Abstract
Previous theoretical research (Authors, 2018a; Authors, 2018b) has revealed conceptual similarities among a number of mathematical learning theories and theories regarding language acquisition. This intersection of ideas led to a novel framework defining four stages of mathematical learning: Receiving, Replicating, Negotiating Meaning, and Producing. Through qualitative research methods and transcripts of student communication and work, this study empirically investigates this theoretical construct. The findings herein demonstrate that this construct is helpful in characterizing where students are in the process of learning mathematics and how to help them attain the next level in the stages of learning.
Highlights
Research in language acquisition and the learning of mathematics continue to evolve
Following the opinions in the literature related to language acquisition and mathematical learning theories, a set of mathematics questions were developed geared towards unpacking student mathematical understanding, communication, and behaviors
Understanding the stages of mathematical learning is essential for educators who are attempting to create curricula and instructional experiences commensurate with a student’s level of mathematical understanding
Summary
Research in language acquisition and the learning of mathematics continue to evolve. Recently, these two realms have intersected and mathematics learning has been shown to share similarities with language acquisition. In investigating the intersection of learning theories from mathematics and language acquisition, Bossé, et al (2018a) and Bossé, Ringler, Bayaga, Fountain, and Slate Young (2018b) have proposed the Math Acquisition Framework, a multistage theory of mathematical learning with potentially far reaching ramifications for education. The stages in this framework include: Receiving, Replicating, Negotiating Meaning, and Producing. There remains a need to empirically apply this construct to further investigate student understanding and learning regarding other fields of mathematics and generally across mathematics. Constraints were necessarily imposed in the initial development of the Math Acquisition Framework and these constraints have been maintained through following articles and studies employing the framework
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