“A Linguistic and Narrative View of Word Problem in Mathematics Education” by Susan Gerofsky discusses the importance and value of mathematical word problem in facing the real life situation. It describes mathematical world problem as a linguistic genre and its pragmatic structure then compares word problems genre and others literary genre. Gerofsky endeavors to explain to what extent word problems are applicable and useful for students. She states the point of view of several scholars who believes word problem in mathematics textbooks do not represent the real world problem because most of them are not the real story. She raises the example of people who are good at solving mathematical problems in the real life but cannot solve some of the word problems of the mathematics textbook.
the author categorizes the word problem in three groups of “set up”, “information” and “questions”, then explains to what extent “set up” part is relevant and helpful in finding “information” and solving the “question”. She believes “too much attention to the story [set up] will distract students from the translation task at hand, leading them to consider “extraneous” factors from the story rather than concentrating on extracting variables and operations from” the text. I am completely agreed with the author that most set up part of word problem distract students from the main part of the question. Students take much time to understand the setup part of the word problem and sometimes they would loose the track of information especially with some extraneous data. In solving the word problem, some of my students, ask why these questions are so long and full of non-useful information, how these part of questions (set up) is relevant to the answer and solution? Set up part frustrates my ELL students who have issues understanding English language. They usually give up answering the question when they face a long word problem. When I ask them (sometimes force them) to read the question, they emphasize that we cannot understand it, we cannot solve it, it is too complicated. However, after reading the questions and carefully translating it, they mostly solve it easily. They laugh and say “it was easy!”
In Gerofsky’s article, there are some reasons behind the importance of the setup parts. Some scholars believe that without setup part, students cannot see the relevant of this question to the real life situations. This part helps them to imagine the real situation that they can use their mathematical knowledge. However, the critics of this viewpoint state that these parts are fictions and do not represent the real situation or even if show a real life, solving the problem relating these situations are not helpful for students. For instance, they bring up the example of a word problem that asks about the time of filling a tub or the amount of water that can be filled in the tub. They wonder how calculating filling time or volume of a tub help students? I think this kind of discussion shows the importance of setup part of a word problem. It means by modifying the setup part of these question, most of these deficiencies will be disappeared. Instead of telling a story about a tub and asking its volume, we can tell a story of a factory that fills the water bottle and asks the volume of water that is needed for each bottle or filling time. So, the question would be practical and useful. Gerofsky believes asking students to propose a word problem will show to what extent students have learned from those word problems that they solved. Studies reveal that most of the students propose questions exactly similar to what they already solved or faced in the school. They usually did not make new question based on their real life situation. It shows that students did not see any real life situation involved in the word problems. They just see the setup part as extraneous words of the question.
These issues highlight the weaknesses of the word problem, however, I believe it does not mean word problems are not required or applicable or useful. I believe we need to understand these issues and address them carefully. My question is what are the issues of current word problem? What are your suggestions to improve word problems? Do you remember any word problem that was not applicable? And finally what is your point of view regarding the word problem? (Is it useful or not or..)
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ReplyDeleteLike you, I have found that teaching math to ELL students can be frustrating. I have also wondered about the “literary genre” of math word problems for these students to learn word meaning and usage. The fact that the mathematical procedures can exist outside of word problems, and that the task becomes extracting the math from the problem makes me question their use. Students do become immune, and start substituting operations for words, like “of” and multiplication.
ReplyDeleteI think that there is a certain human storytelling urge that is satisfied by communicating mathematical ideas as word problems. They can be social. They can be creative. Tricks of multiple interpretations and personal connections can draw students in. But, I also think that word problems should be presented as just that. I appreciate the discussion of them as a linguistic genre.
I found the question of “truth value” interesting, and how mathematics word problems are disposable and interchangeable, in ways that fiction is not. I have found that as an instructor, I model deconstructing word problems but also create small fictions using known people and possible scenarios.
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ReplyDeleteThe idea of having too much in the set-up is interesting. There was a textbook called Math Makes Sense that included ' ethnically diverse' names. I presume the idea was to be inclusive of diversity in schools but the flip side was that when I worked with ELL learners, they were not able to or didn't care to understand these long story lines. The storylines were also typical of math texts, just names were diverse.
ReplyDeleteIt is so interesting how we become 'schooled' or conditioned to generate problems that we have seen before. I think the biggest problem with word problems is to get students to be free to generate things that are applicable to their lives.
On a somewhat funny note and connecting to ethno-mathematics there is a phrase in Punjabi that older women will say when they are asked if they want a cup of tea or chai. Many times older women will responde and will say that they want half a cup of tea. We make a joke of this in my class and carry on to half of a half a cup. I have used this to teach unit conversions; we make a cafe with our names for tea (grande, venti etc gets converted). I hope modelling genuinely authentic problems, building trust and relationship through humour and a common ground helps.
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ReplyDeleteAlso, with regards to this idea that students only come up with problems they see in textbooks, this reminds me of a TED talk called the "Danger of the Single Story' It is by a novelist named Chimamanda Ngozi Adichie who talks about how she only wrote European stories as a child because that is what she read as a child. It is dangerous (and tragic) for us to think that these limited textbook problems are what math is.
ReplyDeleteWord problem in mathematics is very difficult to teach to students where language used as the medium of instruction is their second or third language as practiced in Kenya. The first is Mother tongue, second Swahili and finally English. Students have always failed mathematics and termed it a difficult disciple because of a word not even sentence.I once experienced students failed a mathematics question in a national examination because of the word "abundant", if they could use "more" they would have got it right.
ReplyDeleteTo improve it, is by use of simple mathematical language and symbols, mathematics teachers are forced to teach analytical methods of handling word problem, some of these problems are very lengthy and confuses students.
Fascinating commentary everyone!
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