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Download full textAustin, Christine K.; Kosko, Karl W. – North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
Multiplication and division are vital topics in upper level elementary school. A teacher's pedagogical content knowledge (PCK) influences both instruction and students' learning. However, there is currently little research examining teachers' PCK within this domain, particularly regarding professional education of future teachers. To help address…
Descriptors: Multiplication, Division, Elementary School Teachers, Pedagogical Content Knowledge
Direct linkKosko, Karl W. – Mathematics Teacher: Learning and Teaching PK-12, 2020
Developing multiplicative reasoning is an important milestone for elementary school students, which influences their learning of later mathematical concepts (Hackenberg and Tillema 2009). For children to conceptually understand multiplication, one should move beyond merely counting by ones to dealing with composites (twos, fives, etc.) and other…
Descriptors: Multiplication, Mathematics Instruction, Teaching Methods, Thinking Skills
Kosko, Karl W. – Investigations in Mathematics Learning, 2018
Multiplicative reasoning as articulated through scheme theory suggests that students improve the sophistication of their reasoning as they are able to coordinate additional levels of units, often described through students' use of schemes and operation at particular multiplicative concepts. Theoretical descriptions of the second and third…
Descriptors: Multiplication, Logical Thinking, Mathematical Concepts, Mathematics Tests
Kosko, Karl W.; Singh, Rashmi – The Mathematics Educator, 2018
Multiplicative reasoning is essential for students' engagement with various mathematical concepts. Although the field's understanding of children's multiplicative concepts has grown over the past 30 years, relatively few studies have examined the development of multiplicative concepts with whole numbers, and even fewer have studied this phenomenon…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Multiplication
Kosko, Karl W. – School Science and Mathematics, 2019
Visual representations and manipulatives are a highly advocated mathematical tool for the teaching and learning of multiplication and division. Although there is some prior research on elementary teachers' general use of manipulatives and visual representations, there is little to no specific focus on use of such representations on a specific…
Descriptors: Grade 3, Elementary School Teachers, Mathematical Concepts, Mathematics Instruction
Kosko, Karl W.; Singh, Rashmi – North American Chapter of the International Group for the Psychology of Mathematics Education, 2016
Detailing is a linguistic tool for mathematical argumentation in which given mathematical information is operationalized through one's warrants to support a claim. Recent literature suggests that students' detailing is related to their early algebraization. This study examined 168 elementary students' use of detailing in two mathematical…
Descriptors: Elementary School Students, Number Concepts, Mathematical Logic, Multiplication
