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Rationale
for Use
This article provides teachers
with strategies for identifying and creating opportunities for students to engage
in algebraic thinking. Helping students generalize their mathematical thinking
by routinely expressing and justifying their generalizations will develop students’
capacity to think algebraically and can lead to greater students’ achievement.
Suggestions
for Use
This activity
may be used with elementary school teachers.
Procedures
- Solve
the Handshake Problem. Share and discuss different solution strategies. (The
Handshake Problem: How many handshakes will there be if each person in your group
shakes the hand of every person once? Start with a group of three people, then
increase the group size by one person each time.)
- Compare
the original (Version 1) and “algebrafied” (Version 2) for the handshake
problem (p. 72). Discuss how the two versions are the same and how are they different.
- Read
the article and discuss the authors’ description of algebrafied tasks.
In what ways does the description of algebrafied tasks account for the differences
in the two tasks that you identified in question 2?
Discussion
Questions
- How would you support students’ algebraic
thinking? (e.g., How would deal with Sarah and Stephen’s confusion? How
would you question Tory and Mary so as to shift their focus to algebraic thinking?)
- How would you create a classroom culture that
promotes algebraic thinking?
- What challenges might you encounter in orchestrating
student-centered discussion?
- How does algebrafying tasks support the development
of algebraic ideas as discussed in Principles
and Standards for School Mathematics (see Grade 3–5 Algebra,
pages 158–163) or in Navigations (grades 3–5)?
Extensions
- Select
a task from your own curriculum, and create an algebrafied version of the task,
keeping in mind the description Blanton and Kaput provide on page 72.
- Plan
a lesson around the algebrafied task, taking into account the recommendations
made by Blanton and Kaput for finding and supporting students’ algebraic
thinking.
- Implement
the algebrafied task in your classroom. Document students’ work on the
algebrafied task. Meet with colleagues to discuss what the student responses
tell you about what students know and can do.
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