Teachers’ ability to identify and explain students’ actions in near and far figural pattern generalization tasks

Mouhayar, Rabih El; Jurdak, Murad

doi:10.1007/s10649-012-9434-6

Cited by 25 publications

(14 citation statements)

References 19 publications

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“…To date, only a few studies directly addressed practicing teachers' noticing of student generalizations and justifications (e.g., LaRochelle et al, 2019;Melhuish, Thanheiser, Fasteen, & Fredericks, 2015;Melhuish, Thanheiser, & Guyot, 2020;Mouhayar & Jurdak, 2013). Studies that explored PSTs' noticing of student generalizations and justifications are even more scarce (e.g., Callejo & Zapatera, 2017).…”

Section: Teachers' Noticing Of Student Generalizations and Justificationsmentioning

confidence: 99%

“…They, however, did not interpret student understanding meaningfully. Mouhayar and Jurdak (2013) documented that teachers did not explain how students developed symbolic (algebraic) rules and justified general rules, even though they identified strategies students used to extend given patterns. Many teachers in Melhuish et al's (2020) study relied on surface clues while interpreting student generalizations and justifications without making in-depth observations of student thinking.…”

Section: Teachers' Noticing Of Student Generalizations and Justificationsmentioning

confidence: 99%

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Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records

Magiera

Zambak

2021

IJ STEM Ed

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Background This paper contributes to current discussions about supporting prospective teachers (PSTs) in developing skills of noticing students’ mathematical thinking. We draw attention to PSTs’ initial noticing skills (prior to instruction focused on supporting noticing) as PSTs engage in analyzing written artifacts of student work and video-records. We examined and compared PSTs’ noticing skills as they analyzed how students reason about, generalize, and justify generalizations of figural patterns given student written work and video records. We identified aspects of student thinking about generalizations and justifications, which PSTs addressed and interpreted. We also examined how PSTs respond to students as they analyze student thinking given written artifacts of student work or video-records of small group discussions, and we identified the foci of PSTs’ responding practice. Results Our data revealed that PSTs’ initial noticing skills of student generalizations and justifications differed while accounting for ways in which student thinking was externalized (written work or video-records). PSTs’ attending-and-interpreting and their responding practices were focused on mathematically significant aspects of student thinking to a greater extent in the context of analyzing written artifacts compared to video records. While analyzing students’ written work, PSTs demonstrated greater attention to ways in which students analyzed patterns, students’ generalization strategies, and justifications linked to an understanding of the pattern structure, compared to analyzing student thinking captured via videos. Conclusion Our results document that without providing any intentional support for PSTs’ noticing skills, PSTs are more deliberate to focus on mathematically significant aspects of student thinking while analyzing written artifacts of student work compared to video-records. We believe that the analysis of student written work might demand from PSTs to be more analytical. While examining written representations, PSTs have to reconstruct students’ reasoning. Unlike the videos where the students tell or use gestures to express their thinking, written work provides fewer clues about student thinking. Thus, written work demands a deeper level of engagement from PSTs as they strive to understand student reasoning. Our study extends research on PSTs’ noticing skills by documenting differences in PSTs’ noticing in relation to the nature of artifacts of student work that PSTs analyze. Our work also adds to prior research on PSTs’ noticing by characterizing specific aspects of students’ thinking about pattern generalizations and justifications that PSTs address as they analyze student thinking and respond to students.

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Section: Teachers' Noticing Of Student Generalizations and Justificationsmentioning

confidence: 99%

Section: Teachers' Noticing Of Student Generalizations and Justificationsmentioning

confidence: 99%

Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records

Magiera

Zambak

2021

IJ STEM Ed

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“…Researchers have also attempted to explain teacher knowledge for particular mathematical topics, such as algebra (e.g., functions), probability and statistics (Graeber & Tirosh, 2008). However, there is not much research in the literature about teachers" knowledge and practice of algebra (Doerr, 2004;El Mouhayar & Jurdak, 2013;Wilkie, 2014). The studies in the past about teachers" SMK generally focused on functions, slopes, and equations (e.g.…”

Section: Conceptual Frame Of Teacher Knowledgementioning

confidence: 99%

“…Most of the studies in current research literature have examined algebraic expressions within other algebra topics such as equations, patterns or functions (e.g. El Mouhayar & Jurdak, 2013;Even, 1990;Even et al, 1993;Ferrini-Mundy et al, 2006;Wilkie, 2014). Therefore, there is not much research about teachers" knowledge of manipulation of algebraic expressions as topic-specific knowledge and at middle school level (10-13 years).…”

Section: Teachers' Knowledge Of Algebraic Expressionsmentioning

confidence: 99%

Examining Two Middle School Mathematics Teachers’ Knowledge for Teaching Manipulation of Algebraic Expressions during Lesson Planning and Instruction

Yıldız¹,

Akyüz²

2019

Turkish Journal of Computer and Mathematics Education (TURCOMAT)

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Teachers use their content and pedagogical content knowledge for teaching algebra. For this reason, the examination of how teachers use this knowledge may help shed light on how students learn algebra, especially in determining why they usually have difficulties. The aim of the current study is to reveal what teachers know, and propose what they actually need to know for teaching the simplification and equivalence of algebraic expressions. The multiple-case study design was used for this study to compare and contrast the two middle school teachers" lesson planning and instruction. The data corpus included lesson plans, actual instruction records, and post-observation interviews. Data analysis was conducted using the Mathematical Knowledge for Teaching (MKT) model. The findings indicated that both teachers had a lack of specialized content knowledge about mathematical representations such as algebra tiles. They did not use algebra tiles effectively and could not link algebraic and geometric representations that underlie the idea of multiplication. It was observed that both teachers generally used unknowns and variables interchangeably indicating the inadequacy of their common content knowledge. In the planning process, the two teachers were able to state the common misconceptions that the students generally had and the ways of addressing them. Through the cases of these two teachers, it was observed that teachers need to have a good conceptual mathematical understanding and also knowledge of students" thinking in order to design effective lessons. Based on the findings, the types of knowledge that the teachers need to have are outlined and the theoretical and practical implications of the study are discussed.

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“…The teacher has the important task of advancing and looking out for the inductive reasoning of the students, as well as helping them to recognize its limitations and possibilities (NCTM, 2000). In addition, teachers need the ability to identify abductive and inductive actions in order to notice and explain students' actions when generalizing from particular instances (El Mouhayar & Jurdak, 2013;Rivera & Becker, 2007). In this regard, previous research has shown that teaching and noticing forms of mathematical reasoning, including inductive, has been cognitively challenging for teachers (Callejo & Zapatera, 2017;Herbert, Vale, Bragg, Loong, & Widjaja, 2015;Melhuish, Thanheiser, & Guyot, 2018;Stylianides, Stylianides, & Traina, 2013).…”

Section: Introductionmentioning

confidence: 99%

Characterization of Inductive Reasoning in Middle School Mathematics Teachers in a Generalization Task

Moguel

Landa

Cabañas-Sánchez

2019

Int Elect J Math Ed

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This paper reports on the characterization of the inductive reasoning used by middle school mathematics teachers to solve a task of generalization of a quadratic pattern. The data was collected from individual interviews and the written answers to the generalization task. The analysis was based on the representations and justifications used to move from particular cases to the formulation of the general rule. Three processes characterize the inductive reasoning of the mathematics teachers to obtain a general rule: observation of regularities, establishment of a pattern and formulation of a generalization; while some teachers revealed problems in moving from the observation of regularities to the formulation of a generalization. Therefore, some difficulties in generalizing associated with these processes are also mentioned.

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Teachers’ ability to identify and explain students’ actions in near and far figural pattern generalization tasks

Cited by 25 publications

References 19 publications

Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records

Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records

Examining Two Middle School Mathematics Teachers’ Knowledge for Teaching Manipulation of Algebraic Expressions during Lesson Planning and Instruction

Characterization of Inductive Reasoning in Middle School Mathematics Teachers in a Generalization Task

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