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Taming the Math Monster
Taking a Metacognitive Approach to
Teaching/Learning Mathby
Andrea Johnsonand
Linda Hegeberg
5 + 2(3) =
A storekeeper goes to the bank to get $10 worth of change. She requests twice as many quarters as half dollars, twice as many dimes as quarters, three times as many nickels as dimes, and no pennies or dollars. How many of each coin did the storekeeper get?
Huh??
You’re kidding me. Right???
NO WAY!!!
Taming the Math Monster
Horror
Panic Frust
rationConf
usion Intimidation
So What is Metacognition?
• Awareness or analysis of one's own learning or thinking processes. (Merriam-Webster, 2012)
• Metacognition also includes self-regulation—the ability to orchestrate one's learning: to plan, monitor success, and correct errors when appropriate—all necessary for effective intentional learning… Metacognition also refers to the ability to reflect on one's own performance. (National Research Council, 2000)
• Learning how to learn cannot be left to students. It must be taught. (JP Gall. Tools for Learning, 1990 )
Reading Apprenticeship Conceptual Framework
Personal Math Log
• Examination of self as a learner• A priori attitudes about
math• Set goals• Ongoing reflection
throughout quarter
Personal Math Log Day 1: What attitudes about math do I bring to this class and why? What are my strengths? Weaknesses? What GOALS do I have for myself this quarter? _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.
On-going post-test reflection Exam #1 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Exam#2 _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.
End of Quarter: How has my attitude regarding math changed? Current strengths? Weaknesses? _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.
Math Self-Evaluation• Initiated after mid-term• Salient Self-Reflection:
strategies, changes, and resources
• “Pair Share”
Math Self-EvaluationName: ___________________
Have I reached my goal(s)s at this point? Do I need to set new goals?______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ What are the learning strategies that have worked for me this quarter? What strategies have NOT worked?_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ What changes do I need to make in order to be more successful in math?_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Resources I have tried:
Resources I NEED to try:_____________________________________________________ ______________________________
_______________________________________________________________________________________________________________________________________________________________________________________
Comments: ____________________________________________________________________________________________________________________________________________________________________
Initials Section Points and explanation/plan for completion and peer initials Graded?
______ ______
4.3_________ 4.4_________
_____ ___________________________________________________________________________________ _____ ___________________________________________________________________________________
___________ ___________
______ ______ ______
4.5_________ SummaryExercises_________ 4.6_________
_____ __________________________________________________________________________________ _____ __________________________________________________________________________________ _____ _________________________________________________________________________________
___________ ___________ ___________
______ ______
4.7_________ 4.8_________
_____ __________________________________________________________________________________ _____ _________________________________________________________________________________
___________ ___________
Week #5Totals
Homework Peer-Review Sheet Name______________________________
(4.3 – 4.8) – Due 3/4 Name of Peer: _______________________
Homework Peer Review (Adapted from Calhan Ring)
Chapter(pg. #)
Trouble-Area/Roadblocks(Questions that I have) Strategies, Hints, and Example
Mastered?(If not, what is
my plan?)
Clarification Chart – Chapter(s) _________Use this chart to document your trouble-areas (roadblocks) as you progress through the chapters of the book. As you learn strategies and solutions to your questions, fill in the chart. If you haven’t mastered the concept on your own, try the tutoring center, Study Plan on MML, or ask your instructor. This chart is a great TOOL for exams and should be turned in with HW Packet for credit.
First Day Questionnaire/Syllabus Quiz
Name: Program:
1) Are you a running start student?
2) What is the last math class you can remember taking, when did you take it, and what was your grade?
3) What is one thing you like about Math? And one thing you dislike?
4) Rate yourself as a reader on a scale from 1-5, 1 being illiterate, 5 being a proficient/prolific reader:
1 2 3 4 5
5) Please fill me in on any concerns or comments you have about math and/or reading:
6) I have read and understand the Math 98 Syllabus and Assignment Schedule (yes or no):
7) The Instructor’s name is:
8) How many online MyMathLab (MML) homework assignments are there?
9) When is the Quiz #3 due?
10) How many exams are there?
11) In-class work constitutes 10% of your grade, how do you earn these points?
12) What are 3 things engaged students do?
13) I believe everyone can learn math. You can be successful in this class when you put in the effort. Think about your schedule and where math learning will fit in. Please list 2-3 times and places during your week that you will devote to Math 98 (besides class time):
THINK
WRITE
SHAREPAIR
Read the problem
What do I know about this? What is being asked?
What can I figure out?
Can I estimate an answer?
Your ideas
Knowns
Unknowns
Formulas needed
Start solving
Find a partner
Decide your roles: Problem Solver- “think out loud” while solving the problem.
Assistant- listen to the problem solver, ask clarifying questions, give hints if needed, but not solving the problem.
Share your strategies and roadblocks, then: Problem solver solves
Assistant assists
Switch roles and go through the steps again for another problem
A storekeeper goes to the bank to get $10 worth of change. She requests twice as many quarters as half dollars, twice as many dimes as quarters, three times as many nickels as dimes, and no pennies or dollars. How many of each coin did the storekeeper get?
Answer:5 Half Dollars, 10 Quarters, 20 Dimes, 60 Nickels
Trades Management
Last year, the owner of the Fixum Auto Repair Shop paid a premium of $9.92 per $100 of gross wages for workmen’s compensation insurance. This year his premium will increase by 4%. If he has 8 employees averaging $22 per hour, 40 hours per week for 50 weeks, what will be his total premium for this year?
Answer: Total premium will be $36,315.14
Backyard Baseball
In baseball, the infield is called the “diamond”; it is actually a square. But the DeVito brothers had to improvise in their backyard for infield practice. They made the distance from home to first base 60 feet, the distance from first base to second base 80 feet, the distance from second to third base 60 feet, and the distance from third base to home 80 feet, creating a rectangle. How far is the distance, diagonally, from second base to home plate?
Answer: 100 feet
•Think about the strategies that you could adapt for use in your classroom to help “Tame the Math Monster”
•Write down your ideas
•Pair up and discuss how you would use it in your classroom
•Share - Those who are comfortable, please share your ideas with the rest of the group
Taming the Math Monster
Horror
Panic Frust
rationConf
usion Intimidation
Taming the Math Monster
Empowerment
Clarity
Safety
Enthusiasm Confide
nce
Closing the Loop:
Letter to Incoming Students
