Cover Image
close this bookImproving Student Achievement in Mathematics (IAE - IBE - UNESCO, 2000, 48 p.)
View the document(introduction...)
View the documentThe International Academy of Education
View the documentPreface
View the documentIntroduction
View the document1. Opportunity to learn
View the document2. Focus on meaning
View the document3. Learning new concepts and skills while solving problems
View the document4. Opportunities for both invention and practice
View the document5. Openness to student solution methods and student interaction
View the document6. Small-group learning
View the document7. Whole-class discussion
View the document8. Number sense
View the document9. Concrete materials
View the document10. Students’ use of calculators
View the documentConclusions
View the documentAdditional resources
View the documentReferences
View the documentThe International Bureau of Education-IBE

5. Openness to student solution methods and student interaction

Teaching that incorporates students’ intuitive solution methods can increase student learning, especially when combined with opportunities for student interaction and discussion.

Research findings

Recent results from the TIMSS video study have shown that Japanese classrooms use student solution methods extensively during instruction. Interestingly, the same teaching technique appears in many successful American research projects. Findings from American studies clearly demonstrate two important principles that are associated with the development of students’ deep conceptual understanding of mathematics. First, student achievement and understanding are significantly improved when teachers are aware of how students construct knowledge, are familiar with the intuitive solution methods that students use when they solve problems, and utilize this knowledge when planning and conducting instruction in mathematics. These results have been clearly demonstrated in the primary grades and are beginning to be shown at higher-grade levels.

Second, structuring instruction around carefully chosen problems, allowing students to interact when solving these problems, and then providing opportunities for them to share their solution methods result in increased achievement on problem-solving measures. Importantly, these gains come without a loss of achievement in the skills and concepts measured on standardized achievement tests.

Research has also demonstrated that when students have opportunities to develop their own solution methods, they are better able to apply mathematical knowledge in new problem situations.

In the classroom

Research results suggest that teachers should concentrate on providing opportunities for students to interact in problem-rich situations. Besides providing appropriate problem-rich situations, teachers must encourage students to find their own solution methods and give them opportunities to share and compare their solution methods and answers. One way to organize such instruction is to have students work in small groups initially and then share ideas and solutions in a whole-class discussion.

One useful teaching technique is for teachers to assign an interesting problem for students to solve and then move about the room as they work, keeping track of which students are using which strategies (taking notes if necessary). In a whole-class setting, the teacher can then call on students to discuss their solution methods in a pre-determined and carefully considered order, these methods often ranging from the most basic to more formal or sophisticated ones. This teaching structure is used successfully in many Japanese mathematics lessons.


Boaler, 1998; Carpenter et al., 1988, 1989, 1998; Cobb, Yackel & Wood, 1992; Cobb et al., 1991; Cognition and Technology Group, 1997; Fennema, Carpenter & Peterson, 1989; Fennema et al., 1993, 1996; Hiebert & Wearne, 1993, 1996; Kamii, 1985, 1989, 1994; Stigler & Hiebert, 1997; Stigler et al., 1999; Wood, Cobb & Yackel, 1995; Wood et al., 1993; Yackel, Cobb & Wood, 1991.