Researchers have recommended using tasks that support students in reasoning covariationally to build productive meanings for graphs, rates of change, exponential growth, and more. However, not many recent studies have been done to identify how students reason when engaging in covariational reasoning tasks in undergraduate precalculus courses. In…

Mathematical thinking is a complex, multi-faceted process that has been described as messy and difficult but can also show growth and insights into conceptual understanding and knowing. This paper explores the application of Edward de Bono's practical thinking, in particular, the occurrence of porridge words to examine the mathematical thinking of…

This paper presents Big Ideas of Measurement as a framework of students' thinking about measurement. Drawing from research-based evidence, the framework is a collection of key concepts that students must develop for a robust understanding of measurement and, as such, are key aspects of students' thinking teachers should learn to notice. In a case…

Immersive spatial diagrams (three-dimensional diagrams rendered with immersive stereoscopic displays) offer learners the opportunity to extend practices of diagramming in school geometry into a human-scale, spatial context. Learners can use two or more hands to inscribe simultaneously with digital spatial painting tools, a spatial analog of the…

We investigate the beliefs that influence middle and high school algebra teachers' appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical…

In this paper, the application of fuzzy logic in mathematical education is viewed from the perspective of pre- school education. The aim of the paper is to give a brief overview of examples from the literature related to fuzzy logic and to point out the presence of fuzzy linguistic variables in the everyday life of a preschool child, as well as…

This study examines how elementary preservice teachers notice children's mathematical thinking and how this noticing influences the evaluation of technological resources. In particular, we explore the aspects of thinking to which preservice teachers attend and how they interpret evidence about children's thinking when using the Spatial-Temporal…

Supporting students' in-the-moment perseverance is a vital objective in mathematics education because it promotes learning with understanding. Yet, little is written about if and how student perseverance can improve over time. I examine the specific ways in which secondary students improved their perseverance as they engaged with challenging…

Proportional reasoning is important to the field of mathematics education because it lies at the crossroads of additive reasoning in the elementary school and multiplicative reasoning needed for more advanced mathematics. This research reports on the representations used by pre-service teachers (PSTs) as they responded to tasks involving…

The symposium provides an overview of the Early Years STEM Australia (ELSA) program. The conceptual underpinnings of the program are framed within STEM practices, rather than traditional thinking concerning the integration of discipline content knowledge. We will argue that our focus on practices is more aligned with the play-based and intentional…

This paper represents research that exists at the crossroad of scholarly practice and scholarly inquiry. We share the design, enactment and empirical examination of an elementary methods course activity, Exploring and Supporting Student Thinking (ESST) which engaged 18 prospective teachers in two sessions of one on one problem posing with 3rd…

Supporting students' mathematical reasoning is an important goal of mathematics instruction, but can be challenging for many teachers .We report the results of a study aimed at better understanding and identifying the ways in which teachers support student reasoning when provided with conceptually rich tasks. This study resulted in the Teacher…

Research about teacher noticing of students' mathematical thinking has been an important and ongoing strand of research and practice in mathematics education. Our work extends this agenda by working collaboratively with teachers to learn together how to notice students' mathematical strengths. The lens on strengths runs counter to the prevalent…

Researchers have argued that students can develop foundational understandings for a variety of mathematical concepts through quantitative reasoning. I extend this research by exploring how students' quantitative reasoning can support them in developing meanings for inverse relations that influence their inverse function meanings. After summarizing…

Examples play a critical role in mathematical practice, particularly in the exploration of conjectures and in the subsequent development of proofs. Although proof has been an object of extensive study, the role that examples play in the process of exploring and proving conjectures has not received the same attention. In this paper, we present a…