Students with learning disabilities/difficulties in mathematics often apply ineffective procedures to solve word problems. Given that current mathematics curriculum standards emphasize conceptual understanding in problem solving as well as higher-order thinking and reasoning, the purpose of this study was to evaluate the impact of a model-based…

Drawing on research around the utility of worked examples, we examine how 29 first- and 27 third-grade students made sense of integer subtraction worked examples and used those examples to solve similar problems. Students first chose which of three worked examples correctly represented an integer subtraction problem and used the example to solve a…

Identifying components of teaching that make a difference in children's learning is an ongoing challenge in our field. Focusing on teaching that is responsive to children's fraction thinking, we decomposed responsiveness into the instructional practices of questioning to support and extend children's thinking, noticing children's thinking, and…

This study examines how a PD program to promote teachers' shift toward a student-adaptive pedagogy impacts students' multiplicative reasoning. We describe the underpinnings of this pedagogy and main components of the PD program. Then, we present key features of participants, data collection/analysis methods, and the written assessment used to…

Reform-based math instruction calls for students' construction of conceptual understanding, solving challenging problems and explanation of reasoning. However, existing literature shows that students with learning disabilities (LD) easily get lost in reform-based instruction. As an outcome of collaborative work between math education and special…

This research explores the interplay between students' understandings of proportional and functional relationships. Approximately 90 students participated in an early algebra intervention in Grades 3- 5. Before the intervention and after each year of the intervention, we evaluated their understandings of proportional and functional relationships.…

In this exploratory study, we documented teachers' knowledge of children's mathematical thinking as they engaged in the task of anticipating children's strategies for an equal sharing fraction problem. To elicit an array of knowledge, 18 teachers were deliberately selected with a variety of numbers of years participating in professional…

Currently, language competences in mathematics lessons gain more attention in Germany. The paper reports an interdisciplinary study of linguistics and mathematics education on reasoning. A model to rate the competences in arithmetic reasoning at primary level will be presented for discussion: mathematical reasoning is coded separately from its…

Both additive and proportional reasoning are types of quantitative analogical (QA) reasoning. We investigated the development and nature of primary school children's QA reasoning by offering two missing-value word problems to 3rd to 6th graders. In one problem, ratios between given numbers were integer, in the other ratios were non-integer. These…

This report focuses on key elements of teaching occurring during intensive, one-to-one instruction with 3rd- and 4th-graders. The study involves six cases in all, each consisting of video records of up to eight lessons, each of 30-45 minutes' duration, resulting in the analysis of about 33 hours of video data. A resulting framework of four stages…

While the metaphor of students bringing linguistic, cultural, and community resources to classrooms abounds in mathematics education research with non dominant students, teachers seem not to benefit from such metaphoric language as most of them struggle to figure out how such resources can be used during mathematics instruction. This paper urges a…