Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…

Students with disabilities present a unique instructional design challenge. These students often have qualitatively different ways of processing information, meaning that standard instructional approaches may not be effective. In this study I present a case study of a student with a mathematical learning disability for whom standard instruction on…

In our contribution we focus on the possibility to use an educational tool called Concept Cartoons in future primary school teachers' education, as an instrument for observing how future primary school teachers reason about fractions. In the introduction section we present Concept Cartoons, and also the primary school level of the fractions topic.…

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

The purpose of this study was to replicate and extend the study of the schema-based intervention (SBI) conducted by Jitendra et al. (2015) that demonstrated impact in proportional problem solving for a homogeneous sample of Upper Midwest students and teachers who were predominantly White and middle class. This study was replicated in two…

This report describes efforts to measure teachers' knowledge of their own students' abilities in mathematics and offers preliminary findings. It provides a description of the sample, a description of the study design and its realization, and descriptive statistics for teacher judgment accuracy. The work described here was completed as part of a…

A test project at the University of Puerto Rico in Mayagüez used GeoGebra applets to promote the concept of multirepresentational fluency among high school mathematics preservice teachers. For this study, this fluency was defined as simultaneous awareness of all representations associated with a mathematical concept, as measured by the ability to…

It remains difficult to foster problem-solving and mathematical-reasoning capabilities in classrooms where students and teachers are accustomed to the more traditional forms of education. Several studies suggest that this difficulty might be related to the kind of knowledge students acquire in such environments, which could be fragmented and…

Service-learning provides a versatile pedagogical platform that can improve the academic performance of participating students and open space for a discussion of issues of social justice within a mathematics classroom. We describe our Precalculus course with a service-learning component, in which university students regularly tutor algebra…

We implemented a STEM task that highlights the engineering cycle and engages students in productive struggle. Students problem solved in productive ways and saw tangible benefits of revising their work to achieve mathematical goals.

The aim of this study is to validate an instrument to evaluate the teaching of mathematics through mathematical processes using a structural equation model. To that end, we have administered the instrument to 95 in-service Spanish teachers and we have also analysed the presence of mathematical processes (problem solving, reasoning and proof,…

Creative thinking is the highest level of the kind of high order thinking. In observations at the schools in Indonesia, teachers overly equate all levels of achievement of students' creative thinking to obtain higher order thinking skill improvements in mathematics learning. This condition results in an imbalance in learning practices. Therefore,…

One of the most prevalent features of digital mathematics textbooks, compared to traditional ones, is the provision of automated feedback on students' solutions. Since feedback is regarded as an important factor that influences learning, this is often seen as an affordance of digital mathematics textbooks. While there is a large body of mainly…

Research exists on mathematical interventions to support elementary students experiencing mathematical difficulties, yet little examines the provision of such interventions within an online learning environment. This study explored the online delivery of the virtual-representational-abstract (VRA) instructional sequence, taught via explicit…

This paper presents a case study of the experiences of a special educator named Ms. Montes (pseudonym) teaching standards-based mathematics during Emergency Remote Teaching (ERT) during spring 2020. Ms. Montes was interviewed twice during this period; data were analyzed through inductive thematic analysis. Pre-COVID, Ms. Montes provided her…