We report a qualitative analysis of elementary school students engaged in collaborative problem solving involving mathematical equivalence tasks. We build on previous research showing that students often use strategies based on either operational or relational understandings of the equal sign. We closely analyze three cases and identify nuanced…

The purpose of this study was to explore instructors' perspectives on the effect of using pen-based technology in the online mathematics courses and understand instructors' experiences in online mathematics teaching with pen-based technology. In this study, two instructors who taught online mathematics courses in fourteen weeks used digital pen as…

In this case study, we examine the usage of language -- how teachers used and regulated their language when teaching English language learners (ELLs) with learning disabilities (LD) how to solve mathematics multiplication problems. We focus on types of scaffolds used by teachers to identify how scaffolding helps ELLs with LD build better…

Basic mathematical fluency is a prerequisite for success in a wide array of areas in biology and it has been noted that many students are deficient in this skill. In this paper, the use of a "simulated" peer-assessment activity is investigated as a method to improve performance in numerical problem-solving questions in high school…

This study examined the effects of using an online flexible educational game on students' attitude towards mathematics as compared to the traditional method of solving mathematical problems. Moreover, the study assessed the learning effectiveness of the game and investigated potential gender differences in the game's effectiveness on changing…

Being able to effectively interpret students' thinking and respond effectively in the moment are important skills that preservice teachers (PSTs) need to learn. This study zooms in on 14 PSTs' planning, teaching, and reflections involved in number string lessons, and investigates to what extent PSTs anticipate their students' strategies and…

As part of one of the undergraduate Bachelor of Education units offered as a specialisation unit in primary mathematics education at The University of Notre Dame Australia, the pre-service teachers were asked to complete an assignment. In this assignment they were given 12 typical algebra text book problems which they were asked to solve and then…

There is a need for research in STEM (science, technology, engineering, and mathematics) teacher education that addresses the challenge of building teachers' pedagogical skills in fostering the development of mathematical reasoning in students. The Common Core State Standards for Mathematics provide teachers with guidance on how to promote…

This study addresses the problem of mathematics teachers' resistance to problem-solving models that align with constructivist perspectives because they feel pressure to utilize more teaching approaches that focus on preparing students for high-stakes tests. The purpose of this qualitative study was to explain how ninth grade mathematics students…

This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3-5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modeled by multiplication have an element that represents the scalar and an element that…

Proving in school geometry is not just about validating the truth of a claim. In the school setting, the main function of the proof is to convince someone that a claim is true by providing an explanation. Students consider proving to be difficult; in fact, they find the very concept of proof demanding. Proving a claim in planar geometry involves…

Background/Context: Most reforms in elementary education rely on teacher learning and improved instruction to increase student learning. This study increases our understanding of which types of professional development effectively change teaching practice in ways that boost student achievement. Purpose/Objective/Research Question/Focus of Study:…

Using the Gap Analysis problem-solving framework (Clark & Estes, 2008), this study examined the performance gap experienced by 6th grade students on the math sections of the ISEE (Independent School Entrance Exam). The purpose of the study was to identify and validate the knowledge, motivation, and organization causes of the students' low…

Researchers have suggested that teachers use a specialized type of knowledge specifically attributed to the work of teaching. One aspect of this specific type of knowledge is the ability to analyze children's work. With continued emphasis on a teacher's ability to analyze their students' thought processes, teacher candidates will need to develop…

Teaching advanced programming can be a challenge, especially when the students are pursuing different majors with diverse analytical and problem-solving capabilities. The purpose of this paper is to explore the efficacy of using a particular problem as a vehicle for imparting a broad set of programming concepts and problem-solving techniques. We…