Mathematics majors, including future secondary teachers, should understand the work of pure mathematicians and the crucial role proof plays for the discipline of mathematics. Beyond the textbook proofs seen in most transition-to-proof courses, we conjectured that students might develop a deeper understanding of the discipline of mathematics and…

Two studies were conducted to examine and compare the construct validity of scores on the Junior Metacognition Awareness Inventory (JMAI) and problem-solving interview protocols. Participants consisted of 183 middle and high school students attending a university summer program for academically talented youth. Study 1 results indicated that JMAI…

Reasoning and problem solving are both critical acts in mathematics learning. The author has met many teachers who tell her they would love to highlight them more but feel they cannot because of the pressures of content coverage, pacing guides, and district tests. In this article, she describes a teaching intervention that highlighted problem…

We introduce a template to (i) scaffold the problem solving process for students in the physics 1 course, and (ii) serve as a generic rubric for measuring how expertlike students are in their problem solving. This template is based on empirical studies of the problem solving practices of expert scientists and engineers, unlike most existing…

"English Language Learners" (ELLs) at risk for "math disabilities" (MD) are challenged in solving word problems for numerous reasons such as (a) learning English as a second language, (b) limited experience using math vocabulary, and (c) lack of strategies to improve word-problem-solving skills. As a result of these…