Student Use of Mathematics Discourse during the Taxicab Problem
Creators: name: Vassiliadis, Alexia L.
Publisher: name: No Publisher Supplied
Year: 2024

description: This analytic explores how the four twelfth grade students (Michael, Romina, Brian, and Jeff) used mathematics discourse throughout their problem-solving process of the Taxicab problem. Mathematical discourse refers to the way in which students talk, write, and reason about mathematics, including the use of language, symbols, representations, and practices. While acknowledging that discourse does not only refer to language, the mathematics register can be used to characterize mathematical discourse, as pointed out by Moschkovich (n.d.). The “mathematics register” is a term that refers to the use of specific language, notation, and protocols used in mathematical discourse to communicate mathematical ideas and reasonings. Students are expected to develop this domain-specific register and use more “precise linguistic encoding and expressions” of their mathematics understandings (Sigley &amp; Wilkinson, 2015). The students in this analytic participate in mathematical discourse practices by “talking and acting in the ways that mathematically competent people talk and act when talking about mathematics” (Moschkovich, n.d.).Matute et al. (2022) suggests ways in which students can use mathematics discourse practices and build their mathematics register: “Students need to combine everyday language, symbols, visual displays, and non-linguistic representations to communicate effectively in mathematics” (p. 1823). This analytic observes and identifies events where the students use the different representations of communication according to Matute et al. (2022). Michael, Romina, Brian, and Jeff used all four of the language representations presented by Matute et al. (2022) to communicate their mathematical thoughts, ideas, and reasonings throughout their problem-solving process. Romina used the mathematical symbols x and y in Event 4 to communicate the idea of moving left and right or up or down on the Taxicab grid, respectively. Michael also spoke through symbols to the group when he used binary notation to explain the taxicab’s movements on the grid in Event 6. Throughout these six events, the students are seen using visual displays to share their ideas, like in Event 2 when Romina drew out Pascal’s Triangle and turned the paper to visually show Jeff this mathematical concept. In Event 3, Jeff used a non-linguistic form of communication by using his finger to point to the box he was referring to as he said, “well like to here we would say it’s 35”. This was in response to Researcher Maher’s question, who also used a non-linguistic way of pointing to a specific box on Jeff’s grid and asked, “where does this 10 come from?” This analytic considers the student language used through the lens of the four representations of communication identified by Matute et al. (2022). It aims to illustrate that student communication can be represented in multiple dimensions surrounding their mathematical understandings, reasonings, and ideas. Through problem-solving, students like Michael, Romina, Brian, and Jeff “are accorded opportunities to develop deep understandings of mathematical concepts, acquire the language of mathematics (the mathematics register), and adopt multiple ways of representing mathematical solutions” (Wilkinson, 2018, p. 171). Wilkinson (2018) also emphasizes the importance of the mathematics register by saying that “when students have command of the mathematics register, they represent problems coherently, provide their conclusions, and explain their mathematical knowledge accurately and comprehensively” (p.170), which are the goals of student learning and understanding mathematics. Throughout this problem solving, mathematical discourse helped these students to articulate their thinking, develop reasoning, and engage with mathematical concepts on a deeper level.Taxicab problem:Researcher Maher presented the Taxicab problem to the students. This problem included coordinates on a single (fourth) quadrant with the “taxi stand” located at (0,0) as well as three “pick-up” points: A (blue) at (1,-4), B (red) at (4,-3), and C (green) at (5,-5). The problem statement was as follows: “A taxi driver is given a specific territory of a town, as represented by the grid. All trips originate at the taxi stand. One very slow night, the driver is dispatched only three times; each time, she picks up passengers at one of the intersections indicated on the map. To pass the time, she considers all the possible routes she could have taken to each pick-up point and wonders if she could have chosen a shorter route. What is the shortest route from the taxi stand to each point? How do you know it is the shortest? Is there more than one shortest route to each point? If not, why not? If so, how many? Justify your answers.”References:Matute, K., Catsellón, L., &amp; Kitchen, R. (2022). English Language Learner Students’ Development of the Mathematics Register during a Problem-Solving Lesson. ERIC. https://eric.ed.gov/?id=ED630474Moschkovich, J. (n.d.). WHAT COUNTS AS MATHEMATICAL DISCOURSE? https://files.eric.ed.gov/fulltext/ED501034.pdf Sigley, R., &amp; Wilkinson, L. C. (2015). Ariel’s cycles of problem solving: An adolescent acquires the mathematics register. The Journal of Mathematical Behavior, 40, 75–87. https://doi.org/10.1016/j.jmathb.2015.03.001Wilkinson, L. C. (2018). Teaching the language of mathematics: What the research tells us teachers need to know and do. The Journal of Mathematical Behavior, 51, 167–174. https://doi.org/10.1016/j.jmathb.2018.05.001