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Linchevski, Liora; Williams, Julian

doi:10.1023/a:1003726317920

Cited by 49 publications

(10 citation statements)

References 17 publications

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“…Other research has focused on improving students' sense-making and meaning-making around integers. For example, several design studies aiming to improve integer instruction have focused on providing realistic referents for the meaning of the integers to help students reason about them (e.g., Gregg & Gregg, 2007;Liebeck, 1990;Linchevski & Williams, 1999;Stephan & Akyuz, 2012).…”

Section: Prior Research On Genesis: Symmetry Systems Support Additivementioning

confidence: 99%

Learning to “See” Less Than Nothing: Putting Perceptual Skills to Work for Learning Numerical Structure

Tsang

Blair

Bofferding

et al. 2015

Cognition and Instruction

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Section: Prior Research On Genesis: Symmetry Systems Support Additivementioning

confidence: 99%

Learning to “See” Less Than Nothing: Putting Perceptual Skills to Work for Learning Numerical Structure

Tsang

Blair

Bofferding

et al. 2015

Cognition and Instruction

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“…I have, with colleagues, illustrated the use of some of these in (1) analyses of studentworker communication in the workplace (Williams & Wake 2007a, b) and (2) analyses of learning trajectories in teaching experiments akin to that of Maschietto and Bartolini Bussi (2008), such as in the teaching of negative integers and strategies for two-digit subtraction (Koukkoufis & Williams 2006;Linchevski & Williams 1999;Williams, Linchevski & Kutscher 2008b). I will draw on two of these experiences now to add to the progress made in this volume and to draw attention to two important conceptions not much discussed in the six papers.…”

Section: This Issue-an Appreciation and Hypothesesmentioning

confidence: 99%

Embodied multi-modal communication from the perspective of activity theory

Williams

2008

Educ Stud Math

Self Cite

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I begin by appreciating the contributions in the volume that indirectly and directly address the questions: Why do gestures and embodiment matter to mathematics education, what has understanding of these achieved and what might they achieve? I argue, however, that understanding gestures can in general only play an important role in 'grasping' the meaning of mathematics if the whole object-orientated 'activity' is taken into account in our perspective, and give examples from my own work and from this Special Issue. Finally, I put forward the notion of a 'threshold' moment, where seeing and grasping at the nexus of two or more activities often seem to be critical to breakthroughs in learning.Keywords Activity theory . Unit of analysis . Pedagogy . Threshold moment PrefaceA large dog sat on the floor at the bar next to his owner, balefully eyeing me and other customers. I locked gaze with him and his sad-looking eyes responded; they suggested to me that he had been sitting there too long. I wondered if this was all in my imagination: do dogs speak to humans through their eyes? As I thought about it and about writing this paper, I laughed. The dog looked away; but then after a few moments he looked back at me, apparently to see if I was still watching him. The dog yawned, a huge gaping yawn that seemed to go on forever, and I felt impelled to yawn myself, and then I actually did yawn 1 .Do humans and dogs communicate non-verbally? I recall a dog that, when its owner returned from work, would fetch the lead in its teeth to show him, drop it at his feet, and then run to the front door. Cats on the other hand are very different, at least in their facial expressions-perhaps this is due to a different co-evolution of the two species with human Educ Stud Math (

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“…While positive numbers can be embodied in mind with real objects; about negative numbers, there are not any non-positive objects or object groups in physical world. So, with observing physical world it is not possible to gain informal knowledge (Linchevski & Williams, 1999;Mc Corkle, 2001). …”

Section: Introductionmentioning

confidence: 99%

“…Neutralization models are about negative and positive quantities consisted of concrete objects and number line models emphasized direction meaning of integers (Lytle, 1994). Advocates of these models also claim that they allow students to use the idea of inverse operations and additive inverses by recognizing that one could either take away positives or add negatives to achieve the same result (Semadeni, 1984;Linchevski & Williams, 1999). Some other researchers, on the other hand, criticized neutralization models due to the fact "they involve rules which are not consistent with the rules of mathematics" (Rousset, 2010;Star & Nurnberger-Haag, 2011;Vig, Murray, & Star, 2014).…”

Section: Introductionmentioning

confidence: 99%

Analyzing Problems Posed by Prospective Teachers Related to Addition and Subtraction Operations with Integers

Işik

2018

HES

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In this study, it was aimed to analyze the structure of prospective middle school mathematics teachers" problems posed with regard to given symbolic representation including addition and subtraction operations with integers. The study conducted with 96 last grade elementary school mathematics teacher candidates studying in Faculty of Education of Erciyes University in Turkey at the beginning of 2018 years. A Problem Posing Task including five items regarding addition and subtraction operations with integers and semi-structured interview forms were used as data gathering tools. Results indicated that prospective teachers had difficulties in choosing problem types with regard to the given operation structure. Prospective teachers presented less success in problem posing with integers having different signs. Besides, some of the prospective teachers used signs of integers and operations interchangeably and some others multiplied signs of integers and operations, and they gave meaning to the result of this multiplication while they were posing problems.

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Untitled

Cited by 49 publications

References 17 publications

Learning to “See” Less Than Nothing: Putting Perceptual Skills to Work for Learning Numerical Structure

Learning to “See” Less Than Nothing: Putting Perceptual Skills to Work for Learning Numerical Structure

Embodied multi-modal communication from the perspective of activity theory

Analyzing Problems Posed by Prospective Teachers Related to Addition and Subtraction Operations with Integers

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