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 Activity
Assessing 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=n
tzX6tBVgpk&feature=related
21st Century Learning
Skills
1. Critical Thinking and Problem Solving
2. Collaboration Across Networks
3. 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?
Maria
The Mastery Math Student
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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.
Tanisha
The Understanding Math Student
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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.
Giovanni
The Interpersonal Math Student
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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.
Al
The Self-Expressive Math Student
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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, knowledgeseeking, and problemsolving 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
12% 65%
10% Understanding
1%
22%
20% Self-Expressive
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 Rotation
Mastery
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
Understanding
Three 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.
Interpersonal
Partner 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.
Self-Expressive
Create 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 Rotation
Mastery
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!
Interpersonal
Think 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.
Understanding
Self-Expressive
Here are two linear functions:
Y = 3x – 2 and Y = -4x + 8
Complete 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.
Write 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/Focus
2nd line—Two Descriptive Adjectives
3rd line—Three Action Verbs
4th line—Four-Word Phrase
5th line—One-Word Conclusion
Assessment Menu
Three Levels of Difficulty
Mastery
1. Gather information
2. Organize information
3. Present information
Interpersonal
1. Express feelings
2. Understand feelings
3. Act on feelings
Understanding
1. Examine data
2. Interpret data
3. Extrapolate data
Self Expressive
1. Generate ideas
2. Reorganize ideas
3. Create original work
Three-Way Tie
• Students identify relationships between three
terms or concepts, then develop a summary
or interpretation.
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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/Thoughtf
ul%20Ed/ThoughtfulEdtemplates.htm
• http://www.marshall.k12.ky.us/cd/Curri
culumDocuments.htm