OAASFEP Math Tools Keynote 3-25-10 - thoughtfulclassroom.net · Title: Microsoft Word - OAASFEP...

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OAASFEP Conference | March 25, 2010 | Keynote Presented by Tr. Harvey F. Silver Ed.D. Pam L. Warrick, Ph.D. Silver Strong & Associates

Math Styles and Strategies: How to Differentiate Instruction and Increase Student Engagement in Any Mathematics Classroom


Mathematical Styles and Strategies for Differentiating Instruction and Increasing Student Engagement

Our thoughtful questions:

• Why do some students succeed in mathematics while others do not? Is it a matter of skill or will?

• How can we use research-based teaching tools and strategies to address

the styles of all learners so they succeed in mathematics?

Our workshop is based on the following assumptions: • What teachers do and the instructional decisions they make have a

significant impact on what students learn and how they learn to think.

• Different students approach mathematics using different learning styles and need different things from their teachers to achieve in mathematics.

• Style-based mathematics instruction is more than a way to invite a greater

number of students into the teaching and learning process; it is, plain and simple, good math—balanced, rigorous, and diverse.

In this workshop, you will learn:

• The characteristics of the four basic mathematical learning styles (Mastery, Understanding, Self-Expressive, and Interpersonal) and how to assess your own mathematical teaching style and the mathematical learning styles of your students.

• How to use a variety of mathematical teaching tools to differentiate instruction and increase student engagement.


MEET YOUR NEIGHBOR BY THE NUMBERS

Numbers play an important role in our life experiences, from a person’s age to important dates, to birth order, to college GPA, and so on.

1. Select five’s numbers that are meaningful to you and that will help someone learn a little bit more about you.

2. Next write a sentence or question for each number, leaving a blank line

where the number should go (e.g. The number of people in my family is __.). Share your numbers with your neighbor. See if your neighbor can match the right number to your sentence.

Sentence Answer

1.

2.

3.

4.

5.

3. Meet with two other pairs (to form a group of six) and write each of your

numbers on a “Post-itTM.” Place your numbers on your table and see how many groups you can make that share a common characteristic (e.g. 2, 12, 32—numbers that have the number 2 in the ones column).

4. Visit another table and try to guess the reason for their groupings.

5. Return to your table and discuss how you might use some of the parts of this activity with your students.


WHO AM I AS A LEARNER OF MATHEMATICS?

The three things I remember most from learning mathematics are: 1. 2. 3.

I learn mathematics best when I can:

Mathematics is… Because…

Which of the following math terms best describe you as a learner of mathematics? Circle all that apply.

variable cubical spherical

irrational equilateral congruent

infinite finite rational

point acute factorial

parabolic minimum constant

exponential divisible square

maximum obtuse transformation


MATHEMATICAL ANTICIPATION GUIDE

Complete the first (Before workshop) and last columns (After workshop) by placing an “A” for “Agree” or a “D” for “Disagree” in each box. Share your thoughts with your group and give one or two reasons to support your position. Before After Workshop Workshop

1. Most mathematics teachers use a variety of teaching tools and strategies to teach mathematics.

2. Differences in mathematical teaching styles account for 65% of the reason that students are not successful in mathematics.

3. There is an inverse correlation between writing in mathematics and mathematical achievement.

4. Success in mathematics has more to do with feeling than with thinking.

5. Cooperative learning is a highly effective strategy for learning mathematics.

6. Proficiency in mathematical procedures is more important than understanding mathematical concepts (procedure vs. content).

7. In the United States, teachers of mathematics cover more content in a year than their counterparts in other countries whose students score higher on international tests of mathematical achievement.

8. Access to high-level concepts in mathematics is an important equity issue.

9. Mathematical achievement has little to do with career success.

10. Divergent thinking and creativity are more important to learning in the humanities than they are to learning in mathematics.


WHAT IS MATHEMATICAL LITERACY?

Describe a personal incident in your life using as many mathematical terms as you can. Meet with a neighbor to share and compare your story. As you read, keep count of how many mathematical terms are used. Mathematical Story Answer the following questions, then find the sum of your numbers.

The year you were born: The year of a significant event in your life:

Your age as of December 31, 2010: The number of years from your significant event and present year:

Total


Compare your answers with your partner. How do they compare? How can you explain that you may have been born in different years, may be different ages, and chose an incident that occurred at different times, yet you both have the same total? Now that you understand why everyone’s answer to the problem is the same, find another way to explain why this is the case. You can use a picture, an equation, a diagram, words or numbers, or any other way you can think of to explain the logic.


What Is Mathematical Literacy?

Mastery of procedural and

conceptual knowledge.

_______________________

A language to communicate ideas and

solve real-world problems.

_______________________

Understanding of logical reasoning to

explain and prove a solution.

_______________________

Application of strategies to formulate

and solve problems.

_______________________

What percentage of your classroom practice in mathematics would you estimate you spend in each of these areas? (Write your percentage on the line in each box above) How does your classroom practice compare with the NAEP data?

NAEP data shows that proficiency in these four areas has developed unevenly. In many classrooms, students are able to mimic rules and procedures demonstrated by their teacher: however, students often acquire these skills with little depth of understanding or the ability to use them to solve complex problems (Kowley & Wearing 2000).


Which of the following best represents you as a learner of mathematics? Explain your choice.


WHAT KIND OF PROBLEM SOLVER ARE YOU? Math is all about problem solving. But not all students and not all mathematicians solve problems in the same way. In fact, even though your textbook might tell you otherwise, there are many different ways to solve math problems. Your own preferences as a problem solver can tell you a lot about how your mind works and how you learn best. So, how do you go about solving problems in math? Let’s conduct a little experiment to find out. Read “The Canoe Problem” below. When you feel ready, use the workspace to solve “The Canoe Problem.” But here’s the twist: As you are getting ready to solve the problem and as you are doing the work of problem solving, try to look and listen in on your own mind. What is it doing? What is it saying? How is it attempting to solve the problem? The Canoe Problem Nineteen campers are hiking through Acadia National Park when they come to a river. The river is moving too rapidly for the campers to swim across. The campers have one canoe, which fits three people. On each trip across the river, one of the three canoe riders must be an adult. There is only one adult among the nineteen campers. How many trips across the river will be needed to get all of the children to the other side of the river?


How Four Different Students Solved “The Canoe Problem” Maria Well, the first thing I did was gather up the facts quickly: 19 campers, 1 canoe, 3 people per canoe, etc. Then — don’t think this is crazy — I used a piece of paper to stand for the boat, with one red pen on it to stand for the adult and two blue pens on it to stand for the children. Using actual objects to simulate the problem really helps me — it makes it easier to grasp the problem. To solve the problem I moved step‐by‐step from beginning to end. First, I took the facts I gathered up and set them up carefully on paper. Then, I used basic math to get my answer of 17 trips across the river. Finally, I double checked my calculations to make sure I had done my math correctly.

Giovanni I was very happy when the teacher said we could work with a learning partner. For me, the best way to learn math and solve problems like this one is to talk. I really like it when the teacher comes around and asks me how I’m doing, and I also like when I can work with friends and share my ideas. The best ideas seem to come when people are talking or working together. Anyway, what I really liked about today’s learning partnership with Jody is that we didn’t just get the answer to the problem right and wait around. We also talked about how we solved the problem and what we might do next time to improve as problem solvers.

Tanisha I find that problems like this one often have hidden questions or little tricks in them that aren’t always so obvious. For example, I bet some people missed the fact that every time 2 children get across the river, that’s 2 trips across — one there and one back. By looking for the hidden question, I saw the pattern to the problem pretty quickly: 2out of 18 children get to the other side for every 2 trips across the river. That means it will take 18 trips to get all 18 children across. But here’s another little trick: On the last trip, they only need to go one way and not back again. So the answer’s actually 17. Anyway, once I figured out the answer, I checked to make sure it made logical sense and that it answered the question posed by the problem. In both cases, it did.

Al I need to see the problem in my head. I closed my eyes and actually pictured the river and saw the 18 kids and the 1 adult with that 1canoe. Then, I generated possible answers by sort of playing with the numbers, trying different things out. When I do a problem like this, I try out different ways to solve it. Sometimes, I come up with more than one solution. For this problem, I came up with 9 and 17 as possible answers, so I explored each one to see which one worked. That’s how I came up with 17. Sometimes, I like to imagine cool twists or variations that would make the problem more interesting. For example, what if the boat held only a certain amount of weight and all the campers’ weights were given? Then we would have to find the best way to load the boat on each trip.

What we do as problem solvers is closely related to the way we learn. Everyone learns, but we don’t all learn in the same way. The differences in how people learn are called learning styles. You can see your style in the way you talk, the way you think, and the way you solve problems. Some students, like Maria, solve math problems using step-by-step procedures. Others are like Tanisha. These students prefer to find patterns and discover hidden questions. Students like Al are drawn to problems that are unique and love to speculate on the possible solutions. For students like Giovanni, there’s no better way to solve a challenging math problem than by discussing it with friends and fellow students. Which of these students sounds most like you?


Observations


Four Styles of Mathematical Learners

Working with a group of four, each takes one of the four learners to analyze. Read their responses to the “canoe problem.” Then answer the following questions:

1. What 3 adjectives would you use to describe the learner?

2. What kind(s) of math problem does the student like?

3. How does the student learn best?

4. What problems or challenges may this student have in becoming a better math student?


The T.E.M.P.O. of Style

Mastery (S + T)

Thinking Goal Environment Motivation Process Outcome

Interpersonal (S + F) Thinking Goal Environment Motivation Process Outcome

Understanding (N + T) Thinking Goal Environment Motivation Process Outcome

Self-Expressive (N + F) Thinking Goal Environment Motivation Process Outcome


TEACHING TO, WITH, AND ABOUT STYLE

Many of the students we are consigning to the dust heaps of our classrooms have the abilities to succeed. It is we, not they, who are failing. We are failing to recognize the variety of thinking and learning styles they bring to the classroom, and teaching them in ways that don’t fit them well.

Robert J. Sternberg

IBM Professor of Psychology and Education Yale University

Teaching to is: An individualized approach to suit a particular student’s style who may not be performing to the best of his/her abilities because of a lack of motivation or insufficient mastery of specific knowledge or skills.

Complete and return to your presenter

OAASFEP Keynote

Name: Position/Title:

Organization:

Address:

Work Phone Preferred e-mail (please print clearly):

Three ideas from our work today:

One thing I would tell a friend about this workshop:

Before today I thought: Now I think:

My conference learning experience is best described as a function that is:

Linear

Polynomial (3rd)

Sinusoidal

Exponential Explain your choice

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