Recontexualising items that measure mathematical knowledge for teaching into scenario based interviews: an investigation

AbstractThis paper interrogates the recontextualisation of available assessment items developed forresearch purposes that measure mathematical knowledge for teaching, into scenarios foruse in qualitative studies related to mathematics teachers’ subject matter knowledge. Itdraws from interviews with teacher participants in the Wits Maths Connect-Secondaryproject and their responses to two selected items from the Learning Mathematics forTeaching (LMT) project. The analysis shows that carefully constructed multiple choiceitems in the domain of (mathematics) subject matter knowledge have much potential inprovoking teachers’ talk and their mathematical reasoning in relation to practice-basedscenarios; and exploring with teachers a range of connected knowledge related to theteaching of a particular concept or topic. We argue that productive use of such items furtherrequires that researcher make explicit the mathematical ideas they expect to explore andassess in the developed items

Teacher learning about exemplification in geometry through lesson study

We explore aspects of Malawian teachers’ learning in their first encounter with Lesson Study (LS) professional development. Experienced secondary mathematics teachers from two schools participated in a theory-guided LS focused on geometry. Using data collected during the first LS cycle, we examined dimensions of variation of geometry examples made available, and changes in example sets. Findings show teachers’ take-up of two dimensions of variation in the initial lesson plan, with the third dimension coming into focus during lesson reflection. We argue that theory-guided LS can support teachers to strengthen their knowledge and use of example sets in geometry.This paper is based on postdoctoral fellowship work in the Wits Maths Connect Project at University of the Witwatersrand and in collaboration with the Faculty of Education at University of Malawi

Can improving teachers’ knowledge of mathematics lead to gains in learners’ attainment in mathematics?

It is wellknown that the majority of South African learners achieve extremely poorly in mathematics. Many claim that one of the causes of this poor attainment is teachers’ weak knowledge of mathematics, and propose that improving teachers’ mathematical knowledge would improve learner attainment. However, the evidence-base for this proposed solution is currently relatively weak. We report on a quasi-experimental study examining the learning gains of Grade 10 learners from five secondary schools in the Johannesburg area whose teachers participated in a year-long professional development course aimed at improving the teachers’ knowledge of mathematics for teaching. Statistical analyses of pre- and post-test results show that the intervention group of learners (N = 586) taught by teachers who had participated in the professional development (N = 14) outperformed a matched control group of learners (N = 217) taught by teachers in the same schools (N = 7). An effect size of =0.17 for the intervention group is equivalent to two months’ additional progress. While the learning gains are small, they are statistically significant. These findings provide empirical support for claims that attending to teachers’ mathematical knowledge can impact learners’ attainment. Suggestions are made regarding the form and substance of such professional development

Discourses of mathematical reasoning: analysis of three reform frameworks

Curricula in many countries include mathematical reasoning as an aim, a competence or proficiency that students should acquire. This inclusion has been supported by wide dissemination of frameworks advocating reform that have arisen from the research community. We present the first part of a project aiming to investigate how ideas about reasoning originating in these frameworks are recontextualised in curricula, textbooks and classrooms. We analyse discourses about reasoning in three such frameworks, identifying how each characterises the nature of mathematical reasoning and the ways students are expected to relate to it. We also examine the extent to which reasoning is construed as a goal of mathematics education or as a means to achieving other goals. In this paper, we explain the methods used for analysing reasoning discourse and identify key findings from the analysis

Framework for analysing secondary mathematics teachers’ development of geometric reasoning

Developing geometric reasoning is an important aim of school mathematics. Some influential theoretical frameworks have been used to map progress in geometric reasoning among learners and teachers internationally. We propose an alternate analytical framework, suitable for the context of our work, to analyse secondary mathematics teachers’ development of geometric reasoning as they participate in content-focused professional development. We show how the emerging framework uses conceptual categories drawn from the existing literature on geometric reasoning and empirical levels mapped to analyse teachers’ developing reasoning. We conclude by anticipating ways in which the framework can be used and extended.This paper is based on postdoctoral fellowship work in the Wits Maths Connect Secondary Project at the University of the Witwatersrand, partly funded by the National Research Foundation of South Africa

Patient characteristics associated with objective measures of digital health tool use in the United States: A literature review.

The study sought to determine which patient characteristics are associated with the use of patient-facing digital health tools in the United States.We conducted a literature review of studies of patient-facing digital health tools that objectively evaluated use (eg, system/platform data representing frequency of use) by patient characteristics (eg, age, race or ethnicity, income, digital literacy). We included any type of patient-facing digital health tool except patient portals. We reran results using the subset of studies identified as having robust methodology to detect differences in patient characteristics.We included 29 studies; 13 had robust methodology. Most studies examined smartphone apps and text messaging programs for chronic disease management and evaluated only 1-3 patient characteristics, primarily age and gender. Overall, the majority of studies found no association between patient characteristics and use. Among the subset with robust methodology, white race and poor health status appeared to be associated with higher use.Given the substantial investment in digital health tools, it is surprising how little is known about the types of patients who use them. Strategies that engage diverse populations in digital health tool use appear to be needed.Few studies evaluate objective measures of digital health tool use by patient characteristics, and those that do include a narrow range of characteristics. Evidence suggests that resources and need drive use

Interpretations of, and orientations to, “understanding mathematics in depth”: students in MEC programmes across institutions

In this paper we present initial findings from our study of interpretations and orientations to ‘understanding mathematics in depth’ among students in selected Mathematics Enhancement Courses (MEC) in the UK. The MEC is a 26-week pre-Initial Teacher Education (ITE) ‘mathematics subject knowledge for teaching’ course designed for, and undertaken by, graduates wishing to teach mathematics at secondary level, but do not have a Mathematics degree. It is completed before commencing with a PGCE. A common theme running through the MEC documentation is the importance of ‘understanding mathematics in depth’. We are interested in what and how MEC students interpret and orient themselves towards ‘understanding mathematics in depth’. In designing and conducting our empirical work we have drawn upon a related project in South Africa, which is exploring ‘mathematics for teaching’, specifically what and how mathematics and teaching are co-constituted in mathematics teacher education programmes. The MEC is an interesting empirical context for such study, as it is a mathematics course, or set of courses, specifically designed for future teachers. We have collected data through guided, semi-structured interviews with 18 students and 4 lecturing staff at three different institutions. The interpretations and orientations of MEC students towards mathematics and the notion of ‘understanding mathematics in depth’, we contend, provide additional insight into the developing notion of mathematical knowledge in and for teaching

Troubling "understanding mathematics-in-depth": Its role in the identity work of student-teachers in England

Copyright @ The Author(s) 2013. This article is published with open access at Springerlink.comThis article has been made available through the Brunel Open Access Publishing Fund.In this paper, we focus on an initiative in England devised to prepare non-mathematics graduates to train as secondary mathematics teachers through a 6-month Mathematics Enhancement Course (MEC) to boost their subject knowledge. The course documentation focuses on the need to develop “understanding mathematics in-depth” in students in order for them to become successful mathematics teachers. We take a poststructural approach, so we are not interested in asking what such an understanding is, about the value of this approach or about the effectiveness of the MECs in developing this understanding in their participants. Instead we explore what positions this discourse of “understanding mathematics in-depth” makes available to MEC students. We do this by looking in detail at the “identity work” of two students, analysing how they use and are used by this discourse to position themselves as future mathematics teachers. In doing so, we show how even benign-looking social practices such as “understanding mathematics in-depth” are implicated in practices of inclusion and exclusion. We show this through detailed readings of interviews with two participants, one of whom fits with the dominant discourses in the MEC and the other who, despite passing the MEC, experiences tensions between her national identity work and MEC discourses. We argue that it is vital to explore “identity work” within teacher education contexts to ensure that becoming a successful mathematics teacher is equally available to all.King’s College Londo