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Grades 3 to 5 Overview of
Research
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, p.35). 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.
- Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell (Eds.) (2001) Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy Press.
- Lehrer, Richard. (2003) “Developing Understanding of Measurement.” In Jeremy Kilpatrick, W. Gary Martin and Deborah Schifter (Eds.) A Research Companion to Principles and Standards for School Mathematics (179-192). Reston, VA: NCTM.
- National Council of Teachers of Mathematics (2000) Principles and Standards for School Mathematics. Reston, VA: NCTM.
2. Individual Studies Examine the following tables of studies.)
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Reviewers' Ratings of Research As explained in the Mathematics
Summary page, selection of research for this database has emphasized
studies meeting the definition of quality research as outlined in the
federal No Child Left Behind legislation. Remember that ratings in column
2 apply to the research design, not to the quality of the
intervention studied or how powerful the method, strategy, or approach is
in influencing overall student achievement. Rating levels, as illustrated
by the Gold Standard pyramid, are further defined on the Definitions
page. The review tables below are arranged by column 2, Design Rating,
with highest ratings first.
