We describe here lessons learned in designing an early algebra curriculum to measure early algebra's impact on children's algebra readiness for middle grades. The curriculum was developed to supplement regular mathematics instruction in Grades K-5. Lessons learned centered around the importance of several key factors, including using conceptual…

Prior knowledge has long been recognized as an important predictor of learning, yet the term prior knowledge is often applied to related but distinct constructs. We define a specific form of prior knowledge, ancillary knowledge, as knowledge of concepts and skills that enable learners to gain the most from a target lesson. Ancillary knowledge is…

Prior research shows that self-explanation promotes understanding by helping learners connect new knowledge with prior knowledge. However, despite ample evidence supporting the effectiveness of self-explanation, an instructional design challenge emerges in how best to scaffold self-explanation. In particular, it is an open challenge to design…

This paper demonstrated how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. Using a data-driven approach, we examined: (1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance (i.e. posttest math knowledge scores) prediction; and…

Educational video games can engage students in authentic STEM practices, which often involve visual representations. Specifically, because most interactions within video games are mediated through visual representations, video games provide opportunities for students to experience disciplinary practices with visuals. However, prior research has…

This paper introduces constructivist dialogue mapping (CDM), a new type of concept mapping. CDM encodes what people learn during a non-goal directed learning activity. CDM is a practical means to outline the mini theories users fluidly construct as they explore open-ended learning environments. To demonstrate the method, in this paper we use CDM…

This paper demonstrates how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. We examined: (1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance prediction; and (2) what types of in-game features were associated with student…

In mathematics, learners often spontaneously draw on prior knowledge when learning new ideas. In this study, we examined whether the specific diagrams used to represent more familiar (i.e., whole number division) and less familiar ideas (i.e., fraction division) shape successful transfer. Undergraduates (N = 177) were randomly assigned to…

English Learners benefit from small group sorting activities with clear structures to participate. Early in a lesson, students can sort to surface prior knowledge and develop categories. Later, sorting helps English Learners coordinate and connect multiple representations. As they extend understanding, English Learners can make new connections and…

Many studies investigating inquiry learning in science domains have appeared over the years. Throughout this period, inquiry learning has been regularly criticized by scholars who favor direct instruction over inquiry learning. In this vein, Zhang, Kirschner, Cobern, and Sweller (2022) recently asserted that direct instruction is overall superior…

This paper responds to a 2016 systematic literature review of the research on learning games by Ke (2016). The review paper unpacked the idea of intrinsic integration in learning games, analyzing important emergent themes. The key ideas and the value of this review are discussed in the context of the recent shift to virtual instruction. The…

Many studies have shown that visual representations can enhance student understanding of STEM concepts. However, prior research suggests that visual representations alone are not necessarily effective across a broad range of students. To address this problem, we created a novel, scaffolded form of diagrammatic self-explanation in which students…

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…

The rapid evolution of generative artificial intelligence (GenAI) is transforming science education by facilitating innovative pedagogical paradigms while raising substantial concerns about scholarly integrity. One particularly pressing issue is the growing risk of student use of GenAI tools to outsource assessment tasks, potentially compromising…

This pilot study examined the promise of a Tier 2 sixth grade intervention program for students at-risk for difficulties in mathematics. The study utilized a quasi-experimental design. The final sample included 112 students in treatment (Promoting Algebra Readiness) and 86 students in control (standard district practice) conditions. The Promoting…