Ever wonder why when you give a student a real-life word problem to solve they seem to lose all sense of reason and mathematical ability? Why is it that students resort to simply looking for key words or extracting arithmetic for finding a solution to a real-life word problem? Why is they can do naked number math problems, but put the math in a problem scenario and they’re clueless?
Take for example one of LearnBop's proportion problems at www.learnbop.net/S/7.RP.A.3. As the Common Core Standard 7.RP.A.3 suggests, students need to be able to "use proportional relationships to solve multistep ratio and percent problems." When you look at the data for this problem, what seems like a simple problem can in fact be quite perplexing to students.
As the data indicates, almost half the students who attempted this problem are lacking prerequisite skills in addition/subtraction (49%) and more than a third have trouble completing tables (39%). That's part of the challenge, but looking deeper at the student responses (see the Full Report), it’s clear that many don’t know how to approach the problem, and less than half of them solve it correctly.
Research has shown that students struggle with relating the real-world context of a problem with the mathematical task required to solve it—that is, with mathematizing the problem. According to Lave (1992), this disconnect is a result of word problems not being realistic but rather stylized representations of hypothetical experiences, which results in students not seeing them as math problems. So what can you do to support students in making sense of the problem, and assist them in the process of translating words into mathematics so they can solve the problem?
Word problems are structured around a scenario, information, and question (Gerfosky, 2006). Often information in the problem is arbitrary in relation to the scenario and involves an ambiguous use of verb tense, time, and reference. This can make solving the problem challenging for any student, but especially challenging for English language learners.
Barwell (2005) found three dimensions of word problems that students pay attention to - genre (language), mathematical structure, and personal experience (life). He notes that the three aspects are interrelated. Personal experience makes the underlying mathematical structure meaningful and allows for interpretation of the word problem. That is, understanding the structure of the problem is necessary to mathematize the scenario.
Students are able mathematize situations based on their own real-world problems—problems that they write themselves, for instance. Therefore it makes sense for you to draw upon this ability so that students can mathematize word problems they have not seen before. Examining how students write their own problems can provide insight into the features they are not aware of, not just as a mathematical task, but also as a form of text. In order to do this, Barwell recommends the following activities.
Relating Language and Mathematics
Each activity should be followed by discussion about the language used in the problems and how the language is related to the mathematics task within the problem.
- Students compare two problems with the same mathematical structure and discuss the similarities and differences in the two. Draw attention to the fact that the scenario can change but the essential mathematical structure and calculations do not change.
- Students write word problems for a given calculation and compare the different problems and solutions, then discuss the ways in which the math structure is represented in words.
- Students mathematize word problems by rewriting the problem or changing the mathematical operation required to solve the problem.
Relating Life and Mathematics
- Students update an existing problem to make it more realistic by including current prices or information.
- Students compose and solve world problems relating to current events in their lives.
Relating Life and Language
Following each activity, discuss the role of the scenario in the problem, including the idea that some information is not relevant to the mathematics in solving the problem.
- Students engage with the contexts of problems in different ways by creating pictures, writing stories, or making a model.
- Students share their solutions to the problem presented.
Engaging in activities like these promote an understanding of the structure of word problems. Students who understand the structure of stories make better readers, so it would stand to reason that understanding the structure of word problems would make your students better readers and problem solvers.
I invite you to provide your comments in the comment section below about why you think students struggle with this concept, what prerequisite skills prove to be most challenging, and/or activities, resources, and tools you’ve found beneficial in teaching the prerequisites or concept. In the future, we'll be sharing more about how to use data to identify and address the specific concepts students struggle with. You can stay informed and find additional resources about using data to inform instruction on Facebook, Twitter @LearnBop, and our blog www.learnbop.net/blog.
Please join me on Tuesday, January 28 from 2:00 – 3:00 ET for our first Twitter Chat, where we'll be talking more about how to help students struggling with Unit Rate problems, and CCSS 6.RP.A.3b. We'll be using the hashtag #LBdatachat.
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