Social design produces strategic, systematic solutions or new cultures as a response to the complexity of social changes and, in consequence, designers who are used to the traditional way of ideation may not be well prepared for the requirements of social design. This paper identified the characteristics of the concept generation of industrial…

The National Council of Teachers of Mathematics (NCTM) promotes creating resources that build procedural fluency from conceptual understanding through intentionally sequenced tasks that draw on students' prior knowledge and move from simple, concrete representations to more complex and abstract representations (Boston et al., 2017). Liljedahl…

Here we investigate how college students may conceptualize symbolic algebraic properties. This work uses the theory of Grundvorstellungen (GVs) to analyze how learners' conceptions may or may not align with some desired goals of instruction. Through the analysis of interviews with students across a variety of courses, we describe several…

Research has identified some sources of student difficulty in understanding the horizontal translation of a function. The present study presents and focuses on another source for the difficulties: student conceptions of symbols involved in the horizontal translation of the graph of a function. We explored which student conceptions of the symbols…

Beginning a mathematics lesson involving a challenging task with a carefully chosen preliminary experience is an effective means of activating student cognition. In this article, the authors highlight a variety of preliminary experiences, each with a different structure and form, all designed to support students to more successfully engage with…

An understanding of structure-function relationships in proteins is essential for modern biochemical studies. The integration of common freely accessible bioinformatics tools available online with the knowledge of protein-engineering tools provide a fundamental understanding of the application of protein structure-function for biochemical…

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…

For the past decade, the College of Chemistry at UC Berkeley has iteratively redesigned general chemistry laboratory courses to introduce students to green chemistry concepts, while simultaneously using green chemistry as a relevant context to learn chemistry. To investigate the effectiveness of this curriculum we developed approaches to…

From the experiential learning perspective, this study investigates middle and high school students (n = 1009) who used an online module to learn about wildfire hazards, risks, and impacts through computational simulations of wildfire phenomena. These students were taught by 18 teachers in urban, rural, and suburban schools across the United…

This Family and Practitioner Brief discusses how deaf children who have not had access to a complete language from birth often encounter unique challenges in developing academic language skills, particularly in the realm of inference-making.

Rural adolescents are at risk for firearm-related injury and death. In response, professional organizations have called for communication between adolescents, parents, and providers about firearms. A shared understanding of firearms between providers and families can facilitate effectiveness of health interventions. However, few studies engage…

In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…

This study was an attempt to better understand how law faculty search for and create "linkages between subject matter being taught and law students' existing (that is, prior) knowledge and experience." For faculty who do search for and create these linkages, the study can help them understand, and potentially give them access to,…

This study examined the effects of shared representational guidance (collaborative textural representative tool vs. collaborative graphical representative tool; TR vs. GR) and prior knowledge (low vs. high; LPK vs. HPK) on different levels of individuals' understanding of specific-domain knowledge after collaborative problem solving (CPS). A total…

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…