This study evaluated recent advances in learning progressions for the concept of matter (LPCM) and explored trends by reviewing the literature on the topic published between 2005 and 2021. A total of 21 studies were reviewed. Fifteen studies were devoted to developing LPCM of varying spans and grain sizes. There were six follow-up studies based on…

This dissertation reports on three studies about students' conceptions and learning of the idea of instantaneous rate of change. The first study investigated 25 students' conceptions of the idea of instantaneous rate of change. The second study proposes a hypothetical learning trajectory, based on the literature and results from the first study,…

Critical thinking is essential in academia and the workforce. Although writing can be used as a pedagogical tool for fostering deeper subject matter understanding, increased retention, and critical thinking, relatively few science courses are writing based. This writing-based introductory science course provided an opportunity for students to…

Learning progressions have become increasingly prevalent in mathematics education as they offer a fine-grain map of possible learning pathways a child may take within a particular domain. However, there is an opportunity to build upon this research in ways that consider learning from multiple perspectives. Many current forms of learning…

The "Integrated Development of Key Competences" has been identified as the core idea in education to face competition in the 21st century. Similarly, reform efforts in science education emphasize the importance of integrating scientific practices and disciplinary core ideas. The learning progression (LP) is viewed as a robust tool to…

Big ideas, sometimes referred to as key, core, fundamental or threshold concepts, are widely applicable concepts at the heart of disciplines that are or have been central and influential for their fields. Attention here is particularly directed to meta-concepts common to sister disciplines in the sciences. "Learning thresholds",…

Background and Context: Since the surge of grounded cognition (GC) theories in cognitive psychology, many studies have focused on demonstrating the importance of embodiment and sensorimotor activities on students' conceptual development. In computing education, however, there is not yet a conceptual framework for developing age-appropriate.…

A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…

Learning emphasizing fractions as a part-whole concept causes several limitations in developing fraction knowledge and inhibits proportional reasoning. We use fractions as quotients as the first context introduced in our learning trajectory. We report the teaching experiment results using the improved learning trajectory on thirty 4th grade…

This paper shares findings from the study of a learning sequence designed to support prospective elementary teachers (PTs) in identifying evidence of conceptual understanding and procedural fluency. Conceptual understanding and procedural fluency are widely recognized as important to teaching and learning mathematics, and identifying evidence of…

Learning the content of entrepreneurship arithmetic is an extension of social arithmetic that focuses on mathematical calculations in business or creative economy. Most teachers do not link students' daily activities to classroom teaching and learning on traditional markets around the environment. This significantly affects the interest in…

Learning Trajectories have the potential to be used as a tool to advance equity by explicitly connecting to anti-deficit framing and asset-based instruction. This plenary paper highlights research on three use cases for learning trajectories (LT) with an intentionality around promoting equity: 1) the use of LT based Lesson Study with vertical…

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…

This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the predicate and inference structures among various proofs (in…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…