Fostering Algebraic Thinking - PowerPoint PPT Presentation

1 / 30
About This Presentation
Title:

Fostering Algebraic Thinking

Description:

10:40-11:20 Postage Stamp Discussion. 11:20-11:45 Making a Mathematical Thinking Record ... In groups of four people, work on the Postage Stamps math activity. ... – PowerPoint PPT presentation

Number of Views:52
Avg rating:3.0/5.0
Slides: 31
Provided by: Debbi50
Category:

less

Transcript and Presenter's Notes

Title: Fostering Algebraic Thinking


1
Fostering Algebraic Thinking
  • May 19-22, 2008

2
A core belief underlying Fostering Algebraic
Thinking is that good mathematics teaching
begins with understanding how mathematics is
learned.
3
While the materials provide activities for
teachers to do with students, the primary focus
is on TEACHER learningin the belief that student
learning will also be served.
4
Goals
  • Become familiar with the Fostering Algebraic
    Thinking materials.
  • Examine activities that may be challenging to
    facilitate.
  • Develop plans for implementation at your sites.

5
We will focus on
  • How students think about mathematics.
  • Understanding students thinking through analysis
    of different kinds of data.
  • Understanding how algebraic thinking develops.
  • Instructional implications.

6
Fostering Algebraic Thinking Modules
  • Analyzing Student Written Work
  • Listening to Students
  • Asking Questions of Students
  • Documenting Patterns of Student Thinking

7
Agenda Overview
  • Monday AMIntroductory Session
  • Monday PMAnalyzing Written Student Work
  • Tuesday AMAnalyzing Written Student Work
  • Tuesday PM Listening to Students
  • Wednesday AMAsking Questions of Students
  • Wednesday PMPlanning for Implementation
  • Thursday AMDocumenting Patterns of Student
    Thinking
  • Thursday PMClosing Session

8
Group Norms
  • Begin and end on time.
  • Respect your colleagues ideas and opinions.
  • Monitor your own participation.
  • When working in groups, allow time for group
    members to read and think about the problem
    before beginning your discussion.
  • Only one conversation should take place in a
    group at a time.

9
Agenda
  • 900-930 Announcements
  • 930-955 Introduction to A-HOMs
  • 955-1025 Postage Stamp Problem
  • 1025-1040 Break
  • 1040-1120 Postage Stamp Discussion
  • 1120-1145 Making a Mathematical Thinking
    Record
  • 1145-1200 Group Process Discussion
    Announcements

10
Agenda
  • 100-130 A-HOMs Discussion
  • 130-215 Crossing the River Problem
  • 215-230 Break
  • 230-300 Crossing the River Discussion
  • 300-400 Crossing the River Example Papers

11
Introductory SessionGoals
  • Build the foundations of a comfortable and
    productive study group.
  • Familiarize yourselves with the FAT sessions and
    some of the tools, such as the Mathematical
    Thinking Record (MTR).
  • Explore the concepts of algebraic habits of mind.
  • Become comfortable working on mathematics
    activities together and sharing mathematical
    ideas.

12
Think about the phrase habits of mind.
  • Have you heard this phrase before in the context
    of mathematics?
  • What does the phrase mean to you?
  • What ideas or other phrases does it bring to mind?

13
Look at the Algebraic Habits of Mind Diagram and
Table.
  • The algebraic habits of mind are a language for
    describing algebraic thinking. We will use this
    language as a tool to understand and talk about
    the kinds of thinking that you and your students
    do about mathematics.

14
Look at the features of the different habits of
mind.
  • Which of these lines of thought seem familiar to
    you?
  • Can you think of things you have seen your
    students do that indicate that they are engaging
    in these productive lines of thought?

15
Postage Stamps
  • In groups of four people, work on the Postage
    Stamps math activity.
  • While working on this problem, think about the
    methods people in your small group tried, the
    questions they asked, the process for coming to a
    deeper understanding, and the different ways of
    thinking about the problem.
  • Post your groups work.

16
Postage Stamps Discussion
  • In what ways is this problem algebraic? How
    does it elicit algebraic thinking?
  • You may have noticed yourself working from output
    to input. How did different group members work
    from output to input to answer questions such as
    How can I make 53 worth of postage?

17
  • What computational shortcuts did group members
    use as they worked on the problem?
  • How were these shortcuts useful?
  • What rules did group members come up with to help
    them generate postage values of 5 and 7 stamps?

18
Mathematical Thinking Record (MTR)Postage Stamps
  • What would you like to recall about the different
    strategies and/or solutions used by your
    colleagues? Record the approaches and strategies
    you would like to remember.
  • What would you like to recall about the
    algebraic thinking? Record the specific features
    of habits of mind that you have seen in the
    different solutions.
  • What would you like to recall about the different
    strategies and/or solutions used by your
    students? Record the mathematical approaches or
    strategies you would like to remember.

19
Group Process Discussion
  • How does the way the group works help you develop
    a spirit of inquiry and ask questions about
    algebraic thinking or the teaching of algebraic
    thinking?
  • How could the group do this better?

20
Analyzing Written Student Work Goals
  • Explore the Algebraic Habits of Mind.
  • Examine algebraic thinking in your own and your
    colleagues written work.
  • Use student written work as data during the
    process of exploring algebraic thinking.
  • Explore the range of algebraic ideas that can
    occur in students thinking .
  • Look for potential in students written work.

21
Algebraic Habits of Mind (A-HOMs)
  • Doing-Undoing
  • Building Rules to Represent Functions
  • Abstracting from Computation

22
Doing-Undoing Features
  • Input from output
  • Working backward

23
Building Rules to Represent Functions Features
  • Organizing information
  • Predicting patterns
  • Chunking the information
  • Describing a rule
  • Different representations
  • Describing change
  • Justifying a rule

24
Abstracting from Computation Features
  • Computational shortcuts
  • Calculating without computing
  • Generalizing beyond examples
  • Equivalent expressions
  • Symbolic expressions
  • Justifying shortcuts

25
Crossing the River
  • Work with the members of your group on the
    Crossing the River activity.
  • As you work, think about the strategies you are
    using to solve the problem.
  • Post your groups work.

26
Crossing the River Discussion
  • Did everyone come up with the same solution (or
    partial solution) to the problem? Why or why
    not?
  • What aspects of algebraic thinking were involved
    in the various approaches?
  • What might the strategies for solving this
    problem indicate about understanding the
    algebraic concept of variable?
  • The last question is sometimes difficult for
    students. Why do you think that is?

27
MTRCrossing the River
  • What would you like to recall about the different
    strategies and/or solutions used by your
    colleagues? Record the approaches and strategies
    you would like to remember.
  • What would you like to recall about the
    algebraic thinking? Record the specific features
    of habits of mind that you have seen in the
    different solutions.
  • What would you like to recall about the different
    strategies and/or solutions used by your
    students? Record the mathematical approaches or
    strategies you would like to remember.

28
Crossing the River Example Papers
  • Follow the instructions in Activity 1, pages 5-14.

29
Group Papers
  • The small group discusses What evidence do you
    see in these papers of the habit of mind Building
    Rules to Represent Functions?How did students
    organize information?In what ways do they
    describe any rules they are building?Do any
    other features of Building Rules to Represent
    Functions play out in the student work?
  • What evidence do you see in these papers of
    Doing/Undoing or Abstracting from Computation?

30
For Tuesday
  • Review Sums of Consecutive Numbers activity.
  • Review The Staircase Problem.
  • Select one or two examples of student work to
    bring to the group.
  • Read Algebraic Thinking Tasks.
Write a Comment
User Comments (0)
About PowerShow.com