Study Author
& Title
 |
|
Strategy, Subjects, Results
 |
Description of
Strategy/Program
|
NCTM Math Standards,
Math Topics,
Grades |
|
Table
information is abbreviated. Click "Read full review" links below for full
citations of author and journal names and for details about the
studies. |
|
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.
Grades : 8th to 10th Grades |
|
Study:
E. Harskamp, C. Shure & A. Van
Streun.
Title: The graphics calculator in mathematics
education: An experiment in the Netherlands.
Read full review
math_9-12_15
|
New
Review
4 |
Strategy: Graphing
calculator
Subjects: 294 pre-university Dutch
students, 16-17 years old.
Results: Students in the
treatment group made significantly more use of graphical solutions than
the students in the control group. Males used the graphing calculator
significantly more than females. The graphing calculator had a positive
effect on the weaker math students. |
Description: This study utilized two experimental
conditions and one control condition in a senior high mathematics
classroom. Three classrooms used the graphing calculator throughout the
year with all topics in their textbook. Five classrooms used the graphing
calculator for only one topic for a two-month long implementation and four
classrooms (control group) covered the topics in the textbook without
using the graphing calculator. |
NCTM Math
Standard:
• Algebra
Math
Topics : Functions and graphs, change and derivatives, and
exponential functions
Grade: 12th Grade |
|
Study:
Schoen & Hirsch.
The Core-Plus
Mathematics Project: Perspectives and student achievement.
Read full review
math_9-12_5 |
4 |
Strategy: Core-Plus Mathematics Project
Subjects:
64 high schools in 11 states, cross-section of diverse students from
urban, suburban, and rural communities
Results: Results showed
that all CPMP groups performed significantly better on solving
mathematical tasks set in context than the comparison groups. The
comparison groups performed significantly better with paper-and-pencil
procedures at the end of Course 1, but the results were not significant
for Course 2.
Effect Size on ITED-Q
Course 1 ES=+.19
Course 2
ES=+.04
|
Description: The CPMP curricula consist of a
single core sequence for college-bound and employment-bound students
during the first three years of high school that embody the content,
processes, and teaching principles recommended by the NCTM standards.
Building connections among topics is the primary focus. Strands are also
connected by thinking mathematically, such as visual thinking, recursive
thinking, searching for and explaining patterns, making and checking
conjectures, reasoning with multiple representations, inventing
mathematics, and providing arguments and proofs. Fundamental themes of
data, representation, shape, and change also provide connections across
strands.
Curriculum
development principles include: (1) mathematics as an active science of
patterns, (2) problems that include a context for developing student
understanding of mathematics, (3) the processes of exploration and
experimentation necessarily precede and complement theory, and (4) the use
of graphics calculators and other technology as tools for developing
mathematical understanding and for solving authentic problems. Pedagogical
principles include the importance of students' sense making of mathematics
and real-life contexts. The instructional materials are designed to
reflect the importance of collaborative learning, social interaction, and
communication. |
NCTM Math
Standards
• Algebra
• Geometry
•
Data Analysis &
Probability
• Number &
Operations
Math Topic(s):
Symmetry, functions, matrices,
data analysis, and curve fitting.
9th to 12th
grade.
|
|
Study:
Thompson & Senk.
Title: The effects of curriculum on achievement
in second-year algebra: The example of the University of Chicago
School Mathematics Project.
Read full review
math_9-12_11 |
New
Review
4 |
Strategy: Skills and concepts learned and applied
using the University of Chicago School Mathematics Project (UCSMP)
Advanced Algebra textbook
Subjects: 306
students in heterogeneous classes studying second-year algebra in four
high schools. The high schools selected were in a White middle-class
suburb of Atlanta, a rural area that is becoming a suburb of Chicago, a
small semi-rural community in Mississippi, and an affluent suburb of
Philadelphia. Of the students, 19% were in Grade 10, 76% in Grade 11, and
5% in Grade 12. Additionally, 84% were Caucasian, 3% African American, 1%
Hispanic, while the remainder were classified as other or
unknown.
Results: Students using the UCSMP curriculum
significantly outperformed students in the comparison curriculum
(p=0.0014) on all items of the post-test. However, analysis of
the items all students in the study had the opportunity to learn did not
indicate a significant difference (p=0.108). Performance on the
eight skill items in this last analysis was comparable for the two
curricula. |
Description: UCSMP is a curriculum that uses
reading and problem solving, realistic applications, technology (graphing
calculators and/or computers), a multidimensional approach understanding,
and an instructional format featuring continual review combined with a
modified mastery-learning strategy. It emphasizes
understanding of concepts through multiple representations, realistic
contexts, and the use of technology. There is less emphasis on skills than
in a traditional curriculum. The instructional method often uses
small-group explorations and extended projects, both involving writing
about mathematics. |
NCTM Math
Standard :
•
Algebra
Math Topics:
Linear equations, binomial multiplication, graphs of quadratic
equations, exponential equations, the equation for the inverse-square
function, recursion
Grades: 10th to 12th Grade |
|
Study:
M. A. Huntley et al
Title: Effects of Standards-Based Mathematics
Education: A Study of the Core-Plus Mathematics Project Algebra and
Functions Strand
Read full review math_9-12_14 |
New
Review
3 |
Strategy: Core-Plus Mathematics Project
(CPMP)
Subjects: Third year high school students from
six U.S. schools (two of the sites were in the Southeast, two in the
Midwest, one in the South, and one in the Northwest). The number of
students ranged from 90 - 180 per site with a maximum of 593 students
tested at the conclusion of the study.
Results:
Students in the experimental group outperformed students in the control
group on items that involved applying algebraic concepts to solving
contextual problems. On items that assessed symbol manipulation, the
control group outperformed the experimental group. |
Description: The Core-Plus Mathematics Project
(CPMP) is a four-year integrated high school mathematics curriculum. Major
concepts are developed through investigating concepts in the context of
applied problems and mathematical modeling. In particular, algebraic
concepts are developed using graphic, numeric, and symbolic
representations. Graphing calculators are integral, promoting connections
among the forms of representation, encouraging new methods of problem
solving, and decreasing the need for symbolic manipulation procedures.
Since this study was carried in 1997 the curriculum has been revised (in
2003 and in press) to enhance the in-context approach and also include
more work with procedural algebraic skills. |
NCTM Math
Standard:
•
Algebra
Math
Topics: Functions, algebraic expressions, systems of equations
Grade: 11th Grade |
|
Study:
Webb.
The impact of the
Interactive Mathematics Program on student learning.
Read full review
math_9-12_2 |
3 |
Strategy: Interactive Mathematics Program (IMP)
Subjects: Study 1: 1121 students' transcripts from 3 California
high schools (1 Middle-Sized Area = 2075 students, 1 Metro Area=2000
students, 1 City Area=1600 students)
Study 2: 116 high scoring students
(divided equally between treatment and control group) from the Metro Area
high school.
Study 3: 115 ninth grade, 184 tenth grade, 62 eleventh
grade students
Study 4: 136 ninth grade, 174 tenth grade
students
Study 5: 62 ninth grade, 80 tenth grade
students
Results: Study 1: Total number of students taking more
than three years of college-qualifying math courses was significantly
higher for the treatment group than the control group.
Study 2: No
significance on SAT math test, but there was a significant difference
favoring the IMP students in both math and overall GPA.
Study 3: The
mean scores for the IMP 9th - 11th graders were significantly higher than
the control group.
Study 4: The mean scores for the IMP 9th and 10th
graders were significantly higher than the control group.
Study 5: At
grade 9, the mean score of IMP students was significantly lower than the
control group in a traditional Algebra course enhanced with a unit on
statistics. There was no significant difference for the 10th graders.
|
Description:
IMP is a sequence of college
preparatory courses designed for grades 9-12. It is organized into five to
eight week units that focus on a central problem or theme. It incorporates
technology instruction and applications throughout the program. Students
solve both routine and non-routine problems, using calculators. Students
are encouraged to work cooperatively. They learn to experiment,
investigate, ask questions, make and test conjectures, reflect, and
accurately communicate their ideas and conclusions. Students are assigned
to work on "Problems of the Week" up to five days. They are encouraged to
function as independent learners as a result of using multiple sources of
information, including their teachers, the textbook, classmates, and other
resources. |
NCTM Math
Standards
• Algebra
•
Geometry
• Data Analysis & Probability
Math
Topic(s):
Algebra, geometry, trigonometry, probability, statistics, discrete
mathematics, and matrix algebra.
9th to 12th
grades
|
|
Study:
Lott et al.
Curriculum and
assessment in SIMMS Integrated Mathematics.
Read full review
math_9-12_3 |
3 |
Strategy: SIMMS Integrated Math
Subjects: High
school students (n = 125-280) in intact classes in five studies (four in
Montana and one in El Paso). SIMMS programs levels 1, 2, 4, and 6 versus
non-SIMMS programs.
Results: Montana: On all levels no
significant difference on PSAT. Level 1 - On project constructed questions
called End-of-Year-Tasks (EOYT), SIMMS students scored significantly
higher on the common item. Level 2 - No significant difference on
EOYT.
El Paso: no significant difference on PSAT nor EYOT |
Description:
SIMMS Integrated Math is a
complete mathematics program for grades 9-12. It is constructed in six
levels each consisting of one year of work. Levels 1 and 2 provide basic
mathematical literacy. Levels 3 and 5 are for students with
non-mathematical or non-scientific aspirations, whereas levels 4 and 6
prepare students to complete a post-secondary mathematics
curriculum.
The program has the
following characteristics, it is (1) integrated and interdisciplinary, (2)
problem-centered and applications based, (3) technology based, (4)
sensitive to multiple perspectives and the negative effects of bias and
stereotyping, (5) multi-modal to accommodate multiple learning
styles.
Mathematical modeling
is the basic thread of the curriculum, knitting together mathematics and
other subjects. Students organize, relate, interpret, justify, evaluate,
summarize, and communicate ideas as they explore topics and make inquiries
about real-world and mathematical concepts. They confront complex issues
by "mathematizing" real-world problems, interpret and communicate
solutions, and ultimately reflect on their own performance. |
NCTM Math
Standards
• Algebra
• Geometry
•
Data Analysis &
Probability
Math Topic(s):
Basic math concepts,
pre-algebra, algebra, geometry, and college-prep.
9th - 12th
grades
|
|
Study:
Cichon & Ellis.
The effects of
Math Connections on student achievement, confidence, and
perception.
Read full review
math_9-12_4 |
3 |
Strategy: Math Connections (MC)
Subjects: Summary
of several studies
Results: On CAPT, PSAT and SAT, MC students
scored as well or better than nonparticipants. Students in classes with MC
trained teachers have greater confidence in learning mathematics and see
the usefulness of mathematics to a greater degree than
non-participants.
Case study results of Hispanic and African-American
at-risk students in an inner-city school suggest that all students can
successfully meet the challenge of a mathematically rigorous
course. |
Description: Math Connections is presented to
students as a powerful tool for interacting with their environment. Its
primary goals are to: (1) bridge the worlds of education, students, and
business through mathematics; (2) increase mathematical power of all
students; (3) empower students for their own learning; (4) develop a core
curriculum that reflects the standards of the National Council of Teachers
of Mathematics (NCTM); and (5) empower teachers to meet NCTM's
Professional Standards for Teaching Mathematics.
Math Connections
enables students to investigate a concept in order to recognize patterns
that can be presented as a formula. Each year of the curriculum is based
on a theme that connects and unifies mathematical topics. The theme for
Year 1 is Data, Numbers, and Patterns. Students use data, linear
equations, and graphing calculators to forecast events. Year 2's theme,
Shapes in Space, focuses on properties and measurement of figures. The
principles of congruence and triangulation of polygons are, also,
examined. Students use matrices to solve linear equations and learn to
calculate the volumes of a cone and a sphere. Mathematical Models, is the
theme for Year 3. At this time, logic and the properties of an axiomatic
system are introduced. |
NCTM Math
Standards
• Algebra
• Geometry
•
Data Analysis &
Probability
All Math Topic(s)
9th to 12th
grades
|
|
Study:
Senk.
Effects of the UCSMP
secondary school curriculum on students' achievement.
Read full review
math_9-12_6 |
3 |
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. |
Description:
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:
Calhoon and Fuchs.
The effects of
peer-assisted learning strategies and curriculum-based measurement on the
mathematics performance of secondary students with disabilities.
Read full review
math_9-12_7 |
3 |
Strategy: Peer-Assisted Learning Strategies (PALS) and
Curriculum-Based Measurement (CBM) for secondary special education
students.
Subjects: 92 public high school students in 9th-12th
grades. All students met the state and local eligibility requirements for
having a disability in mathematics. Each participant received math
instruction in one of 10 self-contained special education resource rooms
and every student had an Individualized Education Program (IEP)
mathematics goal. Disability categories were 68 student Learning Disabled,
4 Behavior Disordered, 12 Mentally Retarded and 8 with some other
disability.
Results: The PALS/CBM group significantly
outperformed the control group on computation scores. No significant
difference was found between the experimental and control groups on the
concept/application scores. |
Description: The PALS and CBM treatments
were the two primary components of this study. PALS is a class-wide peer
tutoring strategy used to teach students computation and application
skills. Students received two 30-minute sessions each week. Students were
paired within each treatment class and trained to interact with each other
according to the PALS method. The tutor modeled a verbal rehearsal routine
of specific procedural steps designed to help the tutee to complete the
computation or application activity. The tutors and tutees used verbal and
written interaction, which required that the tutor respond each time the
tutee wrote or spoke an answer. Finally, the two students reversed roles
and repeated the procedure.
CBM is a standardized
method for tracking student proficiency in which the teacher identified
the curriculum and level that the student is expected to master by the end
of the year. The teacher then administered a CBM test at this goal level
once a week. Each CBM test reflected the entire year's curriculum allowing
student performance to be compared at different points in time. Students
could earn external rewards for their performance and also received
detailed feedback about their scores. |
NCTM Math
Standards:
•
Number &
Operations
Math Topic(s): Computation and
concepts/application skills.
9th to
12th grade.
(Also in
Diverse Learners) |
|
Study:
O' Callaghan
Computer-Intensive
Algebra and students' conceptual knowledge of functions.
Read full review
math_9-12_9 |
3 |
Strategy:
Computer-Intensive Algebra (CIA)
Subjects:
Eighty volunteer students with
lower-middle to middle SES status enrolled in a college algebra
course.
Results:
Treatment subjects achieved gains in
the concepts of modeling, translating, and interpreting as they relate to
functions. There was no significant difference in groups in regard to the
concept of reification. |
Description:
CIA teaches college algebra using
computer technology and with a focus on real-world
situations. |
NCTM Math
Standard:
• Algebra
Math
Topics: College algebra, functions, modeling.
12th
grade |
|
Study:
Saxon.
Incremental
development: A breakthrough in mathematics.
Read full review
math_9-12_10 |
2 |
Strategy:
Program Name: Saxon
Algebra
Subjects:
Ninth grade algebra students (n=1382) from twenty Oklahoma
public schools.
Results:
No attempt was made to verify the comparability of the
treatment and control groups prior to performing the experiment,
therefore, although students in the treatment group outscored the control
group, it is not possible to meaningfully attribute these gains to the
intervention. |
Description:
This strategy employs an algebra
text written to provide continuous review of four or five problem sets for
each fundamental part of a skill. Each problem set has only four or five
problems on the new facet of the skill and approximately twenty review
problems of prior facts or skills. This method provides the student a
longer period of time in which to learn a skill or develop a
concept. |
NCTM Math
Standard:
Algebra
Math
Topics: Signed numbers, evaluation, equations, adding terms, math
word problems, adding expressions, exponents, factoring, percent problems,
value problems, radicals, linear equations, simultaneous equations,
scientific notation, integral exponents, and uniform motion.
9th
grade |
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.