Elementary school teachers’ noticing of essential mathematical reasoning forms: justification and generalization

Melhuish, Kathleen; Thanheiser, Eva; Guyot, Layla

doi:10.1007/s10857-018-9408-4

Cited by 33 publications

(29 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This work characterises how four primary-school in-service teachers develop the mathematical practices of conjecturing and proving. Melhuish et al (2018) have recently affirmed that a "teacher must be able to notice mathematical reasoning forms such as justifying and generalizing" (p. 2) (herein named proving and conjecturing). In this regard, the results of this study highlight aspects of these practices (such as the use of examples or the need for more formal mathematical activities) which might report on professional development so that in-service teachers would be able to notice different forms of mathematical reasoning (Hidayah, Sa'dijah, Subanji, & Sudirman, 2020;Lesseig, 2016) in order to foster mathematical practices in the classroom.…”

Section: Resultsmentioning

confidence: 99%

“…This research field may contribute, among others, towards the design of professional development activities, towards the professional noticing of mathematical practices, and consequently towards the promotion of students' understanding of these practices and towards their engagement therein. In this respect, several interesting contributions focus on conjecturing and proving, and include: the research by Knuth (2002), which analyses teachers' conceptions of the role and nature of proof; the study by Ko (2010), which reviews mathematics teachers' conceptions of proof and discusses possible implications for educational research; the paper by Melhuish, Thanheiser, and Guyot (2018) on professional noticing of the mathematical practices of generalising (conjecturing) and justifying (argumentation and proof); and the research by Lesseig (2016), which studies teachers' conjecturing, generalising and justifying behaviour when becoming involved in a classic number theory task that invokes these three mathematical practices. Other recent contributions on this topic by Astawa, Budayasa, and Juniati (2018) and by Oktaviyanthi, Herman, and Dahlan (2018) have studied the process of future mathematics teacher cognition in constructing mathematical conjecture and the way in which future mathematics teacher can prove the limit of a function by formal definition, respectively.…”

mentioning

confidence: 99%

See 1 more Smart Citation

A Case Study on How Primary-School in-Service Teachers Conjecture and Prove: An Approach From the Mathematical Community

2021

View full text Add to dashboard Cite

This paper studies how four primary-school in-service teachers develop the mathematical practices of conjecturing and proving. From the consideration of professional development as the legitimate peripheral participation in communities of practice, these teachers’ mathematical practices have been characterised by using a theoretical framework (consisting of categories of activities) that describes and explains how a research mathematician develops these two mathematical practices. This research has adopted a qualitative methodology and, in particular, a case study methodological approach. Data was collected in a working session on professional development while the four participants discussed two questions that invoked the development of the mathematical practices of conjecturing and proving. The results of this study show the significant presence of informal activities when the four participants conjecture, while few informal activities have been observed when they strive to prove a result. In addition, the use of examples (an informal activity) differs in the two practices, since examples support the conjecturing process but constitute obstacles for the proving process. Finally, the findings are contrasted with other related studies and several suggestions are presented that may be derived from this work to enhance professional development.

show abstract

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

A Case Study on How Primary-School in-Service Teachers Conjecture and Prove: An Approach From the Mathematical Community

2021

View full text Add to dashboard Cite

show abstract

“…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%

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

View full text Add to dashboard Cite

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.

show abstract

“…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). For example, El Mouhayar (2018) points out that recognizing properties and relationships of general aspects of a pattern in far generalization tasks is complex for them.…”

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

View full text Add to dashboard Cite

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.

show abstract

Elementary school teachers’ noticing of essential mathematical reasoning forms: justification and generalization

Cited by 33 publications

References 16 publications

A Case Study on How Primary-School in-Service Teachers Conjecture and Prove: An Approach From the Mathematical Community

A Case Study on How Primary-School in-Service Teachers Conjecture and Prove: An Approach From the Mathematical Community

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

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

Contact Info

Product

Resources

About