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Lamberg, Teruni ; Moss, Diana. (Ed.)The purpose of this report is to share the supports created as part of a mathematics mentoring program in a mid-sized western university. The research is longitudinal, and the current paper will share results from the fourth (of six) years of a project. I use a mixed method approach to examining the efficacy of the mentoring program, and the results indicate that the program may have helped students through the pandemic and to shift back afterwards.more » « less
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Lamberg, T ; Moss, Diana (Ed.)
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Lamberg, T ; Moss, Diana (Ed.)
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Lamberg, Teruni ; Moss, Diana (Ed.)While proving, and more broadly conceived “reasoning and sense-making,” have received a great deal of attention in mathematics education research over the past three decades, recently scholars have argued for the importance of justification as a learning and teaching practice. As teachers work toward realizing goals for more equitable classroom environments, little is known about whether teachers’ conceptions about mathematical practices, such as justification, reflect an understanding of how students’ engagement in those practices can support more than just mathematical achievement. In this paper, we present findings from our analysis of interviews with 10 secondary mathematics teachers engaged in participatory action research to explore connections, and potential disconnections, between teachers’ conceptions of justification and their visions for equitable instruction.more » « less
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Lamberg, Teruni ; Moss, Diana (Ed.)Depth-of-knowledge (DOK) is a means to communicate the cognitive demand of tasks and is often used to categorize assessment items. Webb’s (2002) framework has been applied across content areas. The aim of this two-phase iterative study was to modify Webb’s DOK framework for word problems. Through work with school partners, this iterative design-research based study provides supportive evidence for a modified DOK framework reflecting levels of complexity in word problems. The resulting modified DOK framework presents an opportunity for mathematics educators to reflect on various aspects of cognitive complexity.more » « less
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Lamberg, Teruni ; Moss, Diana (Ed.)
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Lamberg, Teruni ; Moss, Diana (Ed.)
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Lamberg, Teruni ; Moss, Diana (Ed.)Building Thinking Classrooms (Liljedahl, 2021) provides teachers with a new method of designing and sequencing tasks called “thin slicing,” which emerged from variation theory. The results of the present study indicate that an analysis of the dimensions and ranges of variation within such a task offers insights into learning opportunities available. Specifically, identifying instances where variation has not been adequately positioned against a background of sameness can highlight potentially limited opportunities for students to notice the intended mathematics. The results of this analysis can inform design decisions and modifications to the task before implementation increasing the potential of the task to support student learning.more » « less
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Lamberg, Teruni ; Moss, Diana L (Ed.)We investigate teacher beliefs about discourses for equation solving and the challenges these beliefs might pose for the implementation of instructional practices that promote deductive reasoning in algebra. To uncover these beliefs, we recorded three video explanations of solutions to the same linear equation with distinct discursive characteristics and analyzed seven secondary mathematics teachers’ small-group critical discussions of these explanations. Three prevalent themes surfaced in our thematic analysis. Teacher beliefs about discourse for equation solving specified different roles and potential benefits of deductive explanations, estimated students’ capacity to understand deductive explanations, and hypothesized differences between teachers' and students' potential to understand deductive reasoning. We discuss implications of these beliefs for opportunities to engage all learners in conceptual thinking about equations.more » « less
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Worthwhile problems: How teachers evaluate the instructional suitability of contextual algebra tasksLamberg, Teruni ; Moss, Diana L (Ed.)We investigate the beliefs that influence middle and high school algebra teachers’ appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical features, and connections to the real world. We recorded small-group discussions in which teachers shared their responses to this activity, and qualitatively analyzed their discussions for evidence of beliefs that influenced their appraisals of the tasks. The teachers’ beliefs about contextual problems attended to task authenticity, opportunities for mathematical activity, obligations of tasks, and pedagogy and access. Our preliminary findings can inform future efforts to equip teachers with contextual tasks that develop students’ algebraic reasoning and problem solving.more » « less