Having a nice mathematical task is one challenge for a teacher--another is making it come alive for students in the classroom. The pathway to the latter is pedagogy--the range of teaching strategies possessed and activated by the teacher. This article presents a delightful mathematical activity known as Spirolaterals, a geometrical figure formed…

We present a design study developed in an Italian school. Taking inspiration from the work of the Russian psychologist V. V. Davydov, we have reformulated some activities of his curriculum for the first grade, in order to adapt them to a didactic project for a fifth grade class. In the paper we firstly expose our theoretical assumptions and the…

Although the early development of children's number sense is a strong predictor of their later mathematics achievements, it has been overlooked in primary schools in Malaysia. Mainly attributable to underdeveloped number sense of Malaysian primary and secondary school children, their inability to handle simple mathematics tasks, which require the…

It is frequently surprising to new teachers (and even those with experience) when they find that not only do some children need to recount the group they have just counted to be assured of the total but also that this need seems to be resistant to intervention. Although moving from "counting-all" to "count-on" is sometimes…

Learning to count and to produce the correct sequence of number words in English is not a simple process. In NSW government schools taking part in "Early Action for Success", over 800 students in each of the first 3 years of school were assessed every 5 weeks over the school year to determine the highest correct oral count they could…

In this paper we investigate task design in an unusual professional development course for elementary school teachers, conceived and taught by research mathematicians. Prior analysis singled out "relevance for teaching" as a critical design issue for engaging teachers in effective learning. The aim of the current research is to uncover…

Despite the significance of the role, little is known about mathematics leaders in schools. Rachel, a mathematics leader, was observed leading planning meetings with junior primary teachers. Using activity theory, three of Rachel's motivations were identified: influencing teacher affect, developing shared understandings, and avoiding conflict.…

This study explores the understanding levels of pre-service teachers of the elementary school mathematics teacher education undergraduate program about capacitors that they learned in the compulsory Physics-2 course in the second year of the second term, and instructors' predictions about the teachers' responses. A total of 54 pre-service teachers…

In this three-article dissertation, I explore how ten Palestinian fifth and sixth-grade students perceive and engage with science, technology, engineering, mathematics, and art (STEAM) activities within an out-of-school context. I collaborated with a local organization, Al-Roward for Science and Technology which developed the programming for the…

For many decades, the amount of geometry curriculum worldwide has been cut, mathematics curricula have lacked diversity of geometrical phenomena, and geometry teaching has been reduced to a somewhat eclectic mix of activities. Recently, new trends have begun to counteract these tendencies by framing new curricula around fundamental ideas. The…

In Norway, children are encouraged to pose a problem that they can solve using an arithmetical calculation. This is known as 'regnefortelling'. During a larger project, we became interested in a small group of "regnefortelling" which used unusual contexts, contexts that made us uneasy and invoked a feeling of uncertainty about how we…

Instruction geared toward priming the underlying problem structures was suggested as an evidence-based practice for students with a learning disability. Schema-based instruction is one intervention aligned with this principle. We extended prior work by: (1) using a teacher as the implementer; (2) providing teacher flexibility in intervention…

In many educational systems, textbooks are a leading factor for daily instructional practices, and consequently may affect educational outcomes. Whereas in many countries textbook assessment is a common practice in light of evaluating and improving educational effectiveness, in other countries these practices are absent, mainly under the realm of…

Teachers with a high level of self-efficacy and positive attitudes are more likely to use new and constructivist approaches and to create a learning environment in which students may develop 21st-century skills. Examining pre-service teachers' attitudes and beliefs related to teaching allow teacher preparation programs to evaluate their…

Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…