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1. Building “Small Worlds” in online professional development with evidence-based noticing and wondering

   Matranga, A. ; Silverman, J. ( October 2021 , Proceedings of the 43rd Annual Meeting of PME-NA)

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

   Understanding how to design online professional development environments that support mathematics teachers in developing mathematical and pedagogical knowledge is more important than ever. We argue that productive social and sociomathematical (SM) norms have benefits for teachers learning mathematics in online asynchronous collaboration and that particular patterns in interactions can create context for the emergence of such norms. We employed social network analysis to compare the emerging social networks of two iterations of an online asynchronous professional development course focused on functions to understand whether particular scaffolds can support the emergence of specific patterns of interactions. Results suggest that evidence-based noticing and wondering can impact the “small world” properties of a social network and associated potential for the emergence of social and SM norms. 

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2. Translanguaging in Mathematics Learning: Teacher Instructional and Attentional Supports

   Gilmore, M. ( January 2020 , ProQuest dissertations theses global)

   Students from less-dominant linguistic backgrounds generally have less opportunity to participate in classroom mathematical discourse compared to their English-dominant peers. An issue raised by mathematics education researchers concerned with issues of equity and opportunities for students is that status quo classroom practices and norms supported by teachers may be less familiar to students from non-dominant linguistic groups, or even detrimental to their classroom participation. Additionally, students who position themselves as doers of mathematics usually come from dominant cultural and linguistic groups (Abreu & Cline, 2002; Hand, 2012), potentially disposing students to perceive classroom mathematics learning through the lens of dominant cultural norms and practices. Thus, students who do not come from dominant linguistic backgrounds might perceive the mathematics classroom differently than their English dominant peers. However, less research has been conducted on how mathematics teachers attend to or notice norms around language and introduce new ones that encourage a multitude of linguistic practices, therefore heightening student participation. Heightening student participation can have implications for students being more likely to identify with mathematics. Additionally, examining students’ participation when using a multitude of linguistic practices or translanguaging is helpful for teachers attending to their own practice to support emerging bilingual students and bilingual students when engaging in mathematical sensemaking. 

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3. When Am I (N)ever Going to Use This? How Engineers Use Algebra

   Istas, Brooke ; Walkington, Candace ; Leyva, Elizabeth ( July 2021 , 2021 ASEE Virtual Annual Conference)

   Mathematics is an important tool in engineering practice, as mathematical rules govern many designed systems (e.g., Nathan et al., 2013; Nathan et al., 2017). Investigations of structural engineers suggest that mathematical modelling is ubiquitous in their work, but the nature of the tasks they confront is not well-represented in the K-12 classroom (e.g., Gainsburg, 2006). This follows a larger literature base suggesting that school mathematics is often inauthentic and does represent how mathematics is used in practice. At the same time, algebra is a persistent gatekeeper to careers in engineering (e.g., Harackiewicz et al., 2012; Olson & Riordan, 2012). In the present study, we interviewed 12 engineers, asking them a series of questions about how they use specific kinds of algebraic function (e.g., linear, exponential, quadratic) in their work. The purpose of these interviews was to use the responses to create mathematical scenarios for College Algebra activities that would be personalized to community college students’ career interests. This curriculum would represent how algebra is used in practice by STEM professionals. However, our results were not what we expected. In this paper, we discuss three major themes that arose from qualitative analyses of the interviews. First, we found that engineers resoundingly endorsed the importance of College Algebra concepts for their day-to-day work, and uniformly stated that math was vital to engineering. However, the second theme was that the engineers struggled to describe how they used functions more complex than linear (i.e., y=mx+b) in their work. Students typically learn about linear functions prior to College Algebra, and in College Algebra explore more complex functions like polynomial, logarithmic, and exponential. Third, we found that engineers rarely use the explicit algebraic form of an algebraic function (e.g., y=3x+5), and instead rely on tables, graphs, informal arithmetic, and computerized computation systems where the equation is invisible. This was surprising, given that the bulk of the College Algebra course involves learning how to use and manipulate these formal expressions, learning skills like factoring, simplifying, solving, and interpreting parameters. We also found that these trends for engineers followed trends we saw in our larger sample where we interviewed professionals from across STEM fields. This study calls into question the gatekeeping role of formal algebraic courses like College Algebra for STEM careers. If engineers don’t actually use 75% of the content in these courses, why are they required? One reason might be that the courses are simply outdated, or arguments might be made that learning mathematics builds more general modelling and problem-solving skills. However, research from educational psychology on the difficulty of transfer would strongly refute this point – people tend to learn things that are very specific. Another reason to consider is that formal mathematics courses like advanced algebra have emerged as a very convenient mechanism to filter people by race, gender, and socioeconomic background, and to promote the maintenance of the “status quo” inequality in STEM fields. This is a critical issue to investigate for the future of the field of engineering as a whole. 

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4. Factors that influence student mathematical dispositions

   Riling, M. ; Dietiker, L. ; Gibson, K. ; Tukhtakhunov, I. ; Ren, C. ( January 2018 , Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Why do secondary students in the US consistently and increasingly report a lack of interest in mathematics? Lack of interest in mathematics has been well documented in TIMSS responses; students dissatisfaction with mathematics more than doubled by 2011, when 40% of 8th graders reported not liking math, up from 18% as 4th graders in 2007. And, sadly, the trend appears to be worsening; in 2015, 47% of 8th graders indicated not liking math, up from 22% as 4th graders. In order to positively impact student attitudes towards mathematics, it is important to understand factors that may influence secondary students’ relationship with the discipline. This poster presents findings from an exploratory study of student disposition toward mathematics. We designed an online survey to learn about students’ relationship with mathematics, including experiences and settings that contribute to both positive and negative feelings about the subject. We surveyed 275 students, grades 9 to 12, in 11 classes in three schools in three New England districts. Though not randomly chosen, this sample allows us to examine student attitudes across a variety of contexts. We asked students about their feelings towards mathematics over the years, as well as which aspects of class they most enjoyed or disliked. Finally, we included items from the TRIPOD survey (Wallace et al., 2016) and the 2015 NAEP survey, which allows us to compare our sample with the national sample. Initial results indicate that student view their teachers and the topics of study as the central factors influencing their enjoyment of mathematics class. We found a correlation between responses that math is boring and that it is not relevant. Students who like math and those who do not reported different class activity preferences. For example, students who like math reported disliking watching a video in class, while students who dislike math reported disliking learning something new. Both groups of students (those who like math and those who do not) dislike math class when they have to present work to classmates, but hold positive views of solving puzzles and working with other students. Technology seems to appeal equally to both groups. Students who reported disliking math also look forward to playing competitive games. We saw no evidence that gender or race corresponded to students’ level of appreciation math. Finally, students reported liking math class less in high school than in middle school. Identifying factors that influence secondary student mathematical dispositions can inform curriculum designers seeking to improve mathematical attitudes. Future studies can learn if new curricular designs can change student relationships with mathematics to reverse recent trends. 

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5. Factors that influence student mathematical dispositions

   Riling, M. ; Dietiker, L. ; Gibson, K. ; Tukhtakhunov, I. ; Ren, C. ( January 2018 , Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Why do secondary students in the US consistently and increasingly report a lack of interest in mathematics? Lack of interest in mathematics has been well documented in TIMSS responses; students dissatisfaction with mathematics more than doubled by 2011, when 40% of 8th graders reported not liking math, up from 18% as 4th graders in 2007. And, sadly, the trend appears to be worsening; in 2015, 47% of 8th graders indicated not liking math, up from 22% as 4th graders. In order to positively impact student attitudes towards mathematics, it is important to understand factors that may influence secondary students’ relationship with the discipline. This poster presents findings from an exploratory study of student disposition toward mathematics. We designed an online survey to learn about students’ relationship with mathematics, including experiences and settings that contribute to both positive and negative feelings about the subject. We surveyed 275 students, grades 9 to 12, in 11 classes in three schools in three New England districts. Though not randomly chosen, this sample allows us to examine student attitudes across a variety of contexts. We asked students about their feelings towards mathematics over the years, as well as which aspects of class they most enjoyed or disliked. Finally, we included items from the TRIPOD survey (Wallace et al., 2016) and the 2015 NAEP survey, which allows us to compare our sample with the national sample. Initial results indicate that student view their teachers and the topics of study as the central factors influencing their enjoyment of mathematics class. We found a correlation between responses that math is boring and that it is not relevant. Students who like math and those who do not reported different class activity preferences. For example, students who like math reported disliking watching a video in class, while students who dislike math reported disliking learning something new. Both groups of students (those who like math and those who do not) dislike math class when they have to present work to classmates, but hold positive views of solving puzzles and working with other students. Technology seems to appeal equally to both groups. Students who reported disliking math also look forward to playing competitive games. We saw no evidence that gender or race corresponded to students’ level of appreciation math. Finally, students reported liking math class less in high school than in middle school. Identifying factors that influence secondary student mathematical dispositions can inform curriculum designers seeking to improve mathematical attitudes. Future studies can learn if new curricular designs can change student relationships with mathematics to reverse recent trends. 

   more » « less