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Trena L. Wilkerson

How has NCTM leadership shaped the evolution of teaching and learning mathematics? What are your expectations for NCTM leadership?

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Trena L. Wilkerson, Tommy Bryan, and Jane Curry

Using candy bars as models gives students a taste for learning to represent fractions whose denominators are factors of twelve.

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Connie Johnsen and Trena L. Wilkerson

Learning how to modify my teaching style and determining successful methods for reaching struggling students in a beginning algebra class has been an eventful journey for me. My journey began fourteen years ago when I altered my teaching style of straight lecturing to one that incorporated handson activity learning with real-world connections, along with the lectures. In a beginning algebra class, using real-world connections is particularly important because the students have great difficulty connecting the abstract concepts of algebra with their everyday lives. Since research has shown that “50 percent of students sixteen and older function at Piaget's concrete operational level” (Gadanidis 1994, p. 93), high school students need the opportunity for hands-on activities. Businesses require that students not only comprehend but also apply mathematics to qualify for jobs.

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Emiliano Gómez, Risa A. Wolfson, and Introduction by: Trena L. Wilkerson

When selecting mathematical tasks to use in professional development with teachers, in-service or preservice, I am always looking for ones that model effective teaching practices, give opportunities to dig deeply into mathematics, engage the learner in multiple ways, and can readily be used in the classroom. Although there are many to choose from, “Filling Bottles with Water" (Gómez and Wolfson 2012) from Mathematics Teacher, now 10 years old, is one I use that exemplifies all four characteristics.

EFFECTIVE TEACHING PRACTICES

When implementing this task, you see multiple effective teaching practices at play (NCTM 2014

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Michelle L. Stephan, Kathryn B. Chval, Jeffrey J. Wanko, Marta Civil, Michael C. Fish, Beth Herbel-Eisenmann, Clifford Konold, and Trena L. Wilkerson

Mathematics education researchers seek answers to important questions that will ultimately result in the enhancement of mathematics teaching, learning, curriculum, and assessment, working toward “ensuring that all students attain mathematics proficiency and increasing the numbers of students from all racial, ethnic, gender, and socioeconomic groups who attain the highest levels of mathematics achievement” (National Council of Teachers of Mathematics [NCTM], 2014, p. 61). Although mathematics education is a relatively young field, researchers have made significant progress in advancing the discipline. As Ellerton (2014) explained in her JRME editorial, our field is like a growing tree, stable and strong in its roots yet becoming more vast and diverse because of a number of factors. Such growth begs these questions: Is our research solving significant problems? How do we create a system and infrastructure that will provide an opportunity to accumulate professional knowledge that is storable and shareable as we work together to address significant problems (Hiebert, Gallimore, & Stigler, 2002)? How do we “facilitate research and development that is coordinated, integrated, and accumulated” (Lesh et al., 2014, p. 167)?

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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.