The vision of Mathematics Curriculum promoted by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) is based on two guiding principles: “First, activities should grow out of problem situations; and second, learning occurs through active as well as passive involvement with mathematics” (1989, 9). In particular, curriculum should be designed to support students in constructing their own mathematical ideas and connections. Students should solve problems, communicate ideas both orally and in writing, engage in mathematical reasoning, and search for mathematical connections.

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- Author or Editor: Jennifer Earles Szydlik x

### Jennifer Earles Szydlik

### Jennifer Earles Szydlik

In this study, I investigated 27 university calculus students' mathematical beliefs and connections between those beliefs and their understandings of limit. Participants were selected on the basis of questionnaire and interview responses to real-number, infinity, function, and sourcesof- conviction items. Data obtained in a subsequent limit interview suggest a relationship between sources of conviction and understanding of limit; students with external sources of conviction gave more incoherent or inappropriate definitions of limit, held more misconceptions of limit as bound or unreachable, and were less able to justify limit calculations than those with internal sources of conviction. The influence of content beliefs on understanding of limit is less evident.

### Jennifer Earles Szydlik

Three topics worthy of classroom discussions help beginning algebra students create meaning and build understanding as a community.

### Jennifer Earles Szydlik, Amy Parrott and Jason Knight Belnap

Share practice and culture through three explicit discussions about the nature of mathematics.