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1. Student inquiry in interesting lessons

   Nieves, Hector I.; Singh, Rashmi; Dietiker, Leslie (January 2020, Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Sacristán, A. I.; Cortés-Zavala, J. C.; Ruiz-Arias, P. M. (Ed.)

   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. 

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2. Impact of Lesson Design on Teacher and Student Mathematical Questions

   Singh, R.; Nieves, H. I.; Barno, E.; & Dietiker, L. (January 2021, Proceedings of the Psychology of Mathematics Education - North American Chapter)

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

   How does the design of lessons impact the types of questions teachers and students ask during enacted high school mathematics lessons? In this study, we present data that suggests that lessons designed with the mathematical story framework to elicit a specific aesthetic response (“MCLEs”) having a positive influence on the types of teacher and student questions they ask during the lesson. Our findings suggest that when teachers plan and enact lessons with the mathematical story framework, teachers and students are more likely to ask questions that explore mathematical relationships and focus on meaning making. In addition, teachers are less likely to ask short recall or procedural questions in MCLEs. These findings point to the role of lesson design in the quality of questions asked by teachers and students. 

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3. Narrative characteristics of captivating secondary mathematics lessons

   https://doi.org/10.1007/s10649-022-10184-y  

   Dietiker, Leslie; Singh, Rashmi; Riling, Meghan; Nieves, Hector I.; Barno, Erin (January 2022, Educational Studies in Mathematics)

   Why do some mathematics lessons captivate high school students and others not? This study explores this question by comparing how the content unfolds in the lessons that students rated highest with respect to their aesthetic affordances (e.g., using terms like “intriguing,” “surprising”) with those the same students rated lowest with respect to their aesthetic affordances (e.g., “just ok,” “dull”). Using a framework that interprets the unfolding content across a lesson as a mathematical story, we examine how some lessons can provoke curiosity or enable surprise. We identify eight characteristics that distinguish captivating lessons and show how some, such as the average number of questions under consideration at any point in the lesson, are strongly related to student aesthetic experiences. In addition, the lessons that students described as more interesting included more instances of misdirection, such as when students’ false assumptions provide opportunities for surprising results. These findings point to the characteristics of future lesson designs that could enable more students to experience curiosity and wonder in secondary mathematics classrooms. 

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4. "Oh! That's Interesting!"; Captivating students who hate mathematics with mathematical ideas

   Claiborne-Naranjo, B.; Barstow, A.; & Dietiker, L. (October 2023, Psychology of Mathematics Education - North American Chapter)

   Lamberg, T.; Moss, D. (Ed.)

   The positive relationship between students’ attitudes toward mathematics and mathematics achievement is well documented. Yet there is a worsening problem of low appeal of mathematics especially at the secondary level. Therefore, in this paper we focus on three high school students who report a strong dislike of mathematics. By analyzing student surveys, interviews, and lesson observation data, we examined how some mathematical lessons improved these students’ experiences (i.e., their aesthetic dimensions). We found that while student preferences varied, each student was interested in lessons that centered them as sense-makers and in which the content unfolded with suspense. Such lessons led to positive aesthetic responses such as surprise, curiosity, and satisfaction. Thus, lessons can be designed in which even students with the most negative views of mathematics can find mathematical concepts interesting. 

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5. Implementing Mathematical Mindsets in a High School Mathematics Classroom

   Begay, B. (July 2019, NSF Noyce Conference 2019)

   Mathematical mindset theory (Boaler, 2015) indicates student achievement in mathematics has the potential to improve, through the use of, student engagement, collaborative groups, and open-ended problem sets that allow students to discover their own understanding of mathematics. This presentation explores how and when I used methods of mathematical mindsets in my classroom, when it appeared that these types of lessons were not appropriate, and student reactions to lessons using mathematical mindsets versus lessons that did not incorporate this theoretical framework. Lessons learned are also explored. 

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