Influence of students' conversations in constructing mathematical knowledge
Creators: name: Rivera-Dominguez, Alberto
Publisher: name: No Publisher Supplied
Year: 2019

description: The purpose of this study is to investigate how students’ verbal conversation facilitates the exchange of mathematics ideas and the construct of mathematical knowledge when students work in a learning activity. Students often involve artifacts or mathematical models to represent their mathematics ideas and use conversational language to exchange and explain those ideas. In line with these premises, the following questions guided the study: (1) How does student use of semiotic models facilitate the constructing of mathematical ideas? (2) How does the use of conversational language facilitate the communication and appropriation of those ideas? These questions are important as they provide the guidelines to investigate how the use of mathematical models and conversational language by students interplay in their construct of mathematical knowledge.Video data archive files from NSF-funded research stored in the Video Mosaic Collaborative and RBDIL video collections are used to investigate the influence of students’ conversation in constructing mathematical knowledge. This study consists of a fine-grained analysis of a single out-of-school session, lasting 1 hour and1 minute, where a group of five high school junior students, one girl and 4 boys, work in a collaborative activity. The students are invited to solve combinatorics problems related to binomial expansion situations. The video data illustrates how the students involve mathematical models to create meanings to the combinatorics situations they confront, and how they explain their ideas during their mathematics conversations. In approaching the issue of how students’ mathematics conversations influence their construct of mathematical knowledge, I created the concepts of functional linguistic structures (FLS) and functional semiotic models (FSM) as forms of mathematics expressions and representation. Three functional categories of linguistic structures and three functional categories of semiotic models are introduced in this study to investigate how the use of conversational language and mathematical models interact and influence each other in the students’ learning of mathematics.The method of grouping the data in large clusters by functional categories facilitates the coding of the transcripts and data analysis. This unified approach renders visibility to investigate, in a generalized way, how the students construct new mathematics ideas and how they, through verbal conversations, interchange their ideas to construct further mathematical knowledge. The study identifies students’ preferring styles of communicating mathematics ideas and presents forms of mathematics expressions and representation that may be used to improve the teaching and learning of mathematics. This study presents the importance of taking conversational language as one functional resource that interacts with the mathematical models in the learning of mathematics, and demonstrates from data how the FSM and the FLS interact and influence each other in promoting the semantic expansion and growth of mathematical knowledge. The study brings important implications to the learning of mathematics by considering a multi-modal approach taking conversational language as one resource that interacts with mathematical models to create meanings in mathematical discourse. The multi-modal approach facilitates the creation of mathematics ideas and provides alternatives for preferring styles of mathematics communication, which may be used to improve the learning of mathematics in classrooms.