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Geometric Rotations and Angles: How are they Connected?

Presenters: Navy Dixon, Sariah Stevenson, and Dawn Teuscher - Brigham Young University and Shannon Dingman - University of Arkansas, Fayetteville
Location: PMENA in Nashville, Tennessee
Abstract/Description:
With the adoption of the Common Core State Standards for Mathematics 12 years ago, the topic of geometric transformations was shifted from high school to grade 8. In our research with middle grades teachers, they often discussed their difficulty in teaching geometric rotations. Therefore, we analyzed 444 middle grade students’ responses, across four states, to eight rotation questions from the SMART assessment. The results corroborate teachers’ challenges with teaching and student learning of rotations. Results indicate that students have a rigid understanding of angle measure that may be impacting their understanding of geometric rotations. Although angle measure is introduced in grade 4, we hypothesize that teachers need to provide additional opportunities for students to expand their rigid understanding of angle measure.

Using Public Records to Support the Productive Use of Student Mathematical Thinking

Presenters: Ben Freeburn - Western Michigan University, Keith Leatham - Brigham Young University, Sini Graff - Brigham Young University, Nitchada Kamlue - Western Michigan University, Shari Stockero - Michigan Tech University, Blake Peterson - Brigham Young University, and Laura Van Zoest - Western Michigan University
Location: PMENA in Nashville, Tennessee
Abstract/Description:
The more researchers understand the subtleties of teaching practices that productively use student thinking, the better we can support teachers to develop these teaching practices. In this paper, we report the results of an exploration into how secondary mathematics teachers’ use of public records appeared to support or inhibit their efforts to conduct a sense-making discussion around a particular student contribution. We use cognitive load theory to frame two broad ways teachers used public records - manipulating and referencing - to support establishing and maintaining students’ thinking as objects in sense-making discussions.

Conducting a Whole Class Discussion About an Instance of Student Mathematical Thinking

Presenters: Shari Stockero - Michigan Tech University, Blake Peterson - Brigham Young University, Keith Leatham - Brigham Young University, and Laura Van Zoest - Western Michigan University
Location: PMENA in Nashville, Tennessee
Abstract/Description:
Productive use of student mathematical thinking is a critical aspect of effective teaching that is not yet fully understood. 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 third element, Conduct. Based on an analysis of secondary mathematics teachers’ enactments of building, we describe the critical aspects of conducting a whole-class discussion that is focused on making sense of a high-leverage student contribution.

Uses of the Equal Sign and Equation Types in Middle School Mathematics Textbooks

Presenters: Daniel Siebert and Chelsea Dickson, Brigham Young University
Location: PMENA in Nashville, Tennessee
Abstract/Description:
Research suggests that students’ difficulties in studying algebraic topics in middle school can be remedied at least in part by teaching students to use a relational meaning for the equal sign to reason about equations. However, little empirical research has been done to investigate what meanings for the equal sign and equation types are common in middle school mathematics. This study examines two series of 7th and 8th grade mathematics textbooks to identify what equal sign meanings and equation types are being used in middle school mathematics. Three meanings for the equal sign were used in all four textbooks, and each equation type was typically associated with only one meaning of the equal sign. The results imply that students need to develop three different meanings for the equal sign to succeed in middle school mathematics, and that recognizing equation types can help indicate which meaning of the equal sign is being used.

Variable Types in Middle School Mathematics Curricula

Presenters: Daniel Siebert and Ashlyn Rounds, Brigham Young University
Location: PMENA in Nashville, Tennessee
Abstract/Description:
While scholars have noted that variables are used in multiple ways during algebraic activity, little empirical research has been conducted to study which variable types middle school students typically encounter in their mathematics classes. To address this need, we present a study that examined the different types of variables used in three 7th-8th grade mathematics curricula. Using qualitative methods, we identified 8 main variable types. These 8 variable types were present in every year of each curriculum. Most lessons required students to distinguish between 2-5 different variable types. Our findings imply that students need to develop sophisticated and nuanced understandings of variables to meaningfully participate in middle school mathematics.