Research indicates that investigating phenomena, rather than reproducing facts, should be a core experience in the education of prospective mathematics teachers. Corresponding with its centrality to quality teacher education, there are multiple existing methodologies for analyzing the effects of investigation tasks on teachers' mathematical…

This study addresses the need to better describe instructional strategies used by middle grades mathematics teachers. After coding 177 videos of grades 6-8 mathematics instruction for indications of effective instructional practices, we further analyzed 8 of the highly scored videos with specific attention to teachers' implementation of strategies…

This study examined opportunities provided for preservice secondary mathematics teachers (PSMTs) to learn reasoning and proof in algebra from the perspective of college instructors. We analyzed interview transcripts of 15 course instructors recruited from three teacher education programs in the United States. We examined the reported opportunities…

In studies over recent years, there has been an increasing interest in teachers' predicting middle school students' thinking processes. However, as far as we are aware, there are no studies examining students' thinking in terms of mathematical thinking components. This study primarily aimed to determine the mathematical thinking of middle school…

This practitioner article describes a lesson carried out in a high school classroom at the conclusion of a unit on exponential growth. Two teachers use a series of music-related activities to engage students in using and connecting multiple representations of exponential growth while exploring musical frequencies on a piano.

In this study, we investigated mathematics teacher's noticing of students' thinking in the context of mathematical modeling activities (MEAs) related to statistics. One middle-school mathematics teacher participated in the study, which adopted a case study design. Data were collected through interviews with the teacher based on video recordings of…

This qualitative case study of four middle school and secondary school mathematics teachers examines how teachers' reflective practice supported their selection of strategies that align with the needs of current mathematics education according to the 10 dimensions of mathematics education. The findings suggest that teachers' reflection practice,…

Productive use of student mathematical thinking is a critical yet incompletely understood dimension of effective teaching practice. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four elements that comprise it. In this paper we begin to unpack this complex practice by looking closely at…

The use of tasks to promote mathematical reasoning (MR) in teaching practice is essential to meet curricular goals. However, that practice is often a huge challenge for teachers, and particularly for prospective teachers and thus it is essential to highlight it as a goal for initial teacher education. This study focuses on preservice mathematics…

In this article, the author describes a task given to pre-service secondary school mathematics teachers. By exposing them to a relatively simple mathematics process, it was hoped that their ability to plan and implement lessons for their own students would be enhanced.

We investigate the beliefs that influence middle and high school algebra teachers' appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical…

The relationship between teacher interventions and students' mathematical thinking has been the subject of inquiry for quite some time. Using the Pirie-Kieren theory for dynamic growth in mathematical understanding, this study documents teacher interventions that support students' growth toward developing a general understanding of a mathematical…

In this paper, we revisit a long-running conversation about situated learning and the design of environments for disciplinary engagement. Throughout the 1970s and 1980s, scholars advanced an anthropological critique of the then-dominant acquisitionist paradigm of formal schooling with a situated view focused on membership in communities and…

We report our findings and perspective to document the knowledge exhibited by three experienced high school teachers in their instructional decisions for lessons on the equation of an exponential function. We describe the nature of the mathematical ideas and connections teachers promoted in discourse and the decisions that supported the emergence…

Ever try to captivate students with real-world applications only to discover that they live in a very different world? Assigning an Extreme Word Problem activity to students alleviates this dilemma by placing the authorship of a problem squarely into the hands of learners. Rather than trying to be hip and finding word problems that resonate with…