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:
Nye, Hedges & Konstantopoulos.
The long-term effects of small classes in early grades: lasting benefits in mathematics achievement at grade 9.
Read full review
math_k2_23 |
5 |
Strategy: Project STAR - 6-year follow-up
Subjects: Initially 79 elementary schools in 42 school districts participated. Students and teachers in grades K through 3 were randomly assigned to a small class (13 - 17 students), a large class (22 - 26 students), or a larger class with a full-time aide. This study examined the achievement of Project STAR students when they were in grade 9. The results are based on the achievement of the "stayers" - those students for whom they had 9th grade mathematics test scores available (757 out if 1,938 participants).
Results: Small class size led to significantly higher achievement for students at the conclusion of the experiment. The positive effects of small classes in early grades resulted in mathematics achievement gains that persisted through grade 9. |
Description: The students and teachers were randomly assigned to a small class (13-17 students), a large class (22-26 students), or a larger class with a full-time aide |
NCTM Math Standards
• Algebra
• Geometry
• Data Analysis &
Probability
• Measurement
All Topics
K to 3rd Grade |
|
Study:
Fuchs et al.
Enhancing students'
helping behavior during peer-mediated instruction with conceptual
mathematical explanations.
Read full review
math_3-5_8 |
5 |
Strategy:
Peer-mediated
instruction.
Subjects:
200
second to fourth grade students in 40
classrooms.
Results:
Peer-mediated instruction results were significantly
better than the control groups in all groups except the learning disabled
students. |
Description: This study compared the effects of
classroom treatment (peer-mediated instruction, peer-mediated
instruction elaborated, and peer-mediated plus conceptual) on
students in grades 2 to 4. Students were paired up to work on a
skill in which one student provided assistance to another student.
Tutoring assignments were changed every two weeks based on performance
assessments. |
NCTM Standards:
• Number &
Operations
Math Topic(s): Computation
2nd to 4th grade |
|
Study:
Pesek & Kirshner.
Interference of
instrumental instruction in subsequent relational learning.
Read full review
math_6-8_9 |
5 |
Strategy: Instrumental Instruction together with Relational
Instruction vs. Relational Instruction only
Subjects: Six
classes of heterogeneously grouped 5th grade students (n=108) from a
"semi-rural" area participated in this study. Additionally, 6 of these
students, 3 high achieving students and 3 low achieving students (3 boys
and 3 girls) were interviewed.
Effects:
Students in the group that
received both kinds of instruction (instrumental, then relational for a
total of 8 days) scored no better than students receiving only the
sense-making (i.e. relational for a total of 3 days)
instruction.
Effect Size = -0.36 |
Description:
Fifth grade students (n = 108) in six intact classes were
randomly assigned (random stratification) into two groups. One group
received five days of instruction based heavily on rote memorization of
area and perimeter formulas and practiced using those formulas in a
variety of situations involving diagrams and word problems. During this
time, the other group reviewed material unrelated to the content of area
and perimeter. Then, all children were returned to their regular classes
and received three days of instruction based heavily on sense-making and
describing their thinking to their classmates. During these three days
students encountered word problems and diagrams, but were not given any
formulas with which to work. |
NCTM
Standards:
• Geometry
• Measurement
Math
Topic(s):
Area
5th Grade
|
Study:
Carroll and Isaacs.
Achievement of students using the University of Chicago School
Mathematics Project's Everyday mathematics.
Read full review
math_k2_1 |
4 |
Strategy:
Everyday Mathematics (EM)
Subjects:
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);
Longitudinal study (from first grade to fifth
grade) started with 496 first-grade students in five school districts.
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:
Fennema & Carpenter.
A longitudinal study of learning to use children's thinking in mathematics education.
Read full review
math_k2_14 |
4 |
Strategy: Cognitively Guided Instruction
Subjects: 14 classrooms of
first, second, and third grade
students whose teachers taught at the same grade
level for 3 years.
Students ranged from 70-99% white.
Children receiving free or reduced lunch ranged from 4-26%.
Results: Teachers changed their beliefs by year 4. Gains in student achievement appeared to be directly related to changes in teachers' instruction. Students’ concepts and problem solving performance improved without a decline in performance of computational skills.
|
Description: Cognitively Guided Instruction, a teacher development program that focuses on helping teachers understand the learning development of children’s mathematical thinking, was used to identify what impact it would have on teachers’ beliefs, instruction, and on students’ learning. Teachers learned that children could solve problems without being shown procedures for solving them. |
NCTM Math Standards:
• Number & Operations
Topics:
• Solving arithmetic word problems
1st, 2nd, and 3rd Grades |
|
Study:
Cramer, Post & del Mas.
Initial fraction
learning by fourth and fifth-grade students: A comparison of the effects
of using commercial curricula with the effects of using the Rational
Number Project curriculum.
Read full review
math_3-5_3 |
4 |
Strategy:
Rational
Number Project (RNP)
Subjects: 1600+
students of high SES from 66 fourth and fifth grade classrooms in a
suburban school district south of Minneapolis.
67 teachers from 17 schools
chose to participate.
Results:
RNP
students had a stronger conceptual understanding of fractions, were better
able to judge the relative sizes of two fractions. There were no
differences between the RNP students and the control students on items
dealing with equivalence, or symbolic addition and subtraction. A
posttest
Effect Size = +.205 favored the RNP
students. |
Description: The Rational Number Project is a
research-based curriculum that involves students in working with multiple
concrete models, emphasizes translations among and within multiple
representations (manipulatives, pictorial, verbal, symbolic, and real
world) and has students regularly reacting with one another in group
situations. |
NCTM math standards:
• Number &
Operations
Topics:
Fractions
4th
& 5th Grades |
|
Study:
Freiberg, Connell, & Lorentz.
Effects of
consistency management on student mathematics achievement in seven Chapter
I elementary schools.
Read full review
math_3-5_5 |
4 |
Strategy:
Consistency
Management and Cooperative Discipline (CMCD)
Subjects:
543
students in the fourth, fifth, and sixth grades in 6 elementary and 1 middle
school in a high crime rate urban neighborhood in the southwest United
States.
Results:
The
three schools that used CMCD in conjunction with a constructivist math
program showed higher gains in achievement than students from schools that
used only the constructivist math program. On a state mathematics test,
Effect Size = + 0.33 in favor of the CMCD and constructivist math
program combination. |
Description:
This study focused on the
additive effect of CMCD on a constructivist mathematics program (Move It
Math). CMCD is a research-based, classroom-tested model that builds on
shared responsibility for learning and classroom organization between
teachers and students. The teacher creates a consistent but flexible
learning environment. Both teacher and students establish a cooperative
plan for classroom rules, procedures, use of time, and academic
learning. |
NCTM math
standards:
• Algebra
• Geometry
• Data Analysis &
Probability
• Measurement
• Number & Operations
All topics
4th
to 6th Grade |
|
Study:
Hohn & Frey.
Heuristic training
and performance in elementary mathematics problem solving.
Read full review
math_3-5_6 |
4 |
Strategy:
Using
the
SOLVED
heuristic
to solve word problems.
Subjects: (Study One) 31
third graders, 37 fourth graders, and 35 fifth graders in two intact
classes at each grade level.
(Study Two) conducted in the same school
as the first study, but involved 38 third graders, 37 fourth graders, and
45 fifth graders in two different intact classes at each grade
level.
Results: (Study One) Statistically
significant differences were found favoring the experimental
classes.
3rd
grade Effect Size = +1.77
4th grade Effect Size = +1.81
5th grade
Effect Size = +0.56; all in favor of the experimental
classes.
(Study
Two) Statistically significant differences favoring the experimental
classes over time were found for both the third and fifth graders.
Positive gains were observed for the fourth grade experimental class, but
they were not statistically significantly. Gender and ability were not
found to be significant. |
Description:
SOLVED is a new heuristic based on the
classic Polya heuristic, however, it is expanded by including steps for
connecting the new problem to a problem type, to prior experiences with
similar problems, and to visual representations of the
problems.
Study One compared a
specific heuristic (SOLVED) to a textbook-based approach to problem
solving.
Study
Two further analyzed strategy use and the factors of gender and
ability. |
NCTM math standards:
• Number &
Operations
Topics:
Solving
word problems
3rd
to 5th Grade |
|
Study:
Fuchs et al.
Acquisition and
transfer effects of classwide peer-assisted learning strategies in
mathematics for students with varying learning histories.
Read full review
math_3-5_7 |
4 |
Strategy: Peer-Assisted Learning Strategies (PALS) in
Mathematics
Subjects: 9 urban schools. Heterogeneous learners.
40 general educators teaching grades 2-4. The 40 teachers were stratified
by grade level and randomly assigned to two groups. Half randomly assigned
to PALS treatment group and half to contrast group.
Each teacher
identified 3 students for which treatment effects were assessed; students
were selected as follows:
(a) 1 student low-achieving and classified
as learning disabled (LD).
(b) 1 low-achieving but not
referred for
special education assessment.
(c) 1 student with average math
performance.
Results:
Across the types of learners and types of measures, students
in the PALS treatment outperformed those in the contrast group. However,
across treatment groups and types of learners, students grew more on the
operations or acquisition measure than on the concepts/applications
transfer measure. |
Description: A peer-assisted learning strategy
(PALS) is a peer-tutoring method that simultaneously pairs all students
within a class to work on academic material in structured
ways. |
NCTM math standards:
• Number &
Operations
Topics:
Basic
facts
2nd to 4th
Grade |
|
Study:
Good & Grouws.
The Missouri
Mathematics Effectiveness Project: An experimental study
in fourth-grade classrooms.
Read full review
math_3-5_9 |
4 |
Strategy:
The
study investigated the effectiveness of a structured format for short and
long-range lesson planning in whole class
instruction.
Subjects: A volunteer
sample of 40 fourth grade teachers from 27 schools in the Tulsa Public
Schools was studied. Most of the semi-departmentalized schools were in low
socioeconomic status areas.
Results: Students
of treatment teachers outperformed students of control group teachers on
both standardized and content tests. |
Description: The program, in total, represented a
system of instruction where instructional activity is initiated and
reviewed in the context of meaning. Each lesson was structured to
include daily review and mental math, development, seatwork, homework, and
special weekly and monthly reviews so as to enhance involvement and to
minimize student performance errors. The principles of distributed
and successful practice are built into the program and teaching
presentations and explanations are emphasized. |
NCTM math
standards:
• Number &
Operations
All topics
4th
Grade |
|
Study:
McNeil and Alibali.
Learning mathematics
from procedural instruction: externally imposed goals influence what is
learned.
Read full review
math_3-5_10 |
4 |
Strategy: Externally imposed goals for mathematics
achievement
Subjects: 53 children (23 boys and 30 girls) in the
third- and fourth-grade in an elementary parochial school. The students
mean age was 9 years, 7 months.
Results: Students’ conceptual
scores increased the most when given a learning goal and increased the
least when no externally imposed goal was given. Transfer scores on
related equivalence problems favored the experimental group over the
control group. |
Description: This study tested
whether externally imposed goals for mathematics achievement would
increase students’ conceptual, procedural, and transfer abilities on
equivalence problems. The goals were either performance related, (which
encouraged them to get problems correct) or learning related, (which
encouraged them to understand the problems well). The students were
randomly assigned to a control group, a performance goal group, or a
learning goal group. |
NCTM math
standards:
• Algebra
• Number
& Operations
Topics:
Equivalence 3rd & 4 th
Grade |
|
Study:
Wood & Sellers.
Deepening the
analysis: Longitudinal assessment of a problem-centered mathematics
program.
Read full review
math_3-5_12 |
4 |
Strategy:
Longitudinal
assessment of a problem-centered mathematics program.
Subjects:
Students
in grades two, three, and four.
School district has a predominantly
white student population although the background of the students consists
of a wide range of socioeconomic backgrounds.
Results:
After 2 years in problem-centered classes, students have
significantly higher achievement on standardized achievement measures,
better conceptual understanding, and more task-oriented beliefs for
learning mathematics than those in textbook instruction. These results
remain even after the problem-centered students spend a year in a
textbook-based program. |
Description: Based on data from earlier studies,
this experiment examined cognitive models that guide student
activities. In addition to instructional activities, the classroom
setting included pair interactions and total group interactions. The study
made a longitudinal analysis of arithmetical achievement of children in a
problem-centered mathematics program as opposed to students in a
traditional textbook-based program. |
NCTM math standards: • Number & Operations
Topics:
Computation
2nd to 4th
Grade |
|
Study:
Woodward & Baxter.
The effects of an
innovative approach to mathematics on academically low-achieving students
in inclusive settings.
Read full review
math_3-5_13 |
4 |
Strategy: Everyday Mathematics.
Subjects: 205 third
graders; of particular interest was a subset of students who had learning
disabilities or were low achieving in mathematics.
Results:
Results
of the Iowa Test of Basic Skills (ITBS) concepts subtest favored the
intervention group. ITBS results for the low-achieving students indicated
non-significant differences. An individually administered test of
problem-solving abilities strongly favored the intervention
group. |
Description: Everyday Mathematics is an
elementary curriculum developed by the University of Chicago School
Mathematics Project. It de-emphasizes computation in order to
include more topics in mathematics at a greater depth than in a
traditional curriculum. It is a student-centered curriculum that has
a problem-solving approach with an emphasis on conceptual development and
number sense. Students are taught using a variety of tools including
manipulatives and calculators. |
NCTM math standards:
• Number & Operations
All Topics
3rd Grade |
|
Study:
Fuchs, Fuchs, Prentice, Burch, Hamlett,
Owen, Hosp & Jancek.
Explicitly teaching
for transfer: Effects on third-grade students' mathematical
problem-solving.
Read full review
math_3-5_19 |
4 |
Strategy: Explicit teaching of 4 dimensions in which word
problems can be altered, combined with peer-assisted learning and
demonstration.
Subjects: Twenty-four third grade teachers from a
southeast urban school district
Results: Results indicated that
explicit teaching of the methods to solve the problems lead to increased
problem solving ability. Explicit teaching of transfer techniques lead to
increased ability to solve even novel word problems that have been
modified along several dimensions at once. |
Description: Third grade students
were taught solution methods to designated problem types by using explicit
instruction, multiple worked examples, and peer-assisted learning.
Teachers also used specific meta-cognitive skills to facilitate learning
how to transfer these problems to more novel situations. |
NCTM math
standards:
• Number & Operations
Topics:
Arithmetic word problems
Grade: 3rd
grade |
|
Study:
Jitendra, Griffin, McGoey,Gardill, Bhat
& Riley.
Effects of
Mathematical Word Problem Solving by Students At Risk or with Mild
Disabilities.
Read full review
math_3-5_22 |
4 |
Strategy: Explicit Schema-Based Strategy or Traditional
Basal Strategy for the Acquisition, Maintenance, and Generalization of
Mathematical Word Problem Solving.
Subjects: 34 second through
fifth graders in four public schools in the northeastern and southeastern
US. 25 were classified as having mild disabilities (LD), educably mentally
retarded (EMR), or seriously emotionally disturbed (SED). The remaining 9
were low performing students experiencing difficulty in
mathematics.
Results: Both groups' performance increased from
the pretest to the posttest. The differences between groups on the
posttest, delayed posttest, and generalization test were statistically
significant, favoring the schema group. |
Description:
Forty to forty-five minute training sessions were conducted with
small groups of 3 to 6 students. Trained investigators delivered the
treatment, alternating across conditions.
Schema Treatment:
Students were taught to solve three different word problem types by using
the schema strategy. Phase 1: Students practiced identifying the different
problem types (e.g. change, group, and compare) and then mapped the
features of the situation onto schema diagrams. Phase 2: Training began
with a review of the problem schema, but problems, instead of story
situations, were presented. Phase 3: Students were taught to use a second
strategy step (i.e. action schema and strategic knowledge). Students
developed a general rule based on the part-whole concept. Students
received explicit feedback, were guided during practice trials, and
completed worksheets containing either story situations or word
problems.
Traditional
Treatment: Students received instruction using the Addison-Wesley
Mathematics basal mathematics program. Phase 1: The instructor presented
and directed the Think Math activities as specified in the basal program
for the entire instruction period. Phase 2: Instruction entailed the use
of a 5-step checklist procedure to solve word problems: (1) understand the
question, (2) find the data, (3) plan, (4) find the answer, and (5) check
back. Students completed problems of all three types at the end of each
session and received feedback on the correctness of their
solutions. |
NCTM math standards:
• Number &
Operations
Topics:
Problem
Solving
Math
Topic:
Arithmetic word problems
2nd to 5th
grade & Diverse Learners |
|
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 |
4 |
Strategy:
Connected Math (CMP) and Everyday Math (EM)
Subjects:
Standards-Based Instruction vs Matched Traditional Instruction
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
|
Description: Standards-type curricula are
problem-oriented providing 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
4th & 8th
Grades
|
|
Study:
Wood & Sellers.
Deepening the
analysis: Longitudinal assessment of a problem-centered mathematics
program.
Read full review
math_3-5_12 |
4 |
Strategy:
Longitudinal
assessment of a problem-centered mathematics program.
Subjects:
Students
in grades two, three, and four.
School district has a predominantly
white student population although the background of the students consists
of a wide range of socioeconomic backgrounds.
Results:
After 2 years in problem-centered classes, students have
significantly higher achievement on standardized achievement measures,
better conceptual understanding, and more task-oriented beliefs for
learning mathematics than those in textbook instruction. These results
remain even after the problem-centered students spend a year in a
textbook-based program. |
Description: Based on data from earlier studies,
this experiment examined cognitive models that guide student
activities. In addition to instructional activities, the classroom
setting included pair interactions and total group interactions. The study
made a longitudinal analysis of arithmetical achievement of children in a
problem-centered mathematics program as opposed to students in a
traditional textbook-based program. |
NCTM
Math Standards:
• Number & Operations
Topics: Computation
2nd to 4th
Grade |
|
Study:
Fuchs, Fuchs, Prentice, Burch, Hamlett,
Owen, and Schroeter.
Enhancing third-grade
students' mathematical problem-solving with self-regulated learning
strategies.
Read full review
math_3-5_27 |
New
Review
4 |
Strategy:
Self-Regulated Learning (SRL)
Subjects: 395
third graders from high- average-, and low-achievement categories, as well
as students with disabilities
Results: Effects for
high, average, and low-achievement students, as well as students with
disabilities, significantly favored the combination of transfer plus
SRL.
|
Effect Size* |
Immed |
Near |
Far |
| Control vs Transfer |
| High
Achievement |
+1.91 |
+1.75 |
+0.47 |
| Average
Achievement |
+1.78 |
+1.22 |
+0.54 |
| Low
Achievement |
+1.83 |
+1.24 |
+0.69 |
| Students w/Disabilities |
+1.07 |
+0.51 |
+0.24 |
| Control vs Transfer + SRL |
| Students w/Disabilities |
+1.43 |
+0.95 |
+0.58 |
| Transfer vs Transfer + SRL |
| Students w/Disabilities |
+0.23 |
+0.25 |
+0.43 | |
Description:
In SRL students set goals for their performance on independent
practice tasks during instructional sessions, score their performance in
terms of the process of their work and the accuracy of their answers. They
record their scores on individual and class graphs. Students also identify
opportunities to apply mathematical problem solving outside of
instructional sessions, discuss the opportunities with partners, report
them to the class, and plot their results on a class-wide
graph.
*Effect Size -
Immediate, Near Transfer, Far Transfer |
NCTM
Math Standards:
• Number & Operations
Topics:
Problem-solving
Diverse Learners
3rd Grade |
|
Study:
Darch, C.; Carnine, D.; and Gersten,
R.
Explicit instruction
in mathematics problem solving.
Read full review
math_3-5_30 |
New
Review
4 |
Strategy:
Explicit Translation Strategy
Subjects:
Seventy-three fourth graders in a middle-sized school district in the
Northwest who were predominantly Caucasian and from middle income
families.
Results: Seventy-three skill-deficient
fourth graders were assigned to four experimental groups. Those students
in the two explicit treatment groups scored significantly better on a
posttest than those in the basal instruction. Students in the explicit
group receiving extended practice significantly out performed all
groups. |
Description:
One aspect of the treatment was the direct teaching of clearly
articulated strategies for translating multiplication and division word
problems into mathematical equations. Strategies focused on choosing the
correct operation by introducing number families and how to discriminate
between operations. A second aspect involved providing extra practice to
those students who did not master a set of lessons. |
NCTM math
standards:
• Number &
Operations
Math topics:
Translating multiplication and division story problems into number
sentences.
4th
Grade |
|
Study:
Mokros.
Learning to reason
numerically: The impact of Investigations.
Read full review
math_k2_5 |
3 |
Strategy: Investigations in Number, Data, and Space.
Subjects: (First Study) 56 third grade and 40 fourth grade
students from diverse backgrounds located in Massachusetts schools in
urban suburban and rural communities
(Second Study) 46 second grade
students
(Third Study) 125 fourth grade students
Results:
The three studies cited show that students using the
Investigations program perform as well as students in traditional
curricula classrooms on basic facts and algorithms with the four
operations and may even perform better on difficult computations.
Investigations students perform better than their counterparts
from other curricula with respect to word problems, more complex
calculations embedded in word problems, and problems that involved
explaining how an operation worked.
|
Description:
The program has six major goals: (1) To provide meaningful
mathematical problems for students that are based on (a) important
mathematical ideas, (b) are addressed to a wide range of students, (c)
require students to think mathematically, and (d) encourage the use of
different strategies by students with different learning styles; (2) to
develop powerful mathematical thinking, explanation, justification, and
demonstration; (3) to encourage sustained thinking by focusing on a small
set of significant problems within each unit; (4) to provide both
coherence and depth in mathematical content; (5) to support teacher
learning; and (6) to connect students of all abilities to mathematics.
|
NCTM Math
Standards:
• Number & Operations
Topics:
• Basic facts, addition,
subtraction, division, multiplication, and word problems.
2nd to 4th
Grades |
Study:
Fuson.
Achievement results for second and third graders using the standards-based curriculum.
Read full review
math_k2_8 |
3 |
Strategy: Everyday Mathematics (EM)
Subjects: (Study One) Experimental Group: 343 second grade students in 22 classrooms in 11 schools including urban, suburban and rural or small-town schools. Range of SES; two classes were Spanish-speaking bilingual classes.
Control Group: 29 second graders attending a middle to upper class school in San Francisco and 33 Japanese second graders attending a middle-class public school in Tokyo.
(Study Two) Experimental Group: 236 third graders
Control Group: 1,800 students as a subset of 18,033 third graders who took the NAEP and answered all questions
Results: (Study One) On the mathematic achievement test, EM students scored between the Japanese and the US comparison students with the Japanese students scoring significantly higher than the EM students on the six most advanced items. The Everyday Math students were above the national norms for multiple digit addition and at the norm for multiple digit subtraction. |
Description: Students work in small groups or pairs exploring mathematical ideas. Students build their informal knowledge by making connections to everyday experiences. Teachers are advised to use manipulatives in order to scaffold students' thinking during problem solving and discussions. Students build conceptual understanding of number and operations by creating and solving story problems. Paper and pencil, in addition to mental, activities are designed to enable students to develop conceptual understandings of the operations and the standard multi-digit algorithms. Students are encouraged to invent and discuss their own solution methods. |
NCTM Math Standards:
• Geometry
• Data Analysis & Probability
• Measurement
• Number & Operations
Topics:
Multiple digit addition and subtraction, negative numbers, functions, fractions, mental computation, and geometry.
2nd and 3rd Grades |
|
Study:
Carter et al.
Student learning and
achievement with Math trailblazers.
Read full review
math_k2_9 |
3 |
Strategy: Math Trailblazers
Subjects: Third
grade classrooms from eight Chicago-area schools. Six schools were Chicago
public schools and two schools were located in a middle-class suburb of
Chicago. The city schools were comprised of 98% to 100% minority students.
Sixty-one to eighty-one per cent of the subjects were low income students.
In the suburban schools 12% were minority students, predominantly
Hispanic, and approximately 13% were low income.
Results: After
first year of implementation, 6 out of 8 Math Trailblazer schools had a
higher percentage of students meeting or exceeding the state goals than
their historical averages on the IGAP. By the end of the second year, all
8 schools were at levels above their historical averages regardless of the
initial level of student achievement. |
Description:
Math Trailblazers includes the following mathematical
strands: number and operations, including estimation; geometry and spatial
sense; measurement; data analysis, statistics, and probability; fractions
and decimals; and patterns, functions, and algebra. Problem-solving
contexts support student learning in all these areas. A distinctive
feature of the curriculum is the use of Teaching Integrated Mathematics
and Science (TIMS) Project Laboratory Investigations that involve the use
of a scientific method to study classification, length, area, volume, and
mass in all grades. Speed and density are also studied in the fifth grade.
|
NCTM Math Standards:
•
Algebra
• Geometry
• Data
Analysis &
Probability
•
Measurement
• Number & Operations
Topics:
All
3rd
Grade |
|
Study:
Moss & Chase.
Developing
children's understanding of the rational numbers: A new model and an
experimental curriculum.
Read full review
math_3-5_1 |
3 |
Strategy:
Unnamed
devised curriculum for rational numbers.
Subject:
29
fourth-grade students, 10-11 years of age; 16 were from a laboratory
school at a University and 13 from a private school of a similar
population, high SES.
Results:
The
results showed that both groups made improvement; the improvement of the
experimental group was significantly greater. On the Rational Numbers
Test, there was an Effect Size = + 1.78, favoring the experimental
group. |
Description:
The curriculum has three features that were deemed
by the researchers to be particularly effective: (a) beginning with
percents, (b) a uni-dimensional form of number representation – the number
ribbon, and (c) the emphasis on benchmark values for moving among the
various forms of representation. |
NCTM math
standards:
• Number &
Operations
Topics:
Percents and
Fractions
4th
Grade |
|
Study:
Clark & Kamii.
Identification of
multiplicative thinking in children in grades 1-5.
Read full review
math_3-5_2 |
3 |
Strategy:
Intelligence
testing (multiplication) in children.
Subjects:
336
children in grades 1-5 were randomly assigned to heterogeneous and
comparable classes at one public school in a low-to middle-income suburban
Alabama neighborhood. Fifty-one percent of the students were boys and 23%
were nonwhite.
Results:
Multiplicative
thinking is clearly distinguishable from additive thinking. It appears
early and develops very slowly. |
Description: The strategy, which
was a modification of a task devised by Sinclair (1981) and Piaget et al
(1968/1977), involved interviewing children about the relative eating
capacity of three plywood “fish” 5, 10, and 15 centimeters
long. |
NCTM math standards:
• Number &
Operations
Topics:
Multiplication
1st to 5th
Grade |
|
Study:
Helmke & Schrader.
Successful student
practice during seatwork: Efficient management and active supervision not
enough.
Read full review
math_3-5_4 |
3 |
Strategy:
Investigation
of existing factors effecting student practice during
seatwork.
Subjects:
39 fifth
grade classrooms (academically the lower two-thirds of student population)
from 24 primary schools in an area near Munich,
Germany.
Results:
Frequency
and length of practice during seatwork, in itself, were not related to
achievement. Teacher's diagnostic competence positively relates to
achievement when teachers are able to support individual students by
determining who needs support and how much support.
|
Description: This study
investigated the impact on student achievement and different factors
effecting seatwork. Seatwork refers to an instructional context in which
students work independently at written tasks and exercises. Teaching
behavior was observed and teachers’ diagnostic competence was assessed.
This study has no control group; the study was designed to document the
existing factors with respect to seatwork. |
NCTM math standards:
• Number &
Operations
Topics:
Basic algorithms, problem
solving
5th
Grade |
|
Study:
Wearne.
Acquiring meaning for
decimal fraction symbols: a one year follow-up.
Read full review
math_3-5_11 |
3 |
Strategy:
A
one-year follow up of conceptually-based instruction in decimal
fractions.
Subjects: 40 4th-graders in 2 classes from ethnically-mixed
middle schools in the original research treatment.
Class A: 19 students with
median percentile ranking of 55 on standardized math achievement test.
Class B: 21 students with math test ranking of 83. Comparison
group: 29 students in same schools. Class A's comparison group test
scores comparable to its treatment group. Class B's comparison group
identified as above average ability with test ranking of 95
Results:
Average- and lower-achieving students correctly solved questions
and used quantitative reasoning skills more often than a comparison group
who did not receive conceptual instruction. The scores of higher-achieving
students were not statistically different from the comparison group that
did not receive conceptual instruction. |
Description: The instruction focused on
developing a conceptual understanding of decimal fractions. Students used
manipulatives (base ten blocks) to facilitate connections between the
written symbol and the physical representation. Students also used
manipulatives to develop procedures for adding and subtracting decimal
fractions. |
NCTM math standards:
• Number &
Operations
Topics:
Decimal
fractions
4th Grade |
|
Study:
Battistich et al.
Number Power:
An elementary school program to enhance students' mathematical and social
development.
Read full review
math_3-5_15 |
3 |
Strategy:
Number
Power.
Subjects: Second through fifth grade teachers and students
at six urban schools in the San Francisco bay area; schools served
ethnically diverse student populations from working class and middle class
families. Students were 48% white, 5% African-American, 8% Hispanic, and
39% Asian-Pacific Islander. Approximately 15% of the students had little
or no English proficiency, 18% were eligible for subsidized school lunches
and 10% were receiving compensatory education. Teachers were predominantly
female (92%) and White (73%) and had an average of 18 years teaching
experience.
Results: In both Year 1 and Year 2 students in the staff
development condition improved twice as much, on average, as students in
the comparison group.
Number Sense Scores (Effect Size)
Year
1
Curriculum
Only vs. Staff Development
Grade 2: -.33
+1.5
Grade
3: +.18
+
.72
Grade 4: -.14
+.90
Grade 5: -.52
+.30
Year
2
Curriculum
Only vs. Staff Development
Grade 2: +.06
+.33
Grade
3: -.95
-.29
Grade 4: +.30
+.75
Grade
5: +.08
+.48 |
Description: Number Power supplements 1/3 of the
year’s math curriculum. It attempts to help students develop the
ability to reason flexibly with numbers as well as to develop the social
skills to work in collaborative settings. Students are encouraged to
devise their own strategies and informal algorithms and to explain,
discuss, and record their computations. They make estimates, use mental
computation, decide when an estimate or an exact answer is appropriate,
use numbers to support mathematical arguments, and make decisions about
the appropriate use of different computational methods. The progression of
lessons within and across units provides in-depth exploration of number
concepts over time, thereby helping students to build on prior learning
and to reflect on their work. |
NCTM math standards:
• Number &
Operations
Topics:
Number Concepts
2nd to 5th
Grade |
|
Study:
Ysseldyke, Spicuzza, Kosciolek, and
Boys.
Effects of a learning
information system on mathematics achievement and classroom structure.
Read full review
math_3-5_20 |
3 |
Strategy: Accelerated Math
Subjects: 157 fourth
and fifth graders in large urban school district in the
Midwest.
Results:
Researchers found that student achievement
and engagement both increased for students who used the Accelerated Math
program as compared to students who were only involved in the Everyday
Math curriculum.
Effect Size= +.40 |
Description:
Accelerated Math consists of educational software products that
provide students with practice on specific mathematical objectives.
Answers are sent to the computer for scoring. Teachers can then see when
students have demonstrated sufficient knowledge in an area and when
students are ready to be tested. Both students and teachers receive
feedback on students' progress. |
NCTM math
standards:
• Number &
Operations
Topic: Computation
4th and 5th
grades |
|
Study:
Rittle-Johnson & Alibali.
Conceptual and
procedural knowledge of mathematics: Does one lead to the other?
Read full review
math_3-5_21 |
3 |
Strategy: Conceptual vs. procedural
instruction
Subjects: 86 fourth and fifth graders from a
parochial school. The subjects were mostly Caucasian with approximately
equal numbers of girls and boys.
Results: Conceptual groups did
better on transfer tasks and generated a variety of procedures for dealing
with equivalence. Procedural instruction led to increased conceptual
understanding and to adoptions, but only limited transfer of the
instructed procedure. |
Description:
Both strategies, one of conceptual understanding and the other
regarding procedural strategies, included direct instruction. Conceptual
knowledge involves understanding the principles and relationship between
pieces of knowledge. Procedural knowledge involves following a sequence of
steps in order to solve a problem. Instruction was the only factor that
differed between the groups. The control group was given no instruction.
The conceptual group was given a short lecture regarding the concept of
equivalence. The procedural group was given a short lecture demonstrating
one procedure for solving problems involving mathematical
equivalence. |
NCTM math
standards:
• Number &
Operations
Math Topic:
Equivalence
4th and 5th
grades |
|
Study:
Anghileri, Meindert, and Van Putten.
From Informal
Strategies to Structured Procedures: Mind the Gap!
Read full review
math_3-5_23 |
3 |
Strategy: The Realistic Mathematics Education and the
National Numeracy Strategy
Subjects: 553 nine and ten year old
students from ten English and ten Dutch schools around small university
cities.
Results: Work by Dutch students reflected greater
accuracy and more efficient strategies than English students.
|
Description:
In the
Netherlands, the Realistic Mathematics Education (RME) has an early focus
on mental methods and a later development of different levels in written
calculations. The RME approach asks children to solve many real-world
problems guided by interactive teaching rather than direct instruction in
standard algorithms. In England, the National Numeracy Strategy places
early emphasis on mental calculations with a later introduction of written
jottings, but requires a standard written method by the time students are
ten years old. |
NCTM math
standards:
• Number & Operations
Math
Topic: Two-digit whole number
division
4th and 5th
grades |
|
Study:
Shyu.
Using video-based
anchored instruction to enhance learning: Taiwan's experience.
Read full review
math_3-5_24 |
3 |
Strategy: Computer-Assisted videodisk-based anchored
instruction on attitudes toward mathematics and instruction as well as
problem-solving skills.
Subjects: Experiment 1 (Attitude Change)
- 74 fifth graders from suburban area of Taipei City in
Taiwan.
Experiment 2 (Problem- Solving Skills) - 37 fifth graders from
suburban area of Taipei City in Taiwan with two groups considered
high-ability; two medium-ability groups; two low-ability
groups.
Results: Experiment 1 - Students felt more positive
about, interested in and less anxious toward mathematics.
Experiment 2
- In general students' problem-solving skills improved significantly with
anchored instruction.
|
Description: Students view a scene
from a video-based program. The instruction is performed via many
problem-solving steps. The activities in the curriculum include watching
the story from the videodisc, learning strategies for solving problems,
and solving mathematical problems in groups of six. |
NCTM math
standards:
• Number & Operations
Math
Topics:
Basic facts,
arithmetic
5th
Grade |
|
Study:
Ysseldyke et al.
Using a
curriculum-based instructional management system to enhance math
achievement in urban schools.
Read full review
math_3-5_25 |
3 |
Strategy: Accelerated Math (AM)
Subjects: 397
students from a large urban school district in the Midwest. 75% were
students of color, 67% of these received free and reduced-price lunch.
Additionally 30% were English Language Learners and 13% were enrolled in
special education programs.
Results: Significant positive
effects were found with a higher degree of implementation and the effects
were similar for high, middle and low performing students. |
Description:
Accelerated Math is based on six principles: "(1) increased time
to practice essential skills, (2) a match between student skill level and
the level of instruction, (3) direct and immediate feedback to teachers
and learners, (4) personalized goal setting, (5) the use of technology to
process, store, and report information, (6) universal success." Students
are pre-tested and assigned an instructional level based on their
performance. The computer generates practice exercises to which the
students respond. The computer provides immediate feedback to the student
and teacher. Teachers can then use this information to adapt and
individualize instruction. |
NCTM math
standards:
• Algebra
• Geometry
• Data Analysis &
Probability
• Measurement
• Number & Operations
Math
Topics:
Computation, number sense,
measurement, relations, functions, randomness, data investigation, numeric
concepts, and math applications
3rd - 5th
grade |
|
Study:
R. Spicuzza, J. Ysseldyke, A.
Lemkuil, S. Kosciolek, C. Boys, and E. Teelucksingh.
Effects of
curriculum-based monitoring on classroom instruction and math achievement.
Read full review
math_3-5_26 |
New
Review
3 |
Strategy: Curriculum-Based
Monitoring – Accelerated Math (AM) taught with Everyday Math
(EM).
Subjects: Participants were part of a larger
multiple-grade project being conducted at four elementary schools in a
large urban school district in the Midwest from February to June of
1999.
Eight teachers with a total of 137 students volunteered to
implement AM with their classes. Sixty-one fourth and fifth grade students
(not learning AM) from the same schools as the 137 students were chosen as
a comparison group. A third group of students was selected from the rest
of the district for comparison.
Results: This study
showed that the implementation of an instructional management system
(Accelerated Math) served to improve student math achievement and the
classroom instructional environment in the areas of Cognitive Emphasis and
Progress Evaluation. |
Description: Teachers in the district use EM as
their core curriculum. This study trained eight teachers in AM, a
supplementary software program that monitors student progress and gives
work at the appropriate level based on student achievement. The program
creates individualized practice assignments for students using an
algorithm problem generator. Students work on assignments printed by the
program at their seats and then scan their completed answers into the
computer. The program scores assignments and keeps records of student and
class performance. |
NCTM math
standards:
•
Algebra
• Geometry
• Data
Analysis &
Probability
•
Measurement
• Number &
Operations
Math topics:
All topics
4th & 5th
Grade |
|
Study:
Carroll, W.
Results of
third-grade students in a reform curriculum on the Illinois State
Mathematics Test.
Read full review
math_3-5_29 |
New
Review
3 |
Strategy: Everyday Mathematics,
University of Chicago School Mathematics Project
(UCSMP).
Subjects: 1885 third-graders from twenty-six
schools in nine greater Chicago metropolitan area districts were in the
UCSMP group; the comparison groups were nonusers of UCSMP in suburban Cook
County and the state of Illinois. Fourteen of the twenty-six schools had
used the curriculum since kindergarten. The remaining twelve schools
adopted the curriculum during the 1991-92 or 1992-93 school year.
Results: All 26 UCSMP schools scored well above the
average state score and three schools scored below the suburban Cook
County Schools. The fourteen schools who had implemented UCSMP since
kindergarten scored 75 points higher than the state scores - median of 343
as compared to 268. For these UCSMP schools 54% exceeded state standards
and 2% did not meet state standards. |
Description:
The UCSMP is a reform curriculum that incorporates small group
work to explore mathematics in real life contexts and incorporates
calculators and manipulatives. Students are encouraged to use these tools
or invent strategies to solve problems and share solutions as part of
class discussions. |
NCTM math
standards:
•
Algebra
• Geometry
• Data
Analysis &
Probability
•
Measurement
• Number &
Operations
Math topics:
All topics
3rd
Grade |
|
Study:
P. Sindelar, D. Gartland, and R.
Wilson.
The effects of lesson
format on the acquisition of mathematical concepts by fourth graders.
Read full review
math_3-5_31 |
New
Review
3 |
Strategy:
Percent of time allotted for teacher-led activities and seatwork.
Subjects: 108 fourth graders from four elementary
schools in a rural district in Pennsylvania.
Results:
Achievement was significantly greater when 75% of the class time
was teacher-led, however, the results were not consistent across the other
treatments. |
Description:
The purpose of the study was to determine the effects of the
amount of teacher-led instruction. Three lessons on exponents were
structured using four different formats: the 15-minute teacher-led lessons
(with no follow-up work with students) versus 30-minute lessons where
teacher-led instruction composed 25%, 50% or 75% of the time.
|
NCTM math
standards:
• Number &
Operations
Math topics:
Exponents
4th
Grade |
|
Study:
Carroll.
Mental computation of
students in a reform-based mathematics curriculum .
Read full review
math_6-8_8 |
3 |
Strategy: UCSMP (EveryDay Math)
Subjects:
Four classes
of 5 th grade students (3 public, 1 parochial). Students in sample were
presumed to have been in the program since Kindergarten.
Results:
Results
indicate that students in the UCSMP program (EveryDay Math) have a strong
ability to calculate mentally. Students in the UCSMP group outscored the
traditional students on all but 1 item. Moreover, on 21 of the 25 items,
the difference between the groups' means was significant at .05 level.
Notably, students in the UCSMP group outscored students in the traditional
group on the division problems, with the UCSMP students average of 72%
compared to the traditional group’s average of 12%. |
Description: In this K-8 program, students invent
their own algorithms, share multiple solution strategies with peers, use
manipulatives and calculators wisely, and solve in-context problems en
route to developing arithmetic proficiency. Mental arithmetic is
emphasized by the encouragement of invented algorithms and by the verbal
sharing of strategies for mental calculation. Students developed a variety
of strategies such as counting up/down, decomposing, working
left-to-right, re-writing with compatible numbers (for example, changing
76 + 25 to 75 + 25 +1), and switching between operations (for example,
thinking of 2 x 87 as 80 + 80 + 7 +7.) |
NCTM math
standards:
•
Number & Operations
Math topics:
5th
Grade |
|
Study:
Bottge.
Effects of
contextualized math instruction on problem solving of average and
below-average achieving students.
Read full review
math_6-8_10 |
3 |
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:
Outhred & Mitchelmore.
Young children's
intuitive understanding of rectangular area measurement.
Read full review
math_k2_18 |
2 |
Strategy: Not a program or strategy. This is a study
(investigation) of children's thinking about rectangular covering before
they have been taught the area formula.
Subjects: 115 children
randomly selected from 40 classes, grades 1 through 4 at four schools.
Medium socioeconomic area of Sydney, Australia.Approximately equal
number of boys and girls.
Results: There was a gradual
development in children's abilities to represent a rectangular covering
either in a drawing or in an inferred mental image. The significance of
the formation of an iterable row as the foundation of an understanding of
an array structure was key to the children's understanding.
|
Description:
Children were given measurement tasks. The strategies used to
solve problems were then identified. |
NCTM Math Standards:
• Number & Operations
• Measurement
Topics:
• Measurement techniques.
1st to 4th
Grades |
|
Study:
Battista.
Fifth graders'
enumeration of cubes in 3d arrays: Conceptual progress in an inquiry-based
classroom.
Read full review
math_3-5_14 |
2 |
Strategy:
Cognitive
Learning in an Inquiry-Based Classroom.
Subjects: 3 pairs
of 5th grade students taught by a teacher who was highly skilled in
creating a classroom culture of inquiry, problem solving, and sense
making.
Results: On the delayed post-interview, all but one
correctly used a layering strategy. |
Description: Students worked in pairs to predict
how many cubes would fit in a graphically represented box, then checked
their predictions by making the box out of grid paper and filling it with
cubes. The teacher circulated around the classroom, interacting with
student pairs, encouraging collaboration and communication within the
pairs and promoting individual sense making. |
NCTM math standards:
• Number &
Operations
•
Geometry
Topics:
5th Grade |
|
Study:
Pogrow.
A revalidation of the
effectiveness of the HOTS program.
Read full review
math_3-5_16 |
2 |
Strategy: Higher Order Thinking Skills (HOTS)
Project.
Subjects: 52 fourth and fifth graders who were eligible for
Title I attending Elvira Elementary in Tucson, low SES, urban setting,
primarily Native American and Hispanic.
Results:
Students in the experimental group matched or exceeded the performance
of the control group.
Fourth Grade Effect Size = +.74
Fifth Grade Effect Size =
+2.40 |
Description: The goal of the HOTS program is to
improve the academic performance of educationally disadvantaged students
by developing more sophisticated thinking skills. The program uses
computers, specially designed curricular materials, and Socratic teaching
strategies through higher order thinking activities. The first half
of the class period consists of teacher led discussion designed to improve
the thinking skills of (a) metacognition, (b) inference from context, (c)
decontextualization, and (d) information synthesis. During the last half
of the class period students work on the prescribed computer software
while teachers explain the computer activities. |
NCTM math standards:
•
Number & Operations
All topics
4th to 6th
Grade |
|
Study:
Byrnes & Al Wasik.
Role of conceptual
knowledge in mathematical procedural learning.
Read full review
math_3-5_17 |
2 |
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
Topics:
Fractions
4th & 5th
Grades |
|
Study:
Stipek & Salmon.
The value (and
convergence) of practices suggested by motivation research and promoted by
mathematics education reformers.
Read full review
math_3-5_18 |
2 |
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 teachers 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
Topics:
Fractions
4th - 6th
grade |
|
Study:
Lamon.
The development of
unitizing: Its role in children's partitioning strategies.
Read full review
math_6-8_17 |
NA |
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 |
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.