TEACHING MATHEMATICS WORD PROBLEM SOLVING TO DEAF STUDENTS

COMETS WORKSHOP

Review of the Literature:

WORKSHOP

Before the workshop,

1) Have teachers read the Problem Solving Workshop: Pre-readings

2) Have each teacher participant bring some element from their regular math curriculum--lesson plans, text, etc. to be used during the workshop.

3) For the Leader

1. Introduction

The leader identifies that in today's workshop, the emphasis will be on using familiar curriculum but in a new way, to structure lessons for problem-solving strategies. The goal of the workshop is that everyone leaves with a MODEL that can be transferred to their entire math curriculum as they teach it for the remainder of the year.

1. The leader then explains that the teaching of problem-solving will follow a 3-part framework, that we will illustrate during the session. The three parts of this problem-solving sequence involve:

• Teaching the particular problem-solution , perhaps using math materials, employing a set of strategies to be explained

• Metacognitive discussion, to be explained further

• Application of the strategy to a new context , sometimes working independently.

On an adult level, the leader then provides the group with a single, interesting, and challenging problem from mathematics, preferably a challenging word problem.

2. The group is divided into working pairs of teacher-participants who are given the task of generating at least two more if there is time) explanations of what the real problem is (Problem-identification).

3. Pairs then share with the large group what they believe the real core problem to be; through large-group discussion, consensus is reached on the core problem, and it is written clearly by the leader for the group to see.

4. As a large group, ideas are solicited for what
may be some workable alternative ways to go about the solution --not yet trying to solve the problem, but just discussing the OPTIONS for some possibly fruitful avenues to pursue. Preferably, three solution paths would be identified by the large group (Choosing Solutions).

5. Divide the larger group into three sub-groups or teams, and each group then tries to carry out the actual solution according to one solution path; thus each of the teams has a different solution path which they are testing (Executing the Plan). At this stage, it is VERY important that the groups not only carry out their respective plans, but also make notes about the processes used; appointing one member of each group as a recorder will facilitate this process. A group chair should also be appointed.The recorder can note also the "false" starts that the group makes as well.

6. At this point, the chairs of each of the three teams use their recorder's notes to report on their team's solution success by including these several steps:

• Explain the solution process and whether it worked or not.
• Illustrate the process, by writing out on a smartboard or some other medium that the whole group can see, the steps or the algorithms used.
• Description of what did NOT work, and WHY.
• Encourage commentary from the larger group.

7. The large group then discusses whether more than one solution path is usable in this particular problem. The larger group then discusses the process to be used to CHECK the answer for accuracy (Checking the Answer). A set of steps is listed.

8. Now is the opportunity to engage in reflection or
METACOGNITION. The leader should explain that there are at least two dimensions to metacognition:

1. Task-oriented in relation to monitoring the solution to the particular problem (in this case the math problem), and
2. Sstrategic in terms of the selection of a particular strategy which may go beyond the immediate particular problem (Presseisen, 2001).

   Research on deaf learners indicates that the current strategies which are used to teach reading to deaf learners may actually hinder the development of mature metacognitive knowledge, that the low-level reading material that is often given to deaf children may not give them opportunity to develop and practice metacognition, and that deaf students in fact CAN benefit from metacognitive strategy instruction (Strassman, 1997). Martin, Craft, and Zheng (2001) found also that deaf learners in three different countries could carry out metacognitive discussions and gain insights into their problem-solving processes.

9. The leader should now ask participants to reflect on the solution which they selected and the PROCESSES that they used, building around the questions:

• What methods did you use in the solution?

• Why did you use those methods?

• If you were to approach a similar problem tomorrow, what would you do differently? The same? Why?

• How will you approach the next problem you have in math, based on this experience?

 

10. The larger group now discusses the question, "Where else in life are these general strategies useful?" This is known as TRANSFER, moving the participants out from math per se, to applying these strategies in new non-math contexts.
Examples could be making difficult decisions such as seeking a job, purchasing a car, negotiating a reconciliation when two friends have had a serious disagreement, etc.

11. Each individual participant is now asked to take the math curriculum element which they brought with them and select one teaching episode or lesson topic, and then work individually to construct a lesson plan which uses these same strategies which the whole group has just demonstrated and participated in, during this workshop

• problem identification,
• choice of solutions,
• executing a plan,
• checking the answer,
• reflecting on the processes used.
  
  

12. Individual participants then share their lesson plans with one partner, for comparison and also feedback and editing.

13. The large group then comes together again and with the help of the Leader, lists some principles learned from writing the lesson plans as well as from the whole session. This effort is to identify what is COMMON across the various lesson plans, whose actual topics will be probably quite varied.

14. Thus, the experience of the workshop as a whole has demonstrated the three fundamental steps of:

• developing a strategy
• doing metacognition
• and making transfer

within the first or strategy segment have been the basic steps of problem-identification, the choice of solutions, executing the plan, and checking the answers.

15. Final discussion -- What will you do differently now in teaching mathematics? This general sharing should confirm for everyone the primary thrust of this workshop session.

Additional Resources:

Project SOLVE: An Exciting Federally-Funded Project to Enhance Math Word Problem Solving Skills in Deaf Students

Do you have a deaf student in your class? Are you searching for resources to help your deaf student(s) improve word problem solving skills in mathematics? Project SOLVE is a web-based problem-solving mentoring system. Many different algebra and introductory college-level math problems are being placed on the web with various help menus to guide the student in developing skills.

In addition, if you are interested in tailoring this bank of problems to include some of your own problems from your course, please contact us.

Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics

Alan Schoenfeld, a leader in math problem solving, wrote this article, Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics. This article talks about a broad conceptualization of what it means to think mathematically, to summarize the literature relevant to understanding mathematical thinking and
problem solving, and to point to new directions in research, development and assessment consonant with an emerging understanding of mathematical thinking.

Mathematics teachers interested in discussions with other teachers should see the COMETS Discussion Board for sharing successful problem solving and other mathematics education strategies.

The COMETS newsletter will regularly update the network with new additions to the website and progress in the various other grants and research projects. Be sure to join COMETS Network if you are not receiving the newsletter.