This paper explores the specialized knowledge mobilized by a mathematics teacher in the selection and use of examples for teaching sequences. Taking an experimental case study approach, we analyse the examples deployed in a series of third-year secondary level lessons on sequences and identify the different knowledge subdomains activated according…

This article addresses a perceived need for a more comprehensive model of teachers' self-efficacy beliefs, that is, teachers' beliefs about their personal abilities to perform specific tasks related to teaching and learning within specific teaching contexts. It starts with an analysis of current representations, and how they encourage further…

For 30 years, science education researchers and practitioners have waited for the promise of pedagogical content knowledge (PCK) to be fulfilled. PCK has the potential to shape instruction, teacher professional learning, and instructional materials. When the field speaks about PCK in terms of these benefits, a particular kind of PCK is envisioned.…

Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and proving across grade levels and mathematical topics. Although most programs require a course on proof, PSTs often perceive it as disconnected from their future classroom practice. Our design research…

In this paper, we focus on the design of assessments of mathematics teachers' knowledge by emphasizing the importance of identifying the purpose for the assessment, defining the specific construct to be measured, and considering the affordances of particular psychometric models on the development of assessments as well as how they are able to…

Previous research has shown knowledge, perceptions, and attitudes are essential factors during mathematics classroom instruction. The current study examined the effects of a 3-week fraction instructional unit using concrete models, problem-solving, and problem-posing to improve elementary preservice teachers' knowledge, perceptions and attitudes…

Professional knowledge is highlighted as an important prerequisite of both medical doctors and teachers. Based on recent conceptions of professional knowledge in these fields, knowledge can be differentiated within several aspects. However, these knowledge aspects are currently conceptualized differently across different domains and projects.…

Rowland's Knowledge Quartet (KQ) model can provide illuminating insights into teacher practice in mathematics classrooms. This paper explores a framework developed for pedagogical technology knowledge (TPACK) to consider teacher practice in integrated technology classrooms alongside the KQ model. Observations of a Year 11 class in an Australian…

Modeling student knowledge while students are acquiring new concepts is a crucial stepping stone towards providing personalized automated feedback at scale. We believe that rich information about a student's learning is captured within her responses to open-ended problems with unbounded solution spaces, such as programming exercises. In addition,…

As scientific models of student thinking, learning progressions (LPs) have been evaluated in terms of one important, but limited, criterion: fit to empirical data. We argue that LPs are not empirically adequate, largely because they rely on problematic assumptions of theory-like coherence in students' thinking. Through an empirical investigation…

This study has been aimed to propose a conceptual framework that helps researchers examine mathematics teachers' PCK in the context of supporting students' mathematical thinking. "Advancing Children's Thinking Framework" which is a pedagogical model developed by Fraivillig, Murphy and Fuson (1999) that supports the development of…

One of the primary goals of teacher education is to aid preservice candidates in formulating a personal philosophy of teaching that is research-based. Teacher candidates should recognize that their philosophy of teaching and learning must be grounded in research-affirmed theory, certain dimensions of which (e.g., motivation) are critical to…

The purpose of this study was to explain middle school teachers' decisions for planning a science unit of instruction (reflection on action) and their decisions when enacting this planned unit (reflection in action) using the new teacher professional knowledge and skill (TPK&S) model as a guiding framework. In addition, this study specifically…

Technological Pedagogical Content Knowledge, one of the frameworks proposed in order to popularize the use of technology in a classroom environment, has been customized and has taken the form of Web Pedagogical Content Knowledge. The Relational Screening Model was used in this study. It aims to determine whether a profile of preservice teachers…

In this study, I examined the relationship between teachers' mathematical knowledge and instruction. Twenty-one K-8 teachers who were enrolled in a master's program were followed for 3 years to study how their mathematical knowledge and teaching changed over time. The results of multilevel growth models indicated that gains in teachers'…