Many scholars have argued that mathematics classrooms often offer narrow conceptions of mathematical excellence, recognizing only some kinds of thinking and some kinds of people as valuable, and conflating mathematical aptitude with overall intelligence. Play offers the potential to disrupt such classroom mathematical practices, by offering new…

This article describes the results of an investigation based on a Models and Modeling Perspective [MMP]. We present the evolution of the models built by university students when solving a model development sequence designed to promote their learning of the exponential function. As a result, we observed that students' thinking was modified,…

In the mathematical community, two notions of "function" are used: the set-theoretic definition as a univalent set of ordered pairs, and the Bourbaki triple. These definitions entail different interpretations and answers to mathematical questions that even a secondary student might be prompted to answer. However, mathematicians and…

This study aims to describe how preservice secondary mathematics teachers (PSMTs) reason about different function representations. The study focuses on two PSMTs' reasonings across static and dynamic representations of functions. Sfard's (2008) Theory of Commognition guided our analysis. Findings indicate that while static representations restrict…

One important aspect of teaching is reviewing tasks in preparation for instruction. The goal of the multicase study of four secondary teachers was to examine the interplay between their mathematical knowledge for teaching [MKT] and what they attend to when reviewing a mathematics task. We engaged secondary mathematics teachers in a…

Noticing children's mathematical thinking is foundational to teaching that is responsive to children's thinking. To better understand the range of noticing expertise for teachers engaged in multiyear professional development, we assessed the noticing of 72 upper elementary school teachers using three instructional scenarios involving fraction…

We report our findings and perspective to document the knowledge exhibited by three experienced high school teachers in their instructional decisions for lessons on the equation of an exponential function. We describe the nature of the mathematical ideas and connections teachers promoted in discourse and the decisions that supported the emergence…

Dramatic differences in children's math knowledge at school entry are thought to originate in the Home Math Environment (HME), where parents and caregivers are the primary provider of experiences that influence children's early math knowledge development. Little is known about what informs parent decision-making around "mathematical…

Several researchers have promoted reimagining functions and graphs more quantitatively. One part of this research has examined graphing "conventions" that can at times conflict with quantitative reasoning about graphs. In this theoretical paper, we build on this work by considering a widespread convention in mathematics teaching: putting…

Bridging the gap between mathematical learning at home and school has been an issue for education research for decades (Galindo & Sheldon, 2012). Expectations for mathematics do not often align for teachers and parents (Posey-Maddox & Hayley-Lock, 2016) and a limited view of what counts as mathematics persists. What needs more attention is…

This study was conducted to gain understanding about potential influences that learning about quadratic functions has on high school algebra students' action versus process views of linear functions. Pre/post linear functions tests were given to two classrooms of Algebra II students (N=57) immediately before and immediately after they participated…

Isomorphism and homomorphism are topics central to abstract algebra, but research on mathematicians' views of these topics, especially with respect to sameness, remains limited. This study examines 197 mathematicians' views of how sameness could be helpful or harmful when studying isomorphism and homomorphism. Instructors saw benefits to…

This study examines pre-service teachers' (PSTs') views of tasks that engage students in mathematical argumentation. Data were collected in two different mathematics courses for elementary school education majors (n = 51 total PSTs). Analyzed were (a) written journals in which PSTs defined tasks that promote student engagement in argumentation,…

People often view mathematics as abstract, cold, and irrelevant to real-life, and their school experiences influence such views. In this case study, we investigated the mathematics learning experiences of two women who participated in an afterschool girls STEM club 26 years ago. We explored their experiences in and out of school and how such…

As mathematics educators, we teach and research a particular form of knowledge. However, in reacting to Platonic views of mathematics, we often overlook its unique characteristics. This paper presents a Kantian and Piagetian perspective that defines mathematics as a product of psychology. This perspective, based in human activity, unites…