Use of online credit recovery is a growing trend across the country, with the hope that expanding credit recovery options through online courses will help students get back on track toward graduation (e.g., Atkins, Brown, & Hammond, 2007; Gemin, Pape, Vashaw, & Watson, 2015). But expanded use of online credit recovery for high school…

Teachers are constantly looking for new ways to make mathematical procedures such as radical simplification meaningful for students. In classes, teachers discovered what researchers have long known, that students who only memorize a set of steps get confused when their steps do not match a new problem or scenario perfectly. The area and side…

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and…

The ways teachers understand mathematics that is useful for teaching, known as mathematical knowledge for teaching (MKT), has been a center of attention for the research and policy communities. A teacher's MKT has been shown to be a significant factor in predicting student outcomes and positively related to the quality of mathematics instructional…

We describe how we supported middle-school students developing meanings for quadratic growth by bringing together three theoretical framings and designing a task sequence grounded in that framework. Specifically, this framework was assembled from the research on students' quantitative and covariational reasoning, Realistic Mathematics Education,…

This study focused on investigating the ability of 58 pre-service mathematics teachers (PSMTs) to construct-evaluate-refine mathematical conjectures and proofs. The PSMTs enrolled in a three-credit mathematics education course that offered various opportunities to engage with mathematical activities including constructing-evaluating-refining…

Binary operations are one of the fundamental structures underlying our number and algebraic systems. Yet, researchers have often left their role implicit as they model student understanding of abstract structures. In this paper, we directly analyze students' perceptions of the general binary operation via a two-phase study consisting of task-based…

Few high school students associate mathematics with playfulness. In this paper, we offer a series of lessons focused on the underlying algebraic structures of the Rubik's Cube. The Rubik's Cube offers students an interesting space to enjoy the playful side of mathematics, while appreciating mathematics otherwise lost in routine experiences.

In this article we illustrate how one teacher used PhET cannonball simulation as an instructional tool to improve students' algebraic reasoning in a fifth grade classroom. Three instructional phases effective to implementation of simulation included: Free play, Structured inquiry and, Synthesizing ideas.

Facilitating productive mathematical argumentation is challenging; it is critical to develop a specific guiding vision of practices to help teachers learn to teach argumentation. However, what counts as acceptable classroom-based mathematical argumentation remains an open question. In this study, building on Habermas' theory of communicative…

Using correct definitions of the mathematical concepts is crucial for learning and teaching of any mathematical content. Being able to make mathematically correct definition of the concepts is an indicator of teachers' content knowledge. The purpose of this study is to determine how preservice middle school mathematics teachers define the concept…

As educators, it is important for us to recognize that our assessment methods affect student attitudes. If we want students to learn from their mistakes and counteract a fixed-mindset of learning, perhaps we should look at what we incentivize in the classroom. Some professors are attempting to counteract math and test anxiety, poor STEM retention,…

The researchers conducted a microanalysis of two purposefully sampled sessions of a tutor working with a student with a learning disability (LD) engaging with multi-step equations with and without fractions. During the tutoring sessions, the student experienced quick, independent success on equations without fractions, but struggled considerably…

This study aims to investigate the non-algebraic solution strategies that prospective mathematics teachers use to solve word problems and their thought process while they were solving the problems. A total of 76 prospective mathematics teachers were asked to solve two word problems without using algebraic solutions and, then, clinical interviews…

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…