Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem solving that integrates mathematical problem-solving and reading comprehension theories and using constant comparative methodology (Strauss & Corbin, 1994), 98 sixth- and seventh-grade students' problem-solving behaviors were described and classified into five categories. Nearly 90% of problem solvers used one behavior on a majority of problems. Use of context such as units and relationships, recording information given in the problem, and provision of explanations and justifications were associated with higher reading and mathematics achievement tests, greater success rates, fewer errors, and the ability to preserve the structure of problems during recall. These results were supported by item-level analyses.
Beth Herbel-Eisenmann, Nathalie Sinclair, Kathryn B. Chval, Douglas H. Clements, Marta Civil, Stephen J. Pape, Michelle Stephan, Jeffrey J. Wanko and Trena L. Wilkerson
In this commentary, we identify key influences on mathematics education that are largely outside the domain of the academic world in which most mathematics education researchers live. The groups that we identify–including the media, companies and foundations, and other academic domains–affect the public's perception of mathematics and mathematics education. Identifying this set of influences in particular is important because these groups often shape policymakers' viewpoints and decisions, but there is not always agreement between mathematics education researchers and these groups about the ways in which mathematics and mathematics education are framed. Whenever a conflict is brought to the foreground, it can be difficult to raise issues without appearing defensive or sounding querulous. It is helpful, then, to bring to bear a theory that can help us interpret this reality (Mewborn, 2005); theories can provide a way to encode, read, and examine a problem as well as offer insights into the design of new practices (Silver & Herbst, 2007). In this case, we use positioning theory to examine potential conflicts between mathematics education researchers and other groups because it offers interesting interpretive insights into the phenomenon and because it can lead to potential strategies for working toward different positionings for mathematics education researchers. We begin by explaining relevant ideas from positioning theory, including storylines, positions, and communication actions. We then use these ideas to highlight current storylines underlying communication by the abovementioned groups about mathematics and mathematics education and trace some of their historical and contextual roots. We argue that mathematics education researchers can intervene to shift these storylines and positionings and to have greater impact on policy, practice, and public perception in the future. Finally, we end by offering specific suggestions for beginning this work.
Sylvia Celedón-Pattichis, Lunney Lisa Borden, Stephen J. Pape, Douglas H. Clements, Susan A. Peters, Joshua R. Males, Olive Chapman and Jacqueline Leonard
In July 2017, the National Council of Teachers of Mathematics (NCTM) released a new mission statement that shifts the organization's primary focus to supporting and advocating for the highest quality mathematics teaching and learning for all students. A key strategy for achieving this goal is to advance “a culture of equity where each and every person has access to high quality teaching and is empowered as a learner and doer of mathematics” (NCTM, 2017, “Strategic Framework,” para. 2). Increasing equity and ensuring the highest quality mathematics teaching and learning for all students requires systemic change (National Council of Supervisors of Mathematics [NCSM] & TODOS: Mathematics for ALL, 2016). As educators are called to enact NCTM's new mission, we acknowledge that such change is complex. We also acknowledge that our own experiences conducting equity work that is grounded in an asset-based approach are at different stages of development, ranging from beginning levels to lived experiences as diverse mathematics learners and mathematics education researchers. We see this change in mission as a call to both act politically (Aguirre et al., 2017) and to change story lines (i.e., “broad, culturally shared narrative[s]”; Herbel-Eisenmann et al., 2016, p. 104) that dominate the public perception of mathematics learning and teaching. We acknowledge that systemic barriers are part of a larger educational issue, but for the purposes of this commentary, we focus on mathematics.