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                                           Rick's Case Outline

I.                 Setting

1.                 Course: Algebra I, Fairview High School; block schedule, moving at twice the conventional rate (475 minutes per week, with the entire course completed from September to January)

2.                 Students: 9th through 11th grade (about half are higher grade students who are repeating the course; for some, it is the third try); ethnically diverse, but no English language learners.  Much of the class work is done in stable heterogeneous groups.

II.                 Subject matter/problem

1.                 Linear equations, including applications

2.                 Throughout the early portion of the course, students performed adequately on tasks in which a problem was set out in algebraic notation, requiring only symbolic manipulation and computation.  I discovered that whenever a "word problem" was posed, requiring them first to construct an equation to represent a situation described in English, they all froze, giving me their best "deer in the headlights" facial expression.  Given an appropriate equation, they could solve it, but they were unable and/or unwilling to generate a suitable equation.  I assumed that this was an entrenched problem inherited from prior years' math classes, and that it was both worthy of direct attack and amenable to a cure.

III..                 Plans to address the problem

1.                 Initial training and de-mystifying efforts: I provided practice in converting simple sentences to equations, with many hints for translation.  For example, in the sentence, "The width is four more than the length", the verb "is" corresponds to an equal sign, and the phrase "four more than" corresponds to "+4", yielding an equation such as W = L + 4.  Each day, one or more problems requiring a translation to notation were included in the warm-up exercises, regardless of the other content to be covered that day.  After a bit of practice, most were successful; however, more complicated problems still brought them to a screeching halt.

2.                 Attempts at diagnosis: I surmised from their questions that they were having trouble getting started on long or apparently complex problems, perhaps intimidated by the length.  Reading skill did not appear to be an issue.  A methodology for approaching such problems seemed to necessary, so I prepared a "getting started" handout with suggestions for breaking down each problem into smaller stages, and reviewed it with the class using several examples.

3.                 Putting it all together:  I also thought that the usual problems might be too dry to inspire much student interest.  I made up a set of problems using what I knew about one student in each of the groups. For example, one problem dealt with concert tickets for N-Sync (a favorite band of two girls in one group), one dealt with dimensions of a tennis court (for a group including a junior varsity tennis player), and so forth.  A different problem was written for each of the five groups, although each required use of the same mathematical principles for solution.

IV.                 Dashing of hopes

1.                 On the day I had chosen to test progress, I passed out a problem to each group, along with copies of the "getting started" handout previously used.

2.                 After twenty-five minutes, only one group out of five had successfully produced an equation and solved it.  I thought that these problems should have been solved in no more than ten minutes.

V.                 Questions:

1.                 What did I do wrong?

2.                 What did I fail to do?

3.                 What did I overlook, or falsely assume?

Copyright 2000, Karen Hammerness, Stanford University. All the material contained on this site has been produced by Karen Hammerness, Lee Shulman, Linda Darling-Hammond, Kay Moffett, and Misty Sato. These materials can be downloaded, printed and used with proper acknowledgement, including the name and affiliation of the authors and the web-site addess.

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