Brief Summary:
Students have experienced difficulty learning mathematics due to a lack of understanding of the math language. In the given article by Schleppegrell (2007), the Author discussed the many linguistic challenges that hinder the process of learning mathematics with better understanding. She also proposed some pedagogical practices to deal with such challenges for an effective teaching-learning process in mathematics. As every subject area has its own way of using language, mathematics also has its technical language to use with proper knowledge of grammatical structures for understanding it. Author also highlighted the linguistic challenges given by Halliday (1978) under his proposal for "Mathematics Register". In the mathematical register, it has pointed out the idea of using technical math language by translating the informal everyday languages to serve the new functions in math context. The linguistic issues can be viewed through the features involved in the classroom mathematics register that broadly includes 'Multiple semiotic systems' and 'Grammatical patterns' which are imperative to understand for solving math problems.
Multiple semiotic systems include math symbols, oral languages while conversations regarding math problems, written language, graphs, and visual displays (p.141) which are important factors to understand the technical use of math language where ordinary language could not make sense to solve math problems. Grammatical patterns include technical vocabulary, dense noun phrases, being and having verbs, conjunctions with technical meanings, and implicit logical relationships (p.141) affect the understanding of using technical math language in the classrooms. It is interesting to note that linguistic issues are beyond the focus on vocabulary or specialized terminology which addresses the different use of patterns of languages in mathematical reasoning.
The author also suggests some pedagogical practices for the teachers to support the development of 'Math Register' and mathematical knowledge among children. Teachers can use technical language in math classrooms even during casual interactions with students. Teachers must do verbal explanations of math problems which could give students a sense of the process to solve them. Teachers could encourage the habits of expressions among the students to explain their process explicitly. Teachers can introduce mathematical terms by relating with meaning-making terms in everyday life. Teachers can give an outline to think over the given math problem for descriptive results. It is important to receive feedback to recognize the level of knowing mathematics in the given context. "Revoicing" by teachers is the key to making students interactive with their intuitive technical language of mathematics as it focuses on meanings rather than forms.
Important points to discuss:
"The notion of a mathematics register and recognition of the role of language in mathematics learning and teaching cast doubt on the common wisdom that suggests that mathematics is the least language-dependent subject"(p.155). Even in my teaching experience, most of the students and parents have this concept in their fixed mind-set that mathematics is all about to cram formulae and apply to given questions to find its solution. Because of such thinking, many students could not give their best in word-problems, geometry, trigonometry which involves more knowledge of math language to do the process.
Secondly, It is crucial to use technical math language in the classroom and explain its correct grammatical use for maximum understanding in math context. It is indispensable to understand the various English words that have different meanings in math as compared to ordinary language in everyday life. For instance, in trigonometry, elevation and depression for 'angle of elevation' and 'angle of depression' have different meanings in math language as compared to ordinary meanings in english language.
Proposed question:
As per this article, if it is important for the students to suggest some steps to solve math problems for descriptive explanations for their thinking expressions, then where can we as teachers enhance their creative thinking in our math classes?
Thank you for sharing your summary, stops and wonders, Sukh! I feel very strongly about your teaching experience when facing students and parents, as some of them think mathematics is about illogical formulas and theories. How can we as teachers enhance their creative thinking in our math classes? The first strategy that comes to my mind is giving students open-ended problems where multiple solutions are possible, allowing students to experience mathematical creativity. Sometimes I notice that when I give responses to students’ answers or problems, my response was guiding and may have influenced their answer.
ReplyDeleteGood thought, Jianying. So much of the traditions of mathematics teaching has to do with very strong teacher guidance -- sometimes so much so that the teacher is the main person doing math in the room. Peter Liljedahl (SFU)'s Thinking Classroom, as well as all kinds of learning based on open-ended problems (see Japanese Lesson Study) works to give students voice and agency as autonomous problem-solvers.
ReplyDeleteI was going to say the same thing as Jianying! One of my favorite topics in math 9 & 10 is solving a quadratic. There is no one "right way" to do it, only the different routes to get to the end. Helping students to see the different methods to solve problems and be able to talk about the pros and cons of each method and when one is more appropriate than others is a wonderful conversation to have. However, as you mentioned, Sukh, the conversation is very difficult to have when students have not developed the mathematical register, or confidence with the register, necessary to have those deeper, more insightful conversations.
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