scholarly journals Secondary mathematics teachers' informal inferential reasoning : the role of knowledge structures for measures of center, spread and shape

2017 ◽  
Author(s):  
◽  
Christopher Engledowl
Keyword(s):  
Mathematics Teachers ◽  
Secondary Mathematics ◽  
Knowledge Structures ◽  
Future Research ◽  
Inferential Reasoning ◽  
Pedagogical Content ◽  
Secondary Mathematics Teachers ◽  
Informal Inferential Reasoning ◽  
Construct Maps ◽  
Measures Of Center

This study examined middle and secondary mathematics teachers' knowledge structures, informal inferential reasoning (IIR), and pedagogical content knowledge (PCK) for statistics. Using task-based clinical interviews (Goldin, 1997) and cross-case analysis (Creswell, 2013), a stratified purposeful sample (Patton, 2002) of nine teachers responded to the Goals and Outcomes Associated with Learning Statistics (GOALS-2) instrument (Sabbag and Zieffler, 2015), released items from the Levels of Conceptual Understanding in Statistics (LOCUS) assessment (Jacobbe, 2016) and supplemental questions to assess PCK (Watson et al., 2008). Responses were used to construct maps of teachers' knowledge structures for measures of center, spread, and shape (Groth and Bergner, 2013) and knowledge structures were analyzed for common characteristics. Teachers' IIR was coded for the appropriateness of responses (Means and Voss, 1996) and key components of IIR (Makar and Rubin, 2009) were identified. To distinguish teachers' PCK level, descriptions of four hierarchical levels were used (Callingham and Watson, 2011) and knowledge structures were classified as desirable-connected, undesirable-connected, and undesirable-disconnected. Although teachers largely engaged in the inference and data components of IIR, they rarely referenced the uncertainty component. In general, teachers with more connected knowledge structures and fewer undesirable knowledge elements exhibited more acceptable forms of IIR and higher PCK levels. Within IIR contexts, teachers struggled to exhibit acceptable forms of IIR and demonstrated the lowest levels of PCK, but within non-IIR contexts, they exhibited acceptable reasoning more often as well as higher PCK levels. Implications for teacher education are discussed and recommendations for future research are offered.

Interactive Whiteboards

2015 ◽  
pp. 288-307
Author(s):  
Tracy Goodson-Espy ◽  
Lisa Poling
Keyword(s):  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Mathematics Teachers ◽  
Secondary Mathematics ◽  
Technological Pedagogical Content Knowledge ◽  
Interactive Whiteboards ◽  
Mathematical Tasks ◽  
Pedagogical Content ◽  
Secondary Mathematics Teachers ◽  
Critical Mathematics

This chapter examines the literature on the use of Interactive Whiteboards (IWBs) in secondary mathematics instruction and notes barriers and achievements. The chapter links the use of IWBs to models for teaching Technological Pedagogical Content Knowledge (TPACK). Specifically, it proposes ways in which pre-service secondary mathematics teachers can be prepared to use IWBs to help their students develop understanding of critical mathematics ideas while engaging with worthwhile mathematical tasks and engaging in meaningful discourse.

Interactive Whiteboards

TPACK ◽  
2019 ◽  
pp. 401-416
Author(s):  
Tracy Goodson-Espy ◽  
Lisa Poling
Keyword(s):  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Mathematics Teachers ◽  
Secondary Mathematics ◽  
Technological Pedagogical Content Knowledge ◽  
Interactive Whiteboards ◽  
Mathematical Tasks ◽  
Pedagogical Content ◽  
Secondary Mathematics Teachers ◽  
Critical Mathematics

This chapter examines the literature on the use of Interactive Whiteboards (IWBs) in secondary mathematics instruction and notes barriers and achievements. The chapter links the use of IWBs to models for teaching Technological Pedagogical Content Knowledge (TPACK). Specifically, it proposes ways in which pre-service secondary mathematics teachers can be prepared to use IWBs to help their students develop understanding of critical mathematics ideas while engaging with worthwhile mathematical tasks and engaging in meaningful discourse.

scholarly journals Mathematics-for-teaching: Insights from the case of annuities

Pythagoras ◽  
2014 ◽  
Vol 35 (1) ◽  
Author(s):  
Craig Pournara
Keyword(s):  
Content Knowledge ◽  
Mathematics Teachers ◽  
Secondary Mathematics ◽  
Financial Mathematics ◽  
Contextual Knowledge ◽  
Pedagogical Content ◽  
Secondary Mathematics Teachers ◽  
Knowledge For Teaching ◽  
Mathematics Knowledge ◽  
Mathematics For Teaching

Shulman’s notations of subject matter knowledge (SMK) and pedagogical content knowledge (PCK) have been very influential in education research on teachers’ knowledge for teaching. However, there is little empirical evidence in support of these as separate analytical constructs. Furthermore, attempts to distinguish SMK and PCK highlight the complex and multidimensional nature of teachers’ knowledge and hence the difficulty of separating SMK and PCK. The author adopts the notion of mathematics-for-teaching (MfT) and argues that teachers’ knowledge for teaching annuities comprises knowledge of mathematical aspects, knowledge of pedagogical aspects and contextual knowledge of finance. Drawing from a larger study in which the author taught a financial mathematics course to pre-service secondary mathematics teachers, four examples of teachers’ knowledge for teaching annuities are identified, each of which illustrates how knowledge of mathematics, knowledge of pedagogy and contextual knowledge of finance are intertwined.

Pedagogical content knowledge and content knowledge of secondary mathematics teachers.

2008 ◽  
Vol 100 (3) ◽  
pp. 716-725 ◽  
Author(s):  
Stefan Krauss ◽  
Martin Brunner ◽  
Mareike Kunter ◽  
Jürgen Baumert ◽  
Werner Blum ◽  
...  
Keyword(s):  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Mathematics Teachers ◽  
Secondary Mathematics ◽  
Pedagogical Content ◽  
Secondary Mathematics Teachers

scholarly journals Deficits in the Statistical and Probabilistic Literacy of Citizens: Effects in a World in Crisis

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1872
Author(s):  
Laura Muñiz-Rodríguez ◽  
Luis J. Rodríguez-Muñiz ◽  
Ángel Alsina
Keyword(s):  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Mathematics Teachers ◽  
Data Science ◽  
Professional Competence ◽  
Group Discussion ◽  
Real Data ◽  
Secondary Mathematics ◽  
Pedagogical Content ◽  
Secondary Mathematics Teachers

The emergency caused by coronavirus disease 2019 (COVID-19) has revealed significant deficiencies in citizens’ statistical and probabilistic knowledge and in people’s understanding of mathematical and, particularly, stochastic models, which may lead to wrong personal or institutional choices, with critical consequences for the entire population. Mathematics teachers play an essential role in ensuring citizens’ statistical and probabilistic literacy. This study aimed at analyzing the pedagogical content knowledge that teachers utilized to teach statistics and probability through considering contextualized situations. In order to accomplish this purpose, fourteen secondary mathematics teachers participated in a formative and evaluative activity that was designed using the transformational professional competence model. During each evaluative phase, a group discussion was conducted. Participants were asked to reflect on their actions when promoting statistical and probabilistic literacy by considering a range of topics (data science, didactic resources, and methodological approaches) that were addressed during the training phase. A mixed, quantitative–qualitative methodological design was used for the data collection and analysis, which involved open-ended, multiple-choice, or scale-type questions that were moderated by the Metaplan® approach and the Mentimeter® software. The main ideas that emerged from the results indicated the need to reinforce the use of real data, technological resources to handle the visualization of information, the elaboration of different types of graphs besides the classical ones, and the formulation of hypotheses. The initial diagnosis will continue within a research and practice community made up of teachers and researchers. Therefore, a working proposal based on examples and models contextualized within the COVID-19 crisis is presented in order to enhance secondary mathematics teachers’ pedagogical content knowledge.

scholarly journals PCK development of beginning secondary mathematics teachers

2019 ◽  
Author(s):  
◽  
Rebecca Bruton
Keyword(s):  
Mathematics Teachers ◽  
Secondary Mathematics ◽  
Student Understanding ◽  
Curriculum Materials ◽  
First Year ◽  
Detailed Knowledge ◽  
Or Education ◽  
Pedagogical Content ◽  
Secondary Mathematics Teachers ◽  
Use Of Assessment

In this study I examined the development of pedagogical content knowledge of three beginning secondary mathematics teachers. My analysis included the development of the teachers' knowledge of curriculum and their knowledge of student understanding during their first two years of teaching. The participants began the study with little or no experience or education regarding the teaching of mathematics. During the first year of the study, all three participants were enrolled in graduate level mathematics methods courses and were under the guidance of a mentor teacher. Using existing research, I analyzed pre and post interviews as well as 12 interviews conducted during 4 observation cycles. Beyond participant interviews, I analyzed interviews with the mentor teachers and researcher notes regarding their observation of the participants' PCK. Analysis revealed that participants demonstrated little knowledge of curriculum at the beginning of the study. Throughout the study, their knowledge of the curriculum developed differently as they approached teaching in different ways (seen through their goals for instruction) and engaged with their curriculum materials differently. Two of the participants developed detailed knowledge of their students' understanding, which they gained through use of their standards-based curriculum materials and their use of assessment, while the third participant was only able to speak to student understanding at the whole-class level.

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