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Direct linkTzur, Ron; Johnson, Heather L.; Hodkowski, Nicola M.; Nathenson-Mejia, Sally; Davis, Alan; Gardner, Amber – Australian Primary Mathematics Classroom, 2020
Children learn to find answers when multiplying two whole numbers (e.g., 3 × 7 = 21). To this end, they may repeatedly add one number (e.g., 7 + 7 + 7 = 21). But what meanings do they have for multiplication? The authors address this issue while sharing an innovative, playful task called Please Go and Bring for Me (PGBM). Drawing on the…
Descriptors: Mathematical Concepts, Concept Formation, Multiplication, Mathematics Instruction
Download full textJorgensen, Cody; Smith, Amy; Tzur, Ron; Johnson, Heather L. – North American Chapter of the International Group for the Psychology of Mathematics Education, 2019
We address the question: How can a student's conceptual transition, from attending only to singleton units (1s) given in multiplicative situations to distinguishing composite units made of such 1s, be explained? We analyze a case study of one fourth grader (Adam, a pseudonym) during the course of a video recorded cognitive interview. Adam's case…
Descriptors: Multiplication, Thinking Skills, Mathematics Instruction, Mathematical Concepts
Hodkowski, Nicola M.; Gardner, Amber; Jorgensen, Cody; Hornbein, Peter; Johnson, Heather L.; Tzur, Ron – North American Chapter of the International Group for the Psychology of Mathematics Education, 2016
In this paper we examine the application of Tzur's (2007) fine-grained assessment to the design of an assessment measure of a particular multiplicative scheme so that non-interview, good enough data can be obtained (on a large scale) to infer into elementary students' reasoning. We outline three design principles that surfaced through our recent…
Descriptors: Elementary School Students, Mathematics Instruction, Multiplication, Thinking Skills
Tzur, Ron; Johnson, Heather L.; Hodkowski, Nicola M.; Jorgensen, Cody; Nathenson-Mejia, Sally; Wei, Bingqian; Smith, Amy; Davis, Alan – North American Chapter of the International Group for the Psychology of Mathematics Education, 2018
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…
Descriptors: Teaching Methods, Mathematics Instruction, Thinking Skills, Faculty Development
Tzur, Ron; Johnson, Heather L.; McClintock, Evan; Kenney, Rachael H.; Xin, Yan P.; Si, Luo; Woordward, Jerry; Hord, Casey; Jin, Xianyan – PNA, 2013
We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children's thinking, and learning situations…
Descriptors: Multiplication, Constructivism (Learning), Child Development, Educational Experiments
Tzur, Ron; Johnson, Heather L.; McClintock, Evan; Risley, Rachael – North American Chapter of the International Group for the Psychology of Mathematics Education, 2012
In this paper we articulate an approach, termed culturally-mathematically relevant pedagogy (CMRP), for fostering urban English language learners' mathematical progression. CMRP integrates three aspects, the use of (1) adaptive teaching to build on students' funds of knowledge for mathematics, (2) tasks that make sense to students given their…
Descriptors: Culturally Relevant Education, Mathematics Instruction, Teaching Methods, Cultural Background
