Reflections from our work with Harvey Silver, TR

Note: All contents of this power point come from our work with Harvey Silver

Reference:64 Math Tools

Opening ActivityAssessing the Learning Styles of your Students

Think about when you were a student learning math.

Briefly describe “how” you were taught.Describe how you “preferred” to be

taught.

Which of the following best represents you as a learner of mathematics?

Rigor and Student Engagement

A new way of thinking about preparing students for their

futures

http://www.youtube.com/watch?v=ntzX6tBVgpk&feature=related

21st Century Learning Skills

1. Critical Thinking and Problem Solving 2. Collaboration Across Networks3. Agility and Adaptability 4. Initiative and Entrepreneurship 5. Effective Oral and Written Communication 6. Accessing and Analyzing Information 7. Curiosity and Imagination

Canoe 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 did you solve it?

• Read the student cards on your table.

• Which student do you compare yourself to?

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 your talk, the way you think, and the way you solve problems.

Some students are like Maria

Like to solve problems using step-by-step procedures

Others are likeTanisha

These students prefer to find patterns and discover hidden questions.

AL

• Students like Al are drawn to problems that are unique and love to speculate on the possible solutions.

Giovanni

• For these students, there is 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?

MariaThe Mastery Math Student

Mastery Math Students… Want to…learn practical information and set

procedures. Like math problems that…are like problems they

have solved before and that use algorithms to produce a single solution.

Approach problem solving…in a step-by-step manner. Experience difficulty when…math becomes too

abstract or when faced with non-routine problems. Want a math teacher who…models new skills, allows

time for practice, and builds in feedback and coaching sessions.

TanishaThe Understanding Math Student

Understanding Math Students… Want to…understand why the math they learn

works. Like math problems that…ask them to explain,

prove, or take a position. Approach problem solving…by looking for patterns

and identifying hidden questions. Experience difficulty when…there is a focus on the

social environment of the classroom (e.g. on collaboration and cooperative problem solving)

Want a math teacher who…challenges them to think and who lets them explain their thinking.

GiovanniThe Interpersonal Math Student

Interpersonal Math Students…• Want to…learn math through dialogue, collaboration,

and cooperative learning.• Like math problems that…focus on real-world

applications and how math helps people.• Approach problem solving…as an open discussion

among a community of problem solvers.• Experience difficulty when…instruction focuses on

independent seatwork or when what they are learning seems to lack real-world application.

• Want a math teacher who…pays attention to their successes and struggles in math.

AlThe Self-Expressive Math Student

Self-Expressive Math Students• Want to…use their imagination to explore mathematical

ideas.• Like math problems that…are non-routine, project-like

in nature, and that allow them to think “outside the box”.

• Approach problem solving…by visualizing the problem, generating possible solutions, and exploring among the alternatives.

• Experience difficulty when…math instruction is focused on drill and practice and role problem solving.

• Want a math teacher who…invites imagination and creative problem solving into the math classroom.

• Paper Clip: think of themselves as organized and efficient learners. These learners love to build their own competence and take a practical approach to learning.

• Magnifying Glass: tend to emphasize the logical, knowledge-seeking, and problem-solving aspects of learning. These learners love to ask questions and often take an intellectual or analytical approach to learning.

• Slinky: tend to focus on the playful and imaginative sides to learning. These learners love to explore ideas, ask “What if?”, and take a creative approach to learning.

• Teddy Bear: see themselves as teddy bears tend to view learning as a warm and nurturing process. These learners emphasize the human story and the personal and conversational elements of learning, and they look for ways to connect their learning to their experiences and values.

(Silver, Jackson & Moirao, 2011)

Instructional Relevance

• Learning Styles• Task Rotations

General Student Population vs. At-Risk Population

35% Mastery 35% Interpersonal

10% Understanding 20% Self-Expressive

12% 65%

1% 22%

Harvey Silver’s 8 C’s to Student Engagement

ATP Resources

Teaching With Style is:

Implementing a variety of instructional teaching tools, strategies, and activities to differentiate instruction in order to support and challenge each student’s learning profile.

As we imagine our vision of quality instruction, let’s keep the needs our of students in

mind.

Calculus Task RotationMastery

Create a glossary of the vocabulary terms listed below. You can use words, pictures, numbers, and examples to define or illustrate each term. Critical Value Relative Extrema Concavity Point of Inflection

InterpersonalPartner Activity: Each partner creates a polynomial whose graph crosses the x-axis at least twice over the interval [-3,2]. Graph your polynomial on a graphing calculator. Without revealing the function, exchange graphs. Each partner will describe the characteristics of the derivative.

UnderstandingThree Way Tie: Look at the triangle below. Write a sentence along each side of the triangle that connects the word or phrase at each angle of the triangle.

Self-ExpressiveCreate a graph that represents your growth as a math student over the course of this year. Identify critical values, extrema, discuss concavity, and find any points of inflection. Describe the significance of these characteristics as they relate to your experiences.

Algebra I Task RotationMastery

Choose any two points on a coordinate plane:Do the following by showing your work when possible:a.) Write these two points on your graph paper.b.) Plot the two points on a coordinate graph and connect them by using a line. Don’t forget proper use of scale.c) Calculate the slope of the two points.d.) Determine the linear equation for the points above. Write the equation in slope-intercept form and show your work!

InterpersonalThink about where you see the effects of linear functions in your life. Then choose one medium to express your thoughts on linear functions. Each product must have at least four examples of linear functions!a) Journal entry of at least one page.b) Scrapbook page or collage that has explanations of each example.c) YouTube, Powerpoint, or Movie Maker presentation with narration and visuals.

UnderstandingHere are two linear functions:Y = 3x – 2 and Y = -4x + 8Complete the following tasks:a) Graph both of them on a coordinate plane.b) Describe the trends you see in each graph’s rate of change and y-intercept.c) Explain what must be done to the parent graph of Y = x in order to obtain each graph.

Self-ExpressiveWrite a cinquain over any of the following concepts: linear functions; linear graphs; rate of change; y-intercept; linear vs. non-linear or come up with your own based on our linear investigations (make sure it is okay with the teacher). Then follow the formula below:1st line—Title/Focus2nd line—Two Descriptive Adjectives3rd line—Three Action Verbs4th line—Four-Word Phrase5th line—One-Word Conclusion

Assessment MenuThree Levels of Difficulty

Mastery1. Gather information2. Organize

information3. Present information

Interpersonal1. Express feelings2. Understand feelings3. Act on feelings

Understanding1. Examine data2. Interpret data3. Extrapolate data

Self Expressive1. Generate ideas2. Reorganize ideas3. Create original work

Three-Way Tie

• Students identify relationships between three terms or concepts, then develop a summary or interpretation.

• NCTM Standards• Educational Research Base• Instructional Objectives• Learning Style - Understanding

Summary

That Really Smart Thing Wes Said

Three

Way

Tie

Resource for Thoughtful Ed Templates and Activities

• http://www.marshall.k12.ky.us/Thoughtful%20Ed/ThoughtfulEdtemplates.htm

• http://www.marshall.k12.ky.us/cd/CurriculumDocuments.htm