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Programmatic collaborations involving mathematicians and educators in the U.S. have been valuable but complex (e.g., Heaton & Lewis, 2011; Bass, 2005; Bass & Ball, 2014). Sultan & Artzt (2005) offer necessary conditions (p.53) including trust and helpfulness. Articles in Fried & Dreyfus (2014) and Bay-Williams (2012) describe outcomes from similarly collaborative efforts; however, there is a gap in the literature in attending to how race and gender intersect with issues of professional status, culture, and standards of practice. Arbaugh, McGraw and Peterson (2020) contend that “the fields of mathematics education and mathematics need to learn how to learn from each other - to come together to build a whole that is greater than the sum of its parts” (p. 155). Further, they posit that the two must “learn to honor and draw upon expertise related to both similarities and differences” across disciplines, or cultures. We argue that in order to do this, we must also take into account race, gender, language. For example, words like trust or helpfulness can read very differently when viewed from personal and professional culture, gender, or racial lenses. This poster shares personal vignettes from the perspective of three collaborators – one black male mathematician, one white female mathematics educator, and one white woman who was trained as a mathematician but works as a mathematics educator - illustrating some of the complexity of collaboration. 

This paper reports an ongoing effort to address the problem of instructional capacity for high school geometry from a systems improvement perspective. In an effort to understand the system that contains the high school geometry instructional capacity problem, we identified key stakeholders and conducted preliminary interviews to learn about the problem from their perspective. We use these interview data to describe the system in more detail and to identify six major factors contributing to the high school geometry instructional capacity problem. 

Mathematics pre-service teachers must learn how to use tools like scientific calculators, Computer Algebra System (CAS), text processors and dynamic mathematical environments. These tools allow users to work with mathematical objects, perform specialized tasks, respond in a defined mathematical way, and transmit mathematical knowledge (Dick & Hollebrands, 2011). To achieve the integration of technology in Mathematics Education, the teacher’s role is very important, since their beliefs and knowledge will dictate how they use technology in the classroom (Julie et al., 2010). The goal of this research is to determine the beliefs and knowledge about technology and its integration into the teaching of mathematics by a group of pre-service teachers at the beginning of their first course of methodology in the teaching of mathematics at the secondary level (N=11). Interviews were conducted, and a questionnaire was administered to determine the profile participants use of technology at their schools and universities. 

One of the most intransigent problems in mathematics education is the culturally-influenced divide between classroom practice and educational research. This paper describes our explicit attempt to bridge that divide by translating research on instructional practices linked to improving students’ mathematics achievement into a brief guide outlining constructs, features, strategies, routines, and tools for use in a teacher-researcher alliance. We outline the design and development process, share the guide itself, and summarize data addressing the utility of the guide for a research and professional development project in which 100 U.S. Grades 6-8 teachers are collaborating to improve middle grades modeling and problem solving achievement. 

How can we design mathematical lessons that spark student interest? To answer this, we analyzed teacher-designed and enacted lessons that students described as interesting for how the content unfolded. When compared to those the same students describe as uninteresting, multiple distinguishing characteristics are evident, such as the presence of misdirection, mathematical questions that remain unanswered for extended time, and a greater number of questions that are unanswered at each point of the lesson. Low-interest lessons did not contain many special narrative features and mostly had questions that were answered immediately. Our findings offer guidance for the design of lessons that can shift student mathematical dispositions. 

What impact, if any, do interesting lessons have on the types of questions students ask? To explore this question, we used lesson observations of six teachers from three high schools in the Northeast who were part of a larger study. Lessons come from a range of courses, spanning Algebra through Calculus. After each lesson, students reported interest via lesson experience surveys (Author, 2019). These interest measures were then used to identify each teachers’ highest and lowest interest lessons. The two lessons per teacher allows us to compare across the same set of students per teacher. We compiled 145 student questions and identified whether questions were asked within a group work setting or part of a whole class discussion. Two coders coded 10% of data to improve the rubric for type of students’ questions (what, why, how, and if) and perceived intent (factual, procedural, reasoning, and exploratory). Factual questions asked for definitions or explicit answers. Procedural questions were raised when students looked for algorithms or a solving process. Reasoning questions asked about why procedures worked, or facts were true. Exploratory questions expanded beyond the topic of focus, such as asking about changing the parameters to make sense of a problem. The remaining 90% of data were coded independently to determine interrater reliability (see Landis & Koch, 1977). A Cohen’s Kappa statistic (K=0.87, p<0.001) indicates excellent reliability. Furthermore, both coders reconciled codes before continuing with data analysis. Initial results showed differences between high- and low-interest lessons. Although students raised fewer mathematical questions in high-interest lessons (59) when compared with low-interest lessons (86), high-interest lessons contained more “exploratory” questions (10 versus 6). A chi-square test of independence shows a significant difference, χ2 (3, N = 145) = 12.99, p = .005 for types of students’ questions asked in high- and low-interest lessons. The high-interest lessons had more student questions arise during whole class discussions, whereas low-interest lessons had more student questions during group work. By partitioning each lesson into acts at points where the mathematical content shifted, we were able to examine through how many acts questions remained open. The average number of acts the students’ questions remained unanswered for high-interest lessons (2.66) was higher than that of low-interest lessons (1.68). Paired samples t-tests suggest that this difference is significant t(5)=2.58, p = 0.049. Therefore, student interest in the lesson did appear to impact the type of questions students ask. One possible reason for the differences in student questions is the nature of the lessons students found interesting, which may allow for student freedom to wonder and chase their mathematical ideas. There may be more overall student questions in low-interest lessons because of confusion, but more research is needed to unpack the reasoning behind student questions.