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Is a substitute the same? Learning from lessons centering different relational conceptions of the equal sign
Andrea Marquardt Donovan1, Ana Stephens1, Burcu Alapala1
1University of Wisconsin-Madison, Madison, USA.
ZDM : the International Journal on Mathematics Education
|August 2, 2022
Summary
Understanding the equal sign is key for math success. This study explored teaching both "sameness" and "substitutive" equal sign meanings to fourth and fifth graders, finding mixed results on equation-solving approaches.
Area of Science:
- Mathematics Education
- Cognitive Psychology
Background:
- Foundational understanding of the equal sign is crucial for algebraic competence.
- Traditional focus on the equal sign as "the same as" may be insufficient.
- A substitutive conception, where expressions can be interchanged, may enhance algebraic skills.
Purpose of the Study:
- To investigate the impact of an online intervention on fostering relational understanding of the equal sign in elementary students.
- To compare the effectiveness of lessons emphasizing a "sameness" conception versus a dual "sameness and substitutive" conception.
- To assess how these different conceptions influence students' approaches to algebraic equations.
Main Methods:
- An online intervention was administered to 146 fourth and fifth graders.
- Three conditions were compared: sameness conception lessons, dual sameness and substitutive conception lessons, and a control group.
- Student definitions and approaches to missing value equations were analyzed.
Main Results:
- Intervention lessons positively influenced students' ability to produce and endorse both sameness and substitutive definitions.
- The impact on students' approaches to solving missing value equations was less conclusive.
- Further research is indicated to clarify the role of these conceptions in algebraic problem-solving.
Conclusions:
- Teaching both sameness and substitutive conceptions of the equal sign can enhance definitional understanding.
- The direct impact on equation-solving strategies requires further investigation.
- Exploring the interplay between equal sign conceptions and structural algebraic thinking is essential.
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