Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

One reason for the widespread use of the energy concept across the sciences is that energy analysis can be used to interpret the behavior of systems even if one does not know the particular mechanisms that underlie the observed behavior. By providing an approach to interpreting unfamiliar phenomena, energy provides a lens on phenomena that can set…

Prior research has shown negative relations between math anxiety and math performance. We posit that one potential pathway through which math anxiety influences performance of math equivalencies is through help seeking behavior during learning. Here, we examine whether middle school students' behavior, specifically the frequency of hint requests,…

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…

The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students' fraction number line acuity, rational number concepts and procedures.…

This study investigated the effect of visual anthropomorphic stories on students' understanding of the particulate nature of matter and their level of anthropomorphic discourse. This study employed a quasi-experimental research design with pretest and posttest control groups. Science activities supported by visual anthropomorphic stories were…

This article begins by describing a class scenario in which a teacher gives her students the L problem (Watanabe 2008), which involves finding the area of a composite figure. Her students inappropriately extend the area formula for rectangles (A = L x W) to composite figures by multiplying all given dimensions. After class, the teacher concluded…

We investigated the effects of proximal grouping of numbers, problem-solving goals to make 100, and prior knowledge on students' solution strategies in an online mathematics game. Logistic regression on 857 problem-level data points from 227 middle-school students showed that students were more likely to use productive solution strategies on…

Purpose: It has been acknowledged in physical education (PE) that knowledge empowers learners to develop a physically active lifestyle In this study, we consider Cognitive Load Theory (CLT) as a valuable extension of the constructivist learning theory to help articulate the role of three pivotal instructional factors, content knowledge, learners,…

This article is prepared as part of a "Practice Teaching in Science" course of a teacher education program aiming for developing prospective science teachers' teaching through inquiry-based instruction involving practices of science and active learning strategies. During the semester, student teachers are required to prepare four…

Understanding equivalence is fundamental to STEM disciplines, yet misunderstandings and misconceptions inhibit students from fully appreciating or leveraging the concept. Using the game-based algebraic notation system, From Here to There! (FH2T), students explore ideas of equivalence by dynamically transforming expressions or equations among…

As with all learners, English learners (ELs) require more than basic reading and writing skills to successfully engage with rigorous academic content, progress through school, and be fully prepared for postsecondary education and careers. ELs must be able to access grade-level content while simultaneously developing proficiency and autonomy in…

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…

The reading comprehension levels of students who are deaf or hard of hearing (DHH) are low compared to those of their hearing peers. One possible reason for this low reading levels is related to the students' prior knowledge. This study investigated the potential factors that might affected DHH students' prior knowledge, including their degree of…

The current study investigated the effects of interactive picture-book read-alouds on middle school EFL students' word inference ability and attitudes toward reading in English. To this end, two classes of seventh-grade students from a public middle school in Taiwan participated and were randomly divided into two groups: an interactive…