Email filters classify new messages as either spam or not spam based on word frequency, syntax, and metadata. A "classifier" is an algorithm that maps input data into categories based on distinguishing characteristics, or "features." Features can be raw data or attributes derived from that data. "Feature engineering"…

We introduce a new metric--the classification power--to examine the effectiveness of postsecondary mathematics placement policies. This metric addresses the methodological challenges of contextualizing the effectiveness of a single placement policy and comparing the effectiveness of multiple placement policies across different student populations.…

As children progress through the elementary grades, they are expected to begin to use attributes of shapes to name and classify them. When listening to children talk about shapes, it becomes clear that the process of learning to reason geometrically is complex. Recognizing the complex nature of students' geometric reasoning, the authors present in…

This article is motivated by the importance of developing statistically literate students. The authors present a selection of problems that could be used to motivate student interest in probability as well as providing additional depth to the curriculum when used alongside traditional resources. The solutions presented utilise natural frequencies…

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…

This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

Ariadne is a touch-based program for the learning of homotopies of paths, without the use of formalism, by building mental models. Using Ariadne, the user can construct points, paths by dragging points and homotopies by dragging paths as well as compute winding numbers of paths, all on a variety of surfaces, through touch gestures. Ariadne…

Modeling projects in differential equations and engineering courses create an authentic activity and an opportunity to attain the holy grail of "deeper" learning. However, what do we mean by "deeper" learning and how do we create an environment that encourages that? This article describes a proposal and case study in using…

Play-based preschool pedagogy usually relies on informal teaching while policy trends and some research call for increased formalisation of the pedagogy. Using Bernstein's concepts of classification and framing, this article characterises mechanisms that link evaluation of preschool to the push towards the formalisation of teaching in preschool.…

A broad categorisation of different reading styles for mathematics text is generated in this research. The styles derive from those found in literature around academic reading skills. These styles are inductively refined using video transcripts of five specially chosen students studying out loud from a prescribed mathematics textbook. The context…

This paper presents a research framework for investigating the role of language use in mathematics learning. The paper draws on the wider M[superscript 2]EID study, which explores whether differences in languages (English and Irish) and their use by bilingual mathematical students have a differential impact on their mathematics meta-level…

This paper describes a framework for identifying, classifying, and coding student proofs, modified from existing proof-grading rubrics. The framework includes 20 common errors, as well as categories for interpreting the severity of the error. The coding scheme is intended for use in a classroom context, for providing effective student feedback. In…

The authors who are mathematics teacher educators, have found that classifying, composing, and transforming shapes (in particular, rotations and reflections) are areas of difficulty for adults as well as for children. However, these are also some of the most important geometric ideas. They are fundamental topics in the K-8 Geometry and Measurement…

The purpose of this paper is to account for the advancement of questioning in mathematics education. Four sections focus on: (1) Importance of Questioning in Education (a historical perspective of questioning from the 1960s through the 1990s); (2) Cognitive Classification of Questions (Costa's Levels of Thinking, Webb's Depth of Knowledge, and…

Watching a debate can help people understand multiple points of view. At the conclusion of a debate, a consensus might occur after a deep analysis and discussion of the issues. Most students will participate in a class debate at some point in their schooling, but chances are that debate will not take place in math class. What could there be to…