Researchers as Coaches: Developing Mathematics Teaching Capacity Using MEAs for STEM Integration

Mizar as a Tool for Teaching Mathematics

The Mizar system is a proof–assistant based on classical logic. A substantial body of Mizar texts (the Mizar Mathematical Library) has been developed in various areas of mathematics. It has been quite natural to expect using Mizar as a tool for teaching mathematics; the experience in this matter dates back to 1975/76. In this paper we present some historical facts about applying Mizar in educat...

Developing Measures of Teachers’ Mathematics Knowledge for Teaching

Defining, developing, and measuring “Proclivities for Teaching Mathematics”

This article presents a form of teacher reasoning that we call proclivities for teaching mathematics. We define proclivities for teaching mathematics as the beliefs, knowledge, and dispositions that are actionable in the flow of instruction, and we argue that growth in this area contributes to positive change in mathematics instruction. Proclivities for teaching mathematics encompass four domai...

Developing a Healthy Scepticism About Technology in Mathematics Teaching

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Structured Derivations as a Unified Proof Style for Teaching Mathematics

Structured derivations were introduced by Back and von Wright as an extension of the calculational proof style originally proposed by E.W. Dijkstra and his colleagues. Structured derivations added nested subderivations and inherited assumptions to the original calculational style. This paper introduces a further extension of the structured derivation format, and gives a precise syntax and seman...