We investigated whether the content pre-service teachers studied in elementary teacher preparation mathematics courses was related to their performance on a mathematics lesson planning task 2 and 3 years after graduation. The relevant mathematics knowledge was studied when the teachers were freshmen, 5 to 6 years earlier. Results showed that when…

Many students from disadvantaged homes participating in Programme for International Student Assessment (PISA) 2012 were classified as academic resilient (called "disadvantaged high achiever", the DHA in this study). In comparison with peers of comparable home background status, there were also students from advantaged homes performing…

There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…

Mathematics in engineering education causes many thresholds in the courses because of the demand of abstract conceptualisation. Electronics depend heavily on more or less complex mathematics. Therefore the concepts of analogue electronics are hard to learn since a great deal of students struggle with the calculations and procedures needed. A…

Mathematics discourse is a teaching approach that encourages student discussion and reveals an understanding of concepts as students engage in mathematical reasoning and debate (Cobb 2006). Grabowski and Ke (2007) posit that students have significantly higher achievement and positive attitudes toward mathematics after participating in gaming…

In the present chapter, we review the evidence for several principles that are especially promising for improving mathematics instruction. Using the classification scheme proposed by Koedinger et al. (2013), we begin with principles that focus on improving memory and fluency: scaffolding, distributed practice, and feedback. We then move to worked…

Addressed are four key issues regarding concrete instruction: What is concrete? What is a worthwhile concrete experience? How can concrete experiences be used effectively in early childhood mathematics instruction? Is there evidence such experiences work? I argue that concrete experiences are those that build on what is familiar to a child and can…

Beliefs help shape how teachers perceive effective mathematics teaching. Providers of professional development, be they local or from other countries, need to be cognisant of such perceptions. This paper seeks to answer the question, "What do South African teachers perceive as effective and ineffective teaching for developing conceptual…

Learning algebra is critical for students in the USA today, yet many students in the USA struggle in algebra classes. Researchers claim that one reason for these difficulties is that algebra classes often focus on symbol manipulation and procedures above, and many times at the expense of, a more conceptual understanding of the content. Teaching…

Field placements serve as the traditional "clinical" experience for prospective mathematics teachers to immerse themselves in the mathematical challenges of students. This article reports data from a different type of learning experience, that of a clinical simulation with a standardized individual. We begin with a brief background on…

This paper investigates the teaching practices used by university mathematics teachers when lecturing, a topic within university mathematics education research which is gaining an increasing interest. In the study, a view of mathematics teaching as a discursive practice is taken, and Sfard's commognitive framework is used to investigate the…

In the author's experience with this activity, students struggle with the idea of representativeness in probability. Therefore, this student misconception is part of the classroom discussion about the activities in this lesson. Representativeness is related to the (incorrect) idea that outcomes that seem more random are more likely to happen. This…

In this paper, we frame mathematics classrooms as heterogeneous spaces wherein students draw on multiple storylines based on different notions of schooling and school mathematics to both communicate mathematical ideas and position themselves and one another. We focus on a fourth grade (age range 9.4-10.8 years) mathematics classroom discussion in…

Helping students generalise mathematical ideas is an essential component of teaching and learning of mathematics (Lannin, Ellis, Elliott & Zbiek, 2011). However, it can be challenging for primary teachers to assess and promote generalisation. Because generalisation is an essential part of mathematics instruction, the authors highlight the…

FOIL is a well-known mnemonic that is used to find the product of two binomials. We conduct a large sample (n = 252) observational study of first-year college students and show that while the FOIL procedure leads to the accurate expansion of the product of two binomials for most students who apply it, only half of these students exhibit conceptual…