The teaching of mathematics is mostly done with tasks that learners and teachers do or solve, in and outside of class. These tasks, which are used to illustrate concepts in mathematics, are referred to in this paper as examples in mathematics. Examples that teachers choose and use are fundamental to what mathematics is taught and learned, and what…

A grandmother attempts to teach her four-year-old granddaughter the multiplication tables using simple repetition, but they repeatedly start over at 'three fives'; the child keeps coming up with 'thirty-five'. We consider three possible explanations: self-perpetuating frequency of behavior, saliency of memory and Vygotsky's next or proximal zones…

In this paper we present statistical analyses of three textbooks used by Swedish teachers to support year one children's learning of mathematics. One, Eldorado, is authored by Swedish teachers, another, Favorit, is a Swedish adaptation of a popular Finnish series and the third, Singma, is a Swedish adaptation of a Singapore series. Data were coded…

Emotions can influence cognitive development and are key elements to the teaching-learning process. Positive emotions (e.g., engagement) can improve the ability to solve problems, store information, and make decisions. On the other hand, negative emotions (e.g., boredom) reduce the capacity to process information at a deeper level, preventing…

Frameworks can influence the work of mathematics teacher educators (MTEs) in many different ways. Frameworks can suggest a structure around which MTEs design instruction, provide a common language for communicating with prospective teachers, and support prospective teachers as they design their own instruction. This paper reports findings related…

Structures such as rehearsals have been designed within mathematics education to engage teacher candidates in deliberate practice of specific teaching episodes before enacting within classroom settings. Current research has analyzed traditional rehearsals that involve peers acting as K-12 students as the teacher candidate facilitates an activity;…

This research paper presents a digital game-based learning as an innovative methodology that takes full advantage of the educational potential offered by digital games to aid learning of concepts. It focuses on the use of games as a mode of learning in the classroom while exploring all learning theories that supports it. This mode of learning is…

Introductory mathematics courses, including precalculus and calculus, largely influence Black and Latin* students' persistence and sense of belonging in STEM. However, prior research on instruction in these courses for advancing more equitable outcomes is limited. This paper presents findings from a study of 18 Black and Latina/o students'…

International comparative studies on mathematics teaching and learning often provide unitary and harmonious images of classroom practices. This paper aims to complement those studies by describing the complex aspects of those practices. Adopting activity theory as a framework, this paper considers classroom teaching and learning of mathematics as…

Mathematics curricula have traditionally focused on content knowledge, often in the form of a scope and sequence of increasingly difficult mathematics. The importance of using and applying mathematics is recognised in the current Australian Curriculum Mathematics (AC: M) as 'proficiencies' that are intended to be integrated with the content. There…

We examine aspects of professional collaboration in a lesson study conducted with mathematics teachers from the final years of basic education belonging to public schools in the State of Rio Grande do Sul, Brazil. The lesson study, conceived as a professional development approach focused on collaboration and reflection, took place in the 2nd…

To further enhance its usability and better serve teachers' needs a new connected classroom technology, called GeoGebra Classroom was developed. in this paper, we outline the results of the potential uses of GeoGebra Classroom in mathematics teaching and learning. in our Design Research study, we utilized the combination of educational research…

This article documents differences between novice and experienced undergraduate students' processes of reading mathematical proofs as revealed by moment-by-moment, think-aloud protocols. We found three key reading behaviors that describe how novices' reading differed from that of their experienced peers: alternative task models, accrual of…

Ensuring students master their basic facts is a shared priority among teachers, parents, and administrators. As a result, the number of available resources for basic facts instruction, from concrete to virtual, is vast and continues to grow. Basic fact fluency has always been of interest to elementary school teachers and is particularly relevant…

There is widespread belief that addressing differentiation within classroom practice is critical for school improvement in mathematics. School mathematics leaders and consultants are faced with the challenge of interpreting the various models of differentiation that are presented throughout professional learning programs and aligning these with…