Considering representational choices of fourth graders when solving division problems

Students need to build on their own understanding when problem solving. Mathematics reform is moving away from skill and drill types of activities and encouraging students to develop their own approaches to problem solving. The National Council of Teachers of Mathematics emphasizes the importance of representation by including it as a process standard in Principles and Standards for School Mathematics (2000) as a means for students to develop mathematically powerful conceptualization. Students use representation to make sense of and communicate mathematical concepts. This study considers the way fourth grade students view and solve division problems and whether problem type affected the choice of strategy. This study also looked at factors that affect students' score performance. Students in extant classrooms were observed in their regular mathematics instructional settings. Data were collected and quantified from pretests and posttests using questions formatted like students see on the state assessment. The results indicate that students moved from pre-algorithmic strategies to algorithmic strategies between pretest and posttest administration. The results also indicate that problem type did not predict students' choice of strategy and did not have an affect on the students' ability to arrive at a correct solution to the problem. This study found that the students' choice of strategy did play a significant role in their quest for correct solutions. The implication is that when students are able to make sense of the problem and choose an appropriate strategy, they are able to successfully solve division problems.