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Jacobs, Victoria R.; Empson, Susan B.; Case, Joan M.; Dunning, Amy; Jessup, Naomi A; Krause, Gladys; Pynes, D'Anna – Mathematics Teacher: Learning and Teaching PK-12, 2022
In this article, the authors introduce and illustrate a new activity that involves "follow-up equations," which are equations that follow up on ideas children have already expressed when solving fraction story problems. Specifically, teachers pose story problems and purposely attend to fraction ideas that arise in children's strategies…
Descriptors: Fractions, Mathematics Education, Problem Solving, Equations (Mathematics)
Baker, Katherine; Jessup, Naomi A.; Jacobs, Victoria R.; Empson, Susan B.; Case, Joan – Mathematics Teacher: Learning and Teaching PK-12, 2020
Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.
Descriptors: Mathematics Instruction, Problem Solving, Teaching Methods, Student Problems
Empson, Susan B.; Jacobs, Victoria R. – North American Chapter of the International Group for the Psychology of Mathematics Education, 2021
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…
Descriptors: Mathematics Instruction, Fractions, Thinking Skills, Grade 3
Jacobs, Victoria R.; Empson, Susan B. – ZDM: The International Journal on Mathematics Education, 2016
This case study contributes to efforts to characterize teaching that is responsive to children's mathematical thinking. We conceptualize "responsive teaching" as a type of teaching in which teachers' instructional decisions about what to pursue and how to pursue it are continually adjusted during instruction in response to children's…
Descriptors: Case Studies, Children, Mathematics Skills, Thinking Skills

Empson, Susan B. – Teaching Children Mathematics, 2001
Discusses examples of children's invented equal-sharing strategies that lay a foundation for reasoning about equivalence by connecting ideas from multiplication, division, and fractions. (KHR)
Descriptors: Arithmetic, Division, Elementary Education, Fractions

Empson, Susan B. – Cognition and Instruction, 1999
This study explored first graders' fraction learning when the teacher elicited and built on children's informal knowledge of fractions during discussions of equal-sharing tasks; the study focused on key classroom interactions resulting in cognitive change. Findings suggest that thinking about fractions is influenced by the structure of the child's…
Descriptors: Arithmetic, Context Effect, Elementary School Mathematics, Elementary School Students

Empson, Susan B. – Teaching Children Mathematics, 1995
Describes a case study of a first-grade class in fractions, presents preliminary findings suggesting that students in others grades can learn fractions in similar ways, and offers ideas for action research. (MKR)
Descriptors: Action Research, Case Studies, Elementary School Mathematics, Elementary School Students