This article expressed the broad and in-depth scenario of Genre analysis to understand the teaching-learning process in math education. The author has explained the meaning of Genre analysis as it is a part of discourse analysis which helps to acknowledge the hidden parts of the related concepts. Genre analysis is not only to address the versatility of math education; however, it also shows us the way, where we may approach or can reach at. Genre analysis can be the reflection on the everyday dialogue to the reflection on the official documents, which could show the reader or listener to the various possibilities and aspects in those related situations.
The author has explained the meaning for this analysis by considering two case studies as its Genre:
(1) Mathematical word problems as a Genre.
(2) Initial calculus lectures as a Genre.
In the first case study, she related the word problem with parables, riddles and puzzles to explain its picture in math education. She succinctly explained the hidden factors of word-problems with their characteristics as "unrelated with real life/lived experiences, anomalous use of verb tenses, no truth value, just solve to get the right answer at the end" (p.38). The main difference between word problems and parables is that word problems in mathematics are meant to find the correct answers without relating to the conceptual or lived experiences. Once the word problem finished in the class; it would closed forever for teachers as well as for students. Whereas, parables are meant for discussions in everyday religious practices.
In the second case, she explained the Genre as initial calculus lectures of four mathematics professors in SFU. In their lectures, their way of speaking and acknowledging their ways to make their lectures more convincing were observed. The major issue of 'hard sell' has been observed in which lecturers or teachers want to put a fake pressure on their students through their fake questions and prepared answers. Where teachers want to be more authoritative and influential without considering their listener in the classes.
The Author has also explained the use of Genre analysis in her pedagogical practices for the growth and development of teaching-learning experiences in the classrooms. She wanted to address the issue of 'hard-sell' in her classes and become a facilitator to uplift the voices of their students. She also explained that it is important to understand the viewpoint of a listener while learning in the math classes.
Points to consider:
- "The word problem in mathematics education is not the reflection or imitation of life but of the other word problems" (p.37). I did not think of the word problems in-depth before reading this article. It is so true that word problems in math education represent a new or different context in front of students, because of that they won't be able to relate with their near surroundings, which results in ambiguity in their minds as well as attempting the word problems in their own ways. It is a crucial concept in mathematics which is to be addressed in future research.
- "Beyond specific classroom activities in the high school where I teach, there is a change in the tone of teaching that has come as a part of my awareness of pedagogical genre" (p.45). Through this point of view of genre analysis, I came to know more crucially the productive use of genre analysis in the teaching and learning practices to make our math classroom more engaging in a holistic way.
How 'Genre analysis' would be productive in designing word problems in mathematics education?
As math teachers, we often joke about how bad word problems are. It’s interesting to read that the word problem “is not the reflection or imitation of life but of the other word problems.” Even though most of us seem to dislike word problems, we continue using them! Why is that? It seems hard to break a tradition in math education. There were classic word problems like the Ferris wheel problem in trigonometry or the height of a tree with the length of shadow problem. I did these problems as a student and now see them as a teacher. We seem to pass them on generations after generations.
ReplyDeleteWhenever thinking about word problems, I often think of Dan Meyer’s TED talk “Math class needs a makeover” (https://www.youtube.com/watch?v=qocAoN4jNwc). He talked about “aversion to word problem” and demonstrated how to turn a textbook word problem into a more engaging activity. I think genre analysis can be beneficial. When we better understand word problems as a genre, we can improve them. Now, this idea that word problems are “meant to find the correct answers” is slowly changing. Earlier in my career, I tried to make word problems more engaging by using students’ names in the problems and making numbers more realistic (by searching for real prices of products, for example). Then, I started using more open-ended problems where there wasn’t one correct answer. For instance, I did a “shopping spree” problem where students researched prices themselves and did calculations of discounts and taxes. However, there are also good word problems that only lead to one correct answer or do not connect to real-life situations, but they can be still engaging. Perhaps genre analysis can help us better understand what makes a good word problem.
I like the likening of word problems to riddles and parables. They all share the alternative world attributes that are like the real world but with only “relevant” facts and constraints revealed. Word problems strip situations and stories of most of the details retaining only what is necessary to answer the question. Encountering a situation and being able to extract what “math” is in there is a relevant skill. I have been recently reading about learning mathematics through stories and there is a place for them that is not filled by word problems. I am changing my view of word problems; I am beginning to see them as puzzles. Like with logic puzzles, the “story” in the word problem helps to construct mental images and draw the listener in. It also provides words to discuss the problem. (Saying “what is the number of goats?” versus “what is the number of objects?”).
ReplyDeleteAs word problems are not set in the real world, what then are real-world word problems? Is trying to force word problems into the real world, right? I find constructing more complicated and more like real world word problems difficult, both on teachers and students. As the word problems become more “real” just how unreal they are becomes clearer. I once did a mini project with students planning out their university education, but the goal was to practice decimal operations. The fees and other figures were not estimated which was unrealistic. Considerations like quality and interest of the schools were not considered. All students had to calculate how much will need to be paid after average financial assistance. These are just some of the unrealistic things that I remember. In general the students would probably do something similar but the constraints in word problems don’t provide a real representation. I think we should stop trying to push word problems into the real world, they are fine in the hypothetical alternative world.
Wonderful discussion!! We will be talking more about the word problem genre in class this evening, and the points raised here -- about the long, unbroken history of word problems, and the intriguing imagery they offer -- are important points that I hope will come up in our class as well.
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