Prior research highlights a positive effect of incorrect worked examples on mathematics learning. Yet the mechanisms underlying these benefits are unclear. To investigate potential mechanisms of the benefits of various worked example types, we examined process data from a previously published classroom-based experiment. More specifically, we…

This study investigated the role of tools in supporting students to reason about even and odd numbers. Participants included Kindergarten, Grade 1, and Grade 2 students (ages 5-8) at two schools in the USA. Students took part in a cross-sectional early algebra intervention in which they were asked to generalize, represent, justify, and reason with…

Mathematical learning has an important role and is often prioritized in education. In K-16 education, algebra is one of the most vital mathematical content domains: it represents one of the top barriers for students pursuing a postsecondary education. Game-based learning has been effective in fostering classroom math learning environments that are…

The aim of the exploratory method research centered on the presence of mathematical tools in STEM through three main questions: Is mathematics an essential tool in the field of STEM? Can mathematics complete projects solely with mathematical and digital tools? Does understanding mathematical modeling affect STEM teaching? A better understanding of…

Gaming the system is a persistent problem in Computer-Based Learning Platforms. While substantial progress has been made in identifying and understanding such behaviors, effective interventions scarce. This study uses a method of causal moderation known as Fully Latent Principal Stratification to explore the impact of two types of interventions --…

Gaming the system is a persistent problem in Computer-Based Learning Platforms. While substantial progress has been made in identifying and understanding such behaviors, effective interventions remain scarce. This study uses a method of causal moderation known as Fully Latent Principal Stratification to explore the impact of two types of…

In paired experiments, participants are grouped into pairs with similar characteristics, and one observation from each pair is randomly assigned to treatment. The resulting treatment and control groups should be well-balanced; however, there may still be small chance imbalances. Building on work for completely randomized experiments, we propose a…

Fraction knowledge and algebraic skill are closely linked. Algebra is a gatekeeper for advanced courses (Booth & Newton, 2012; Brown & Quinn, 2007). This study uses the person-centered approach of latent profile analysis to examine individual differences in middle schoolers' (N = 350) algebra performance at the end of the year (EOY). The…

Adoption of online resources to support instruction and student performance has amplified with technological advances and increased standards for mathematics education. Because teachers play a critical role in the adoption of technology, analysis of data pertaining to how and why teachers utilize online resources is needed to optimize the design…

When one sets out to solve a mathematics problem, a feeling of satisfaction and accomplishment comes with finding the answer and knowing it is correct. In contrast, a student performing the correct process to solve an algebra equation and getting an answer such as 3 = 0 may be left perplexed and not understanding what--if anything--he or she did…

This study aimed to learn the learning outcomes of associate-degree students attending a Vocational School (VS) in a CAS-supported learning environment within the scope of the limit-continuity subject. The study was conducted using the action research method, and the worksheets prepared by Ertem Akbas (2016) were used. While evaluating and…

Emergent graphical shape thinking (Moore & Thompson, 2015) is a way of reasoning that is critical across numerous STEM fields. However, evidence indicates that the underlying component ideas for emergent thinking are underdeveloped in school mathematics education (e.g., Thompson & Carlson, 2017), and few studies directly report on…

After teaching last 10 years and analyzing student work, I realize that in developmental and Elementary Algebra courses there is a disconnection between the students conceptual understanding in context in contrast to their procedural fluency. In some cases, students can perform the procedure, but do not understand when the procedure is valid. In…

Research has shown that tape diagrams are beneficial for algebra learning. However, it is unclear whether certain visual features of tape diagrams have implications for learning. We investigated, with undergraduate students and math teachers, whether tape diagrams with different visual features (color, presence of outer lines, and position of the…

Research in this study investigates teachers' perceptions of professional development (PD) and the characteristics that make up an effective professional development. This study will explore Algebra 1 teachers' perceptions of their PD needs, including their preferred method of PD, preferred time frame, materials, and content they deem to be the…