Students' attitudes toward mathematics and the strength of their mathematics preparation typically go hand in hand such that their specific effects are difficult to disentangle. Employing the method of propensity weighting of a continuous variable, we built hierarchical linear models in which mathematics attitudes and preparation are uncorrelated.…

The study aimed to analyze the interaction effect teaching models and cognitive style field dependent (FD)-field independent (FI) to students' mathematical problem-solving ability (MPSA), as well as students' MPSA differences based on teaching models and cognitive styles. Participants in this study were 145 junior high school students, with…

This study reports an analysis of inductive reasoning of Mexican middle school mathematics teachers, when solving tasks of generalization of a quadratic sequence in the context of figural patterns. Data was collected from individual interviews and written answers to generalization tasks. Based on Cañadas and Castro's inductive reasoning model, we…

Many teachers of intermediate algebra or precalculus use an activity where balls are dropped from known heights and the heights of the bounces are recorded. The "bounce height" will be a roughly constant fraction of the "drop height." Then one can plot each bounce height against its bounce number, an exponential function can…

To date, the way that academic misconduct is manifested in undergraduate mathematics coursework has been unexamined in the literature, with the consequence that policy and preventive education can fail to address it appropriately. This paper describes the particular features of the responses expected in mathematical tasks and provides concrete…

Beginning a teaching career and working to prepare and support beginning teachers is a roller-coaster of successes and puzzling moments. In this article, author Cassandra (Cassie) Seiboldt shares how she learned to manage her first years of teaching by purposefully planning through anticipating student thinking and solutions, and the positive…

In this article, the authors suggest a number of ways in which NAPLAN could be made into a more engaging and enriching experience for both teachers and students. They highlight the importance of making productive errors in the interests of furthering learning. The authors share the journey they have taken as they attempted to get their teeth into…

Math and language are inextricably connected. Math cannot be taught without naming certain concepts and finding ways to express mathematical ideas. With the increasing demands on teachers to meet the needs of diverse learners, the role of language development in the mathematics classroom must be at the forefront of instruction. Identifying and…

This article dives into the importance of engaging students in investigating the mathematics of businesses that pressure their members to recruit new members as a basis for success, also referred to as multi-level marketing (MLM). The mathematics behind these businesses are discussed, and a sample student task is given.

The complexity of understanding unit fractions is often underappreciated in instruction. We introduce a continuum of children's understanding of unit fractions to explore this complexity and to help teachers make sense of children's strategies and recognize milestones in the development of unit-fraction understanding. Suggestions for developing…

Mathematics is a human creation, which has been developing for more than four thousand years. It emerged as a response to different social and economic needs of civilizations. Historical development of mathematics stresses that mathematics as a science has always been connected to economic and social context and development of society. There is…

This paper suggests implications for researchable questions about mathematics teacher development. We ask the following: what is necessary for research that includes mathematics specialists or other hidden school-based roles within a project beyond classroom teachers and students? Mathematics specialists (e.g. mathematics coaches, mathematics…

This text aims to present new research perspectives on teacher training. In particular, it is dedicated to analyzing the training of teachers who teach mathematics from a historical perspective. To this end, it uses the concepts of mathematics to teach and mathematics for teaching, indicating research results, characterizing the professional…

A simple in-class demonstration of integral Calculus for first-time students is described for straightforward whole number area magnitudes, for ease of understanding. Following the Second Fundamental Theorem of the Calculus, macroscopic differences in ordinal values of several integrals, [delta]"F"(x), are compared to the regions of area…

What is the connection between advanced mathematics and teaching secondary mathematics? I address this question, drawing on insights from the Special Issue on "Personal Mathematical Knowledge in the Work of Teaching" ("CJSMTE" 13(2), 2013) and reflecting on my personal teaching experience.