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
2nd to 4th 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 Math Standards:
Number & Operations
Topics: Computation
2nd to 4th grade |
|
Study:
Carpenter, Fennema, Peterson, Chiang,
Loef.
Using knowledge of
children's mathematics thinking in classroom teaching: an experimental
study.
Read full review
math_k2_2 |
4 |
Strategy: Cognitively Guided Instruction -
CGI
Subjects: 40 first grade teachers and their students from
Madison, Wisconsin and four smaller communities, 22 public and 2 Catholic
schools. Children with special needs were omitted from the
study.
Results: Differences in student achievement were modest,
but consistently favored the experimental group. The results documented
that a focus on problem solving does not necessarily result in a decline
in computation skills and that giving teachers access to research-based
knowledge about students' thinking and problem solving can affect
teachers' beliefs and their students' achievement and beliefs. Effect Size
= + 0.497 on ITBS (level 7) in favor of CGI. |
Description: This program helps teachers
understand how children develop addition and subtraction concepts and
provides them the opportunity to explore how they might use that knowledge
for instruction. Teachers learned to classify problems and to identify
children's processes to solve different problems. |
NCTM Math
Standards
Number & Operations
Topics:
Addition and Subtraction
1st Grade
|
|
Study:
Hiebert & Wearne.
Title: Instructional Tasks, Classroom Discourse,
and Students' Learning in Second-Grade Arithmetic.
Read full review
math_k-2_24
|
New
Review
4 |
Strategy: Problem-based instructional tasks and
solicited student discourse
Subjects: 135
second-grade students from six classrooms in one rural/suburban school.
Students had a mean achievement level slightly above
average.
Results: Results showed that working more
problems does not lead to higher performance, neither does requiring fewer
problems worked mean higher performance. The authors suggest that in
mathematics classrooms, certain kinds of instructional tasks and discourse
encourage more productive ways of thinking and increase achievement.
|
Description: Relationships between teaching and
learning mathematics were examined in six second-grade classrooms.
Teaching was evaluated by examining tasks presented to the students and
the nature of the classroom discourse. Students were assessed on place
value understanding, routine computation, and novel computation.
|
NCTM Math
Standard:
Number & Operations
Math
Topics: Place value, multi-digit addition and subtraction of
whole numbers
Grade: 2nd 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:
Villasenor & Kepner.
Arithmetic from a
problem-solving perspective: An urban implementation.
Read full review
math_k2_4 |
4 |
Strategy: Cognitively Guided Instruction -
GCI
Subjects: Experimental and control groups comprised of 144
first grade students from 11 public schools and one private school; 57-99%
minority children.
Results: The experimental classroom students
used advanced strategies in solving word problems significantly more than
the control group. The experimental classroom students scored
significantly higher on all three post-tests than the control group.
Effect Size = +6.63 in favor of CGI.
|
Description:
CGI is a staff development program that builds on the
knowledge that students already have and helps them analyze their own
thinking. Teachers encourage their students to build on their natural
problem-solving strategies by encouraging them to listen to each other,
ask questions, and explain how they solve problems. |
NCTM Math
Standards
Number &
Operations
Topic:
Arithmetic word problems
1st Grade
|
|
Study:
Klein, Beishuizen & Treffers.
The empty number line
in Dutch second grades: Realistic versus gradual program
design.
Read full review
math_k2_6 |
4 |
Strategy: Realistic Program Design vs.Gradual Program
Design
Subjects: 10 second grade classrooms (N = 275) from 9
middle class primary schools in the Netherlands
Results: There
were no differences found in the procedural competence or the flexibility
in using computation procedures and strategies; however, the use of the
empty number line had an impact on childrens learning. Second grade
students who used the empty number line approach for a year scored higher
than third graders in their ability to subtract numbers. |
Description:
Realistic Program Design (constuctivist view) stressed
flexible use of strategies by making connections to children's informal
strategies. Context problems were chosen to reflect everyday experience
and to elicit informal and varied solution strategies. A bead string was
used prior to the empty number line.
Gradual Program Design used more
structured instruction -- multiple strategies were not introduced early so
that they would not confuse the average or lower ability students.
Arithmetic blocks were used in a linear way to introduce the number line.
|
NCTM Math
Standards:
Number &
Operations
Topics:
Addition and
subtraction
Number
line. 2nd Grade |
|
Study:
Fuson & Briars.
Using a base-ten
blocks learning / teaching approach for first- and second-grade
place-value and multi-digit addition & subtraction.
Read full review
math_k2_7 |
4 |
Strategy: Use
of base ten blocks
Subjects: Study One: 169 first and
second graders (for addition), from a small city on the border of Chicago;
75 second graders (for subtraction). Low, average, and high achieving
students were included in the study.
Study Two: 132 second graders in
Pittsburgh.
Results: Study One: Students showed
performance above that ordinarily shown by second graders receiving
traditional instruction.
Study Two: Results similar to
Study One. |
Description:
Teachers used a brief overview of instruction, lesson
plans, student worksheets, and tests. |
NCTM Math
Standards:
Number &
Operations
Topics:
Multi-digit addition and
subtraction 1st and 2nd 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 1st, 2nd, & 3rd 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 childrens 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:
van Essen, Gerard & Hamaker.
Using self-generated
drawings to solve arithmetic word problems.
Read full review
math_k2_21 |
4 |
Strategy: Student-generated pictorial representation for
word problems.
Subjects: (Study 1): 24 first graders and 29
second graders from elementary schools in Amsterdam.
(Study 2): 50
fifth graders from four elementary schools in Amsterdam with a mean age of
7.5 years.
Results: (Study 1): no significant differences
between treatment and control groups, but the treatment group did generate
more accurate drawings than the control group.
(Study 2): The 2x4
ANOVA with condition as the between factor and problem category as the
within factor revealed a significant condition effect, F(1, 48)=8.73,
p<0.01, and problem category effect, F(3, 144)=4.96; p<0.01.
|
Description:
Study 1: Three lessons over 4 weeks time where the
experimenter read aloud six word problems (each time, progressively more
difficult) to groups of four children and requested that students make
drawings showing what was happening in the story. The researcher also
generated drawings to illustrate what a drawing might look like. When all
children had produced a pictorial representation of the problems, the
experimenter asked each child to explain his/her drawing and the
experimenter shared his drawing as another possible representation, but
not as a model that others should follow. Students were also told that
word problems are sometimes difficult to understand and that making a
drawing is a useful technique for understanding. Study 2: Used the same
intervention with the exception that the word problems varied in content
and the sessions were two half-hour sessions. |
NCTM Math Standards:
Number &
Operations
Topic:
Arithmetic word problems
Grade
Levels:
Study One: 1st and 2nd Grades
Study Two: 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 & 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:
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:
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 operation, 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 mathematics. |
NCTM Math Standards:
Algebra
Geometry
Data Analysis &
Probability
Measurement
Number
& Operations
Topics:
All
3rd
Grade |
|
Study:
Burton.
Young childrens'
choices of manipulatives and strategies for solving whole number division
problems.
Read full review
math_k2_10 |
3 |
Strategy: Using manipulatives to help second graders solve
division problems.
Subjects: 117 second graders (61 female and
56 male) from 5 second grade classrooms in two schools.
Results:
When students used manipulatives that matched the problem context
these students did significantly better than when the manipulatives chosen
did not match. Furthermore, the study showed that these students rarely
used a dealing strategy when solving partition problems. Finally,
contrary to previous research findings, these students did equally well on
measurement and partition type division problems. |
Description:
Manipulatives (contextual/matchable or distraction-free)
are used to solve three types of division word problems (no remainder,
remainder not used, and remainder used). The type of manipulative chosen
for each problem was recorded by an observer. How each manipulative was
used was also recorded. Also, the use of calculators was observed and
recorded. |
NCTM Math Standards:
Number &
Operations
Topics:
Partition Division and
Measurement Division
2nd Grade
|
|
Study:
Jones, Thornton, Putt, Hill, Mogill,
Rich, VanZoest.
Multi-digit number
sense: A framework for instruction and assessment.
Read full review
math_k2_15 |
3 |
Strategy: A
Framework for Multi-Digit Number Sense Using Four Constructs: Counting,
Partitioning, Grouping, and Number Relationships
Subjects:
Validation Study: Six randomly selected students in 1st grade and six in 2nd
grade.
Implementation Study: 40 first grade students. Students were
placed in two groups. There was no control group.
Results:
Performances of the students were not significantly different for the
two groups in the implementation study. |
Description:
Teachers were encouraged to: (1) use the multi-digit
number sense framework to assess and build on students' understanding, (2)
present challenging problems to the students, (3) guide students to
construct their own solutions to the problems, (4) maximize opportunities
for pairs of students to engage in collaborative problem solving, and (5)
encourage students to negotiate one or more suitable solutions to the
problems. |
NCTM Math
Standards:
Number &
Operations
Topic:
Number sense
1st and 2nd
Grades |
|
Study:
Kato, Kamii, Ozaki & Nagahiro.
Young children's
representations of groups of objects: The relationship between abstraction
and representation.
Read full review
math_k2_19 |
3 |
Strategy:
Using groups of objects to study the understanding of young children's
relationship between abstraction and representation.
Subjects:
60 Japanese students from ages 3 to 7 divided into subgroups of 4, 5, 6,
and 7 year olds. There were more boys in younger 2 groups and fewer boys
in older two groups. All came from middle class homes.
Results:
The relationship between levels of abstraction and representation was
significant. No child was at a higher level in representation than
abstraction. |
Description:
This study did not involve a program or intervention. The
strategy was to focus on children's thinking and see the relationship
between abstraction and representation.
Three tasks were
given to each child and the interviews were videotaped. |
NCTM Math Standards:
Number &
Operations
All topics
Kindergarten
to 2nd Grade |
|
Study:
Jacobson & Lehrer.
Teacher appropriation
and student learning of geometry through design.
Read full review
math_k2_22 |
3 |
Strategy: Cognitively Guided Instruction (CGI) and
professional development in Geometry
Subjects: Four grade-two
classrooms (of four CGI trained teachers; A, B, C, and D) comprised of 18,
16, 18, and 13 students. Teachers A and B had professional development in
transformational geometry.
Results: Students in classes A and B
learned more about transformational geometry than those in classes C and
D. Students in classes A and B also retained their knowledge over time - a
month later - more than those in classes C and D. |
Description:
Teachers used a thoughtfully designed sequence of tasks
and computer tools to assist students in their learning of
transformational geometry. The curriculum, Geometry in Design, used
software to design quilts. Teachers used questioning to analyze student
thinking. |
NCTM Math Standards:
Geometry
Number & Operations
Topics:
Symmetry, Composition of
transformations
Grade 2
|
|
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:
Brent & N. DiObilda.
Effects of Curriculum
Alignment versus Direct Instruction on Urban Children
Read full review
math_k-2_25 |
New
Review
2 |
Strategy: Direct Instruction
Subjects:
Ninety-nine second-grade students (including 23 stable and 76 mobile
students) were in the direct-instruction classrooms. Ninety second-grade
students (27 stable and 63 mobile students) were in the control classrooms
using a district curriculum that had been aligned with standardized
testing.
Results: On the Comprehensive Test of Basic
Skills (CTBS), the direct-instruction students scored significantly higher
than the traditional students on mathematics computation. The stable
traditional students scored significantly higher than the mobile
traditional students and the stable direct-instruction students on
mathematical concepts and applications. On the Metropolitan Achievement
Test (MAT), the direct-instruction stable students scored significantly
higher than traditional stable students in total mathematics and two
sub-scores -- computation and mathematics concepts. |
Description: Oregon direct instruction is a
unified system of instruction that provides teachers with highly
structured scripts that entail positive reinforcement and immediate
corrective feedback. It is designed according to a clearly defined set of
principles, for example, analysis of the objectives in order to form
teachable component concepts and sets of concepts, identification of
pre-skills, and selection and sequences of examples. |
NCTM Math
Standards:
Number &
Operations
Math
Topics: Basic facts, computation, math concepts
Grade: 2nd Grade |
|
Study:
Carpenter,
Franke, Jacob, Fennema & Empson.
A
longitudinal study of invention and understanding in children's multidigit
addition and subtraction.
Read full review
math_k2_11 |
2 |
Strategy: Student Invented Strategies
Subjects:
82 children in grades 1 - 3 from three schools (1) rural, 99%
white and 4% SES (2) urban, 70% white, 26% SES, (3) urban, 91% white, 8%
SES.
Results: By the end of the study, 88% of the
students had used invented addition strategies and 68% had used
subtraction strategies. Students who used invented strategies demonstrated
basic understanding of base- ten number concepts. These students also used
them flexibly and made fewer systematic errors than students using
algorithms.
|
Description:
No curricular materials or specific guidelines for
instruction were provided. This was not an intervention or strategy but a
study of children's thinking and how invented addition and subtraction
strategies related to an understanding of base-ten number concepts.
|
NCTM Math
Standards:
Number &
Operations
Topics:
Multi-digit addition and
subtraction
1st to 3rd
Grades |
|
Study:
Clements, Swaminathan, Zeitler,
Hannibal, and Sarama.
Young children's
concepts of shape.
Read full review
math_k2_13
|
2 |
Strategy:
No strategy or program was implemented.
Subjects:
97 middle-class children; two pre-schools and one elementary
school (two kindergarten classes); ages 3.5 6.9 years; grouped as 4, 5,
and 6 year olds; 48 boys and 49 girls.
Results:
Students were interviewed to identify their level of
understanding geometric shapes.
In younger children there was a
significant positive relationship between correct responses and their
ability to recognize the properties of a square. |
Description:
Shape selection tasks were used to identify childrens
understanding of geometric shapes. |
NCTM Math Standards:
Geometry
Number & Operations
Topics:
Characteristics of geometric
shapes
Spatial reasoning Kindergarten
|
|
Study:
Pepper & Hunting.
Preschoolers'
counting and sharing.
Read full review
math_k2_17 |
2 |
Strategy: Counting Skills Tasks
Subjects: 25
pre-school, ages 4-6, mean age was 5 years 4 months
Results: No
relationship was found between children's ability to count and their
ability to share/partition objects. |
Description:
Observational, not experimental. Students were given 7
counting tasks and 3 sharing tasks and were categorized as poor,
developing, or good. Childrens ability to identify quickly without
counting the number of items in a group was analyzed. |
NCTM Math
Standards:
Number &
Operations
Topic:
Counting Pre-K
|
|
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:
McClain & Cobb.
An analysis of
development of sociomathematical norms in one
first-grade
classroom.
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math_k2_12 |
1 |
Strategy: Patterning & partitioning sequence,
structuring number sequences, arithmetic rack
Subjects: 1
classroom of 1st grade students in large suburban area and their highly
motivated teacher
Results: Students made significant progress in
their ability to mentally compute and estimate numbers up to 100.
|
Description: Students utilized whole class
discussions with their teacher as facilitator with clearly defined
expectations for the classroom. |
NCTM Math Standards:
Number &
Operations
Topics:
Mental computation and
estimation.
1st Grade
|
|
Study:
Funkhouser.
Developing number
sense and basic computational skills in students with special
needs.
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math_k2_16 |
1 |
Strategy:
Using a Concrete Manipulative called a 5-Frame
Subjects:
Twelve kindergarten and 1st grade students.
Results: At the
end of a 4-week period, all students were consistently successful (over
90%) in using the 5-frame to recognize and match the numbers 0 5 and to
add sums up to five. The teacher also reported that time-on-task and pupil
independence increased using the 5-frame procedures. |
Description: A concrete manipulative called a
5-frame was used to teach K-1 learning disabled students subitizing
(recognizing a number of objects in a set without actually counting them)
in mathematics. |
Standards:
Number &
Operations
Topics:
Addition and number sense
Kindergarten
and 1st Grade |
|
Study:
Carpenter and Levi.
Developing
conceptions of algebraic reasoning in the primary grades
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math_k2_20 |
1 |
Strategy: Cognitively Guided Instruction -
CGI
Subjects: (Pilot Study) 1 first grader and 7 second graders;
(Study Two) 20 students in a combination first and second grade
classroom
Results: Equal sign can be introduced and understood
as expressing a relation as early as first grade. Students in primary
grades can engage in formulating, representing, and justifying
conjectures, even though their justifications might not always be
sufficient to validate all the conjectures they are capable of
identifying.
|
Description:
This is an observational study.
Study 1: Teacher
worked with students with 8 lessons over a one month time frame.
True-false number sentences were discussed and students discovered
that = was not an operation, but a relation. Students then used open
number sentences to generalize properties of numbers and to make
generalizations.
Study 2: Teacher worked with students twice a week on
equal sign expresses a relation, conjectures and justifications in number
sentences, introduced algebraic notation by using open number sentences to
represent conjectures. |
NCTM Math Standards:
Algebra
Number & Operations
Topics:
Equivalence
Properties of
Numbers
Algebraic Notation
1st and 2nd
Grades
|
Reviewers' Ratings of Research