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Cognition and Instruction Volume 28, 2010 - Issue 3
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Original Articles

From Addition to Multiplication … and Back: The Development of Students’ Additive and Multiplicative Reasoning Skills

Wim Van Dooren Katholieke Universiteit Leuven
,
Dirk De Bock Katholieke Universiteit Leuven and Hogeschool-Universiteit Brussel
&
Lieven Verschaffel Katholieke Universiteit Leuven
Pages 360-381 | Published online: 05 Jul 2010

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Simone Passarella. (2022) Emergent modelling to introduce the distributivity property of multiplication: a design research study in a primary school. International Journal of Mathematical Education in Science and Technology 53:10, pages 2774-2796.
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Asha K. Jitendra, Michael R. Harwell, Stacy R. Karl, Soo-hyun Im & Susan C. Slater. (2021) Investigating the Generalizability of Schema-Based Instruction Focused on Proportional Reasoning: A Multi-State Study. The Journal of Experimental Education 89:4, pages 587-604.
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Margaret M. Flores & Jessica H. Milton. (2020) Teaching the Partial Products Algorithm Using the Concrete-representational-abstract Sequence. Exceptionality 28:2, pages 142-160.
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Rukiye Ayan & Mine Isiksal-Bostan. (2019) Middle school students’ proportional reasoning in real life contexts in the domain of geometry and measurement. International Journal of Mathematical Education in Science and Technology 50:1, pages 65-81.
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Tine Degrande, Lieven Verschaffel & Wim Van Dooren. (2017) Spontaneous Focusing on Quantitative Relations: Towards a Characterization. Mathematical Thinking and Learning 19:4, pages 260-275.
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Asha K. Jitendra, Barbara Dougherty, Victoria Sanchez, Michael R. Harwell & Sydney Harbour. (2023) Building Conceptual Understanding of Multiplicative Reasoning Content in Third Graders Struggling to Learn Mathematics: A Feasibility Study. Learning Disabilities Research & Practice 38:4, pages 285-295.
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Juan Manuel González-Forte, Ceneida Fernández, Jo Van Hoof & Wim Van Dooren. (2022) Incorrect Ways of Thinking About the Size of Fractions. International Journal of Science and Mathematics Education 21:7, pages 2005-2025.
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Constanze Schadl & Stefan Ufer. (2023) Beyond linearity: Using IRT‐scaled level models to describe the relation between prior proportional reasoning skills and fraction learning outcomes. Child Development.
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Silvia Regina De Souza, Gabriele Gris, Jonas Gamba, Maria Luiza F. da Rocha & João Dos Santos Carmo. (2023) Adapted digital domino game: Teaching multiplication to children. CES Psicología 16:2, pages 46-61.
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Jérôme Proulx. (2023) Relative Proportional Reasoning: Transition from Additive to Multiplicative Thinking Through Qualitative and Quantitative Enmeshments. International Journal of Science and Mathematics Education.
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Robert Schoen, Ian Whitacre & Zachary Champagne. (2023) Word Problem Performance of U.S. First Graders in the 20th Century and Common Core Era. Journal for Research in Mathematics Education 54:1, pages 24-42.
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Yasemin Copur-Gencturk, Clare Baek & Tenzin Doleck. (2022) A Closer Look at Teachers’ Proportional Reasoning. International Journal of Science and Mathematics Education 21:1, pages 113-129.
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L. Verschaffel, B. De Smedt, K. Luwel, P. Onghena, J. Torbeyns & W. Van Dooren. 2023. Mathematical Challenges For All. Mathematical Challenges For All 25 50 .
Zhenzhen Miao, Christian Bokhove, David Reynolds & Charalambos Y. Charalambous. (2023) Rational numbers and proportional reasoning in Chinese primary schools: Patterns, latent classes, and reasoning processes. Asian Journal for Mathematics Education 1:4, pages 408-436.
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María Burgos & Juan D. Godino. (2021) Prospective Primary School Teachers’ Competence for the Cognitive Analysis of Students’ Solutions to Proportionality TasksDie Kompetenz angehender Grundschullehrkräfte zur kognitiven Analyse von Schülerlösungen zu Proportionalitätsaufgaben. Journal für Mathematik-Didaktik 43:2, pages 347-376.
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Elien Vanluydt, Lieven Verschaffel & Wim Van Dooren. (2022) The role of relational preference in word-problem solving in 6- to 7-year-olds. Educational Studies in Mathematics 110:3, pages 393-411.
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Surani Joshua & Mi Yeon Lee. (2022) Incoherencies in elementary pre-service teachers’ understanding of calculations in proportional tasks. International Electronic Journal of Mathematics Education 17:4, pages em0698.
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María Burgos & Juan D. Godino. (2020) Prospective primary school teachers’ competence for analysing the difficulties in solving proportionality problem. Mathematics Education Research Journal 34:2, pages 269-291.
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Christian Thurn, Daniela Nussbaumer, Ralph Schumacher & Elsbeth Stern. (2022) The Role of Prior Knowledge and Intelligence in Gaining from a Training on Proportional Reasoning. Journal of Intelligence 10:2, pages 31.
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María José Castillo Céspedes & María Burgos Navarro. (2022) Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons. Eurasia Journal of Mathematics, Science and Technology Education 18:6, pages em2121.
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Jenny R. Root, Sarah K. Cox & M. Addie McConomy. (2022) Teacher-Implemented Modified Schema-Based Instruction with Middle-Grade Students with Autism and Intellectual Disability. Research and Practice for Persons with Severe Disabilities 47:1, pages 40-56.
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E. Vanluydt, L. Verschaffel & W. Van Dooren. (2022) The role of relational preference in early proportional reasoning. Learning and Individual Differences 93, pages 102108.
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Pınar Anapa Saban & Merve Koçyiğit Gürbüz. (2021) Authentic Investigation Activities for Reasoning Ratio Concept. Acta Didactica Napocensia 14:2, pages 257-274.
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Rukiye AYAN CİVAK, Mine IŞIKSAL & Seçil YEMEN KARPUZCU. (2021) Erken Orantısal Akıl Yürütmeye Yönelik Öğrenme Rotasının Geliştirilmesi: Bir Tasarı AraştırmasıDevelopment of a Learning Trajectory for Early Proportional Reasoning: A Design Research. Mersin Üniversitesi Eğitim Fakültesi Dergisi 17:3, pages 433-461.
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Kübra AÇIKGÜL. (2021) Developing a Two-Tier Proportional Reasoning Skill Test: Validity and Reliability StudiesDeveloping a Two-Tier Proportional Reasoning Skill Test: Validity and Reliability Studies. International Journal of Assessment Tools in Education 8:2, pages 357-375.
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Karen Zwanch & Jesse L. M. Wilkins. (2020) Releasing the conceptual spring to construct multiplicative reasoning. Educational Studies in Mathematics 106:1, pages 151-170.
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Jill Cheeseman, Ann Downton, Anne Roche & Sarah Ferguson. (2020) Investigating young students’ multiplicative thinking: The 12 little ducks problem. The Journal of Mathematical Behavior 60, pages 100817.
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Virginia J. Flood, Anna Shvarts & Dor Abrahamson. (2020) Teaching with embodied learning technologies for mathematics: responsive teaching for embodied learning. ZDM 52:7, pages 1307-1331.
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Mike Askew & Hamsa Venkat. (2020) Deconstructing South African Grade 1 learners’ awareness of number in terms of cardinality, ordinality and relational understandings. ZDM 52:4, pages 793-804.
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Tine Degrande, Lieven Verschaffel & Wim Van Dooren. (2020) To add or to multiply in open problems? Unraveling children’s relational preference using a mixed-method approach. Educational Studies in Mathematics 104:3, pages 405-430.
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Muhammet ARICAN. (2020) Investigating Preservice Teachers’ Determination and Representation of Proportional and Nonproportional Relationships in Terms of Problem ContextsÖğretmen Adaylarının Orantısal Olan ve Olmayan İlişkileri Belirleyebilme ve Temsil Edebilmelerinin Problem İçerikleri Açısından İncelenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi 14:1, pages 629-660.
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Sarah R. Powell, Katherine A. Berry & Sarah A. Benz. (2020) Analyzing the word-problem performance and strategies of students experiencing mathematics difficulty. The Journal of Mathematical Behavior 58, pages 100759.
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Margaret M. Flores, Alexcia J. Moore & Jill M. Meyer. (2020) Teaching the partial products algorithm with the concrete representational abstract sequence and the strategic instruction model. Psychology in the Schools 57:6, pages 946-958.
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Soo-hyun Im & Asha K. Jitendra. (2020) Analysis of proportional reasoning and misconceptions among students with mathematical learning disabilities. The Journal of Mathematical Behavior 57, pages 100753.
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Carly Sawatzki, Ann Downton & Jill Cheeseman. (2019) Stimulating proportional reasoning through questions of finance and fairness. Mathematics Education Research Journal 31:4, pages 465-484.
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Muhammet Arican. (2018) Preservice Mathematics Teachers’ Understanding of and Abilities to Differentiate Proportional Relationships from Nonproportional Relationships. International Journal of Science and Mathematics Education 17:7, pages 1423-1443.
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Tine Degrande, Lieven Verschaffel & Wim Van Dooren. (2019) To add or to multiply? An investigation of the role of preference in children's solutions of word problems. Learning and Instruction 61, pages 60-71.
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Keiko Hino & Hisae Kato. (2018) Teaching whole-number multiplication to promote children’s proportional reasoning: a practice-based perspective from Japan. ZDM 51:1, pages 125-137.
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Tine Degrande, Lieven Verschaffel & Wim Van Dooren. (2017) Beyond additive and multiplicative reasoning abilities: how preference enters the picture. European Journal of Psychology of Education 33:4, pages 559-576.
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Tine Degrande, Jo Van Hoof, Lieven Verschaffel & Wim Van Dooren. (2017) Open word problems: taking the additive or the multiplicative road?. ZDM 50:1-2, pages 91-102.
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Rukiye Ayan & Mine Isiksal Bostan. (2016) Middle School Students’ Reasoning in Nonlinear Proportional Problems in Geometry. International Journal of Science and Mathematics Education 16:3, pages 503-518.
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M Irfan, Sudirman & R Rahardi. (2018) Characteristics of students in comparative problem solving. Journal of Physics: Conference Series 948, pages 012007.
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Jessica M. Namkung, Lynn S. Fuchs & Natalie Koziol. (2018) Does initial learning about the meaning of fractions present similar challenges for students with and without adequate whole-number skill?. Learning and Individual Differences 61, pages 151-157.
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Kerstin Larsson, Kerstin Pettersson & Paul Andrews. (2017) Students’ conceptualisations of multiplication as repeated addition or equal groups in relation to multi-digit and decimal numbers. The Journal of Mathematical Behavior 48, pages 1-13.
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Daniel D. Hutto, Michael D. Kirchhoff & Dor Abrahamson. (2015) The Enactive Roots of STEM: Rethinking Educational Design in Mathematics. Educational Psychology Review 27:3, pages 371-389.
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Perihan Dinc Artut & Mustafa Serkan Pelen. (2015) 6th Grade Students’ Solution Strategies on Proportional Reasoning Problems. Procedia - Social and Behavioral Sciences 197, pages 113-119.
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Jill Fielding-Wells, Shelley Dole & Katie Makar. (2014) Inquiry pedagogy to promote emerging proportional reasoning in primary students. Mathematics Education Research Journal 26:1, pages 47-77.
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Annette Hilton, Geoff Hilton, Shelley Dole & Merrilyn Goos. (2013) Development and application of a two-tier diagnostic instrument to assess middle-years students’ proportional reasoning. Mathematics Education Research Journal 25:4, pages 523-545.
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Ceneida Fernández, Salvador Llinares & Julia Valls. (2012) Learning to notice students’ mathematical thinking through on-line discussions. ZDM 44:6, pages 747-759.
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Ruma Falk, Patricia Yudilevich-Assouline & Adily Elstein. (2012) Children’s concept of probability as inferred from their binary choices—revisited. Educational Studies in Mathematics 81:2, pages 207-233.
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Ceneida Fernández, Salvador Llinares, Wim Van Dooren, Dirk De Bock & Lieven Verschaffel. (2011) The development of students’ use of additive and proportional methods along primary and secondary school. European Journal of Psychology of Education 27:3, pages 421-438.
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