International Symposium Elementary Maths Teaching Equity and diversity in elementary mathematics education Charles University Faculty of Education Prague, the Czech Republic August 20 – 25, 2017 International Symposium Elementary Maths Teaching Prague, the Czech Republic Charles University, Faculty of Education August 20 - 25, 2017 Proceedings Equity and diversity in elementary mathematics education Edited by Jarmila Novotná and Hana Moraová Prague 2017 International Symposium Elementary Mathematics Teaching Prague, the Czech Republic Charles University, Faculty of Education August 20 - August 25, 2017 International Programme Committee Olive Chapman (Canada), Chair, Marie-Pierre Chopin (France), Brian Doig (Australia), Rose Griffiths (United Kingdom), Alena Hospesova (Czech Republic), Antonin Jancarik (Czech Republic), Esther Levenson (Israel), Jarmila Novotna (Czech Republic), Marta Pytlak (Poland), Petra Scherer (Germany) Advisory Board: Tuba Gökcek (Turkey), David Pugalee (USA), Annie Savard (Canada), Ewa Swoboda (Poland), Dina Tirosh (Israel) Organizing Committee Jarmila Novotná, Hana Moraová, Antonín Jančařík The papers presented at SEMT ‘17 have all undergone a rigorous blind reviewing process by members of the International Programme Committee and Advisory Board. Posters represent work in progress and are not reviewed. Since all papers and other presentations here are presented in English, which is not usually the first language of the presenters, the responsibility for spelling and grammar lies with the authors of the papers themselves. © Charles University, Faculty of Education, Prague, 2017 ISBN 978-80-7290-955-1 TABLE OF CONTENTS Plenary lectures………………………………………...……………………………... 9 H. P. Ginsburg & C. Uscianowski: Stories, stories and more math stories ………… 9 M. Graven: Blending elementary mathematics education research with development for equity – an ethical imperative enabling qualitatively richer work …………… 20 T. Janík: From content to meaning: Semantics of teaching in the tradition of Bildung- centred didactics ……………..…………………………….……………………. 31 E. S. Levenson: Promoting mathematical creativity in heterogeneous classes….…... 42 Research reports ...……………………………………………………………………. 53 L. Bacon, N. Bednarz, C. Lajoie, J.-F. Maheux & M. Saboya: Two perspectives on diversity based on the pedagogical consultant’s work on problem-solving in a teaching context ……………………………………………………………….… 53 Y. Biton, S. Hershkovitz, M. Hoch, B. Ben-David & O. Fellus: Assessment issues that trouble mathematics teachers……………….....................................………………. 63 N. Blundell, K. Bentley, B. A. Temple & D. K. Pugalee: Kinesthetic & Creative Approaches to Pre-K Spatial Geometry Learning: A Qualitative Case Study.….. 72 G. Bolondi, C. Cascella & C. Giberti: Highlights on gender gap from Italian standardized assessment in mathematics ………………………………………… 81 M. Brožová: The use of textbooks in different approaches – Hejny method, Montessori and traditional approach in the Czech Republic………………..….... 91 M. Bruna & R. Havlíčková: Parameters influencing difficulty of word problems – A case of four word problems in grade 4 ..……………..…………………………... 100 I. Budínová: Progressive development of perception of the concept of a square by elementary school pupils ……………...…………...……………………………. 109 R. Cabassut: Diversity of teachers’ beliefs on modelling through a French-Spanish comparison …......……………………………………………………………….. 119 C. Chambris: Changes in the teaching of numbers and ratios in the primary curriculum...………………………………………………………………...….… 128 O. Chapman: Prospective elementary school teachers’ learning trajectory of the numeration system……………………………………………………………….. 138 V. Cifarelli, M. Stephan, D. K. Pugalee & C. Wang: Implementing an instructional sequence for solving net worth problems ….………………………………….… 148 A. Duatepe-Paksu, Ľ. Rybanský & K. Žilková: The content knowledge about rhombus of Turkish and Slovak pre-service elementary teachers ...………….……………. 158 F. Favilli: Mirror curves and basic arithmetics …………...………………………… 168 D. Goetze: Language- and mathematics-integrated intervention for understanding division and divisibility…………………………………….……………….…… 177 K. Hähn: Analyses of learning situations in inclusive settings: a coexisting learning situation in a geometrical learning environment...…...……….….……………… 187 H. Haydar: Elementary Mathematics Teachers Celebrating Student Voice: The Clinical Interview Again and Again……………………………………..………. 197 A. Hošpesová, I. Stuchlíková & I. Žlábková: Introduction of formative peer assessment in primary mathematics from the pupils’ perspective....…………..… 205 3 J. Hunter & J. Miller: Using cultural tasks to develop growing pattern generalisations For young culturally diverse students ……............................................................. 215 A. Jančařík: The potential of the chess environment in mathematics education – Pre- service teachers’ perspective ...………………………………………….……….. 225 D. Jirotková & J. Slezáková: Do teachers understand their pupils?..….……………... 235 D. Jirotková & J. Slezáková: Student teachers’ didactical competences in mathematics …...………………………………………………………………… 245 M. Kaslová: Diversity of results in research in the domain of pre-school mathematics at kindergarten ...………….……………………………………………………... 255 L. Kasmer, D. Harrison & E. Billings: Equitable learning opportunities: Textbook language accessibility in English medium classes….…………………………… 265 J. Kopáčová & K. Žilková: Pyramid or triangle - Isn’t it and the same? (A case study) 272 L. Korten: The investigation of co-operative-interactive learning situations in an inclusive arithmetic classroom………………..……………………….……...…. 282 R. Lambert, P. Baddouh, E. Merrill, A. Ferrara, C. Wang & C. Martin: The implementation of a statewide kindergarten entry assessment of object counting... 292 B. Lazić & J. Milinković: Using multiple representations of fractions to enhance problem solving ……………………………………………………………….…. 301 A. Lipovec & J. Ferme: The use of the reference point strategy for measurement estimation ….……………………………………………………………….……. 311 A. Lipovec & M. Podgorošek: Students’ visual representation of fractions and exponentiation …………………………………………..……………………….. 319 C. Martin, R. G. Lambert, C. Wang & D. Polly: Supporting mathematics learning through project based learning: A fifth grade case study ………...……………... 328 H. Moraová & J. Novotná: Higher order thinking skills in CLIL lesson plans of pre- service teachers …...……………………………..…………………...………….. 336 A. Sáenz-Ludlow: Children’s progressive construction of number and numerals by means of numerical diagrams……………………………………………….….... 345 L. Samková: Planning and conducting inquiry based mathematics course for future primary school teachers ………………………………………………………..... 354 P. Scherer: Preparing pre-service teachers for inclusive mathematics classrooms – concepts for primary education …………………………………………….…..... 364 C. Schöttler & U. Häsel-Weide: Students constructing meaning for the decimal system in dyadic discussions: epistemological and interactionist analyses of negotiation processes in an inclusive setting ……………………………….….... 373 J. Slezáková, D. Jirotková & J. Kloboučková: Student portfolio as a tool for development of pre-service primary teachers’ competences in teaching mathematics ………………..……………………………………………….….... 383 D. Stott: Interactive gesturing: deepening understanding of mathematical activity with young learners in a South African context…………………………….….... 393 E. Thanheiser & R. Philipp: Do prospective elementary teachers (in the United States) notice cultural aspects of mathematics in a teaching scenario?……..….... 403 V. Tůmová: How do pupils of the 5th and 6th grade structure space ….…………..... 411 N. Venuto & L. C. Hart: First graders write about mathematics: A teaching experiment …………………………….………………………………………..... 421 J. Višňovská & J. L. Cortina: Learning to support all students’ fraction understanding 430 N. Vondrová & J. Novotná: The influence of context and order of numerical data on the difficulty of word problems for grade 6 pupils……...……………….….......... 440 4 D. Walter: On the representation of quantities with multi-touch at the ‘Math- Tablet’……………………………………………………………………………. 449 R. Zemanová, D. Jirotková & J. Slezáková: Practical component of mathematics education of pre-service primary school teachers: students’ perspective ……….. 459 K. Žilková, J. Kopáčová & Ľ. Rybanský: Similarities and differences in identification of rectangles of fourth-grade pupils………………………………………….….... 466 Workshops .…………………………………………………………………………… 477 D. Clarke, C. Mesiti, J. Novotná, H. Moraová & M. C. E. Chan: Speaking in and about the mathematics classroom……………………………………….………. 477 B. Doig & S. Groves: Mathematical tasks stimulating student problem solving strategies ……………………………………………………………………….... 479 L. Samková: A pathway to inquiry..………………………….....…………………... 480 A. Savard & E. Polotskaia: Shifting paradigm in problem solving: algebraic versus arithmetic thinking………………………………………………………....…….. 482 P. Scherer, K. Hähn, C. Rütten & S. Weskamp: Primary students explore mathematics at the university – Activities for all ……………………………….. 484 D. Tirosh, P. Tsamir, E. Levenson & R. Barkai: Using tablets in preschool: patterns and number concept ……………………………………...……………………… 486 Posters ......…………………………………………………………………………...... 489 A. Duatepe-Paksu & B. Boz-Yaman: Evoking and examining geometric habits of mind while constructing tetrahedron by modular origami..……………………... 489 A. Hošpesová & M. Tichá: Problem posing in prospective primary school