How should Texas prepare teachers so that their students benefit the most? This question is hard to answer, but important to address, particularly in the critical areas of high school mathematics and science. The goal of this project was to assess the quality of science and mathematics teachers prepared by UTeach and other university-based teacher…

We investigated the impact of assistance on learning and affect during problem-solving activities with a computer tutor we built using the Cognitive Tutor Authoring Tools framework. The tutor delivered its primary form of assistance in the form of worked-out examples. We manipulated the level of assistance the examples in the tutor provided, by…

Number sense is the foundation of arithmetic and algebra, yet relatively little research has deeply investigated what children do as they develop number sense. This case study provides insights into that development as it occurred during interactions with a multi-touch mathematics digital game, including conceptually congruent gestures. Findings…

The design of interactions among peers plays a key role in collaborative learning. Various strategies have been applied to assist learners in collaborating and creating a continuous effort to construct and maintain shared knowledge, such as utilizing a concept map as a representational tool during discourse. Some previous studies have revealed its…

Grade inflation is pervasive in American high schools. Is rampant grade inflation cause for concern? How teachers' grading standards affect student success is an empirical question--one that the author addresses in this article in a new study of roughly 350,000 North Carolina students taking Algebra I between 2006 and 2016. The author first…

The design of the Cognitive Tutor Algebra I (CTA1) intelligent tutoring system assumes that students work through sections of material following a pre-specified order, and only move on from one section to the next after mastering the first section's skills. However, the software gives teachers the flexibility to override that structure, by…

Requiring that students enrolled in college algebra to spend hours in a computer lab has been a practice in colleges and universities to improve success and retention. In part, because students come with different backgrounds, skills, and the computer lab environment allows for personalized supplemental instruction and tutoring. However, the way…

National standards and frameworks for mathematics, computer science, and technology emphasize the importance of teaching all children computational thinking (CT) skills. These skills are important for preparing citizens that are literate in science, technology, engineering, and mathematics and for participation in a society that is rapidly…

This study features data from middle school Algebra co-teachers and their students with and without disabilities, who completed questionnaires about their co-teaching experiences. Although most students with disabilities believed the general educator was in charge of lessons, students without disabilities also credited the special educator. Most…

The concept of determinant plays a central role in many linear algebra concepts and is also applied to other branches of mathematics and science. In this study, we focus on the application of determinant and inverse matrix concepts, in solving systems of equations by a group of 116 in-service mathematics teachers who were studying the topic at a…

This study describes how nine university professors managed their teaching when a shift from lecturing to inquiry-based learning was mandated in a large enrollment course, linear algebra for math majors. We describe the tensions that emerged and how they were resolved, in part via the production of worksheets that were used in teaching. We…

We describe results of a long-term design experiment focused on promoting mathematics learning among multilingual ninth graders classified as English Learners. The intervention at a linguistically diverse public high school in the US focused on a unit introducing concepts related to linear rates of change. We analyze results from a…

The development of six online quizzes to support students' study of an introductory mathematics masters module at The Open University is described and their use evaluated. The quizzes were implemented using the "STACK" online e-assessment system, which is powered by a computer-algebra engine. Evaluation of student feedback and an initial…

This paper reports findings from a study that establishes empirical support for Harel's (Zentralblatt für Didaktik der Math 40:893-907 2008b) inclusion of "mathematical ways of thinking" as a component of teachers' professional knowledge base. Specifically, we examined the role of "quantitative reasoning" (Smith and Thompson,…

This article presents the results of a design-based research study related to slope that took place in a high school algebra 1 classroom. In the study, students explored situations related to making predictions. As students engaged with these situations, they reinvented and made meaningful multiple subconstructs of slope. I present the findings in…