Understanding large number data is essential for making sense of real-world problems. For the research reported here, our intent was to find connections between quantitative cognitive science studies and our prior qualitative study about participants' understanding of the relative size of large numbers. While all 23 cognitive science research…

While conceptual understanding of properties, operations, and the base-ten number system is certainly associated with the ability to access math facts fluently, the role of math fact memorization to promote conceptual understanding remains contested. In order to gain insight into this question, this study looks at the results when one of three…

Place value understanding requires the same activity that students use when developing fractional and algebraic reasoning, making this understanding foundational to mathematics learning. However, many students engage successfully in mathematics classrooms without having a conceptual understanding of place value, preventing them from accessing…

This study examines data from college students who worked in pairs to make decisions about a list of potential definitions of prime number. Analysis focused on the evidence each student pair cited when they decided whether or not a statement could be used as a definition for prime number. The purpose of this paper is to describe patterns in the…

To investigate the structure of number sense and then to assess its uses in fifth-grade children's number sense development, a computerized number sense scale was developed and evaluated. The findings of the study indicate that the newly developed scale, with four dominant factors identified and reconfirmed, is internally consistent and…

This paper describes the author's attempt to design assignments that engage preservice elementary teachers in original mathematical thinking. In particular, the choice of integer operations as the focus of a structured writing assignment that takes students two weeks to complete is explained and justified. Exemplary student work is quoted.…

This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress (NAEP). A set of eight instructional modules was developed and tested. The study involved 7…

A short story is presented which uses as its characters rational and irrational numbers and numbers involving fractional exponents. (DT)

Mathematical Induction is used for direct proofs of many theorems; its logical equivalent, the Well-Ordering Property, replaced it to yield indirect proofs by contradiction. The author claims the later property is easier to comprehend and that it affords a non-geometrical example of proof by contradiction. (JP)

A recreational activity providing practice in computation is described. Examples are provided and the underlying mathematics is analyzed. (DT)

Four hundred and three 3rd- and 5th-grade Chinese students took the Multiplication Estimation Test or participated in the interview on it, designed to assess their computational estimation performance on whole-number multiplication. Students perform better when tasks are presented visually than orally. Third graders tend to use rounding based…