Investigating Mathematical Knowledge for Teaching Proof in Professional Development

Lesseig, Kristin

doi:10.21890/ijres.13913

Cited by 31 publications

(34 citation statements)

References 47 publications

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“…Justification and proof can have different levels. According to Lesseig (2016), the students' progress is from inductive or empirical justifications, towards deductive arguments. She developed a classification, organized in five levels of justification, that the students can present in a task (p. 260):…”

Section: Articulation Between Experimentation and Justification (Dimementioning

confidence: 99%

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Using tasks to develop pre-service teachers’ knowledge for teaching mathematics with digital technology

Rocha

2020

ZDM Mathematics Education

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Teacher education is central to the development of the professional knowledge of pre-service teachers. The main goal of this paper is to reflect on the development that the analysis (done by a group of pre-service secondary teachers) of a set of tasks, based on elements related to domains of KTMT-Knowledge for Teaching Mathematics with Technology-can bring to the knowledge of pre-service teachers of mathematics. Specifically, the goal was to investigate the following questions: (1) What are the factors that guide the pre-service teachers' task discussion? (2) Which KTMT domains are emphasized by pre-service teachers during task discussion? The elements taken into account are the characteristics of the tasks (focus on cognitive level, structuring level and technology role), the use of representations (focus on balance and articulation of representations), and the equilibrium between experimentation (focus on digital technology affordances) and justification (focus on argumentation and proof). The methodology of this case study involves a qualitative approach. The main conclusions suggest that influences in the pre-service teachers' discussion of tasks fell into the following categories: the potentialities of technology, the type of tasks, and the prospective teachers' experience with a set of tasks, and analysis of some real students' reports. With regard to KTMT, although it was possible to identify some global development, Teaching and Learning and Technology Knowledge was the domain in which stronger development took place.

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Section: Articulation Between Experimentation and Justification (Dimementioning

confidence: 99%

“…They are thus placing students in an external role regarding justification, assuming it should be based on an external element, in this case, the teacher. That is, they are considering justification at one of the lower levels of the Lesseig's (2016) classification.…”

Section: Stagementioning

confidence: 99%

Using tasks to develop pre-service teachers’ knowledge for teaching mathematics with digital technology

Rocha

2020

ZDM Mathematics Education

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“…These accomplishments are, in the researcher's view, important subject content knowledge (SCK) considerations. Lesseig [7] describes SCK as knowledge of students' typical conceptions and misconceptions of a specific content area.…”

Section: Research Question and Objectivesmentioning

confidence: 99%

High School Students’ Language Related Struggles with Contextualized Differential Equations

Ndemo¹

2019

IJAMTP

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Upon observing with concern that the majority of high school students experienced severe language related difficulties when solving contextualized differential equations, the researcher then decided to investigate the kinds of such challenges and their impact on students' learning of differential equations. A sample of 10 mathematics students was selected from one urban high school in one province in Zimbabwe. Written tasks and follow up interviews were employed as data collection tools for the study. Content analysis technique was applied to the written responses and interview transcriptions to obtain a revealing picture of how the kinds of the language related challenges interfere with the growth of mathematical content. The study revealed that the students struggled with interpreting and formulating differential equations from given mathematical situations. Further, interpretation of given initial conditions posed a challenge to the learners. A major consequence of these language related challenges was that the students could not generate complete solutions and lack of interplay between conceptual and procedural fluency was one of the insights generated from this study with regards to the learning of differential equations. The study findings have important implications for instruction in high school mathematics lessons such as the need to develop and foster the students' abilities to engage in adaptive reasoning and use multiple modes of presenting content in order to promote students' understanding of contextualized differential equations.

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“…The ability to think critically can be seen in their proofing ability in identifying several onto and one-to-one functions, or justify several theorems related to functions. Study of mathematical proof could develop the students' ability to think critically in other domains of explanation (Dawkins & Weber, 2017;Lesseig, 2016;Mata-Pereira & da Ponte, 2017;Reid, 2005). Seeing students' misconceptions in proving functions is one technique to see ability to think critically.…”

Section: Introductionmentioning

confidence: 99%

Identification of students’ misconceptions in proving onto and one-to-one function in abstract algebra using certainty response index

Mukmin

Fa'ani

2020

IJTLM

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<p>This research is aimed to identify students’ misconceptions in proving onto and one-to-one function in Abstract Algebra using CRI (Certainty Response Index), which is an instrument to distinguish misconceptions and errors. This research uses qualitative method. There are eighteen research participants, and they are Mathematics Education students in 3rd semester. Researcher asked participants to solve some problems related to mathematical proof. Then, participants gave score based on their belief or level of certainty. The result shows that ten students get misconceptions. They were weak in understanding the definition of onto and one-to-one function, and are not yet trained to proof onto and one-to-one function in Abstract Algebra. Further, this research also find that the errors of participants in proving mathematics are mainly influenced by errors in algebraic operation.</p>

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Investigating Mathematical Knowledge for Teaching Proof in Professional Development

Cited by 31 publications

References 47 publications

Using tasks to develop pre-service teachers’ knowledge for teaching mathematics with digital technology

Using tasks to develop pre-service teachers’ knowledge for teaching mathematics with digital technology

High School Students’ Language Related Struggles with Contextualized Differential Equations

Identification of students’ misconceptions in proving onto and one-to-one function in abstract algebra using certainty response index

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