skip to main content


Title: Abstraction in students’ mathematics strategies: Productive starting points for introducing CT concepts.
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.  more » « less
Award ID(s):
1738677
NSF-PAR ID:
10183081
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
The Journal of computers in mathematics and science teaching
Volume:
38
Issue:
3
ISSN:
1943-5908
Page Range / eLocation ID:
267-298
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. In many discussions of the ways in which abstraction is applied in computer science (CS), researchers and advocates of CS education argue that CS students should be taught to consciously and explicitly move among levels of abstraction (Armoni Journal of Computers in Mathematics and Science Teaching, 32(3), 265–284, 2013; Kramer Communications of the ACM, 50(4), 37–42, 2007; Wing Communications of the ACM, 49(3), 33–35, 2006). In this paper, we describe one way that attention to levels of abstraction could also support learning in mathematics. Specifically, we propose a framework for using abstraction in elementary mathematics based on Armoni’s (2013) framework for teaching computational abstraction. We propose that such a framework could address an enduring challenge in mathematics for helping elementary students solve word problems with attention to context. In a discussion of implications, we propose that future research using the framework for instruction and teacher education could also explore ways that attention to levels of abstraction in elementary school mathematics may support later learning of mathematics and computer science. 
    more » « less
  2. The U.S. Nation’s Report Card reveals that lower performing students exhibited greater achievement decline than their average/high performing peers based on 2022 long-term trend mathematics assessments for age 9 students. Technology, including computer-assisted instruction, plays an important role in today’s dynamic learning environments. Currently, there is a lack of computer-assisted intervention programs that systematically teach generalized word problem-solving skills that are driven by mathematical models. Model-based problem solving (MBPS) is one of the essential emphases in the Common Core mathematical practice standards. This study investigated the effects of a web-based computer tutor, MBPS, on enhancing word problem-solving performance of elementary students who are struggling in mathematics. The MBPS tutor incorporates best practices that are identified by the Institute of Educational Sciences’ (IES) latest practice guide, including providing systematic instruction, visual and verbal supports, and teaching of precise mathematical language. Findings indicate that the MBPS tutor boosted participants’ performance above and beyond the business-as-usual comparison group.

     
    more » « less
  3. Incorporating computational thinking (CT) ideas into core subjects, such as mathematics and science, is one way of bringing early computer science (CS) education into elementary school. Minimal research has explored how teachers can translate their knowledge of CT into practice to create opportunities for their students to engage in CT during their math and science lessons. Such information can support the creation of quality professional development experiences for teachers. We analyzed how eight elementary teachers created opportunities for their students to engage in four CT practices (abstraction, decomposition, debugging, and patterns) during unplugged mathematics and science activities. We identified three strategies used by these teachers to create CT opportunities for their students: framing, prompting, and inviting reflection. Further, we grouped teachers into four profiles of implementation according to how they used these three strategies. We call the four profiles (1) presenting CT as general problem-solving strategies, (2) using CT to structure lessons, (3) highlighting CT through prompting, and (4) using CT to guide teacher planning. We discuss the implications of these results for professional development and student experiences. 
    more » « less
  4. Abstract: This paper reports on a study of the dynamics of a Research-Practice Partnership (RPP) oriented around design, specifically the co-design model. The RPP is focused on supporting elementary school computer science (CS) instruction by involving paraprofessional educators and teachers in curricular co-design. A problem of practice addressed is that few elementary educators have backgrounds in teaching CS and have limited available instructional time and budget for CS. The co-design strategy entailed highlighting CS concepts in the mathematics curriculum during classroom instruction and designing computer lab lessons that explored related ideas through programming. Analyses focused on tensions within RPP interaction dynamics and how they were accommodated when RPP partners were designing for co-design activities, a critical component that leads to curricular co-design itself. We illustrate these tensions with examples of clusters of activity that appeared repeatedly among the research and practice team members when “designing for co-design”. 
    more » « less
  5. Clark Chinn Edna Tan Carol Chan Yael Kali (Ed.)
    This paper reports on a study of the dynamics of a Research-Practice Partnership (RPP) oriented around design, specifically the co-design model. The RPP is focused on supporting elementary school computer science (CS) instruction by involving paraprofessional educators and teachers in curricular co-design. A problem of practice addressed is that few elementary educators have backgrounds in teaching CS and have limited available instructional time and budget for CS. The co-design strategy entailed highlighting CS concepts in the mathematics curriculum during classroom instruction and designing computer lab lessons that explored related ideas through programming. Analyses focused on tensions within RPP interaction dynamics and how they were accommodated when RPP partners were designing for co-design activities, a critical component that leads to curricular co-design itself. We illustrate these tensions with examples of clusters of activity that appeared repeatedly among the research and practice team members when" designing for co-design". 
    more » « less