This study examined how community college students' reflective sentiments about learning with the Intelligent Tutoring System (ITS) ALEKS evolved in three developmental pre-Algebra Mathematics courses and how students' sentiments related to their metacognitive awareness and learning performance. Thirty-nine students participated in this study.…

This study concerns preservice teachers' knowledge of student thinking at the secondary level. In particular, it examines in what ways a three-week unit integrating content and student thinking was beneficial in developing preservice teachers' knowledge of student thinking associated with big ideas in algebra--such as variation, Cartesian…

In this article, we examine eighth graders' incorrect responses to a specific task on a national standardized assessment of mathematics. The task asked students to write the formula for the perimeter of a given figure as a function of a variable. We focus on incorrect responses to better understand students' difficulties with the algebraic…

This quantitative study examined the impact of a multi-subject double-dose STEM intervention on the academic achievement of underprepared 9th-grade males. The intervention consisted of heterogeneously grouped core classes of Algebra 1 and biology accompanied by a second multi-subject (Algebra 1 and biology) support class. This nine-week study did…

Attending to students' mathematics identities is necessary to provide all students with the opportunity to learn mathematics. Studies of students' mathematics identities must consider the context of the mathematics classroom. My overarching research question was, "How does the teacher to student discourse that takes place in rural, secondary…

The current study investigated the effectiveness of three distinct educational technologies--two game-based applications (From Here to There and DragonBox 12+) and two modes of online problem sets in ASSISTments (an Immediate Feedback condition and an Active Control condition with no immediate feedback) on Grade 7 students' algebraic knowledge.…

The current study investigated the effectiveness of three distinct educational technologies--two game-based applications (From Here to There and DragonBox 12+) and two modes of online problem sets in ASSISTments (an Immediate Feedback condition and an Active Control condition with no immediate feedback) on Grade 7 students' algebraic knowledge.…

Computer-assisted learning platforms (CALPS) increasingly include gamified elements to improve student outcomes by enhancing their engagement with content. Although evidence exists that gamified programs increase engagement and learning outcomes, there is little causal research on what programmatic mechanisms drive the effect between engagement…

This study examines the creative responses of pre-service mathematics teachers in their lesson plays designed to address sixth-grade students' misconceptions about algebraic expressions. This research employs a qualitative descriptive research design, involving 78 third-year students enrolled in an elementary mathematics education program. Using…

This study explores learning vector addition and demonstrating the understanding of vector addition. Vector addition is a key skill in mathematics and science education, but there is a limited amount of research that focuses on this topic. My study investigates how an instructional design framework "concreteness fading" can be used for…

A method based on oblique projection is presented for construction of sundials. The derived formulas are classical, but usage of vectors and projections renders a coherent presentation rather than a number of special cases. The presented work is aimed to be useful for those taking a beginning module on vector algebra.

Over the years, we have noticed our students constructing proofs that commutativity is preserved by isomorphism that do not explicitly use the fact that the isomorphism is surjective. These proofs are typically valid otherwise. However, such proofs are invalid because they would prove the false claim that commutativity is preserved by any…

Persistent difficulties in learning abstract algebraic concepts--particularly among preservice mathematics teachers--continue to hinder students' mathematical development. While prior studies have documented general misconceptions, few have grounded their analysis in comprehensive learning theories. Addressing this gap, the present study adopts…

A positive physics identity is crucial for women and minorities who are underrepresented in the field of physics. Pedagogical methods that focus heavily on math rather than concepts present a deterrent to many students in physics courses. This research aimed to determine how a 'gamified' physics curriculum with immediate feedback affects students'…

We analyzed the solution pathways and errors found in the written responses of 469 prospective teachers solving an equation containing fractions. The majority (332, or 70%) used an algebraic method; 141 of the 332 (42%) were correct, and 22% of the algebraic methods were abandoned before a solution was obtained. We identified the steps in the…