We discuss how research on student difficulties was used as a guide to develop, validate, and evaluate a Quantum Interactive Learning Tutorial (QuILT) to help students learn how to determine the completely symmetric bosonic or completely antisymmetric fermionic wave function and be able to compare and contrast them from the case when the particles…

As the most influential figure in the field of learning science, Piaget's research on children's concepts and consciousness, his concept of 'Piagetian education', his contribution to constructivism have been greatly adopted in education. However, the weaknesses of his work have been criticised by many scholars. This paper illustrates how Piaget's…

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…

The author relates their involvement in the process of testing a picture storybook to teach science concepts. The project asked: If children were learning through a story where the science content was explicit, would children be able to explain the science in the context of the story and then in real-world contexts? Would the learning become…

Research-based assessments (RBAs) measure how well a course achieves discipline-specific outcomes. Educators can use outcomes from RBAs to guide instructional choices and to request resources to implement and sustain instructional transformations. One challenge for using RBAs, however, is a lack of comparative data, particularly given the skew in…

Learning progressions (LPs) are descriptions of students' growing sophistication in the understanding of a particular construct through a curricular sequence. They are particularly useful for organizing complex constructs for which students do not necessarily connect concepts as taught in different courses. However, they are challenging to…

This article shares two activities geared toward students in middle school that engage students in analyzing measures of center, specifically the arithmetic mean, and using transnumerative thinking with the ultimate goal of improving students' statistical literacy. Both activities support the Common Core standard, 6.SP.B.5 "Summarize and…

In this paper, we introduce a technology-enhanced pedagogical sequence for supporting lower secondary school students' sense-making of the concept of volume in a non-procedural and non-formula-driven way. Specifically, we illustrate a novel approach of using dynamic geometric environment (DGE) to introduce the meaning of volume and then deriving…

Much like one's experiences with the wonders of the world, concrete and multiperspective representations of mathematical concepts are key to understanding. Ideally, "learning environments should give students the opportunity to get to know different representations of a mathematical object in order for them to develop an appropriate…

The abstract nature of quantum mechanics makes it difficult to visualize. This is one of the reasons it is taught in the language of mathematics. Without an opportunity to directly observe or interact with quantum phenomena, students struggle to develop conceptual understandings of its theories and formulas. In this paper we present the process of…

The overarching theme of this book can be simply stated: Building on a foundation of biologically based abilities, children construct number via sensorimotor and mental activity. In this chapter, we return to this theme, and we connect it to three additional themes that emerge across chapters: comparing competing models for conceptual change;…

Statistical methods are indispensable to the practice of science. But statistical hypothesis testing can seem daunting, with P-values, null hypotheses, and the concept of statistical significance. This article explains the concepts associated with statistical hypothesis testing using the story of "the lady tasting tea," then walks the…

Acquiring conceptual understanding seems to be one of the main challenges students face when studying organic chemistry. Traditionally, organic chemistry presents an extensive variety of chemical transformations, which often lead students to recall an organic transformation rather than apply conceptual knowledge. Strong surface level focus and…

M3CA is a model of mastery learning developed in a college classroom, and an acronym for Mastery, Concept Maps, Critical Thinking, Collaboration and Assessment. The M3CA model is a formative model of skill based mastery learning and assessment that produces high levels of academic achievement and empowers students with a feeling of fairness.…

All students should have opportunities to develop their ability to reason mathematically. Gersten and Chard (1999) support this stance with respect to students with learning disabilities: "Even if students are not automatic with basic facts, they still should be engaged in activities that promote the development of number sense and…