Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…

Research has been carried out on the application of "mindfulness" to a number of different populations in varying contexts, some of which traverse the field of educational psychology. This discussion paper explores what is understood as mindfulness and outlines the breadth of its application. As well as more extensive research into the use of…

Identifying mathematical and didactical conditions under which mathematics learners can encounter an intellectual need for defining and proving is recognized as a challenging research enterprise. This paper presents a particular configuration of conditions under which a group of pre-service mathematics teachers successfully constructed a…

This study looks at a mixed ability group of 21 Year 5 primary students (aged 9-10 years old) who had previously never had formal instruction using letters to stand for unknowns or variables in a mathematics context; nor had they been introduced to formal algebraic notation. Three lessons were taught using the computer software "Grid Algebra"…

This pilot study investigated the impact of an oral narrative intervention program implemented with 24 children who attended a College of Education on campus laboratory school for children with specific language learning difficulties. Oral narratives were elicited before and after treatment and underwent T-unit and story grammar component…

This paper shows how to teach a mathematics for liberal arts class in an inquiry-based way using ideas from music to launch the mathematical activities. No musical knowledge is required to understand and teach the material. The main activity is analyzing the differences between two kinds of rhythmic palindromes. The content is mathematically…

Most treatments for stereotypy involve arrangements of antecedent or consequent events that are imposed entirely by a therapist. By contrast, results of some studies suggest that self-recording, a common component of self-management interventions, might be an effective and efficient way to reduce stereotypy. Because the procedure typically has…

We illustrate a method, which is modeled on "breaching experiments," for studying tacit norms that govern classroom interaction around particular mathematical content. Specifically, this study explores norms that govern teachers' expectations for the doing of word problems in school algebra. Teacher study groups discussed representations of…

Dewey's conception of scientific explanation, which has been neglected by both philosophers of science and philosophers of education, facilitates overcoming the seeming divide between teaching a highly technical and specialized subject matter and encouraging students to successfully engage in the experience of being philosopher-scientists. By…

Central values promoted in a national curricula are often uncontested (Arnot, Hopman, & Molander, 2007; Colnerud, 2004; Popkewitz, 2009). Therefore, a critical understanding of these values is crucial, as is an understanding of how students are affected by interpretations of certain values as fundamental. The aim of this study is to cast light…

While teaching auditing using cases is regarded as an effective approach, spatial separation of students and teachers in online contexts can restrict the application of case teaching. This study examines an undergraduate auditing course implemented to address this challenge by integrating case teaching with ePortfolio assessment. Students' written…

This dissertation builds on and extends research on the relationship between equity-minded mathematics teaching, specifically teaching mathematics for social justice, complex instruction, and project-based learning, and students' learning and identity development. Although different in their structures and strategies, equity-minded mathematics…

The goal of this study was to explore the educational potential of Minecraft. This project was conducted with 118 elementary-school students from Canada during the 2016-2017 school year. To explore the educational potential of Minecraft on the students, we designed a "Minecraft challenge" for students. 10 game levels of ascending…

Within the "Australian Curriculum: Mathematics" the Understanding proficiency strand states, "Students build understanding when they connect related ideas, when they represent concepts in different ways, when they identify commonalities and differences between aspects of content, when they describe their thinking mathematically and…

Two suggestions for instruction in chemical equilibrium are presented, along with the evidence that supports these suggestions. The first is to use diagrams to connect chemical reactions to the effects of reactions on concentrations. The second is the use of the majority and minority species (M&M) strategy to analyze chemical equilibrium…