Functional thinking is an established route into algebra. However, the learning mechanisms that support the transition from arithmetic to functional thinking remain unclear. In the current study we explored children's pre-instructional intuitive reactions to functional thinking content, relying on a conceptual change perspective and using mixed…

Algebraic knowledge transfer is considered an important skill in problem-solving. Using algebraic knowledge transfer, students can connect concepts using common procedural similarities. This quasi-experimental study investigates the influence of algebraic knowledge in solving problems in a chemistry context by using analogical transformations. The…

The algebraic structure is one of the axiomatic mathematical materials that consists of definitions and theorems. Learning algebraic structure will facilitate the development of logical reasoning, hence facilitating the study of other aspects of axiomatic mathematics. Even with this, several researchers say a lack of algebraic structure sense is a…

The purpose of this study was to determine the effectiveness of co-teaching versus inclusive non-co-teaching for students with disabilities (SWD) using algebra I end-of-course scores (EOC) and whether these effects differed by gender. Participants included 244 ninth-grade algebra I SWD. The research design consisted of a posttest only with a…

This quantitative, ex post facto study is to examine what differences exist, if any, in ACT Aspire math scores based on gender, instructional method, and the interaction between gender and instructional method among ninth grade students taking Algebra 1 in a school district located in Northeast Arkansas. Using a two-way ANOVA, the first main…

Fractions are foundational for success in algebra and STEM, but they are notoriously difficult for students. In past work, two separate branches of research from psychology and math education have studied fractions knowledge using different, isolated approaches. In this dissertation, I synthesize research from both fields about proportional…

One pedagogical technique that promotes conceptual understanding in mathematics learners is self-explanation integrated with worked examples (e.g., Rittle-Johnson et al., 2017). In this work, we implemented self-explanations with worked examples (correct and erroneous) in a software-based Intelligent Tutoring System (ITS) for learning algebra. We…

Supporting students with mathematics learning difficulties (MLD) as they transition from arithmetic to algebra remains a challenge within the special education and mathematics education research communities. This dissertation includes 3 manuscripts focused on how fifth graders with MLD develop algebraic understandings related to equivalence and…

The purpose of this study was to design, develop, and test the effects of digital game-based learning on undergraduate students' learning motivation, mathematics achievement, and learning retention in a college algebra course. Digital games utilize interactive digital media that offer rules-based challenges and react to the individual's choices.…

Teachers are among the most important inputs in the education production function. One mechanism by which teachers might affect student learning is through the grading standards they set for their classrooms. However, the effects of grading standards on student outcomes are relatively understudied. Using administrative data that links individual…

The standard technique for solving equations with radicals is to square both sides of the equation as many times as necessary to eliminate all radicals. Because the procedure violates logical equivalence, it results in extraneous solutions that do not satisfy the original equation, making it necessary to check all solutions against the original…

This study examined the extent to which college algebra instructors employ pedagogical practices previously found to assist students master difficult STEM content material and address their own previous math deficits. Faculty classroom behaviors were assessed with a modified version of the Generalized Observation and Reflection Platform (GORP).…

This research analyzed the effect of digital storytelling (DST) on the development of pedagological content knowledge (PCK) of prospective secondary school mathematics teachers on mistakes made by students in algebra. The research applied sub-domains of PCK, the knowledge of content and students (KCS) and the knowledge of content and teaching…

This study explores the effectiveness of GeoGebra in enhancing students' understanding of vectors in mathematics education. The research compares traditional teaching methods with the application of GeoGebra to determine its impact on conceptual and procedural knowledge acquisition. Vectors are often challenging for students to grasp due to their…

Unfortunately, too many young people come to Algebra I with significant gaps due to instructional inconsistencies and interruptions in their mathematics learning over several years. Given the long-term impact of academic success on young people's lives, it is critical to help more students succeed in Algebra I. TNTP asked the question: "How…