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DEFINITION

LESSON I: BASIC VARIABLES

LESSON II: PROBABILITY SPREADSHEETS

LINKS

BIBLIOGRAPHY

METACOGNITION: A DEFINITION

SHAUN WERSTED

Many high school math teachers would probably agree that the number one problem they have is that "...many students don't feel good about math, largely as a result of the way they have been taught. Because of the prevalent belief that classroom mathematics consists of mastering formulas, these students do not understand how mathematics can be meaningful." There is a growing number of people who believe that the answer to this problem lies in metacognition. Metacognition has been defined as "having knowledge (cognition) and having understanding, control over, and appropriate use of that knowledge" (Tei & Stewart, 1985 ). To use metacognition in the classroom a teacher must develop a plan of action, maintain and monitor that plan, and evaluate the plan once it is presented to students. The following paper attempts to present two lesson plans for a high school level algebra class that uses metacognition in their implementation.

LESSON I: BASIC VARIABLES

Objectives:

1. Assign values to a variable.

2. Collect information about variables and be able to use the information to solve for an unknown variable.

Materials Needed:

For each group of 3 students: 8 small containers and 80 small countable objects code sheet prepared by teacher.

SET: Explain to students that today we will play a game in which they try to solve other teamsí "Secret numbers."

REVIEW: Go over solving equations. Ensure everyone remembers how to solve equations. Explain that today they will learn how to write equations.

PROCEDURE:

1. Divide the class into groups of 3 or 4. Instruct each group to select a recorder to keep an account of the events beginning in step 6. Distribute 8 containers and 80 counters to each group.

2. Each group is assigned a different letter of the alphabet and each of the groupís 8 containers is labeled with the lowercase form of that letter. If the same lesson is taught repeatedly, the same containers can be used over and over.

3. Each group chooses a "secret number" between one and ten and informs teacher of their choice. The teacher keeps a record of all "secret numbers" on his code sheet.

4. Have each group place the "secret number of counters in each of their eight containers.

5. Each group will now have 8 containers, each of which contain the same number of counters and the same letter of the alphabet. Discuss ways to express the total number of counters in all 8 containers. For example: m+m+m+m+m+m+m+m or x+x+x+x+x+x+x+x. Build on that idea: 8m or 8x.

6. Have each group exchange some containers with one other group. For example, 3 mís are exchanged for 3 xís. Each group records its holdings in the following manner: m+m+m+m+m+x+x+x or 5m + 3x and x+x+x+x+x+m+m+m or 5x +3m.

7. Each group confers with the teacher who checks the code sheet to tell them the total number of counters their groups is holding. For example, the first group has 5m + 3x counters. The teacher tells them they have 22 counters.

8. Discuss if necessary how to write an equation to express the total number of counters. For example, 5m + 3x = 22.

9. Each group solves the equation they have developed to solve for the unknown variable.

10. Students continue to trade until they have discovered each groupís "secret number" or until time has run out.

11. Encourage students to keep solutions within their group so each group can make their own discoveries on their own.

CLOSURE:

Have students return to their desks. Explain that they now should be familiar with how to write algebraic expressions to represent real objects.

ASSESSMENT: Students will be assessed through informal observation and formal written evaluation on a written test.

LESSON II: PROBABILITY SPREADSHEETS

OVERVIEW:

Students pair up and toss coins to learn probability of coin tosses and then make a spreadsheet and graph to record the data.

PURPOSE:

To increase the knowledge of probability and how it affects a simple coin toss and then apply computer skills in using spreadsheets.

OBJECTIVES:

Students will be able to: Team up and (1) create probability outcomes,(2) record data and(3) create a spreadsheet using the probability data and then a (4) graph for visual reference.

RESOURCES/MATERIALS:

Computers, Microsoft Spreadsheet on the Works program, work sheet, coins, dice, cards or other devices to devise a probability ratio, printer, and web editor if placing on the Internet.

ACTIVITIES AND PROCEDURES:

Students are paired off, one recorder and one does the probability experiment. Student rolls dice or flips coins (50 times using the worksheet provided as the guide), the other student records the data.

Students add up the results and using the MS Works program show their results in a digital format.

Activity may be placed in a booklet for all and/or published on the web site.

Note: Could easily use the scientific method before attempting the experiment.

TYING IT ALL TOGETHER:

To show students how the probability system works and show how the computer can enhance a difficult task of teaching.

EVALUATION:

Students see how they apply skills with the computer to everyday events, sheet will have all data posted as on the worksheet.

BIBLIOGRAPHY

http://mathforum.org/~sarah/Discussion.Sessions/Schoenfeld.html

http://www.lessonplanspage.com/MathVariablesAndSolvingForUnknownVars78.htm

http://www.lessonplanspage.com/MathCIProbSpreadsheets6HS.htm

LINKS TO OTHER SITES

LESSON PLANS AND TEACHER CHAT ROOMS

http://7-12educators.about.com/cs/mathalgebra/index.htm

http://www.teachers.net

http://psrtec.clmer.csulb.edu/21stcent.htm#lpr

http://mathforum.org/discussions

SITES ON METACOGNITION

http://mathforum.org/~sarah/Discussion.Sessions/Schoenfeld.html

http://www.indiana.edu/~eric_rec/ieo/digests/d96.html

GOOD SITE FOR STUDENTS TO GET HELP WITH THEIR ALGEBRA

http://library.thinkquest.org/10030/algecon.htm

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