Mathematics Learning Through the Lens of Language Acquisition

Abstract

Previous theoretical research 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.

The Language That Grade R Students Use to Achieve the Envisaged Mathematics Outcomes, a South African Perspective

“…For students like S1S1, S1S2, S2S2, S3S1 and S5S1 who had problems in matching the items to the correct numerical values, such problems emanate from a misunderstanding of mathematical language. It is argued that communicating mathematically requires an in-depth comprehension of the mathematical language and the multiple illustrations employed in communicating mathematical concepts [5]. Some of the students, for example, S1S1, S2S1, S4S2 and S5S1 when counting the bottle-tops in Figure 1a and b counted in English, listening carefully to their counting, skipped some of the numbers which is an indication that they are not yet conversant counting in English.…”

“…Some of the students, for example, S1S1, S2S1, S4S2 and S5S1 when counting the bottle-tops in Figure 1a and b counted in English, listening carefully to their counting, skipped some of the numbers which is an indication that they are not yet conversant counting in English. Literature highlights that students in the advanced stage of language native-language acquisition can easily extend vocabulary, and good comprehension of the second language [5]. This implies that students need to be thoroughly developed in HL to have access to the Second Language (SL).…”

“…Research confirms that ESL performs low in mathematics compared to their counterparts EFL speakers [3]. Numerous research studies in language acquisition and mathematical learning have developed along mostly discrete trajectories, for example, studies examining the links between linguistic and mathematical literacy [4], the functions of language in the math classroom [5] established the framework defining the four stages of mathematical learning: Receiving, Replicating, Negotiating meaning and Producing. However, few studies have investigated the language that Grade R students use to navigate the mathematics space to achieve the envisaged outcomes of the policy.…”

From Receiving Mathematics to Negotiating Meaning: Development of Students' Understanding of Geometric Concept

“…Simultaneously, research has developed an understanding of how students learn mathematics and geometry. Recent investigations regarding the intersection of SLA and mathematics learning theories have suggested that mathematics is learned in a manner similar to SLA and has led to the development of the Mathematics Acquisition Framework (MAF), through which four stages of mathematical learning are recognized: receiving, replicating, negotiating meaning, and producing mathematics (Bossé, et al, 2018b).…”

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This study applies a framework for mathematical cognition and learning (Bossé, et al, 2018a;Bossé et al, 2019;Bossé et al, 2018b) to examples of students' comprehension of geometric concepts related to angles. This framework utilizes key concepts from second language acquisition (SLA) to elucidate processes involved in mathematical learning.

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