ERIC Number: EJ1228007
Record Type: Journal
Publication Date: 2019-Jul
Abstractor: As Provided
Levels of Abstraction in Students' Mathematics Strategies: What Can Applying Computer Science Ideas about Abstraction Bring to Elementary Mathematics?
Rich, Kathryn M.; Yadov, Aman; Zhu, Marissa
Journal of Computers in Mathematics and Science Teaching, v38 n3 p267-298 Jul 2019
Moving among levels of abstraction is an important skill in mathematics and computer science, and students show similar difficulties when applying abstraction in each discipline. While computer science educators have examined ways to explicitly teach students how to consciously navigate levels of abstraction, these ideas have not been explored in mathematics education. In this study, we examined elementary students' solutions to a commonplace mathematics task to determine whether and how students moved among levels of abstraction as they solved the task. Furthermore, we analyzed student errors, categorizing them according to whether they related to moves among levels of abstraction or to purely mathematical steps. Our analysis showed: (1) students implicitly shift among levels of abstraction when solving "real-world" mathematics problems; (2) students make errors when making those implicit shifts in abstraction level; (3) the errors students make in abstraction outnumber the errors they make in purely mathematical skills. We discuss the implications for these findings, arguing they establish that there are opportunities for explicit instruction in abstraction in elementary mathematics, and that students' overall mathematics achievement and problem-solving skills have the potential to benefit from applying these computer-science ideas to mathematics instruction.
Descriptors: Mathematics Instruction, Computer Science Education, Elementary School Mathematics, Elementary School Students, Common Core State Standards, Logical Thinking, Problem Solving, Mathematics Skills, Error Patterns, Computation, Thinking Skills, Grade 4, Grade 5, Elementary School Teachers
Association for the Advancement of Computing in Education. P.O. Box 719, Waynesville, NC 28786. Tel: 828-246-9558; Fax: 828-246-9557; e-mail: firstname.lastname@example.org; Web site: http://www.aace.org
Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Education; Grade 4; Intermediate Grades; Grade 5; Middle Schools
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Grant or Contract Numbers: 1738677