Mathematics classrooms have reflected little change over the past century, consisting of the learning of inert, disjoint procedures with few connections between mathematics concepts and students’ everyday experiences. However, problem posing, that is, the reformatting of existing problems and the generation of new ones, has been promoted by the National Council of Teachers of Mathematics (NCTM, 1989) as a valuable practice for deepening students’ mathematical thinking. It has also been shown to be associated with problem-solving ability, conceptual understanding, and mathematical habits of mind such as divergent thinking. Furthermore, educational policy and research have promoted collaborative student interactions in mathematics.
In this study, I investigated the process of group problem posing for beginning problem posers. That is, I explored characteristics of an individual student’s engagement with the activity, as well as students’ interactions with one another, so as to understand the successes and struggles of student participation and collaboration. In addition, I explored the products of group problem posing, that is, what kinds of problem scenarios beginning problem posers would create. Because the linear function is a foundational topic for high-school Algebra students, and because mathematical connections and multiple representations have been promoted by the NCTM (2000), I analyzed how students incorporated visual representations, as well as the rate of change and the y-intercept.
I led a five-day intervention in an Integrated Mathematics 2 classroom with five groups of students (3-4 students per group) in an ethnically-diverse high-school in a small, mid-Atlantic town. Students were heterogeneously grouped according to gender, mathematics disposition, and mathematics performance. As Activity Theory served as the basis for the intervention, students were daily provided with mediating artifacts (i.e., criteria, cultural artifacts, “I Notice, I Wonder” chart) to support their daily creation of problem scenarios. Students were also given the opportunity to periodically define, enact, and negotiate roles within their groups to promote student collaboration. In addition, to encourage their incorporation of representations and mathematics concepts, students participated in daily lessons regarding the rate of change and y-intercept, which fostered connections between concepts and between representations. Problem scenarios from all five groups were coded and analyzed with respect to how student groups incorporated representations and mathematics concepts into their scenarios. Videotaped sessions of one group of three students were recorded, transcribed, and analyzed to investigate student interactions and engagement.
The results indicated that all student groups created problem scenarios that included both mathematical information and everyday items (e.g., food or beverages) from the cultural artifacts. However, student groups faced difficulties with incorporating visual representations into their scenarios that were mathematically meaningful, that had explicit purposes, and that were explicitly mathematically connected. Regarding mathematics topics, most student groups often found difficulties with incorporating the rate of change and the y-intercept in productive ways. Furthermore, each of the three students varied in the degree and ways in which they participated in group problem posing throughout the intervention. As two of the students took a more cooperative, rather than collaborative, approach to group problem posing, the third student struggled to participate in the activity. Further results and implications of the findings for practitioners and researchers are discussed.
|Advisor:||Hohensee, Hartmut C.|
|Commitee:||Hiebert, James, Morris, Anne, Cai, Jinfa|
|School:||University of Delaware|
|Department:||School of Education|
|School Location:||United States -- Delaware|
|Source:||DAI-A 81/2(E), Dissertation Abstracts International|
|Subjects:||Mathematics education, Mathematics, Education|
|Keywords:||Activity theory, collaboration, Group problem posing, Linear functions, Problem posing, Representations|
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