Examples play a central role in mathematics learning and teaching. Although they involve specific situations, their purpose is to exemplify more general mathematical principles. A critical task of teaching, therefore, is to choose appropriate examples and implement them in pedagogically productive ways. This study considers the examples used by…

We report on a two-year "concept study" in which a cohort of middle school teachers collectively deconstructed and reconstructed the concept of multiplication. Defining concept study as a collaborative structure through which mathematics educators identify, interpret, interrogate, invent, and elaborate images, metaphors, analogies, examples,…

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…

In this study subjects are presented with sequences of heads and tails, derived from flipping a fair coin, and asked to consider their chances of occurrence. In this new iteration of the comparative likelihood task, the ratio of heads to tails in all of the sequences is maintained. In order to help situate participants' responses within…

Using calculus, we explore the long term dynamical behavior of exponential functions under iteration for all initial points.

Interpretation of correlation is often based on rules of thumb in which some boundary values are given to help decide whether correlation is non-important, weak, strong or very strong. This article shows that such rules of thumb may do more harm than good, and instead of supporting interpretation of correlation--which is their aim--they teach a…

In this note, we construct infinite series using M-bonacci numbers in a manner similar to that used in previous studies and investigate the convergence of the series to an integer. Our results generalize the ones obtained for Fibonacci numbers.

This article presents the authors' response which consists of three main parts. The first involves recapping the general thrust of their focus article. The second part consists of some general points that they hope will clarify issues raised by the commentators that were not made as clearly as they should have been in the focus article. The third…

This study is a literature review to investigate the effects of implementing technology into a high school mathematics classroom. Mathematics has a hierarchical structure in learning and it is essential that students get a firm understanding of mathematics early in education. Some students that miss beginning concepts may continue to struggle with…

Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

In this paper, we report on the impact of four activities and two interviews on the organization of an introductory statistics course attended by future mathematics teachers at the University of Sao Paulo, Brazil. The activities were designed to enhance students' learning and collaborative knowledge construction, based on Vygotsky's…

The purpose of this study was to assess the relative contribution of teacher and tutor ratings of inattentive behavior in two different instructional settings in predicting students' performance on fraction concepts and whole-number calculations. Classroom teachers rated each student's attentive behavior in a whole-class setting and tutors rated…

To help researchers understand potential issues one can encounter when conducting propensity matching studies in complex settings, this paper describes methodological complications faced when studying schools using deeper learning practices to improve college and career readiness. The study uses data from high schools located in six districts…

In my personal interactions with elementary preservice teachers (EPSTs) at a large Midwestern university in United States, many EPSTs held negative beliefs and attitudes about geometry learning. Although finding ways to help EPSTs change their negative beliefs and attitudes is an important issue, it can be best addressed by first investigating how…

This study purposed to determine the effect of an endogenously designed instructional game on conceptual understanding of the associative and distributive properties of multiplication. Additional this study sought to investigate if performance on measures of conceptual understanding taken prior to and after game play could serve as predictors of…