Problem solving has long been a priority in mathematics education, and the first Common Core mathematical practice (SMP1) focuses on this priority through the language of "Make sense of problems and persevere in solving them." We present findings from a survey about how prospective elementary teachers' (PTs) make sense of potential…

This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

Some of mathematics teaching is routine, like an exercise from a textbook for which you have received instruction and already know what to do. On other occasions, however, teaching mathematics is challenging, involving problems of teaching for which the solutions may not be readily apparent. These situations require the application of mathematical…

The article contains general information about the use of specialized mathematics software in the preparation of math teachers. The authors indicate the reasons to study the mathematics software. In particular, they analyze the possibility of presenting basic mathematical courses using mathematical computer tools from both a teacher and a student,…

This paper documents the ways mathematical knowledge for teaching (MKT) and curriculum materials appear to contribute to the enactment of a 7th grade "Connected Mathematics Project" lesson on comparing ratios. Two teachers with widely differing MKT scores are compared teaching this lesson. The comparison of the teachers' lesson enactments suggests…

A steady stream of research has shown that many elementary school teachers have weak mathematical knowledge in some areas, including place value and fractions. Since a teacher's mathematical knowledge affects their students' performance, improving elementary school teachers' knowledge is critical. A better understanding of the mathematical…

Ambitious teaching is a form of teaching that requires a high level of teacher responsiveness to what students do as they actively engage with the subject matter. Thus, a teacher enacting ambitious teaching is often confronted with uncertainties about how to advance students' learning while also building on students' contributions. In…

We report the development of a multiple-choice instrument that measures the mathematical knowledge needed for teaching arithmetic with fractions, decimals, and proportions. In particular, the instrument emphasizes the knowledge needed to reason about such arithmetic when numbers are embedded in problem situations. We administered our instrument to…

One special characteristic of any exponential growth or decay function f(t) = Ab[superscript t] is its unique doubling time or half-life, each of which depends only on the base "b". The half-life is used to characterize the rate of decay of any radioactive substance or the rate at which the level of a medication in the bloodstream decays as it is…

This article presents our plans and initial work to explore how mathematics teacher education programs can prepare teachers for diverse middle grades classrooms. It describes the start-up of a five-year National Science Foundation project to design, develop, and test technology-enriched teacher preparation strategies to address equity in algebra…

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…

This report presents the results of an experiment conducted in Alabama beginning in the 2006/07 school year, to determine the effectiveness of the Alabama Math, Science, and Technology Initiative (AMSTI), which aims to improve mathematics and science achievement in the state's K-12 schools. This study is the first randomized controlled trial…

This article presents data from a group of secondary pre-service teachers who used vee diagrams to illustrate their conceptual and methodological analyses of a problem, as part of a required mathematics methods course assignment. The individually constructed vee diagrams were analysed in terms of the extent to which they displayed principles and…

Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their…

US and China are reforming mathematics teaching by shifting from students' attainment of facts and procedures toward development of competencies in reasoning, communication, connections, and problem solving, and application of these in real life contexts. Differences in students' overall performance, curricula, and teachers' knowledge and…