Adapted by Susan Muir Created by:DeniseTarlinton

Original Terms New Terms Evaluation Synthesis Analysis Application Comprehension Knowledge Creating Evaluating Analysing Applying Understanding Remembering (Based on Pohl, 2000, Learning to Think, Thinking to Learn, p. 8)

3 How to Take Student Learning to the Next Level

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5 Inspiring Spaces

Look like.. Sound like… Feel like…?

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9 Taking Student Learning to the Next Level

10 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.

11 Creating Opportunities for Higher Level Thinkers

12 Students need to self assess and be assessed, with immediate feedback so growth can happen quickly.

13 Tools to Assess Student Learning mQKiPV2cmw mQKiPV2cmw Vocaroo ects Voice Thread Photo Story to evaluate student thinking and use of Formal Math Language

Remembering The learner is able to recall, restate and remember learned information. –Recognising –Listing –Describing –Identifying –Retrieving –Naming –Locating –Finding Can you recall information?

Classroom Roles for Remembering Teacher roles Directs Tells Shows Examines Questions Evaluates Student roles Responds Absorbs Remembers Recognises Memorises Defines Describes Retells Passive recipient

Remembering: Potential Activities and Products 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. –Interpreting –Exemplifying –Summarising –Inferring –Paraphrasing –Classifying –Comparing –Explaining Can you explain ideas or concepts?

Classroom Roles for Understanding Teacher roles Demonstrates Listens Questions Compares Contrasts Examines Student roles Explains Describes Outlines Restates Translates Demonstrates Interprets Active participant

Understanding: Potential Activities and Products 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 Shows Facilitates Observes Evaluates Organises Questions Student roles Solves problems Demonstrates use of knowledge Calculates Compiles Completes Illustrates Constructs Active recipient

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. –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 Probes Guides Observes Evaluates Acts as a resource Questions Organises Dissects Student roles 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. –Checking –Hypothesising –Critiquing –Experimenting –Judging –Testing –Detecting –Monitoring Can you justify a decision or course of action?

Classroom Roles for Evaluating Teacher roles Clarifies Accepts Guides Student roles 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. –Designing –Constructing –Planning –Producing –Inventing –Devising –Making Can you generate new products, ideas, or ways of viewing things?

Classroom Roles for Creating Teacher roles Facilitates Extends Reflects Analyses Evaluates Student roles Designs Formulates Plans Takes risks Modifies Creates Proposes Active participant

Creating: Potential Activities and Products 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 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 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 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 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