Iowa Content Network
Overviews of Research – Mathematics
Overview – Research on Pre-Kindergarten through Grade 2 Teaching and Learning
It is essential that students have a strong foundation in mathematical content and the development of mathematical processes. Research results related to improving students’ achievement in mathematics in prekindergarten through grade 2 may be summarized into three categories: curriculum materials (textbooks), supplementary programs, and teaching strategies.
A set of curriculum materials that has been found to be effective is Everyday Mathematics (Fuson, 2000). An integral component of Everyday Mathematics is the focus on problem-based instruction. Other problem-based or problem-centered mathematics programs have indicated positive results in achievement (Wood & Sellers, 1997; Hiebert & Wearne, 1993).
A supplementary program that indicated positive results is Cognitively Guided Instruction (CGI) (Jacobson & Lehrer, 2000;Carpenter et al, 1999; Villasenor & Kepner, 1993; Fennema & Carpenter, 1996). Another supplementary program that indicated significant improvements in achievement is the “Explicit Schema-Based Strategy” (Jitendra et al, 1998). These programs include a training component for teachers on teaching strategies for helping students solve word problems.
Teaching strategies with positive results include the use of peer-mediated instruction (Fuchs et al, 1997) and peer-assisted learning (Fuchs et al, 1995). The emphasis was on students working with each other. Use of manipulatives is another teaching strategy showing improved student achievement; these strategies included using the empty number line (Klein et al, 1998), base-ten blocks (Fuson & Briars, 1990), and other manipulatives (Burton, 1992). Using self-generated drawings for solving word problems was yet another effective teaching strategy (van Essen et al, 1990).
In addition, a longitudinal study indicated that small class sizes in grades K- 3 made a difference in student achievement gains that persisted through grade nine (Nye et al, 2001).
The research studies supporting this overview are found in the following
table. (Go to mathematics_k2.htm
to examine a table of studies.)
Overview – Research on Grades 3 to 5 Teaching and Learning
Based on Individual Studies Reviewed by the Iowa Content Network and Prominent Published Reviews of Collections of Research
Nearly three-fourths of U.S. fourth graders report liking mathematics. To maintain their enthusiasm, the mathematics in grades 3-5 must be interesting and understandable with instruction designed so the students are actively engaged in making sense of mathematics. Three central mathematical themes for grades 3-5 are identified in the Principles and Standards for School Mathematics. These themes–multiplicative reasoning, equivalence, and computational fluency–are interwoven across content areas (NCTM, 2000).
A number of studies evaluated the content strands in the grade 3-5 curriculum (algebra, data analysis and probability, geometry, measurement, and number and operations). These studies compared NCTM-standards-based to traditional curriculum; in all cases the students in the standards-based curriculum outperformed the students studying the traditional curriculum. (See NCTM-Standards-based Overview). In two studies, greater achievement was reported using a standards-based curriculum with Accelerated Mathematics rather than implementing just the standards-based curriculum (Ysseldyke et al. 2003, Spicuzza et al. 2001).
A longitudinal study indicated that small class sizes in grades K-3 made a difference in student achievement gains that persisted through grade nine (Nye et al. 2001).
The number of studies that involved only algebra, data analysis and probability, geometry, and measurement were limited. There were a large number of studies that involved evaluation of number and operations; some of these studies involved general teaching strategies that may or may not be transferable to other topics.
Algebra, Data Analysis, and Probability
There were no separate
studies related to algebra, data analysis, and probability.
Geometry and Measurement
In addition to the studies
reported above, one study (Carroll, 1998) reported a growth in students’
geometric reasoning by evaluating Van Hiele levels as a result of implementing
Everyday Math in contrast to a traditional curriculum.
Reasoning with respect to one-, two- and three-dimensions adds to the complexities of developing proficiency for linear, area and volume measurements. The development of conceptual understandings and procedural competence in measurement are closely related and need to be thoughtfully integrated in instruction (Lehrer 2003; Kilpatrick et al. 2001). In one study students who received conceptual instruction for 3 days did just as well as students who had the same instruction plus an additional 5 days of rote learning for area and perimeter topics (Pesek et al. 2000). A class culture of inquiry, problem solving, and sense making was effective in helping students develop volume concepts through a layering strategy (Battista 1999).
Number and Operations
Multiplicative reasoning, identified in the Principles and Standards for School Mathematics as a central theme for grades 3-5, develops slowly (Clark et al. 1996). As students are provided more experiences, they develop more sophisticated strategies for unitizing and partitioning, part of multiplicative reasoning (Lamon 1996).
Studies involving basic facts and whole number algorithms showed no differences between standards-based curricula and traditional curricula in regular or inclusion classrooms. In studies that evaluated word problems, more complex computations, and student explanations, results favored the standards-based groups (Wood et al. 2003; Mokros, 2003). For the development of rational numbers, results for average and lower ability students favored curricula that were based on conceptual understanding, including multiple representations, benchmarks, and connections (Cramer, et al. 2002; Moss, 1999; Wearne 1990).
Positive results with respect to greater accuracy, more efficient strategies, better conceptual understanding, and higher scores for standardized achievement tests were also found for problem-centered curricula or curriculum based on real world problems as compared to traditional textbooks (Anghileri et al. 2002; Wood et al. 1997). (Also, see overview of research for using problem-based instructional tasks.)
Teaching explicit strategies to solve word problems or to develop more sophisticated thinking strategies resulted in positive differences for average and low ability students (Fuchs et al. 2003; Darch et al. 2001; Hohn et al. 2002; Pogrow 1995).
Other effective teaching strategies include promoting more student responsibility for learning by having students set and regulate their learning goals and having them work in pairs (Fuchs et al. 1997; Fuchs et al. 1995; Fuchs, Fuchs, Prentice, Burch, Hamlett, Owen, Hosp, and Jancek 2003; Fuchs, Fuchs, Prentice, Burch, Hamlett, Owen, and Schroeder 2003).
Professional development makes a difference. Student test scores improved significantly when teachers participated in staff development while implementing standards-based curricula in contrast to no staff development during implementation (Battistich et al. 2003). Gains in student achievement also appeared to be directly related to changes in teacher instruction and beliefs as a result of Cognitively Guided Instruction (CGI), a teacher development program (Fennema et al. 1996).
The research supporting this overview falls into two categories – prominent published reviews of collections of research, and individual studies. These two categories are presented below.
1. Prominent Published Reviews of Collections of Research These nationally-recognized reviews of substantial bodies of research have been written by experts in the field and reviewed by peers.
2. Individual Studies (Go to mathematics_35.htm to examine a table of studies.)
Overview – Research on Grades 6 to 8 Teaching and Learning
Based on Individual Studies Reviewed by the Iowa Content Network and Prominent Published Reviews of Collections of Research
The traditional U. S. middle grades mathematics curriculum has been limited in depth and breadth and the weakest area in both international and domestic comparisons with respect to mathematics proficiency is middle school students’ performance in geometry (NCTM, 2000). In order to strengthen students’ backgrounds and increase their options in life and career opportunities, it is recommended in the Principles and Standards for School Mathematics that a significant amount of both algebra and geometry need to be integrated in the middle grades curriculum for all students (NCTM, 2000).
A number of studies evaluated the content strands in the grade 6-8 curriculum (algebra, data analysis and probability, geometry, measurement, and number and operations); these studies compared NCTM standards-based to traditional curriculum. In all cases the test scores of students in the standards-based curriculum was comparable or exceeded test scores of students studying the traditional curriculum. (See NCTM Standards-based Summary).
Three studies focused on ability grouping. When comparing homogeneous to heterogeneous groupings, low ability or average students were more likely to make gains in heterogeneous classes. Performances of high ability students were not effected. (Hunt 1996; Linchevski et al. 1998; Leonard 2001). These results are consistent with summaries on the effects of ability grouping including data from international studies that support the assumption that all students can learn mathematics and work within heterogeneously grouped classes (Kilpatrick 2001).
Greater student gains were the result of teaching strategies that included presenting problem solving situations in context using videos, organizing instruction around big ideas, teaching explicit strategies, guiding through scaffolding, and including review that requires students to apply their knowledge (Arthurs et al.1998; Bottge, 1999; Grossen 2000). Other factors contributing to student gains included teachers who had acquired a mathematics major; who participated in professional development in developing higher-order thinking strategies, and who implemented teaching strategies such as hands-on learning and higher-order thinking skills (Wenglisky 2002).
The number of studies that involved only algebra, data analysis and probability, geometry, and measurement were limited to nonexistent (although several studies addressed all strands together). There were a larger number of studies that involved evaluation of number and operations.
Algebra
Only one study involved only algebra; no differences in achievement were found between the Saxon Algebra text and conventional textbooks on linear combinations; the control group (conventional textbooks) performed significantly better on one subscale measuring definitions and theory. The experimental group had a significantly more positive attitude in every area except for study habits (Johnson et al. 1987).
Geometry
In addition to the studies reported above, one study (Carroll 1998) reported a growth in students’ geometric reasoning by evaluating van Hiele levels as a result of implementing Everyday Math in contrast to a traditional curriculum. The van Hieles’ theory of levels of geometric reasoning provides a framework for curriculum and teaching and most traditional textbooks do not provide a curriculum that requires students to develop higher levels of geometric reasoning across the grades (Clements 2003).
Number and Operations
Mental computation is not only a practical skill but it also helps students develop number and operation sense; in recent decades this topic has not been included in the U.S. traditional curriculum (Kilpatrick 2001). Mental computation skills were enhanced for groups using the standards-based curriculum, Everyday Math (Carroll 1996). Another study found that mental computation skills improved when representations were presented through a computer environment (Ainsworth et al. 2002).
Research on rational numbers relates student difficulties to weak conceptual understandings of rational numbers and a lack of connecting fractions and decimals. Approaches such as standards-based curriculum that build on students’ informal understandings and incorporate representations and contexts offer more promise than rule-based programs (Kilpatrick 2001). Student achievement on fractions was enhanced when teachers were committed to implementing a reform curriculum in contrast to teachers who had no interest (Stipek et al. 1998). See Summaries on Fractions and Problem-based Instruction.
Another study that focused on student understanding involved proportional reasoning. Students made greater gains in proportional reasoning when studying curriculum where they developed their own concepts and procedures (Ben-Chaim et al. 1998).
With respect to the role of calculators and instruction, the factor in greater achievement in solving problems was learning problem-solving strategies rather than calculator use. Additionally, students who used calculators had more positive attitudes towards math and their computation scores were not significantly different (Szetela et al. 1998).
The research supporting this overview falls into two categories – prominent published reviews of collections of research, and individual studies. These two categories are presented below.
1. Prominent Published Reviews of Collections of Research
These nationally-recognized reviews of substantial bodies of research have been written by experts in the field and reviewed by peers.
2. Individual Studies (Go to mathematics_68.htm to examine a table of studies.)
Overview – Research on Teaching with Problem-Based Instructional Tasks
Based on individual studies reviewed by the Iowa Content Network and prominent published reviews of collections of research
The use of problem-based instructional tasks as an instructional strategy to increase student achievement in mathematics is strongly supported by research. This strategy is also referred to as teaching through problem solving, using a problem-based approach, or a problem-centered approach. The strategy is implemented by getting students actively engaged in solving, explaining, and reasoning about rich problems focused on important mathematics. This strategy focuses on the teaching paradigm of “understand and apply,” rather than the traditional paradigm of “memorize and practice.”
Research suggests that teaching mathematics through problem solving is both possible and effective. For example: "What do the findings from research suggest about the feasibility and efficacy of teaching mathematics through problem solving? The research reviewed herein suggests both the feasibility and efficacy of of such approaches" (Stein, Boaler, & Silver, 2003, pp.255-256). “Problem solving should be the site in which all of the strands of mathematics proficiency converge” (Kilpatrick, Swafford, & Findell, 2001, p. 421). Strands referred to here are not the content strands, but rather the strands, or types, of mathematical knowledge such as concepts, skills, and problem solving. More precisely, the strands are: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. Thus, research suggests that problem solving should be the context in which all these types of mathematical knowledge should be taught.
The research supporting the use of problem-based instructional tasks falls into three categories – (1) prominent published reviews of collections of research, (2) research on problem-based textbooks (such as the NSF-funded, NCTM-Standards-based curricula), and (3) individual studies of problem-solving instructional interventions. These three categories are presented below.
1. Prominent Published Reviews of Collections of Research about Teaching through Problem Solving These nationally-recognized reviews of substantial bodies of research have been written by experts in the field and reviewed by peers.
2. Individual Studies of Problem-Solving Instructional Interventions
The following table contains entries from the main tables on the Content Network site.
Study Author & Title  |
Design Rating |
Strategy, Subjects, Results  |
Description of Strategy/Program  |
NCTM Math Standards, Math Topics, Grades |
|
Study: Title: Instructional Tasks, Classroom Discourse, and Students' Learning in Second-Grade Arithmetic. math_k-2_24 |
4 |
Strategy: Problem-based instructional tasks and
solicited student discourse |
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: Math Topics: Place value, multi-digit addition and subtraction of whole numbers Grade: 2nd Grade |
|
Study: Arithmetic from a problem-solving perspective: An urban implementation. 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 Topic:
1st Grade |
|
Study: Deepening the analysis: longitudinal assessment of a problem-centered mathematics program. math_3-5_12 |
4 |
Strategy: Longitudinal assessment
of a problem-centered mathematics 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: Topics: Computation 2nd to 4th Grade |
|
Study: Multi-digit number sense: A framework for instruction and assessment. math_k2_15 |
3 |
Strategy: A
Framework for Multi-Digit Number Sense Using Four Constructs: Counting,
Partitioning, Grouping and Number Relationships |
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: Topic:
1st and 2nd Grades |
|
Study: How schools matter: The link between teacher classroom practices and student academic performance. math_6-8_15 |
3 |
Strategy: This
study links teacher classroom practices and achievement on the NAEP eighth
grade mathematics assessment. |
Description: Using various classroom practices such as writing about math, solving real world problems, having students work with objects, having students talk about math, working in small groups, etc. |
NCTM math
standards: Math topics:
8th Grade
|
3. Research on Problem-Based Textbooks (such as the NSF-funded, NCTM-Standards-Based curricula):
Study Author & Title |
Design Rating |
Strategy, Subjects, Results |
Description of Strategy/Program |
NCTM Math Standards, Math Topics, Grades |
|||||||||||||||||||||||
|
Study: Student learning and achievement with Math trailblazers. 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: Topics: 3rd Grade | |||||||||||||||||||||||
|
Study: Achievement of students using the University of Chicago School Mathematics Project's Everyday mathematics. math_k2_1 |
4 |
Strategy:
Subjects:
Results:
|
Description: |
NCTM
math standards: Math
Topics: K to 6th Grades | |||||||||||||||||||||||
|
Study: Achievement results for second and third graders using the standards-based curriculum. 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: Topics:
2nd and 3rd Grades
| |||||||||||||||||||||||
|
Study: Learning to reason numerically: The impact of Investigations. 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: Topics:
2nd to 4th Grades | |||||||||||||||||||||||
|
Study: Results of third-grade students in a reform curriculum on the Illinois State Mathematics Test. math_3-5_29 |
3 |
Strategy: Everyday Mathematics,
University of Chicago School Mathematics Project
(UCSMP). |
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: Math topics:
3rd Grade | |||||||||||||||||||||||
|
Study: The effects of an innovative approach to mathematics on academically low-achieving students in inclusive settings. math_3-5_13 |
4 |
Strategy: Everyday Mathematics. |
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: All Topics 3rd Grade | |||||||||||||||||||||||
|
Study: Geometric knowledge of middle school students in a reform-based mathematics curriculum. math_6-8_1 |
4 |
Strategy: Everyday Math |
Description: This study is a quasi-experimental design. The intervention was an on-going treatment (the EveryDay Math curriculum) to which students had not been randomly assigned. Rather, the students had been either exposed to the UCSMP or a traditional curriculum since kindergarten and were being assessed as to their level of geometry thinking (according to the van Hiele theory) after those experiences |
NCTM
math standards: Math Topic(s): 5th & 6th grades | |||||||||||||||||||||||
|
Study: Mathematics in Context - Preliminary evidence about student outcomes. math_6-8_2 |
3 |
Strategy:
Mathematics in Context (MiC) |
Description: Mathematics in Context is a standards-based curriculum for grades 5-8 designed to help students progress from informal to formal mathematical reasoning in number, geometry (and measurement), algebra, statistics, and probability. The curriculum focuses on placing students in realistic situations that they must resolve. During their resolution process, students progress from informal notions toward formal mathematical reasoning and representations to model and solve non-routine problems. Throughout the curriculum, students develop conceptual knowledge first and re-visit it as necessary. |
NCTM math
standards: Math topics:
5th to 8th Grades
| |||||||||||||||||||||||
|
Study: 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)]. math_6-8_6 |
4 |
Strategy:
Connected Math (CMP) and Everyday Math (EM) |
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: Math topics:
4th & 8th Grades
| |||||||||||||||||||||||
|
Study: Student attainment in the Connected Mathematics curriculum. math_6-8_5 |
4 |
Strategy: Connected Math (CMP) Subjects: 5 Midwest, 2 West, and 2 East schools, 2 CMP classes and 1 nonCMP in each school
|
Description: A problem-oriented curriculum which provides a broad range of mathematical topics with a focus on concept development and student discussion prior to written work. |
NCTM math
standards: Math
topics: 6th to 8th Grades | |||||||||||||||||||||||
|
Study: Assessing the impact of standards-based middle grades mathematics curriculum materials on student achievement. math_6-8_24 |
4 |
Strategy:
Standards-based middle grades mathematics curriculum.
Subjects: Two thousand eighth grade students from six
school districts. Students were matched for prior mathematics achievement,
SES (free and reduced lunch), the same building configuration, and
geographic location. |
Description: Eighth grade students used standards-based mathematics curriculum materials (specifically MathThematics and Connected Mathematics) for at least two years. |
NCTM Math
Standards: Math
Topic(s): 6th to 8th grades | |||||||||||||||||||||||
|
Study: Middle grades MATH thematics: The STEM project. math_6-8_3 |
3 |
Strategy: MATH
Thematics - STEM Project |
Description: A Standards-based curriculum for grades 6, 7, and 8 characterized as problem-oriented with a focus on concept development and student discussion prior to written work. Students are expected to actively do mathematics by investigating, discovering, and applying mathematics to new situations. Students must be able to communicate their ideas effectively through cooperative groups and whole-class discussions. |
NCTM math
standards: Math topics:
6th to 8th Grades
| |||||||||||||||||||||||
|
Study: Proportional reasoning among seventh grade students with different curricular experiences. math_6-8_7 |
4 |
Strategy: Connected Mathematics Program
(CMP) Subjects: 187 eighth graders, 6 classes in Michigan, 1 in San Diego and 1 in Pittsburgh 128 seventh graders, 3 classes in Michigan, 1 in Toledo, 1 in San Diego, 1 in Pittsburgh Results: Seventh graders outperformed control students 53% to 28% on collections task and on each individual problem |
Description: The treatment group was taught using CMP materials for one school year. In this reform curriculum, students are encouraged to construct their own conceptual and procedural knowledge through collaborative problem-solving activities. The data for this study were generated by five proportion problems focusing on rate or population density. |
NCTM math
standards: Math
Topic(s): seventh and 8th grades | |||||||||||||||||||||||
|
Study: Effects of the UCSMP secondary school curriculum on students' achievement. math_9-12_6 |
3 |
Strategy:
University of Chicago School Mathematics Project
(UCSMP) |
Description:
UCSMP is composed of courses called Transitional Mathematics (Algebra; Geometry; Advanced Algebra; Functions, Statistics, and Trigonometry; and Precalculus and Discrete Mathematics). Algebra uses variables to develop linear, exponential, and quadratic patterns. Geometry presents coordinates, transformations, measurement formulas, along with work involving writing proofs. Advanced Algebra studies functions, equations, and inequalities. The Functions, Statistics, and Trigonometry course integrates statistical and algebraic concepts. Precalculus and Discrete Mathematics incorporate many topics required for success in Calculus and Computer Science. The content strands of applied mathematics, prealgebra, and elementary geometry are woven throughout the six courses. |
NCTM Math
Standards All Math Topic(s) 7th to 12th grades
| |||||||||||||||||||||||
|
Study: The Core-Plus Mathematics Project: Perspectives and student achievement. math_9-12_5 |
4 |
Strategy: Core-Plus Mathematics Project Subjects: 64 high schools in 11 states, cross-section of diverse students from urban, suburban, and rural communities Results: Results showed that all CPMP groups performed significantly better on solving mathematical tasks set in context than the comparison groups. The comparison groups performed significantly better with paper-and-pencil procedures at the end of Course 1, but the results were not significant for Course 2. Effect Size on ITED-Q Course 1 ES=+.19 Course 2 ES=+.04 |
Description: The CPMP curricula consist of a
single core sequence for college-bound and employment-bound students
during the first three years of high school that embody the content,
processes, and teaching principles recommended by the NCTM standards.
Building connections among topics is the primary focus. Strands are also
connected by thinking mathematically, such as visual thinking, recursive
thinking, searching for and explaining patterns, making and checking
conjectures, reasoning with multiple representations, inventing
mathematics, and providing arguments and proofs. Fundamental themes of
data, representation, shape, and change also provide connections across
strands.
Curriculum development principles include: (1) mathematics as an active science of patterns, (2) problems that include a context for developing student understanding of mathematics, (3) the processes of exploration and experimentation necessarily precede and complement theory, and (4) the use of graphics calculators and other technology as tools for developing mathematical understanding and for solving authentic problems. Pedagogical principles include the importance of students' sense making of mathematics and real-life contexts. The instructional materials are designed to reflect the importance of collaborative learning, social interaction, and communication. |
NCTM Math
Standards Math Topic(s): 9th to 12th grade.
| |||||||||||||||||||||||
|
Study: Title: The effects of curriculum on achievement in second-year algebra: The example of the University of Chicago School Mathematics Project. math_9-12_11 |
4 |
Strategy: Skills and concepts learned and applied
using the University of Chicago School Mathematics Project (UCSMP)
Advanced Algebra textbook |
Description: UCSMP is a curriculum that uses reading and problem solving, realistic applications, technology (graphing calculators and/or computers), a multidimensional approach understanding, and an instructional format featuring continual review combined with a modified mastery-learning strategy. It emphasizes understanding of concepts through multiple representations, realistic contexts, and the use of technology. There is less emphasis on skills than in a traditional curriculum. The instructional method often uses small-group explorations and extended projects, both involving writing about mathematics. |
NCTM Math
Standard : Math Topics: Linear equations, binomial multiplication, graphs of quadratic equations, exponential equations, the equation for the inverse-square function, recursion Grades: 10th to 12th Grade | |||||||||||||||||||||||
|
Study: Title: Effects of standards-based mathematics education: A study of the Core-Plus Mathematics Project algebra and functions strand math_9-12_14 |
3 |
Strategy: Core-Plus Mathematics Project
(CPMP) |
Description: The Core-Plus Mathematics Project (CPMP) is a four-year integrated high school mathematics curriculum. Major concepts are developed through investigating concepts in the context of applied problems and mathematical modeling. In particular, algebraic concepts are developed using graphic, numeric, and symbolic representations. Graphing calculators are integral, promoting connections among the forms of representation, encouraging new methods of problem solving, and decreasing the need for symbolic manipulation procedures. Since this study was carried in 1997 the curriculum has been revised (in 2003 and in press) to enhance the in-context approach and also include more work with procedural algebraic skills. |
NCTM Math
Standard: Math Topics: Functions, algebraic expressions, systems of equations Grade: 11th Grade | |||||||||||||||||||||||
|
Study: The impact of the Interactive Mathematics Program on student learning. math_9-12_2 |
3 |
Strategy: Interactive Mathematics Program (IMP)
|
Description: |
NCTM Math
Standards Math
Topic(s): 9th to 12th grades
| |||||||||||||||||||||||
|
Study: Curriculum and assessment in SIMMS Integrated Mathematics. math_9-12_3 |
3 |
Strategy: SIMMS Integrated Math |
Description: SIMMS Integrated Math is a complete mathematics program for grades 9-12. It is constructed in six levels each consisting of one year of work. Levels 1 and 2 provide basic mathematical literacy. Levels 3 and 5 are for students with non-mathematical or non-scientific aspirations, whereas levels 4 and 6 prepare students to complete a post-secondary mathematics curriculum. The program has the following characteristics, it is (1) integrated and interdisciplinary, (2) problem-centered and applications based, (3) technology based, (4) sensitive to multiple perspectives and the negative effects of bias and stereotyping, (5) multi-modal to accommodate multiple learning styles. Mathematical modeling is the basic thread of the curriculum, knitting together mathematics and other subjects. Students organize, relate, interpret, justify, evaluate, summarize, and communicate ideas as they explore topics and make inquiries about real-world and mathematical concepts. They confront complex issues by "mathematizing" real-world problems, interpret and communicate solutions, and ultimately reflect on their own performance. |
NCTM Math
Standards Math Topic(s): 9th - 12th grades
| |||||||||||||||||||||||
|
Study: The effects of Math Connections on student achievement, confidence, and perception. math_9-12_4 |
3 |
Strategy: Math Connections (MC) Subjects: Summary of several studies Results: On CAPT, PSAT and SAT, MC students scored as well or better than nonparticipants. Students in classes with MC trained teachers have greater confidence in learning mathematics and see the usefulness of mathematics to a greater degree than non-participants. Case study results of Hispanic and African-American at-risk students in an inner-city school suggest that all students can successfully meet the challenge of a mathematically rigorous course. |
Description: Math Connections is presented to
students as a powerful tool for interacting with their environment. Its
primary goals are to: (1) bridge the worlds of education, students, and
business through mathematics; (2) increase mathematical power of all
students; (3) empower students for their own learning; (4) develop a core
curriculum that reflects the standards of the National Council of Teachers
of Mathematics (NCTM); and (5) empower teachers to meet NCTM's
Professional Standards for Teaching Mathematics.
Math Connections enables students to investigate a concept in order to recognize patterns that can be presented as a formula. Each year of the curriculum is based on a theme that connects and unifies mathematical topics. The theme for Year 1 is Data, Numbers, and Patterns. Students use data, linear equations, and graphing calculators to forecast events. Year 2's theme, Shapes in Space, focuses on properties and measurement of figures. The principles of congruence and triangulation of polygons are, also, examined. Students use matrices to solve linear equations and learn to calculate the volumes of a cone and a sphere. Mathematical Models, is the theme for Year 3. At this time, logic and the properties of an axiomatic system are introduced. |
NCTM Math
Standards All Math Topic(s) 9th to 12th grades
| |||||||||||||||||||||||
|
Study: Computer-Intensive Algebra and students' conceptual knowledge of functions. math_9-12_9 |
3 |
Strategy:
Subjects: Results: |
Description: |
NCTM Math
Standard: Math Topics: College algebra, functions, modeling. 12th grade | |||||||||||||||||||||||
Overview – Research on NCTM-Standards-Based (NSF-Funded) Curricula, K-12
Numerous projects, funded by the National Science Foundation in the 1990s, developed K-12 curriculum materials, which are designed to include more important mathematics and enhance student learning. These curricula are referred to variously as Standards-based curricula, NSF curricula, alternative curricula, or reform curricula. Key content and equity issues leading to reform were concerns that the U.S. mathematics curriculum was not internationally competitive, the high school curriculum focused on math/science-based college preparation at the expense of mathematics for all students and all potential college majors, and large numbers of K-12 students failed or stopped studying mathematics with a disproportionate number of nonwhite students in this category (Schoenfeld, 2002).
An NCTM-Standards-based curriculum is cohesive and comprehensive; it includes the content strands of number and operations, algebra, geometry, measurement, and probability and data analysis (Trafton, et al., 2001). Connections are developed across grade levels, and across and within topics so that mathematics is perceived as being coherent and an integrated whole. Connections to real life contexts are the basis of mathematical tasks so that applications become part of understanding and interpreting math. Standards-based materials develop topics in depth and promote sense making, as the focus is on conceptual development and understanding. Standards-based materials engage students through intriguing tasks; the learning is student-centered with problem solving as a vehicle for both learning and teaching mathematics. Multiple and connected representations are used to explore and develop concepts. Calculators and computing technology are used as tools for learning.
It should be noted when reviewing research results that the goals for these alternative Standards-based curricula are not the same as the traditional textbook programs. The goals for the new curricula are much more ambitious mathematically, including deep conceptual understanding, powerful problem solving ability, and solid skill proficiency. From both domestic studies and international comparisons, it is reasonable to set more ambitious goals for our students and students can understand significant mathematics without sacrificing skill proficiency (Hiebert, 2003).
Conceptual Understanding and Problem Solving – In K-12 studies on conceptual understanding and problem solving, students using NCTM-Standards-based curricula out performed students from traditional curricula on such measures as ITED, ITEPS, ITBS, Balanced Assessment, Massachusetts and Illinois State Assessments, NAEP, PSAT and SAT. Students in reform programs made even greater gains when the programs were implemented with fidelity for longer periods of time or teachers were involved in professional development. Similar results were reported across suburban, urban, and rural populations and other subgroups such as low income, minority, and low achieving students.
Procedural Skills – In some studies, skill differences initially favored the traditional textbook groups but the differences were not significant after the second year of implementation (Ridgway, et al., 2003, Schoen, et al., 2003). In one study, the control group outperformed the Core-Plus Mathematics experimental group on procedural symbol manipulation, although the Core-Plus group out performed the control group on applying algebraic concepts to solving contextual problems (Huntley, 2000). Subsequent revisions of Core-Plus Mathematics have included more work with procedural algebraic skills. Overall, skill performance between students in traditional and NCTM-Standards-based curricula were not significantly different.
The research supporting the use of Standards-based curricula falls into two categories – prominent published reviews of collections of research, and individual studies of curricula. These two categories are presented below.
1. Prominent Published Reviews of Collections of Research about Standards-Based Curricula
These nationally-recognized reviews of substantial bodies of research have been written by experts in the field and reviewed by peers.
2. Individual Studies of Standards-Based Curricula (Tables for Grades K-2, 3-5, 6-8, 9-12)
Grades K-2
Study Author & Title |
Design Rating |
Strategy, Subjects, Results |
Description of Strategy/Program |
NCTM Math Standards, Math Topics, Grades |
Study: Student learning and achievement with Math trailblazers. 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: Topics: 3rd Grade |
Study: Achievement of students using the University of Chicago School Mathematics Project's Everyday mathematics. math_k2_1 |
4 |
Strategy: Subjects: Results: |
Description: |
NCTM math standards: Math Topics: K to 6th Grades |
Study: Achievement results for second and third graders using the standards-based curriculum. 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: Topics: 2nd and 3rd Grades
|
Study: Learning to reason numerically: The impact of Investigations. 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: Topics: 2nd to 4th Grades |
Grades 3-5
Study Author & Title |
Design Rating |
Strategy, Subjects, Results |
Description of Strategy/Program |
NCTM Math Standards, Math Topics, Grades |
Study: 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)]. math_6-8_6 |
4 |
Strategy: Connected Math (CMP) and Everyday Math (EM) |
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: Math topics: 4th & 8th Grades
|
Study: Results of third-grade students in a reform curriculum on the Illinois State Mathematics Test. math_3-5_29 |
3 |
Strategy: Everyday Mathematics, University of Chicago School Mathematics Project (UCSMP). |
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: Math topics: 3rd Grade |
Study: Effects of curriculum-based monitoring on classroom instruction and math achievement. math_3-5_26 |
3 |
Strategy: Curriculum-Based Monitoring – Accelerated Math (AM) taught with Everyday Math (EM). |
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: Math topics: 4th & 5th Grade |
Study: Achievement of students using the University of Chicago School Mathematics Project's Everyday mathematics. math_k2_1 |
4 |
Strategy: Subjects: Results: |
Description: |
NCTM math standards: Math Topics: K to 6th Grades |
Study: Achievement results for second and third graders using the standards-based curriculum. 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: Topics: 2nd and 3rd Grades
|
Study: Student learning and achievement with Math trailblazers. 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: Topics: 3rd Grade |
Study: Geometric knowledge of middle school students in a reform-based mathematics curriculum. math_6-8_1 |
4 |
Strategy: Everyday Math |
Description: This study is a quasi-experimental design. The intervention was an on-going treatment (the EveryDay Math curriculum) to which students had not been randomly assigned. Rather, the students had been either exposed to the UCSMP or a traditional curriculum since kindergarten and were being assessed as to their level of geometry thinking (according to the van Hiele theory) after those experiences | NCTM math standards: Math Topic(s): 5th & 6th grades |
Study: Mathematics in Context - Preliminary evidence about student outcomes. math_6-8_2 |
3 |
Strategy: Mathematics in Context (MiC) |
Description: Mathematics in Context is a standards-based curriculum for grades 5-8 designed to help students progress from informal to formal mathematical reasoning in number, geometry (and measurement), algebra, statistics, and probability. The curriculum focuses on placing students in realistic situations that they must resolve. During their resolution process, students progress from informal notions toward formal mathematical reasoning and representations to model and solve non-routine problems. Throughout the curriculum, students develop conceptual knowledge first and re-visit it as necessary. |
NCTM math standards: Math topics: 5th to 8th Grades
|
Study: The effects of an innovative approach to mathematics on academically low-achieving students in inclusive settings. math_3-5_13 |
4 |
Strategy: Everyday Mathematics. |
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: All Topics 3rd Grade |
Study: Learning to reason numerically: The impact of Investigations. 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: Topics: 2nd to 4th Grades |
Study: Number Power: An elementary school program to enhance students' mathematical and social development. math_3-5_15 |
3 |
Strategy: Number Power. Year 2 |
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: Topics: 2nd to 5th Grade |
Grades 6-8
Study Author & Title |
Design Rating |
Strategy, Subjects, Results |
Description of Strategy/Program |
NCTM Math Standards, Math Topics, Grades |
|||||||||||||||||||||||
Study: Student attainment in the Connected Mathematics curriculum. math_6-8_5 |
4 |
Strategy: Connected Math (CMP) Subjects: 5 Midwest, 2 West, and 2 East schools, 2 CMP classes and 1 nonCMP in each school
|
Description: A problem-oriented curriculum which provides a broad range of mathematical topics with a focus on concept development and student discussion prior to written work. |
NCTM math standards: Math topics: 6th to 8th Grades |
|||||||||||||||||||||||
Study: 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)]. math_6-8_6 |
4 |
Strategy: Connected Math (CMP) and Everyday Math (EM) |
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: Math topics: 4th & 8th Grades
|
|||||||||||||||||||||||
Study: Assessing the impact of standards-based middle grades mathematics curriculum materials on student achievement. math_6-8_24 |
4 |
Strategy: Standards-based middle grades mathematics curriculum. Subjects: Two thousand eighth grade students from six school districts. Students were matched for prior mathematics achievement, SES (free and reduced lunch), the same building configuration, and geographic location. |
Description: Eighth grade students used standards-based mathematics curriculum materials (specifically MathThematics and Connected Mathematics) for at least two years. |
NCTM Math Standards: Math Topic(s): 6th to 8th grades |
|||||||||||||||||||||||
Study: Mathematics in Context - Preliminary evidence about student outcomes. math_6-8_2 |
3 |
Strategy: Mathematics in Context (MiC) |
Description: Mathematics in Context is a standards-based curriculum for grades 5-8 designed to help students progress from informal to formal mathematical reasoning in number, geometry (and measurement), algebra, statistics, and probability. The curriculum focuses on placing students in realistic situations that they must resolve. During their resolution process, students progress from informal notions toward formal mathematical reasoning and representations to model and solve non-routine problems. Throughout the curriculum, students develop conceptual knowledge first and re-visit it as necessary. |
NCTM math standards: Math topics: 5th to 8th Grades
|
|||||||||||||||||||||||
Study: Middle grades MATH thematics: The STEM project. math_6-8_3 |
3 |
Strategy: MATH Thematics - STEM Project |
Description: A Standards-based curriculum for grades 6, 7, and 8 characterized as problem-oriented with a focus on concept development and student discussion prior to written work. Students are expected to actively do mathematics by investigating, discovering, and applying mathematics to new situations. Students must be able to communicate their ideas effectively through cooperative groups and whole-class discussions. |
NCTM math standards: Math topics: 6th to 8th Grades
|
|||||||||||||||||||||||
Study: Effects of the UCSMP secondary school curriculum on students' achievement. math_9-12_6 |
3 |
Strategy: University of Chicago School Mathematics Project (UCSMP) |
Description:
UCSMP is composed of courses called Transitional Mathematics (Algebra; Geometry; Advanced Algebra; Functions, Statistics, and Trigonometry; and Precalculus and Discrete Mathematics). Algebra uses variables to develop linear, exponential, and quadratic patterns. Geometry presents coordinates, transformations, measurement formulas, along with work involving writing proofs. Advanced Algebra studies functions, equations, and inequalities. The Functions, Statistics, and Trigonometry course integrates statistical and algebraic concepts. Precalculus and Discrete Mathematics incorporate many topics required for success in Calculus and Computer Science. The content strands of applied mathematics, prealgebra, and elementary geometry are woven throughout the six courses. |
NCTM Math Standards All Math Topic(s) 7th to 12th grades
|
|||||||||||||||||||||||
Study: Achievement of students using the University of Chicago School Mathematics Project's Everyday mathematics. math_k2_1 |
4 |
Strategy: Subjects: Results: |
Description: |
NCTM math standards: Math Topics: K to 6th Grades |
|||||||||||||||||||||||
Study: Geometric knowledge of middle school students in a reform-based mathematics curriculum. math_6-8_1 |
4 |
Strategy: Everyday Math |
Description: This study is a quasi-experimental design. The intervention was an on-going treatment (the EveryDay Math curriculum) to which students had not been randomly assigned. Rather, the students had been either exposed to the UCSMP or a traditional curriculum since kindergarten and were being assessed as to their level of geometry thinking (according to the van Hiele theory) after those experiences | NCTM math standards: Math Topic(s): 5th & 6th grades |
|||||||||||||||||||||||
Study: Proportional reasoning among seventh grade students with different curricular experiences. math_6-8_7 |
4 |
Strategy: Connected Mathematics Program (CMP) Subjects: 187 eighth graders, 6 classes in Michigan, 1 in San Diego and 1 in Pittsburgh 128 seventh graders, 3 classes in Michigan, 1 in Toledo, 1 in San Diego, 1 in Pittsburgh Results: Seventh graders outperformed control students 53% to 28% on collections task and on each individual problem |
Description: The treatment group was taught using CMP materials for one school year. In this reform curriculum, students are encouraged to construct their own conceptual and procedural knowledge through collaborative problem-solving activities. The data for this study were generated by five proportion problems focusing on rate or population density. |
NCTM math standards: Math Topic(s): seventh and 8th grades |
|||||||||||||||||||||||
Grades 9-12
Study Author & Title |
Design Rating |
Strategy, Subjects, Results |
Description of Strategy/Program |
NCTM Math Standards, Math Topics, Grades |
Study: The Core-Plus Mathematics Project: Perspectives and student achievement. math_9-12_5 |
4 |
Strategy: Core-Plus Mathematics Project Subjects: 64 high schools in 11 states, cross-section of diverse students from urban, suburban, and rural communities Results: Results showed that all CPMP groups performed significantly better on solving mathematical tasks set in context than the comparison groups. The comparison groups performed significantly better with paper-and-pencil procedures at the end of Course 1, but the results were not significant for Course 2. Effect Size on ITED-Q Course 1 ES=+.19 Course 2 ES=+.04 |
Description: The CPMP curricula consist of a single core sequence for college-bound and employment-bound students during the first three years of high school that embody the content, processes, and teaching principles recommended by the NCTM standards. Building connections among topics is the primary focus. Strands are also connected by thinking mathematically, such as visual thinking, recursive thinking, searching for and explaining patterns, making and checking conjectures, reasoning with multiple representations, inventing mathematics, and providing arguments and proofs. Fundamental themes of data, representation, shape, and change also provide connections across strands.
Curriculum development principles include: (1) mathematics as an active science of patterns, (2) problems that include a context for developing student understanding of mathematics, (3) the processes of exploration and experimentation necessarily precede and complement theory, and (4) the use of graphics calculators and other technology as tools for developing mathematical understanding and for solving authentic problems. Pedagogical principles include the importance of students' sense making of mathematics and real-life contexts. The instructional materials are designed to reflect the importance of collaborative learning, social interaction, and communication. |
NCTM Math Standards Math Topic(s): 9th to 12th grade.
|
Study: Title: The effects of curriculum on achievement in second-year algebra: The example of the University of Chicago School Mathematics Project. math_9-12_11 |
New 4 |
Strategy: Skills and concepts learned and applied using the University of Chicago School Mathematics Project (UCSMP) Advanced Algebra textbook |
Description: UCSMP is a curriculum that uses reading and problem solving, realistic applications, technology (graphing calculators and/or computers), a multidimensional approach understanding, and an instructional format featuring continual review combined with a modified mastery-learning strategy. It emphasizes understanding of concepts through multiple representations, realistic contexts, and the use of technology. There is less emphasis on skills than in a traditional curriculum. The instructional method often uses small-group explorations and extended projects, both involving writing about mathematics. |
NCTM Math Standard : Math Topics: Linear equations, binomial multiplication, graphs of quadratic equations, exponential equations, the equation for the inverse-square function, recursion Grades: 10th to 12th Grade |
Study: Title: Effects of standards-based mathematics education: A study of the Core-Plus Mathematics Project algebra and functions strand math_9-12_14 |
3 |
Strategy: Core-Plus Mathematics Project (CPMP) |
Description: The Core-Plus Mathematics Project (CPMP) is a four-year integrated high school mathematics curriculum. Major concepts are developed through investigating concepts in the context of applied problems and mathematical modeling. In particular, algebraic concepts are developed using graphic, numeric, and symbolic representations. Graphing calculators are integral, promoting connections among the forms of representation, encouraging new methods of problem solving, and decreasing the need for symbolic manipulation procedures. Since this study was carried in 1997 the curriculum has been revised (in 2003 and in press) to enhance the in-context approach and also include more work with procedural algebraic skills. |
NCTM Math Standard: Math Topics: Functions, algebraic expressions, systems of equations Grade: 11th Grade |
Study: The impact of the Interactive Mathematics Program on student learning. math_9-12_2 |
3 |
Strategy: Interactive Mathematics Program (IMP) |
Description: |
NCTM Math Standards Math Topic(s): 9th to 12th grades
|
Study: Curriculum and assessment in SIMMS Integrated Mathematics. math_9-12_3 |
3 |
Strategy: SIMMS Integrated Math |
Description: SIMMS Integrated Math is a complete mathematics program for grades 9-12. It is constructed in six levels each consisting of one year of work. Levels 1 and 2 provide basic mathematical literacy. Levels 3 and 5 are for students with non-mathematical or non-scientific aspirations, whereas levels 4 and 6 prepare students to complete a post-secondary mathematics curriculum. The program has the following characteristics, it is (1) integrated and interdisciplinary, (2) problem-centered and applications based, (3) technology based, (4) sensitive to multiple perspectives and the negative effects of bias and stereotyping, (5) multi-modal to accommodate multiple learning styles. Mathematical modeling is the basic thread of the curriculum, knitting together mathematics and other subjects. Students organize, relate, interpret, justify, evaluate, summarize, and communicate ideas as they explore topics and make inquiries about real-world and mathematical concepts. They confront complex issues by "mathematizing" real-world problems, interpret and communicate solutions, and ultimately reflect on their own performance. |
NCTM Math Standards Math Topic(s): 9th - 12th grades
|
Study: The effects of Math Connections on student achievement, confidence, and perception. math_9-12_4 |
3 |
Strategy: Math Connections (MC) Subjects: Summary of several studies Results: On CAPT, PSAT and SAT, MC students scored as well or better than nonparticipants. Students in classes with MC trained teachers have greater confidence in learning mathematics and see the usefulness of mathematics to a greater degree than non-participants. Case study results of Hispanic and African-American at-risk students in an inner-city school suggest that all students can successfully meet the challenge of a mathematically rigorous course. |
Description: Math Connections is presented to students as a powerful tool for interacting with their environment. Its primary goals are to: (1) bridge the worlds of education, students, and business through mathematics; (2) increase mathematical power of all students; (3) empower students for their own learning; (4) develop a core curriculum that reflects the standards of the National Council of Teachers of Mathematics (NCTM); and (5) empower teachers to meet NCTM's Professional Standards for Teaching Mathematics.
Math Connections enables students to investigate a concept in order to recognize patterns that can be presented as a formula. Each year of the curriculum is based on a theme that connects and unifies mathematical topics. The theme for Year 1 is Data, Numbers, and Patterns. Students use data, linear equations, and graphing calculators to forecast events. Year 2's theme, Shapes in Space, focuses on properties and measurement of figures. The principles of congruence and triangulation of polygons are, also, examined. Students use matrices to solve linear equations and learn to calculate the volumes of a cone and a sphere. Mathematical Models, is the theme for Year 3. At this time, logic and the properties of an axiomatic system are introduced. |
NCTM Math Standards All Math Topic(s) 9th to 12th grades
|
Study: Effects of the UCSMP secondary school curriculum on students' achievement. math_9-12_6 |
3 |
Strategy: University of Chicago School Mathematics Project (UCSMP) |
Description:
UCSMP is composed of courses called Transitional Mathematics (Algebra; Geometry; Advanced Algebra; Functions, Statistics, and Trigonometry; and Precalculus and Discrete Mathematics). Algebra uses variables to develop linear, exponential, and quadratic patterns. Geometry presents coordinates, transformations, measurement formulas, along with work involving writing proofs. Advanced Algebra studies functions, equations, and inequalities. The Functions, Statistics, and Trigonometry course integrates statistical and algebraic concepts. Precalculus and Discrete Mathematics incorporate many topics required for success in Calculus and Computer Science. The content strands of applied mathematics, prealgebra, and elementary geometry are woven throughout the six courses. |
NCTM Math Standards All Math Topic(s) 7th to 12th grades
|
Overview – Research on Teaching and Learning Fractions
Students have a great deal of difficulty in working with fractions. Research results related to improving students’ understanding of fractions may be summarized into three categories: K–12 curriculum materials (textbooks), add-on curriculum programs, and individual instructional strategies.
Improvement in achievement resulted from the implementation of the Connected Math Program (Ben-Chaim et al, 1998; Ridgway et al, 2003; Riordan & Noyce, 2001) and Everyday Mathematics (Riordan & Noyce, 2001), which are two standards-based mathematics curricula. Fractions are one of the topics imbedded in these curricula.
Regarding add-on curriculum programs, positive effects were documented for The Missouri Mathematics Effectiveness Project (Good & Grouws, 1979), which was a program that provided a very structured time-on-task daily routine for the classroom. Each lesson was structured to include daily review and mental math, development, seatwork, homework and special weekly and monthly reviews. The Rational Number Project (Cramer, Post & del Mas, 2002) was also effective in helping students understand fractions. Students worked with manipulatives and focused on multiple representations (i.e. concrete manipulatives, pictorial, verbal, symbolic, and real world). Mathematics in the Mind’s Eye (Woodward, et al, 1999) is another program showing evidence of helping students specifically improve achievement in decimals and percents. This program utilizes visual representations and lots of physical manipulatives, followed by drill and practice.
Several individual instructional strategies also resulted in achievement gains in fractions. Moss & Chase (1999) specifically focused on rational numbers and found that beginning with percent, the use of the manipulatives, the number ribbon, and emphasis on benchmark values for moving among the various forms of representation had positive results. Wearne (1990) found that the use of another manipulative, base-ten blocks, was beneficial in helping students connect the written symbol and the physical representation. It is important to note that in this study the manipulatives were found to be beneficial to average and lower-achieving students; however, there were no significant differences for higher-achieving students. Two instructional units, Enhanced Anchored Instruction (Bottge et al, 2002) and Conceptually Oriented Instruction (Madsen et al., 1995) found that teaching fractions within a context improved students’ understanding of fractions. In addition, Madsen et al. found a benefit to using a conceptual approach, compared to a procedural drill and practice approach.
Overall, key components in successful teaching and learning of fractions involve the use of manipulatives and teaching fractions in context and with meaning.
The research studies supporting this overview on fractions research are found in the following table. Back to top menu
Study Author & Title |
Design Rating |
Strategy, Subjects, Results |
Description of Strategy/Program |
NCTM Math Standards, Math Topics, Grades |
|||||||||||||||||||||||
|
Study: Achievement results for second and third graders using the standards-based curriculum. 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: Topics:
2nd and 3rd Grades
| |||||||||||||||||||||||
|
Study: 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. math_3-5_3 |
4 |
Strategy:
Rational
Number Project (RNP)
|
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:
Topics: 4th & 5th Grades | |||||||||||||||||||||||
|
Study: The Missouri Mathematics Effectiveness Project: An experimental study in fourth-grade classrooms. 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. |
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: All topics 4th Grade | |||||||||||||||||||||||
|
Study: The effects of an innovative approach to mathematics on academically low-achieving students in inclusive settings. math_3-5_13 |
4 |
Strategy: Everyday Mathematics. |
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: All Topics 3rd Grade | |||||||||||||||||||||||
|
Study: Developing children's understanding of the rational numbers: A new model and an experimental curriculum. math_3-5_1 |
3 |
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: Topics: 4th Grade | ||||||||||||||||||||||||
|
Study: Acquiring meaning for decimal fraction symbols: a one year follow-up. math_3-5_11 |
3 |
Strategy:
A
one-year follow up of conceptually-based instruction in decimal
fractions. |
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: Topics: 4th Grade | |||||||||||||||||||||||
|
Study: Effects of contextualized math instruction on problem solving of average and below-average achieving students. math_6-8_10 |
3 |
Strategy:
Contextualized mathematics instruction on problem solving
|
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: Math topics:
8th Grade | |||||||||||||||||||||||
|
Study: Role of conceptual knowledge in mathematical procedural learning. math_3-5_17 |
2 |
Strategy: Dynamic Interaction
View |
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: Topics: 4th & 5th Grades | |||||||||||||||||||||||
|
Study: The value (and convergence) of practices suggested by motivation research and promoted by mathematics education reformers. math_3-5_18 |
2 |
Strategy: Strategies and teacher
practices designed to focus on learning and understanding mathematics
concepts. |
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: Math Topic(s): 4th to 6th grade | |||||||||||||||||||||||
|
Study: The effects of an innovative approach to mathematics on academically low-achieving students in inclusive settings. math_3-5_13 |
4 |
Strategy: Everyday Mathematics. |
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: All Topics 3rd Grade | |||||||||||||||||||||||
|
Study: Weighing the benefits of anchored math instruction for students with disabilities in general education classes. math_6-8_27 |
4 |
Strategy: Enhanced Anchored Instruction
(EAI) |
Description: Students were placed in four small groups of 10 to 11 for instruction. Students in the EAI classroom also spent time, in the technology education classroom, solving related problems. The instruction was divided among math teacher, special education teacher, and a technology education teacher. Students, in the treatment and control groups, solved problems aligned with NCTM standards. |
NCTM math
standards: Math Topics: Computation, fractions, arithmetic word problems Grade: seventh Grade
| |||||||||||||||||||||||
|
Study: Student attainment in the Connected Mathematics curriculum. math_6-8_5 |
4 |
Strategy: Connected Math (CMP) Subjects: 5 Midwest, 2 West, and 2 East schools, 2 CMP classes and 1 nonCMP in each school
|
Description: A problem-oriented curriculum which provides a broad range of mathematical topics with a focus on concept development and student discussion prior to written work. |
NCTM math
standards: Math
topics: 6th to 8th Grades | |||||||||||||||||||||||
|
Study: 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)]. math_6-8_6 |
4 |
Strategy:
Connected Math (CMP) and Everyday Math (EM) |
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: Math topics:
4th & 8th Grades
| |||||||||||||||||||||||
|
Study: Proportional reasoning among seventh grade students with different curricular experiences. math_6-8_7 |
4 |
Strategy: Connected Mathematics Program
(CMP) Subjects: 187 eighth graders, 6 classes in Michigan, 1 in San Diego and 1 in Pittsburgh 128 seventh graders, 3 classes in Michigan, 1 in Toledo, 1 in San Diego, 1 in Pittsburgh Results: Seventh graders outperformed control students 53% to 28% on collections task and on each individual problem |
Description: The treatment group was taught using CMP materials for one school year. In this reform curriculum, students are encouraged to construct their own conceptual and procedural knowledge through collaborative problem-solving activities. The data for this study were generated by five proportion problems focusing on rate or population density. |
NCTM math
standards: Math
Topic(s): seventh and 8th grades | |||||||||||||||||||||||
|
Study: How group composition influenced the achievement of sixth-grade mathematics students. math_6-8_12 |
3 |
Strategy:
Comparison of heterogeneous vs. homogeneous grouping. |
Description: Sixth-grade students were grouped heterogeneously and homogeneously to determine how groups differ in mathematics achievement and what influence group composition has on student interactions in heterogeneous and homogeneous small groups. Students were assigned to one of three homerooms. The research was conducted for two consecutive academic years. The first year students were grouped heterogeneously by ability. The second year students were grouped homogeneously. |
NCTM math
standards: Math topics:
6th Grade | |||||||||||||||||||||||
|
Study: Using everyday knowledge of decimals to enhance understanding. math_6-8_18 |
2 |
Strategy: Collaborative Learning on Contextual Problems
with Decimals Subject: 16 students ages 11 and 12, low SES Effects: Significance of p=.002 Contextual group: The low ranked students improved from 19% pretest to 32% posttest. The high ranked students improved 34% pretest to 48% posttest. |
Description: Pairs of students were presented with two types of sentence problems, contextualized and noncontextualized. Contexts included different sizes of soft drink bottles, monetary exchanges between countries, and other uses of metric measurement. There were three categories of decimal fractions problems: magnitude, addition and subtraction, and multiplication and division. The problems addressed misconceptions about decimals. |
NCTM math
standards: Math
Topic(s): seventh Grade | |||||||||||||||||||||||
|
Study: Does conceptually oriented instruction enhance computational competence? math_9-12_1 |
4 |
Strategy: Conceptually Oriented Instruction Subjects: Two ninth grade general math classes from a Midwest suburban high school with a population of 700 students. Subject students ranged from 14-17 years old. The average age was 15 years old. First semester: the “conceptually oriented” class had 28 students and the “computational” class had 19 students. Second semester: the “conceptually oriented” class had 23 students and the “computational” class had 21 students. Results: Students in the conceptually oriented class outperformed students in the drill and practice class on a test of computation. Effect Size = +0.96. |
Description: |
NCTM
Math Standards: Math
Topic(s): 9th grade | |||||||||||||||||||||||
Path: State of Iowa > Educate > PK-12 Education > Educator Quality > Professional Development > Iowa Professional Development for Student Achievement > Content Network
Updated 11-7-2006