and student discussion prior to written work.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

6th to 8th Grades

Study:
Riordan & Noyce.

The impact of two standards-based mathematics curricula on student achievement in Massachusetts ["standards-based" instruction is identified as Connected Math (cmp) and/or Everyday Math (em)].

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math_6-8_6

Strategy: Connected Math (CMP) and Everyday Math (EM)
Subjects: Standards-Based" Instruction Traditional Instruction Matched
EM1 n=48 schools 4+ years using EM n=51 schools
EM2 n=19 2-3 years using EM n=27
CMP1 n=1 4+ years using CMP n=4
CMP2 n=20 2-3 years using CMP n=30
Results: Massachusetts’ students in the standard-based programs performed significantly better on the 1999 statewide mathematics tests than did Massachusetts’ students in traditional programs attending matched comparison schools.
Effect Size: Late implementation of EM= +0.15
Early implementation of EM and CMP= +0.34

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

4th & 8th Grades

Study:
Ben-Chaim et al.

Proportional reasoning among seventh grade students with different curricular experiences.

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math_6-8_7

Description: The treatment group was taught using CMP materials for one school year. In this reform curriculum, students are encouraged to construct their own conceptual and procedural knowledge through collaborative problem-solving activities. The data for this study were generated by five proportion problems focusing on rate or population density.

NCTM math standards:
• Number & Operations

Math Topic(s):
Rational numbers, proportionality (rate, density, ratio)

7th & 8th grades

Study:
Hunt.

The effect on mathematics achievement and attitude of homogeneous and heterogeneous grouping of gifted sixth-grade students.

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math_6-8_11

Strategy: Homogeneous vs. heterogeneous grouping.
Subjects: 208 sixth grade students at a middle school in a suburban Southwestern city.
Racial background of 6th gr. Teams - 46% African American, 28% Hispanic American, 16% White, 10% Asian American
Racial background of gifted group - 29% African American, 29% White, 26% Asian American, 17% Hispanic American
Results:No significant differences in math achievement were found regardless of ability group. There were significantly more activities completed by the gifted and average-ability students when grouped homogeneously. The low-ability students had significantly more activities completed when grouped heterogeneously.

Description: Students were randomly selected for placement in 5 classes of heterogeneously grouped students and 5 classes of homogeneously grouped students. Groups used self-paced mathematics learning guides, three weeks in length involving three levels of activities -- regular, extension, and exploratory.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Computation, problem solving

6th Grade

Study:
Linchevski & Kutscher.

Tell me with whom you're learning, and I'll tell you how much you've learned: Mixed-ability versus same-ability grouping in mathematics.

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math_6-8_13

Strategy: TAP (Together and APart) Project.
Subjects: 1730 seventh grade students in the 12 Israeli junior high schools that participated in the TAP project
389 8th grade students in 4 of the 12 Israeli junior high schools
Results: The gap between better and weaker students learning together in mixed-ability settings for a certain period of time was not different from the gap that would be expected on the basis of initial differences between the two groups. Placement in heterogeneous classes does significantly increase intermediate and low-ability students’ achievement while not significantly impacting the high-ability student.

Description: TAP’s main principle is to keep students together as one learning unit while responding to the different needs of the students. Teaching was conducted within four major settings: (1) students working in a whole-class setting, (2) students working in small mixed-ability groups, (3) students working in small homogeneous groups, and (4) students working in large homogeneous groups.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Seventh and eighth grade algebra, problem solving, and geometry.

7th & 8th Grades

Study:
Arthurs, DeFranco, and Young.

An examination of the impact of tuning students' attention to information in a mathematics problem on their problem-solving performance.

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math_6-8_23

Description: Two 6th grade classrooms were shown the videodisc "Rescue at Boone's Meadow." The experimental group was "tuned" to the information in the video by receiving a presentation on bald eagles prior to problem solving. The control group was provided information on inductive reasoning via the software package "The King's Rule." The intervention lasted nine days. Students' problem-solving skills were evaluated.

NCTM math standards:
• Algebra
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Problem solving, data gathering

6th Grades

Study:
Reys, Reys, Lapan, and Holliday.

Assessing the impact of standards-based middle grades mathematics curriculum materials on student achievement.

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math_6-8_24

Strategy: Standards-based middle grades mathematics curriculum. Subjects: Two thousand eighth grade students from six school districts. Students were matched for prior mathematics achievement, SES (free and reduced lunch), the same building configuration, and geographic location.
Results: After two years in a standards-based curriculum, the treatment group equaled or exceeded the comparison group. Students in each of the three districts using standards-based curriculum scored significantly higher in two content strands (algebra, and data analysis and probability).

Description: Eighth grade students used standards-based mathematics curriculum materials (specifically MathThematics and Connected Mathematics) for at least two years.

NCTM Math Standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Number &   Operations

Math Topic(s):
All topics, including discrete mathematics.

6th to 8th grades

Study:
W. Szetela and D. Super

Title: Calculators and Instruction in Problem Solving in Grade 7

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math_6-8_28

New
Review

4

Strategy: Problem solving strategies and calculator usage
Subjects: 823 seventh-grade students from an urban-rural area, in three groups, (a) experimental group, problem-solving strategies with calculators (n=290); (b) experimental group, problem-solving strategies without calculators (n=195); and (c) control group, no special problem-solving strategies and no calculators (n=338).
Results: Students who were taught problem-solving strategies (with or without calculators) scored significantly higher than the control group who were not taught problem-solving strategies. Students who used calculators scored significantly higher on their attitude toward mathematics than students in the control group and did not score significantly lower on computation.

Description: Students were taught problem-solving strategies, such as, guessing and checking, making a systematic list, making a simpler problem, searching for a pattern, and drawing a diagram.

NCTM Math Standards: Number & Operations

Math Topic: Computation

7th Grade

Study:
Romberg & Shafer.

Mathematics in context - preliminary evidence about student outcomes.

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math_6-8_2

Strategy: Mathematics in Context (MiC)
Subjects: 17 schools from 2 suburban and 2 urban districts
54 teachers in grades 5-8, 80% have used MiC curriculum
2225 students in the program 1,2, or 3 years
Results: The degree of implementation of the Mathematics in Context curriculum varied throughout the four districts. According to data, students in the MiC program outperformed students in the conventional program on Number, Geometry, Algebra, and Statistics/Probability. However, the percentages of correct responses varied among all groups.

Description: Mathematics in Context is a standards-based curriculum for grades 5-8 designed to help students progress from informal to formal mathematical reasoning in number, geometry (and measurement), algebra, statistics, and probability. The curriculum focuses on placing students into realistic situations that they must resolve. During their resolution process, students progress from informal notions toward formal mathematical reasoning and representations to model and solve non-routine problems. Throughout the curriculum, students develop conceptual knowledge first and re-visit it as necessary.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

5th to 8th Grades

Study:
Billstein & Williamson.

Middle grades MATH thematics: The STEM project.

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math_6-8_3

Strategy: MATH Thematics - STEM Project
Subjects: Study 1 treatment group: 115 midwestern MATH Thematics 6th graders in middle-class suburban school.
Study 1 control group: 46 non-MATH Thematics students from another school district.
Study 2: longitudinal; rural western school; 2 groups of 9th graders tested at different times (1993 & 1997 ITEDS). 1993 9th graders had not completed the MATH Thematics curriculum, whereas1997 9th graders had completed MATH Thematics curriculum for grades 6 - 8.
Study 3: Suburban 6th & 8th graders at a MATH Thematics field-test site had used MATH Thematics at the seventh grade level for 4 years.
Results: Study 1: no significant difference
Study 2: 1993 Non MATH-Thematic students ranked 44th percentile on ITEDs; 1997 MATH Thematic students ranked 89th percentile on ITEDs
Study 3: Treatment students scored 12% higher on ITBS
Study 4: After statistical corrections, 14 of 42 CRT objectives favored MATH-Thematic students, 1 of 42 CRT objectives favored control students

Description: A standards-based curriculum for grades 6, 7, and 8 characterized as problem-oriented with a focus on concept development and student discussion prior to written work. Students are expected to actively do mathematics by investigating, discovering, and applying mathematics to new situations. Students must be able to communicate their ideas effectively through cooperative groups and whole-class discussions.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

6th to 8th Grades

Study:
Carroll.

Mental computation of students in a reform-based mathematics curriculum .

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math_6-8_8

NCTM math standards:

• Number &   Operations

Math topics:

5th Grade

Study:
Leonard.

How group composition influenced the achievement of sixth-grade mathematics students.

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math_6-8_12

Strategy: Comparison of heterogeneous vs. homogeneous grouping.
Subjects: 177 6th grade students, approx. 10% of total school enrollment on free or reduced lunch
suburban elementary school in Maryland
Results: Low achieving and middle achieving students scored significantly better in heterogeneous grouping than homogeneous. High-achieving students’ scores were not significantly different. Follow-up interviews indicate that group cohesiveness may impact achievement more than ability grouping.

Description: Sixth-grade students were grouped heterogeneously and homogeneously to determine how groups differ in mathematics achievement and what influence group composition has on student interactions in heterogeneous and homogeneous small groups. Students were assigned to one of three homerooms. The research was conducted for two consecutive academic years. The first year students were grouped heterogeneously by ability. The second year students were grouped homogeneously.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Number concepts, whole numbers, mixed numbers and fractions, decimals, measurement, data, and problem solving

6th Grade

Study:
Threadgill-Sowder & Julips.

Manipulatives versus symbolic approaches to teaching logical connectives in junior high school: An aptitude x treatment interaction study.

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math_6-8_14

Strategy: Manipulative versus symbolic approaches to teaching logical connectives
Subjects: One-hundred forty-seven seventh-grade students from two junior high schools in Calgary, Alberta, Canada participated in the study. The students included the total seventh-grade population from the two schools, with the exception of absent students or those with severe behavioral problems. The schools were located in Canadian middle-class communities.
Results: Results indicated no significant difference between the treatment groups (use of manipulative materials or symbolic instruction) in the mean scores on the achievement post-test or the test that measured ability to transfer knowledge to more general logical connective statements. However, students with very low scores on the Mathematics Concepts and Mathematics Problem Solving Tests received higher scores on the achievement post-test when instructed with manipulative materials and students with high scores on the Mathematics Concepts and Mathematics Problem Solving Tests found the symbolic instruction more beneficial.

Description: The treatment students were taught logical connectives over the course of three class periods; instruction was either a manipulative or symbolic approach. Control students received no instruction on this topic.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
Logical connectives (including conjunction, disjunction, and negation).

7th Grade

Study:
Wenglisky.

How schools matter: The link between teacher classroom practices and student academic performance.

Read full review

math_6-8_15

Strategy: This study links teacher classroom practices and achievement on the NAEP eighth grade mathematics assessment.
Subjects: 7,146 8th grade students who took the 1996 NAEP Mathematics Assessment
Results: The study found a positive relationship between student achievement on NAEP and teachers with a major in mathematics, professional development in higher-order thinking skills and diversity, using hands-on learning and higher-order thinking skills in the classroom. The influence of these teacher qualities was greater than the influence of SES as a student characteristic on students taking the NAEP assessment.

Description: Using various classroom practices such as writing about math, solving real world problems, having students work with objects, having students talk about math, working in small groups, etc.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

8th Grade

Study:
Ainsworth, Bibby & Wood.

Examining the Effects of Different Multiple Representational Systems in Learning Primary Mathematics.

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math_6-8_21

Description: CENTS is designed to help 9-12 year olds learn some of the knowledge and skills required for computational estimation. Using both pictorial (splatwall and archery target) and mathematical (numerical and histogram) MREs, learners make predictions about a particular estimate, perform the estimation, and then judge the accuracy of their predictions. Rounding and truncation (front-end) were the estimation strategies.

NCTM math standards:
• Number & Operations

Math Topic(s):
Computational estimation, multi-digit multiplication

5th and 6th Grades

Study:
Grossen

The BIG Accommodation Model: The direct instruction model for secondary schools.

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math_6-8_25

Strategy: BIG Accommodation Model
Subjects: 518 students in the seventh and eighth grades from "the lowest performing middle school in one of the lowest performing districts in northern California." Ninety-five percent of the students received free or reduced lunch; 56% lived with families that qualified for ADC; about 40% were ELL (English Language Learners); and 91% were various minorities.
Results: Grades 7 and 8 results were combined and reported by the percentages of students at different grade levels. The median-score student increased two grade levels during the first year of the program.

Description: The BIG Accommodation Model is described as a new generation direct instruction program that is organized around big ideas. It includes: a presentation of big ideas, concepts, and principles that facilitate the most efficient and broad acquisition of knowledge, teaching conspicuous strategies, pre-teaching background knowledge, guiding through scaffolding, reviewing that requires students to apply previously learned knowledge, and blending new and old knowledge to build big ideas.

NCTM math standards:
• Algebra
• Geometry
• Data Analysis &
  Probability
• Measurement
• Number &   Operations

Math topics:
All topics

7th & 8th Grades

Study:
Byrnes & Al Wasik.

Role of conceptual knowledge in mathematical procedural learning.

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math_3-5_17

Strategy: Dynamic Interaction View
Subjects: Experiment 1: Nineteen children from the fourth grade of a middle-class elementary school (M = 9 years, 11 months) and 51 children from the sixth grade of a middle-class junior high school (M = 12 years, 1 month).
Experiment 2: Fifty-one fifth graders  (M = 10 years, 9 months).
Results: Experiment 1: The total conceptual knowledge items were uncorrelated with LCD scores.
Experiment 2: None of the average gain scores in the three groups differed significantly.

Description: The simultaneous activation view is compared to the dynamic intervention view.  Proponents of simultaneous activation as described by the authors propose remediating computational errors through the use of concrete models (manipulatives) and that conceptual knowledge is both necessary and sufficient for the correct use of procedures.  The authors propose that conceptual knowledge is necessary but not sufficient.  They describe dynamic intervention as arguing for distinct systems that interact diachronically and for a progressive independence of procedural knowledge with expertise.  Experiment 1 looked for a correlation between conceptual knowledge and procedural knowledge.  In experiment 2 the intervention strategy for dynamic intervention consisted of telling students that fractions could not be added like whole numbers (making a distinction between the category of fractions and the category of whole numbers). 

NCTM math standards:
• Number & Operations

Math Topic(s): Fractions

4^th and 5^th Grades

Study:
Stipek & Salmon.

The value (and convergence) of practices suggested by motivation research and promoted by mathematics education reformers.

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math_3-5_18

Strategy: Strategies and teacher practices designed to focus on learning and understanding mathematics concepts.
Subjects: 624 students in fourth through sixth grade: 46 African American, 358 Latino, 49 Asian, 92 White, 26 other ethnic group, remainder no ethnic data available.
Twenty-four teachers divided into three groups.  Two groups expressed commitment for reformed mathematics while the last group had no interest in reformed mathematics practices.
Results: Comparing teachers' practice and student learning; the average gain of 4.25 of the 13 conceptual items for students of teacher with the five highest scores compared to the average gain of 2.39 items achieved by students of teachers with the five lowest scores.

Description: A “Learning Orientation” with nine dimensions of teacher practices was analyzed for teachers implementing “Seeing Fractions” (a replacement unit that was developed to be consistent with the California Mathematics Framework) and for traditional teachers covering addition and comparisons of fractions using traditional textbooks.  The nine dimensions were: (a) the degree to which teachers emphasized student effort and conveyed the message that effort will eventually pay off; (b) the degree to which the teaches emphasized and encouraged students to focus on learning, understanding, and mastery; (c) the degree to which teachers emphasized performance;  (d) the degree to which the teachers encouraged and gave opportunities for students to work autonomously; (e) the frequency with which teachers made social comparisons;  (f) the kind of affect teachers displayed; (g) the level of teachers’ enthusiasm and interest in mathematics; (h) the type of environment the teachers fostered; and (i) the degree to which teachers emphasized speed in completing tasks.

NCTM math standards:
• Number & Operations

Math Topic(s):
Fractions

4^th to 6^th grade

Study:
Irwin.

Using everyday knowledge of decimals to enhance understanding.

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math_6-8_18

Description: Pairs of students were presented with two types of sentence problems, contextualized and noncontextualized. Contexts included different sizes of soft drink bottles, monetary exchanges between countries, and other uses of metric measurement. There were three categories of decimal fractions problems: magnitude, addition and subtraction, and multiplication and division. The problems addressed misconceptions about decimals.

NCTM math standards:
• Measurement
• Number & Operations

Math Topic(s):
Decimal fractions

7th Grade

Study:
Reys and Yang.

Relationships between computational performance and number sense among sixth- and eighth-grade students in Taiwan.

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math_6-8_22

Description: Students completed a written computation test (WCT) and in the next week they completed a number sense test (NST). The WCT answers were scored as 1 (correct) or 0 (incorrect). The NST answers were scored with a maximum of two points. The investigators then checked for correlations between the two tests.

NCTM math standards:
• Number & Operations

Math Topic(s):
Arithmetic, Place Value, Computation, Mental Math

6th & 8th Grade

Study:
Lamon.

The development of unitizing: Its role in children's partitioning strategies.

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math_6-8_17

Strategy: Partitioning Strategies
Subjects: N = 346: fourth grade=63
Fifth grade=60
Sixth grade = 72
Seventh grade= 69
Eighth grade = 82
Effects: As students have more experience, they are more likely to use more sophisticated strategies.

Description: The students were given eleven partitioning tasks and asked to draw pictures to show how they would share various types of food among given numbers of people.

NCTM math standards:
• Number & Operations

Math Topic(s):
Partitioning

5th and 6th Grades

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