How Students Verify Conjectures: Teachers’ Expectations

Bergqvist, Tomas

doi:10.1007/s10857-005-4797-6

Cited by 31 publications

(17 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As learners re-engage with tasks, informal mathematical conjectures often have their beginnings (Calder, Brown, Hanley, & Darby, 2006). Other researchers have noted that the development of mathematical conjecture and reasoning can be derived from intuitive beginnings (Bergqvist, 2005;Dreyfus, 1999).…”

Section: Introductionmentioning

confidence: 99%

Mathematics in student-centred inquiry learning: Student engagement

Calder

2013

tandc

View full text Add to dashboard Cite

. It is directed towards a professional audience and focuses on contemporary issues and research relating to curriculum pedagogy and assessment. ISSN 1174-2208 Notes for ContributorsTeachers and Curriculum welcomes:• research based papers with a maximum of 3,500 words, plus an abstract or professional summary of 150 words, and up to five keywords;• opinion pieces with a maximum of 1500 words; and• book or resource reviews with a maximum of 1000 words. FocusTeachers and Curriculum provides an avenue for the publication of papers that• raise important issues to do with the curriculum, pedagogy and assessment;• reports on research in the areas of curriculum, pedagogy and assessment;• provides examples of informed curriculum, pedagogy and assessment; and• review books and other resources that have a curriculum, pedagogy and assessment focus. Teachers and Curriculum, Volume 13, 2013ii Teachers and Curriculum, Volume 13, 2013Submitting articles for publication The article should clearly show where each is to appear within the text. All submissions must be submitted as word documents. Only the first page of the article should bear the title, the name(s) of the author(s) and the address to which reviews should be sent. In order to enable 'blind' refereeing, please do not include author(s) names on running heads. Foot/End Notes: These should be avoided where possible; the journal preference is for footnotes rather than endnotes.Referencing: References must be useful, targeted and appropriate. The Editorial preference is APA style; see Publication Manual of the American Psychological Association (Sixth Edition). Please check all citations in the article are included in your references list and in the correct style.Covering letter: When submitting a manuscript to Teachers and Curriculum, authors must, for ethical and copyright reasons, include in a covering letter a statement confirming that a) the material has not been published elsewhere, and b) the manuscript is not currently under consideration with any other publisher. A fax and email contact should also be supplied. Editorial: All contributions undergo rigorous peer review by at least two expert referees. The Editors reserve the right without consulting the author(s) to make alterations that do not result in substantive changes. The Editors' decisions about acceptance are final. Copyright: Publication is conditional upon authors giving copyright to the Faculty of Education, The University of Waikato. Requests to copy all or substantial parts of an article must be made to the Editors. Acknowledgement of ReviewersThe Editors would like to acknowledge the contribution of the reviewers.

show abstract

Section: Introductionmentioning

confidence: 99%

Mathematics in student-centred inquiry learning: Student engagement

Calder

2013

tandc

View full text Add to dashboard Cite

show abstract

“…In a related study, Tsamir, Tirosh, Dreyfus, Barkai, and Tabach () found teachers had very high expectations for students’ proof work, expecting students’ proofs to be both correct and minimal, when they examined arguments from hypothetical students. On the other hand, Bergqvist () found teachers initially underestimated students’ levels of reasoning, expecting few students to possess high enough levels of reasoning to verify the given conjectures. When presented with hypothetical student work, however, the teachers described more accurate expectations for students’ arguments.…”

Section: Related Literaturementioning

confidence: 99%

“…Teachers’ expectations for student arguments are likely related to their mathematical knowledge for teaching proof (MKT‐P) as described by Stylianides and Ball () and others. Previous research on teachers’ and prospective teachers’ expectations of students’ mathematical proof work primarily examined the accuracy of those expectations through their analysis of students’ proof attempts (Bergqvist, ) or other mathematical work (Pemberton & Galbraith, ). Little research has been conducted analyzing the rationales given by prospective secondary teachers regarding their expectations for students’ work in argumentation and proof.…”

mentioning

confidence: 99%

Prospective mathematics teachers’ expectations for middle grades students’ arguments

Suominen

Conner

Park

2018

School Sci & Mathematics

View full text Add to dashboard Cite

In this study, 15 prospective secondary (grades 6–12) mathematics teachers were asked to situate themselves as middle school (grades 6–8) mathematics teachers and validate arguments purported to prove that the sum of the first n odd natural numbers isn2. We examined their stated expectations for middle school students’ mathematical arguments and the rationales given for these expectations. Even though the participants were situated as middle grades teachers when evaluating hypothetical student arguments, not all of the participants embraced this perspective when discussing their expectations for middle school students’ arguments. In fact, only six participants embraced the teacher perspective, whereas nine participants relied, at least in some part, on their own experiences as students to determine their expectations for student work. In this article, we report five representative participants’ expectations and rationales to illustrate three emerging perspectives on prospective teachers’ expectations for middle school students’ arguments.

show abstract

“…Researchers often consider them as generalised statements, containing essences distilled from a number of specific examples (e.g. Bergqvist, 2005). They are often contextualised and constrained by defining statements, for which they hold true, unless identified as false conjectures.…”

Section: The Notion Of Conjecturementioning

confidence: 99%

Forming conjectures within a spreadsheet environment

et al. 2006

View full text Add to dashboard Cite

This paper is concerned with the use of spreadsheets within mathematical investigational tasks. Considering the learning of both children and pre-service teaching students, it examines how mathematical phenomena can be seen as a function of the pedagogical media through which they are encountered. In particular, it shows how pedagogical apparatus influence patterns of social interaction, and how this interaction shapes the mathematical ideas that are engaged with. Notions of conjecture, along with the particular faculty of the spreadsheet setting, are considered with regard to the facilitation of mathematical thinking. Employing an interpretive perspective, a key focus is on how alternative pedagogical media and associated discursive networks influence the way that students form and test informal conjectures. The study to be described was part of an ongoing research programme exploring how spreadsheets might function as pedagogical media, as compared with pencil and paper methods. As a tool for investigation, we asked, how might the study inform our understanding of the ways spreadsheets filter the learning experience? In particular, we asked how might spreadsheets influence learner's perceptions and understandings of mathematical phenomena? One aspect of this programme, to be pursued here, was to identify the ways in which participants approached mathematical investigations. We explored how they negotiated the requirements of the tasks, and how they produced their conjectures and generalisations.We commence by outlining the three core themes and some literature upon which these themes are premised. First, we introduce a hermeneutic theoretical perspective in which the process of understanding mathematical phenomena is seen as oscillating between individual encounter and social discourse. Understanding here is considered to be a function of the learner's interpretation and reflection, where such engagement gets fixed as conceptual phenomena. These concepts, however, evolve through further cycles of encounter as understanding develops. This understanding is thus manifest in what students say, and what they do. It is our contention that through an examination of participants' social interaction and output, we will gain insight into the ways students internalise mathematical understandings.Second, we review literature that underpins our concern with the particular qualities that spreadsheets bring to investigative mathematical processes. This enables us to differentiate patterns in the dialogue and output better, and, as a consequence, pinpoint the influence of spreadsheets on the learner's investigative trajectories. The assumption here is that spreadsheets filter

show abstract

How Students Verify Conjectures: Teachers’ Expectations

Cited by 31 publications

References 6 publications

Mathematics in student-centred inquiry learning: Student engagement

Mathematics in student-centred inquiry learning: Student engagement

Prospective mathematics teachers’ expectations for middle grades students’ arguments

Forming conjectures within a spreadsheet environment

Contact Info

Product

Resources

About