Mathematics

This chapter focuses on the design of simulation assessments to learn about pre-service teachers’ capabilities with eliciting and interpreting student thinking. We present a simulation assessment and show what a performance on that assessment can reveal about a pre-service teacher’s eliciting and interpreting skills, as well as their mathematical knowledge for teaching. We consider the specific design features that make it possible to appraise pre-service teachers’ capabilities.

We evaluated the effects of three instructional interventions designed to support young children’s understanding of area measurement as a structuring process.

In this chapter, we examine what aspects of Mathematical Knowledge for Teaching of Proving (MKT-P) can be observed in written scenarios of classroom interactions, produced by pre-service teachers (PSTs) of mathematics. A group of 27 elementary and middle school PSTs completed an online interactive module, intended to trigger reflection on, and crystallization of their knowledge of the roles of examples in proving.

Although teacher education is the formal means by which novices are prepared for teaching, they come having already had significant experience in schools. Preservice teachers have formed habits of “teaching” which influence their learning to teach. This article reports a study of the specific knowledge of and skills with teaching practice that novices bring to teacher education with respect to one teaching practice, eliciting student thinking in elementary mathematics, and describes the use of a standardized teaching simulation to learn about novices’ skills.

The theory of realistic mathematics education establishes that framing mathematics problems in realistic contexts can provide opportunities for guided reinvention. Using data from a study group, I examine geometry teachers' perspectives regarding realistic contexts during a lesson study cycle. I ask the following. (a) What are the participants' perspectives regarding realistic contexts that elicit students' prior knowledge? (b) How are the participants' perspectives of realistic contexts related to teachers' instructional obligations?

Measurement is paired with data as a fundamental domain of K–grade 5 mathematics in the Common Core State Standards, and it is one of five core content areas in NCTM’s Principles and Standards for School Mathematics. This book presents lively activities that dovetail with standards and research-based stages of development to support students’ steady growth of understanding of measurement.

Amidon, J., Chazan, D., Grosser-Clarkson, D., & Fleming, E. (2017). Meet me in Azul’s room: Designing a virtual field placement for learning to teach mathematics. Mathematics Teacher Educator, 6(1), 52–66. DOI10.5951/mathteaceduc.6.1.0052

To make sense of the Common Core State Standards mathematical practice (MP) 8, this article illustrates what “repeated reasoning” means, why looking for and expressing regularity in it is such a valuable mathematical habit of mind, and how that differs from analyzing structure (MP 7) and from finding patterns in numerical results.