Search Results

You are looking at 1 - 5 of 5 items for

  • Author or Editor: Jennifer A. Czocher x
Clear All Modify Search
Restricted access

Jennifer A. Czocher and Keith Weber

To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a collection of necessary and sufficient conditions. We argue that defining the proof category in this way renders the definition incapable of accurately capturing how category membership is determined. We propose an alternative account—proof as a cluster category—and demonstrate its potential for addressing many of the intractable challenges inherent in previous accounts. We will also show that adopting the cluster account has utility for how proof is researched and taught.

Restricted access

Jennifer A. Czocher and Diana L. Moss

Have you ever thought about teaching mathematics through making connections to logic and philosophy? This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5–9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with mathematics (NGAC 2010). It also gives students of all ages a glimpse into the development of mathematics by introducing a reason to think about infinite convergent series.

Restricted access

Jennifer A. Czocher and Diana L. Moss

Along with previous learning, general knowledge and personal encounters influenced students when the Letter Carrier problem was delivered to them.

Restricted access

Jennifer A. Czocher, Diana L. Moss and Luz A. Maldonado

Conventional word problems can't help students build mathematical modeling skills. on their own. But they can be leveraged! We examined how middle and high school students made sense of word problems and offer strategies to question and extend word problems to promote mathematical reasoning.

Restricted access

Diana L. Moss, Jennifer A. Czocher and Teruni Lamberg

For these sixth graders, transitioning from arithmetic to algebraic thinking involved developing new meanings for symbols in expressions and equations.