In learning, errors are ubiquitous and inevitable. As these errors may signal otherwise latent cognitive processes, tutors--and students alike--can greatly benefit from the information they provide. In this paper, we introduce and evaluate the Systematic Error Tracing (SET) model that identifies the possible causes of systematically observed…

Counting problems offer rich opportunities for students to engage in mathematical thinking, but they can be difficult for students to solve. In this paper, we present a study that examines student thinking about one concept within counting, factorials, which are a key aspect of many combinatorial ideas. In an effort to better understand students'…

An empirical study has been carried out to evaluate the potential of word order matching and static comparison as explanatory models of reversal error. Data was collected from 214 undergraduate students who translated a set of additive and multiplicative comparisons expressed in Spanish into algebraic language. In these multiplicative comparisons…

The objective of the proposed study is three-fold: to identify middle school student levels of estimation self-efficacy and student engagement, to address student multiplication estimation performance under differing teacher expectations and cultural learning contexts, and to understand how student levels of efficacy and engagement mediate their…

South Africa participated in TIMSS from 1995 to 2015. Over these two decades, some positive changes have been reported on the aggregated mathematics performance patterns of South African learners. This paper focuses on the achievement patterns of South Africa's high-performing Grade 9 learners (n = 3378) in comparison with similar subsamples of…

This study is about prospective secondary mathematics teachers' understanding and sense making of representational quantities generated by algebra tiles, the quantitative units (linear vs. areal) inherent in the nature of these quantities, and the quantitative addition and multiplication operations--referent preserving versus referent…

Using qualitative data collection and analyses techniques, we examined mathematical representations used by sixteen (N=16) teachers while teaching the concepts of converting among fractions, decimals, and percents. We also studied representational choices by their students (N=581). In addition to using geometric figures and manipulatives, teachers…

The "Census in Schools Educator Update" is sent to educators and educational organizations periodically to keep them informed about current and upcoming census data and to provide ideas about how to use data in the classroom. This issue of the "Census in Schools Educator Update" newsletter focuses on the following topics: (1) Census in Schools is…

A grounded theory approach was employed to explore the variation in strategies used by students when solving mental multiplication problems. Metacognitive prompts, externally generated stimuli that activate thoughtful cognition, were automatically generated via computer during the solving of mental multiplication problems to elicit awareness,…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

This article explores the mathematics involved in the NCAA basketball tournament including data analysis, basic probability, expected value, and the multiplication principle. A fun activity is presented that applies these concepts and involves students shooting Ping-Pong balls to discover a best strategy. (Contains 3 tables and 3 figures.)

The National Science Foundation funded Calculators and Mathematics Project, Los Angeles (CAMP-LA) developed curriculum materials focused solely on the use of calculators. The project was developed in three stages. The first stage studied the mathematics curriculums from different states and identified topics that are not included but should be if…

The Calculators and Mathematics Project, Los Angeles (CAMP-LA), funded by the National Science Foundation for developing use of technology in the classroom, developed curriculum materials focused solely on the use of calculators. The project was developed in three stages. The first stage studied the mathematics curriculums from different states…

The National Science Foundation funded Calculators and Mathematics Project, Los Angeles (CAMP-LA) developed curriculum materials focused solely on the use of calculators. The project was developed in three stages. The first stage studied the mathematics curriculums from different states and identified topics that are not included but should be if…