Using data from teaching experiments and theories from quantitative reasoning, we built second-order accounts of students' mathematics with regards to how they conceived rate of change through operating on existing quantities. In this report, we explain three different ways STEM undergraduates structurally conceive rate of change as they…

This paper draws on numerous data sources to better understand the shift from additive to multiplicative thinking in years 4 to 9. Research studies that have used the Scaffolding Numeracy in the Middle Years assessment tasks have found that while students can be supported to move through the early and upper zones of the Learning and Assessment…

Literature typically describes mathematization, the process of transforming a real-world situation into a mathematical model, in terms of desirable actions and behaviors students exhibit. We attended to STEM undergraduate students' quantitative reasoning as they derived equations. Analysis of the meanings they held for arithmetic operations (+, -,…

Mathematical relationships are crucial elements to consider for learning mathematics. However, too often students pay more attention to the calculations to be done rather than the reasons for doing them. Relying on the relational paradigm to support elementary school students, we proposed two specially designed tasks to help students recognize and…

Previous studies have repeatedly shown that children often incorrectly use an additive model for multiplicative word problems, and a multiplicative model for additive word problems. The present study aimed to investigate which model upper primary school children tend to choose in word problems that are open to "both" ways of reasoning.…

Distinguishing between sources of variability in mathematics performance may contribute to a more comprehensive theory of mathematics skills. Research has examined student differences based upon scores on achievement tests, which provide overall proficiency, but may not provide the detailed information for identifying and remediating difficulties.…

The study explored the effects of a computer-assisted COnceptual Model-based Problem-Solving (COMPS) program on multiplicative word-problem-solving performance of students with learning disabilities or difficulties. The COMPS program emphasizes mathematical modeling with algebraic expressions of relations. Participants were eight fourth and fifth…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

Suggestions for teaching problem solving which include the use of general models, variation of illustrations and terminology, and diagrams are illustrated for comparison multiplication word problems. (MN)

Over 600 pupils in grades five, seven, and nine in Italian schools were asked to choose the operation needed to solve 26 multiplication and division word problems. The findings seemed to confirm the impact of the repeated addition model on multiplication and of the partitive model on division. (MNS)

Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…

After a year of instruction, 70 kindergarten children were individually interviewed as they solved basic, multistep, and nonroutine word problems. Thirty-two used a valid strategy for all 9 problems, and 44 correctly answered 7 or more problems. Modeling provided a unifying framework for thinking about problem solving. (Author/MDH)

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…