Gerofsky explores the goals of using world problems in school by using linguistic analysis on the structure of mathematics word problems used in schools. There are usually 3 components seen in a typical word problem: 1. the exposition, 2. some information to solve the problem, and 3. the question. Gerofsky pays special attention to the first component which establishes the characters and places of the story, and argued that it only worked as a statement which is actually irrelevant to the question. The author continued to examine the structure of word problems with the lens of linguistics analysis. It is pointed out that there is a mutual understating over the inconsistency of the tense used in word questions (sometimes, it is all present tense, while in others it is mixed with present and future tense), which might be explained by the philosophy behind word problems: hypothetical solutions to hypothetical situations. Gerofsky argued that most questions could be rewritten in a standardized form: Suppose condition A exists. Then, if conditions B and C held, what would be the answer to D. This leads to an interesting argument that word problems are hardly a fiction genre as word problems don’t present “truth values”. Gerofsky invites us to think of word problems as parables, but also cited contradictory studies about the analogy. According to her, delineating the boundaries of word problems as a genre opens a door to generate more productive discussion over the rationale for using word problems at school.
Stop:
While many teachers hold the belief that word problems help students to learn “adaptive” or “contextual” mathematics, the author invites us to look closely at the elements, structure and variance of world problems. There is no doubt that students have developed an “immune system” to word questions, as they skip the story and quickly search for numbers and key phrases which are useful for plugging in to formulas. With that mindset, students gain a limited understanding of goal setting, planning, and do not develop a positive attitude toward problems.
Question:
Do you prefer “real world” word problems with the three elements mentioned, or abstract problems that cut to the chase?
My first reaction to your question is: do I have to choose only one? I think that both these type of problems can have a place in mathematics classrooms. Students do need problem solving and critical thinking skills in the 21st century and those skills need to be implicitly taught. Often, the easiest way to get students to connect to the word problems is to provide them with real world contexts.
ReplyDeleteHowever, teaching students to solve abstract problems is also important, particularly in leading students towards higher-level maths. My teaching style has always followed the widely held pattern of teaching math concretely, then pictorially and finally abstractly.
My current class of Grade 7s is able to see how the solving of “real world” word problems pictorially is connected to abstract mathematics and has made their transition to the first example of abstract math, algebra, less challenging.
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ReplyDeleteI suppose the word problems with real world example is easier for teachers to contextualize mathematics class as well as for students to understand given situations and questions. Some students have obstacles to imagine the given contents in non-real world word problems. However, as Nancy mentions, students need to confront word problems of both real world and abstract. I believe abstract word problems can improve students logical thinking skills and to build their idea for given situations.
ReplyDeleteI am curious whether word problems with real world or abstract is better for English Language Learners (ELLs) to understand given situations and problems. As Cummins (1984) identifies language skills into BICS (Basic Interpersonal Communication Skills) and CALP (Cognitive Academic Language Proficiency), there might be various language factors that can influence their mathematics understanding. I guess ELLs, especially people who are familiar with current abstract word problems, get higher score in abstract word problems than real world ones, while they actually understand the real world word problems contents more than abstract ones.