This study explores preservice teachers engaging in a ratio activity connecting the wages of men and women to the number of men and women in government positions. Mathematical learning expands the critical literacy framework reading and writing the word situating mathematics as the world itself. Furthermore, the bridging of mathematics, the self…

In this study, the elements of the design and results of the implementation of a Massive Open Online Course (MOOC) based on the problem solving and the use of digital technology are analyzed and discussed. The results show that the design of the activities, the intervention of the MOOC design team in the discussion forums and the interaction among…

Mathematical play has a fairly short history, with strong roots further back in time (e.g., Papert, Montessori), and understanding the role of mathematical play from early childhood to adulthood is, as yet. unmapped. This working group will build on the success of last year's working group and continue to provide a community space to explore and…

Embodied cognition is growing in theoretical importance and as driving a set of design principles for curriculum activities and technology innovations for mathematics education. The central aim of the EMIC (Embodied Mathematical Imagination and Cognition) Working Group is to connect with inspired colleagues in this growing community of discourse…

Opportunities matter when it comes to students' math attitudes and performance. Over two semesters, across treatment sections of college algebra students, we implemented a set of dynamic computer activities linking animations and graphs. Across all sections, we administered a fully online survey of students' attitudes toward math. Using mixed…

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…

This study compared area lessons from Korean textbooks and US standards-based textbooks to understand differences and similarities among these textbooks, as well as how these textbooks address known learning challenges in area measurement. Several well-known challenges have been identified in previous studies, such as covering, array structure,…

In this article, we report how a geometric task based on the ACODESA methodology (collaborative learning, scientific debate and self-reflection) promotes the reformulation of the students' validations and allows revealing the students' aims in each of the stages of the methodology. To do so, we present the case of a team and, particularly, one of…

In this exploratory study, our goal was to engage students in dynamic experiences of area as a continuous quantity that can be measured by multiplicatively composing two linear measures (lengths), an approach we refer to as 'dynamic measurement,' or DYME. In this paper, we present the learning trajectory constructed from two cycles of teaching…

Teachers' efforts to support students, both academically and socially, can play a role in how high school students productively engage with mathematics in the moment. To examine the connection between teacher support and student engagement, we conducted an exploratory mixed-methods study combining data from 20 high school classroom observations…

In this theoretical paper, I consider reversibility as a defining characteristic of mathematics. Inverse pairs of formalized operations, such as multiplication and division, provide obvious examples of this reversibility. However, there are exceptions, such as multiplying by 0. If we are to follow Piaget's lead in defining mathematics as the…

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…

This paper uses multimodal discourse analysis to show that discursive form, in addition to words, gestures and sound dimensions of speech, is an important linguistic resource for expressing mathematical meaning. During a collaborative task, a student spoke an insight about an algebraic property five times over a few minutes, in slightly different…

Studies on cognition have capitalized on the role of contexts and experience in shaping our cognitive competence. In the past few decades, the mathematical education research field has begun to pay increased attention to the mathematics practices of both adults and children that take place in non-academic settings. As a result, theoretical fields…

The [National Council of Teachers of Mathematics] NCTM research committee made a recent, urgent call for mathematics education researchers to "examine and deeply reflect on our research practices through an equity lens." With this in mind, we use this paper to reflect on the ways in which Steffe's work has contributed to three facets of…