# Papers and Presentations

As the project continues, we will post papers and presentations here.

## PME-NA 43 – “That’s Crazy”: An Exploration of Student Exclamations in High School Mathematics Lessons

*Brief research report by Sarina Simon, **Rashmi Singh, and **Leslie Dietiker
*

In this study, we explore the relationships between the types of student exclamations in an enacted lesson (e.g., “Wow!”) and the varying dramatic tensions created by the unfolding content. By analyzing student exclamations in six specially-designed high school mathematics lessons, we explore how the dynamic tension between revelations of mathematical ideas at the moment and what is yet to be known connects with the aesthetic pull to react by the student. As students work through novel problems with limited information, their joys and frustrations are expressed in the form of exclamations.

## PME-NA 43 – Impact of Lesson Design on Mathematical Questions

*Brief research report by **Rashmi Singh, Hector I. Nieves, Erin Barno, and **Leslie Dietiker
*

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 suggesting that lessons designed with the mathematical story framework in order to elicit a specific aesthetic response (“MCLEs”) have a positive influence on the types of teacher and student questions asked 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.

## PME-NA 42 – What Makes a Mathematics Lesson Interesting to Students?

*Research report by Leslie Dietiker, Rashmi Singh, Meghan Riling, and Hector I. Nieves.*

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 described 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.

## PME-NA 42 – Characterizing Coherence within Enacted Mathematics Lessons

*Research brief report by Jaepil Han, Meghan Riling, Hector I. Nieves, Leslie Dietiker, and Rashmi Singh.*

The importance of curricular coherence has been emphasized by leaders in mathematics education, who explain that coherence enhances deeper understanding by enabling students to see connections between mathematical ideas. Although there are different forms of curricular coherence in teaching and learning mathematics, the coherence within a lesson has received considerably less attention. In particular, little is known about what constitutes coherent lessons or how to measure the degree of coherence. Using lesson data from a larger study in which lessons are intentionally designed for coherence, we propose a tool for examining lesson coherence and describe characteristics of the lessons with different levels of coherence.

## PME-NA 42 – Student Inquiry in Interesting Lessons

*Poster by Hector I. Nieves, Rashmi Singh, and Leslie Dietiker*

What impact, if any, do interesting lessons have on the types of questions students ask? We analyzed 145 student questions from 12 lessons, developing a rubric of student questions: factual, procedural, reasoning, and exploratory. Initial results suggest high-interest lessons contain more exploratory questions, and had more student questions arise during whole class discussion.

## MCLE at AMTE 2021 – virtual!

The MCLE team will be presenting at AMTE 2021!

Presentation title: Fostering Positive Student Participation by Supporting Teachers' Discursive Tactics

Time: Friday, Feb 19, 3:00-3:45pm

To combat negative perceptions of mathematics among secondary students, we describe multiple discursive strategies ("tactics") used by six experienced high school mathematics teachers to elicit student interest, engagement, and agency as they implemented lessons designed to captivate students.

During the workshop, we will be sharing clips from high school lessons for workshop attendees to watch and discuss.

## MCLE Presents Results at NSF CADRE Conference

The MCLE team presented a poster for the NSF CADRE Conference that describes the results of 4 years of research. In it, an overview of the MCLE design approach, using the mathematical story framework, is given. In addition, the comparison data for 8 classrooms (for 6 high school teachers across 3 different schools) is provided, showing how there was an improvement in student experiences in nearly all classes. Also provided: an example of the difference in the structure of content between MCLEs and non-MCLEs, the impact on questioning (both teacher and student) in MCLEs when compared to non-MCLEs, and an analysis of the characteristics of the content that differ between MCLEs and non-MCLEs. Check it out!

## Student Engagement in MCLEs

Undergraduate research team member Sarina Simons recently shared her analysis of student engagement during MCLEs.

*Engagement in a classroom is always a topic of conversation in a math classroom. Over the course of the semester, I observed two lessons in six public high school math classrooms, with the goal of isolating key characteristics of a high engagement math class. The purpose of this study is to observe the lessons and analyze student interviews and post surveys to better understand the differences in students engagement in MCLEs and Non-MCLEs. I noticed that students were generally more engaged in the MCLE lessons than the lessons that were randomly selected in the same classes (non-MCLE). After listening to student interviews and analyzing post-class surveys, I recognized that the Mathematics Story Framework is the key to students being engaged in the classroom. Students were curious and therefore able to understand more in the MCLE classes because of its contrast to the routine classroom notes. Based on this evidence, teachers should adopt these MCLE lessons because they provide experiential learning which allows students to be more engaged and better understand the topic.*

## New findings will soon be available

Our project team is publishing two sets of findings as part of the proceedings of the Psychology of Mathematics Education - North American Chapter (PME-NA) organization. Although the conference has been rescheduled to occur in Spring 2021, the research report *What makes a mathematics lesson interesting to students?* (authors Leslie Dietiker, Rashmi Singh, Meghan Riling, & Hector I. Nieves) and brief research report *Characterizing coherence within enacted mathematics lessons* (authors Jaepil Han, Meghan Riling, Hector I. Nieves, Leslie Dietiker, and Rashmi Singh) will be published soon. Check back soon as we will update the website with final publications shortly!

## MCLE workshop at AMTE 2020

During this workshop, participants will get the chance to explore the various aesthetics that can be experienced while doing mathematics, get to know one of the MCLE lessons and discuss how it can be thought of as a story, and examine teachers' design processes in order to think about how they enabled teachers to design a captivating lesson and to develop aesthetic mathematical knowledge for teaching.