Adapted by Susan Muir
Created by:DeniseTarlinton
Original Terms
New Terms
• Evaluation
•Creating
• Synthesis
•Evaluating
• Analysis
•Analysing
• Application
•Applying
• Comprehension
•Understanding
• Knowledge
•Remembering
(Based on Pohl, 2000, Learning to Think, Thinking to Learn, p. 8)
How to Take Student Learning
to the Next Level
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Inspiring Spaces
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Look like..
Sound like…
Feel like…?
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Taking Student Learning to the Next Level
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How do I get my students
here?
Problem Solving Strategies- Demonstrating solving in more than one way and
extending thinking
Reasoning and Proof- justify and support/ explain/ extend solution to other cases
Communication- audience (forms of writing) / use of formal math language and use
of mathematical notation
Connections- Mathematical connection to problem and used to extend the solution
Representation- multiple representations / making connections from one
representation to another to clarify and show thinking.
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Creating Opportunities for
Higher Level Thinkers
http://blogs.gssd.ca/smuir/?p=1743
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Students need to self assess and be assessed, with immediate
feedback so growth can happen quickly.
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Tools to Assess Student
Learning
http://vocaroo.com/?media=vi7Fqfb
mQKiPV2cmw
Vocaroo
http://mrsdevlin.wikispaces.com/Math+Proj
ects
Voice Thread
http://springkinder.blogspot.com/2011/02/capacity.html
Photo Story to evaluate student thinking and use of
Formal Math Language
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Remembering
The learner is able to recall, restate and
remember learned information.
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Recognising
Listing
Describing
Identifying
Retrieving
Naming
Locating
Finding
Can you recall information?
Classroom Roles for
Remembering
Teacher roles
Student roles
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Directs
Tells
Shows
Examines
Questions
Evaluates
Responds
Absorbs
Remembers
Recognises
Memorises
Defines
Describes
Retells
Passive recipient
Remembering: Potential
Activities and Products
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What is a factor?
Make a time line of your typical day.
Write a list of formal math words you know about….
Make a chart showing…
Can you identify the different place values in the metric
system?
• State the mode, mean, median, and range from your set
of data.
• How do you reproduce a circle using a compass?
Understanding
The learner grasps the meaning of information by
interpreting and translating what has been
learned.
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Interpreting
Exemplifying
Summarising
Inferring
Paraphrasing
Classifying
Comparing
Explaining
Can you explain ideas or concepts?
Classroom Roles for
Understanding
Teacher roles
Student roles
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Demonstrates
Listens
Questions
Compares
Contrasts
Examines
Explains
Describes
Outlines
Restates
Translates
Demonstrates
Interprets
Active participant
Understanding: Potential
Activities and Products
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Write in your own words…
Cut out, or draw pictures to illustrate…
Report to the class…
Retell in your own words.
Classify polygons by regularity, concavity, and line
symmetry.
• Explain how to convert between fractions, decimals, and
percents.
• What is your interpretation of the data expressed on the
graph?
Applying
The learner makes use of information in a context
different from the one in which it was learned.
– Implementing
– Carrying out
– Using
– Executing
Can you use the information in another
familiar situation?
Classroom Roles for Applying
Teacher roles
Student roles
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• Solves problems
• Demonstrates use of
knowledge
• Calculates
• Compiles
• Completes
• Illustrates
• Constructs
• Active recipient
Shows
Facilitates
Observes
Evaluates
Organises
Questions
Applying: Potential Activities
and Products
• How do you calculate the percent of a
given whole?
• Solve for area of a rectangle by using A= l
x w.
• What information do you consider when
graphing data derived from a survey?
Analysing
The learner breaks learned information into its
parts to best understand that information.
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Comparing
Organising
Deconstructing
Attributing
Outlining
Finding
Structuring
Integrating
Can you break information into parts to explore
understandings and relationships?
Classroom Roles for Analysing
Teacher roles
Student roles
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Probes
Guides
Observes
Evaluates
Acts as a resource
Questions
Organises
Dissects
Discusses
Uncovers
Argues
Debates
Thinks deeply
Tests
Examines
Questions
Calculates
Investigates
Inquires
Active participant
Analyzing: Potential Activities
and Products
• What methods can be used to compare and
order fractions?
• How are multiplication and division related?
• What factors do you consider when formulating
a plan for problem solving?
• How many ways can you deconstruct the
number 34?
Evaluating
The learner makes decisions based on in-depth
reflection, criticism and assessment.
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Checking
Hypothesising
Critiquing
Experimenting
Judging
Testing
Detecting
Monitoring
Can you justify a decision or course of action?
Classroom Roles for Evaluating
Teacher roles
Student roles
• Clarifies
• Accepts
• Guides
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Judges
Disputes
Compares
Critiques
Questions
Argues
Assesses
Decides
Selects
Justifies
Active participant
Evaluating: Potential Activities
and Products
• Evaluate the expression after changing the
order of operations.
• Describe how to solve a problem using the 4
step method.
• Justify your reason for choosing the strategy
selected.
• Prove that 23 is a small number.
Creating
The learner creates new ideas and
information using what has been previously
learned.
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Designing
Constructing
Planning
Producing
Inventing
Devising
Making
Can you generate new products, ideas, or
ways of viewing things?
Classroom Roles for Creating
Teacher roles
Student roles
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Facilitates
Extends
Reflects
Analyses
Evaluates
Designs
Formulates
Plans
Takes risks
Modifies
Creates
Proposes
Active participant
Creating: Potential Activities
and Products
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Can you design a model to?
Can you see a possible solution to...?
Why don't you devise your own way to...?
What would happen if ...?
How many ways can you...?
Can you create new and unusual uses for...?
• Can you develop a problem which
would...?
Now it’s your turn…
Sample Unit : Number
Remembering
Cut out…. pictures from a magazine. Make a display or a
collage. List space words (Alphabet Key). List the names of …. in
…. List all the things an mathematician would need for/to….
Understanding
Make …. into , Make an... Use it to tell what an …. does. Make
a model of …..
Applying
Keep a journal of your thinking. What sort of … would you need
to …? Make a list of questions you would ask ….
Analysing
Make an... Compare…. Distinguish between the ...
Evaluating
Compare the benefits of…. Choose a strategy and give reasons
why you chose that strategy. Explain why…
Creating
Write a ….Use the …. strategy to design a…. Create a…...
Prepare a…. Design a…..
A good teacher makes
you think even when
you don’t want to.
(Fisher, 1998, Teaching Thinking)
Questions for Remembering
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What happened after...?
How many...?
What is...?
Who was it that...?
Can you name ...?
Find the definition of…
Describe what happened after…
Who spoke to...?
Which is true or false...?
(Pohl, Learning to Think, Thinking to Learn, p. 12)
Questions for Understanding
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Can you explain why…?
Can you write in your own words?
How would you explain…?
Can you write a brief outline...?
What do you think could have happened next...?
Who do you think...?
What was the main idea...?
Can you clarify…?
Can you illustrate…?
Does everyone act in the way that …….. does?
(Pohl, Learning to Think, Thinking to Learn, p. 12)
Questions for Applying
• Do you know of another instance
where…?
• Can you group by characteristics such
as…?
• Which factors would you change if…?
• What questions would you ask of…?
• From the information given, can you
develop a set of instructions about…?
(Pohl, Learning to Think, Thinking to Learn, p. 13)
Question for Analysing
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Which events could not have happened?
If. ..happened, what might the ending have been?
How is...similar to...?
What do you see as other possible outcomes?
Why did...changes occur?
Can you explain what must have happened when...?
What are some or the problems of...?
Can you distinguish between...?
What were some of the motives behind..?
What was the turning point?
What was the problem with...?
(Pohl, Learning to Think, Thinking to Learn, p. 13)
Questions for Evaluating
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Is there a better solution to...?
Judge the value of... What do you think about...?
Can you defend your position about...?
Do you think...is a good or bad thing?
How would you have handled...?
What changes to.. would you recommend?
Do you believe...? How would you feel if. ..?
How effective are. ..?
What are the consequences..?
What influence will....have on our lives?
What are the pros and cons of....?
Why is ....of value?
What are the alternatives?
Who will gain & who will loose?
(Pohl, Learning to Think, Thinking to Learn, p. 14)
Questions for Creating
• Can you design a...to...?
• Can you see a possible solution to...?
• If you had access to all resources, how would
you deal with...?
• Why don't you devise your own way to...?
• What would happen if ...?
• How many ways can you...?
• Can you create new and unusual uses for...?
• Can you develop a proposal which would...?
(Pohl, Learning to Think, Thinking to Learn, p. 14)
Credit for most slides: Denise Tarlinton