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Critical Thinking

Intro to Critical Thinking in Math & Literacy

Jess LaBella

on 21 March 2013

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Transcript of Critical Thinking

Introduction to Critical Thinking Skills
in Literacy & Math Presented by
Yolanda Robinson, Math Coach
& Jessica LaBella, Literacy Coach The Very Hungry Caterpillar Teach Me to Think What is Critical Thinking? Focused Thinking

Thinking with a definite purpose (goal).

Can be a complex & involved process.

An active process that involves constant questioning.
You are given a 5 gallon jug and a 3 gallon jug. How can you use these two jugs to measure out exactly 4 gallons of water? Title I Parent Workshop
March 21, 2013 It's What Sets Us Apart! Critical Thinkers & Critical Thinking Critical thinkers:
Distinguish between fact and opinion
Ask questions
Make detailed observations
Uncover assumptions and define their terms
Make assertions based on sound logic and solid evidence.

-Ellis, D. (1997) Becoming a Master Student Critical thinking is best understood as the ability of thinkers to take charge of their own thinking. This requires that they develop sound criteria and standards for analyzing and assessing their own thinking and routinely use those criteria and standards to improve its quality.
-Elder, L. and Paul, R. (1994, Fall) "Critical thinking: why we must transform our teaching." Journal of Developmental Education. Why & Who Uses Critical Thinking Skills? Everyday & Everywhere
Academics, professionals, scientists, teachers , & students, and everyone who makes choices

Decision making, solving problems & puzzles, making connections, understanding issues, evaluating evidence and discovering new information Who?
Everyone who makes choices

Solve problems & Puzzles
Make connections
Understand issues
Evaluate evidence
Discover new information How Are Critical Thinking Skills Developed? Think about your thinking.
Think about why you make your choices and decisions.
Think about why the world is the way it is.
Practice every day!

Word problems
Math problems
Games of strategy What Questions Promote Critical Thinking? Socratic Questions

1. Ask for clarification
2. Probe assumptions
3. Probe reasons & evidence
4. About views & perspectives
5. Probe implications & consequences
6. Questions about the questions Four Types of Questions

1. Summary & definition
2. Analysis questions
3. Hypothesis questions
4. Evaluation questions Thinking About Thinking Students who think about thinking:

Know what they know and what they don’t

Can plan a strategy to produce results.

Are aware of the process they are going through to solve a problem, and keep track of the steps they are going through.

Reflect on the process they went through judging how effective they were. Aware of the effect their actions have on themselves, others and the environment. Judge what changes they would make if they were to do a similar activity again. Solution:
1. Fill the 3 gallon jug and pour it into the 5
gallon jug.
2. Fill it again and pour the water from the 3
gallon jug into the 5 gallon jug until it is full.
3. This will leave exactly 1 gallon in the 3 gallon
4. Next pour out the 5 gallon jug and pour the 1
remaining gallon of water into the 5 gallon jug.
5. There is 1 gallon of water in the 5 gallon jug.
6. Fill the 3 gallon up again and pour it into the 5
7. This will give you 4 gallons of water!! Do not readily find solutions for students. Instead, identify even the simplest tasks as a problem for them to solve. Children often get upset if they do not immediately have a chair to sit in, cannot find the crayon they want, or accidentally rip the paper they are working on. It is easy to say "get a chair from over there," "here is a red crayon," or "get some tape," but it is far better to respond, "let's think about how we can solve this problem." GRADE 3 MATH TASK

Jasper used the expression 5x(10+3) to find the area of a rectangular closet floor, in square feet.

On the grid, draw a rectangle that Jasper could have measured.

Jasper wants to use some of the remaining tile to cover the floor of a kitchen. The kitchen is 7
feet long and 12 feet wide.

Does Jasper have enough tiles to cover the kitchen floor? Show how you got your answer.
You may use drawings, mathematical expressions/equations, and words. GRADE 4 MATH TASK

Mr. Torres sold a total of 30 boxes of sports cards at his store on Monday. These boxes contained only baseball cards and football cards.

• Each box contained 25 sports cards.
• He earned $3 for each sports card he sold.
• He earned a total of $1134 from the football
cards he sold.

What amount of money did Mr. Torres earn from the baseball? Use pictures, numbers, and/or words to show how you got your answer. Grade 5 Math Task

Mrs. Phelps bought 4 boxes of crayons at the store to share with her students. Each box contained a total of 64 crayons.

Part A
What is the total number of crayons Mrs. Phelps bought at the store? Explain your answer using diagrams, pictures, mathematical expressions and/or words.

Part B
Mrs. Phelps wants to give each of her students an equal number of the crayons she bought. There are 32 students in Mrs. Phelps’ class. How many crayons should each student get?

Part C
How many more boxes of crayons does Mrs. Phelps need if she wants each of her students to get 12 crayons? Explain your answer using diagrams, pictures, mathematical expressions

Students can:

Clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others.

Students can solve a range of well-posed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies.

Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency to demonstrate understanding of the place value system.

Apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace. GRADE 4 MATH PROBLEM: CRITICAL THINKING STRATEGIES

Students can:

Communicate and support their reasoning clearly and precisely constructing viable arguments where they base arguments on concrete referents such as objects, drawings, diagrams, and actions.

Critiquing the reasoning of others - Distinguish correct logic or reasoning from that which is flawed and if there is a flaw in the argument explain what it is.

Explaining and applying mathematical concepts

Carrying out mathematical procedures with precision and fluency - by extending their understanding of fraction equivalence and ordering. GRADE 3 MATH TASK: CRITICAL THINKING STRATEGIES

Students can:

Communicate and support their reasoning by clearly and precisely constructing viable arguments

Critique the reasoning of others - Distinguish correct logic or reasoning from that which is flawed and if there is a flaw in the argument explain what it is.

Explain and apply mathematical concepts

Carry out mathematical procedures with precision and fluency - by recognizing perimeter as an attribute of plane figures and distinguish between linear and area measures. What critical thinking skills would a student need in order to solve this problem? Critical Thinking Puzzle:
The Water Jug Riddle Here are a few tips to keep in mind: * Get an Early Start – Even with young kids, prompt a discussion about how they reach conclusions. Encourage them to explain to you how they came to those conclusions. Discuss if other possible conclusions can be made, and what they may be.

* Foster and Encourage LOTS of Questions – Promote curiosity, and a willingness to be open to alternative perspectives. If things must be done a certain way, explain the reasons why.

* Introduce a Variety of Issues – Recognize that critical thinking does not have to be limited to scientific problems.

* Classification – Encourage kids to practice classifying items (by shape, size, color, etc.) and to explain how and why they classified things a certain way.

* Hands-On Experiences – Provide plenty of hands-on activities for little ones. Do some “experiments:” See if certain objects will sink or float, Melt ice and observe what happens, make bricks out of mud.

* Use Science Tools – Once your child understands the proper way to use simple science tools as such a scale, ruler, or magnifying glass, try to make these available for everyday activities.
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