The research article in this article is part of a larger study that examines an initiative to expand teacher expertise in facilitating mathematical problem solving within the framework of developing and field-testing pedagogical resources. We focus on one year of the study and report on the complex process of professional development as teachers…

Many educators share the vision of the Equity Principle--teachers holding high expectations for all students. However, according to National Assessment of Educational Progress (NAEP) reports, minority students continue to lag behind white students in mathematics achievement. Furthermore, the discrepancies are more pronounced on the extended,…

Many researchers assume that people are creative, but their degree of creativity is different. The notion of creative thinking level has been discussed .by experts. The perspective of mathematics creative thinking refers to a combination of logical and divergent thinking which is based on intuition but has a conscious aim. The divergent thinking…

Research in the field of Automated Planning is largely focused on the problem of constructing plans or sequences of actions for going from a specific initial state to a goal state. The complexity of this task makes it desirable to find "generalized" plans which can solve multiple problem instances from a class of similar problems. Most approaches…

Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of…

This study examines how students solve problems that involve the concept of absolute value. One hundred seventeen students participated in the first (written) part of the study, 24 students participated in the second part (interview). Particular attention was paid to the actual process of problem solving and to the students' ability to establish…

Dice are considered one of the oldest gambling devices and thus many mathematicians have been interested in various dice gambling games in the past. Dice have been used to teach probability, and dice rolls can be effectively simulated using technology. The National Council of Teachers of Mathematics (NCTM) recommends that teachers use simulations…

Almost every adult in Australia has played Noughts and Crosses at some time in their life--it is that sort of game, a universal classic. Very few Australian adults play Noughts and Crosses, adult against adult, unless they are bored, witless and cannot think of anything better to do. Adults stop playing this game. Many will say it is boring, while…

This article discusses the concept of an invariant item ordering (IIO) for polytomously scored items and proposes methods for investigating an IIO in real test data. Method manifest IIO is proposed for assessing whether item response functions intersect. Coefficient H[superscript T] is defined for polytomously scored items. Given that an IIO…

Little is known about how best to teach mathematics to students with learning disabilities. This study explored the performance and self-reported calculator use of 13 sixth-grade and 15 seventh-grade students with learning disabilities educated in either standards-based or traditional mathematics curricula on multiple-choice and open-ended…

The Problems of the Week (PoWs) are creative, non-routine math challenges for elementary-, middle-, and high-school-level students. They are designed to stimulate student interest in problem solving and to encourage them to communicate their mathematical thinking. This Teacher's Guide describes program features and provides strategies for…

Useful for small groups or one-on-one instruction, this book offers successful math interventions and response to intervention (RTI) connections. Teachers will learn to target math instruction to struggling students by: (1) Diagnosing weaknesses; (2) Providing specific, differentiated instruction; (3) Using formative assessments; (4) Offering…

This study investigated the influence of regular structured writing about problem solving on college algebra students' locus of control, flexibility of articulation, and accuracy in responding to written problem tasks. The writing assignments, acronym PSOLVE, provided students a framework for expressing their thoughts about mathematical actions,…

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich…