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Olanoff, D. ; Johnson, K. ; Spitzer, S. M. (Ed.)Argumentation is widely used in teaching mathematics, but little research has been done on argumentation in teaching integrated mathematics and coding. As part of a larger study investigating collective argumentation in teaching mathematics, science, and coding, we classified the warrants given by elementaryage students who were engaged in argumentation in mathematics and coding. Three ma}or categories  calculation, visual, and unformalized knowledge  accounted for the majority of warrants given. Further analysis revealed differences in types of warrants when the primary focus of the argument was coding versus when the primary focus of the argument was mathematics. Our results suggest that expecting students to provide reasons for modifying their code, similar to what is expected in mathematics arguments, helps move them away from a trialanderror to a more structured approach to coding.more » « less

Olanoff, D. ; Johnson, K. ; Spitzer, S. M. (Ed.)Productive use of student mathematical thinking is a critical yet incompletely understood dimension of effective teaching practice. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four elements that comprise it. In this paper we begin to unpack this complex practice by looking closely at its first element, establish. Based on an analysis of secondary mathematics teachers' enactments of building, we describe two critical aspects of establish—establish precision and establish an object—and the actions teachers take in association with these aspects.more » « less

Olanoff, D. ; Johnson, K. ; Spitzer, S. M. (Ed.)In this paper we examine how teachers who are pursuing their Elementary Mathematics Specialist certification—Elementary Mathematics Specialists in Training (EMSTs)—are positioned in their advice and information networks for mathematics. We analyzed the instructional networks of six elementary schools in one Midwestern school district. Our analysis suggests that EMSTs did occupy central positions in their networks. EMSTs were sought out by more individuals compared to other teachers, and when sought out by others, provided advice and information at a greater frequency than formal leaders. We also considered the school’s informal and formal structure, finding that EMSTs’ positioning was related to the broader school’s information seeking behavior and whether there is a mathspecific formal leadermore » « less

Olanoff, D. ; Johnson, K. ; Spitzer, S. M. (Ed.)The EnCoMPASS project (Emerging Communities for Mathematical Practices and Assessment) at Drexel University has produced a webbased software tool for the assessment of student work. This paper discusses research on the impact of this tool on teachers’ attitudes toward engaging with students in the software environment. The tool supports teachers adopting a more dialogic perspective towards learning and teaching through cycles of problem solving, discussion and mathematical development. It is suggested that the tool aids teachers’ transition toward this more interactive approach to teaching mathematics while also acknowledging and addressing concerns about the time it takes to engage in more detailed dialogue and thinking about mathematics with their students.more » « less

Olanoff, D. ; Johnson, K. ; Spitzer, S. M. (Ed.)Mathematics education needs measures that can be used to research and/or evaluate the impact of professional development for constructs that are broadly relevant to the field. To address this need we developed the Priorities for Mathematics Instruction (PMI) survey consisting of two scales focused on the constructs of Explicit Attention to Concepts (EAC) and Student Opportunities to Struggle (SOS) – which have been linked to increased student understanding and achievement. We identified the most critical assumptions that underlie the proposed interpretation and use of the scale scores and then examined the related validity evidence. We found the evidence for each assumption supports the proposed interpretation and use of the scale scores.more » « less

Olanoff, D. ; Johnson, K. ; Spitzer, S. M. (Ed.)

Olanoff, D. ; Johnson, K. ; Spitzer, S. M. (Ed.)

Olanoff, D. ; Johnson, K. ; Spitzer, S. M. (Ed.)