Solving mathematical problems is cognitively complex, involving strategy formulation, solution development, and the application of learned concepts. However, gaps in students' knowledge or weakly grasped concepts can lead to errors. Teachers play a crucial role in predicting and addressing these difficulties, which directly influence learning outcomes. However, preemptively identifying misconceptions leading to errors can be challenging. This study leverages historical data to assist teachers in recognizing common errors and addressing gaps in knowledge through feedback. We present a longitudinal analysis of incorrect answers from the 2015-2020 academic years on two curricula, Illustrative Math and EngageNY, for grades 6, 7, and 8. We find consistent errors across 5 years despite varying student and teacher populations. Based on these Common Wrong Answers (CWAs), we designed a crowdsourcing platform for teachers to provide Common Wrong Answer Feedback (CWAF). This paper reports on an in vivo randomized study testing the effectiveness of CWAFs in two scenarios: next-problem-correctness within-skill and next-problem-correctness within-assignment, regardless of the skill. We find that receiving CWAF leads to a significant increase in correctness for consecutive problems within-skill. However, the effect was not significant for all consecutive problems within-assignment, irrespective of the associated skill. This paper investigates the potential of scalable approaches in identifying Common Wrong Answers (CWAs) and how the use of crowdsourced CWAFs can enhance student learning through remediation.
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How Common Are Common Wrong Answers? Exploring Remediation at Scale.
The process of synthesizing solutions for mathematical problems
is cognitively complex. Students formulate and implement strate-
gies to solve mathematical problems, develop solutions, and make
connections between their learned concepts as they apply their
reasoning skills to solve such problems. The gaps in student knowl-
edge or shallowly-learned concepts may cause students to guess at
answers or otherwise apply the wrong approach, resulting in errors
in their solutions. Despite the complexity of the synthesis process in
mathematics learning, teachers’ knowledge and ability to anticipate
areas of potential difficulty is essential and correlated with student
learning outcomes. Preemptively identifying the common miscon-
ceptions in students that result in subsequent incorrect attempts can
be arduous and unreliable, even for experienced teachers. This pa-
per aims to help teachers identify the subsequent incorrect attempts
that commonly occur when students are working on math problems
such that they can address the underlying gaps in knowledge and
common misconceptions through feedback. We report on a longi-
tudinal analysis of historical data, from a computer-based learning
platform, exploring the incorrect answers in the prior school years
(’15-’20) that establish the commonality of wrong answers on two
Open Educational Resources (OER) curricula–Illustrative Math (IM)
and EngageNY (ENY) for grades 6, 7, and 8. We observe that incor-
rect answers are pervasive across 5 academic years despite changes
in underlying student and teacher population. Building on our find-
ings regarding the Common Wrong Answers (CWAs), we report on
goals and task analysis that we leveraged in designing and develop-
ing a crowdsourcing platform for teachers to write Common Wrong
Answer Feedback (CWAF) aimed are remediating the underlying
cause of the CWAs. Finally, we report on an in vivo study by analyz-
ing the effectiveness of CWAFs using two approaches; first, we use
next-problem-correctness as a dependent measure after receiving
CWAF in an intent-to-treat second, using next-attempt correctness
as a dependent measure after receiving CWAF in a treated analysis.
With the rise in popularity and usage of computer-based learning
platforms, this paper explores the potential benefits of scalability
in identifying CWAs and the subsequent usage of crowd-sourced
CWAFs in enhancing the student learning experience through re-
mediation.
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- Award ID(s):
- 1931523
- PAR ID:
- 10443558
- Date Published:
- Journal Name:
- Proceedings of the Tenth ACM Conference on Learning@Scale (L@S '23), July 20-22, 2023, Copenhagen, Denmark.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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