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Developing Higher Level Thinking

Developing Higher Level Thinking. After School PD November 2010. Cleaning Up. Object of the race Move down and around the chair and back to the start line You must stay on the paper If you walk on the floor, you have to start over. Warm-Up. What is π ?. Instrumental. Relational.

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Developing Higher Level Thinking

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  1. Developing Higher Level Thinking After School PDNovember 2010

  2. Cleaning Up • Object of the race • Move down and around the chair and back to the start line • You must stay on the paper • If you walk on the floor, you have to start over

  3. Warm-Up What is π ?

  4. Instrumental Relational • Memorizing and routinely applying procedures and formulas • Does not focus on “why” you solve problems the way you do • Explaining, reasoning, relying on multiple representations • Helping students develop their own understanding of content Two Approaches to Teaching

  5. Comparing and Contrasting Instrumental vs. Relational Learning • Benefits for instrumental understanding are: • usually easier to understand • the rewards are more immediate and apparent • students receive quicker answers due to the fact that less knowledge is involved • Advantages of relational understanding include: • adaptable to new tasks, • easier to remember (although harder to learn, there is less re-learning involved), • relational understanding is a more natural path to promote independent learning

  6. What does the research say? “Teach for meaning initially, or risk never getting students beyond a superficial understanding that leaves them unprepared to apply their learning.” Leinwand, Steve, and Steve Fleishchman. "Teach Mathematics Right the First Time." Educational Leadership. 62.1 (2004):

  7. What are some easy ways to do this? • Open Ended Questions • Can be a great way to differentiate instruction • Can also be a good way to assess your students • Writing Strategies • Can help students develop meaning and make connections • Can also be a good way to assess your students

  8. Open Ended Questions • Describe the picture below by using a mathematical equation • To which fact family does the fact 3x4 =12 belong to? X XXX X XXX X XXX

  9. Open Ended Question Strategies • Turn Around A Question • Ask for similarities and differences • Replace a number with a blank • Asking for a number sentence • Change an existing question From : Small, Marian. Good Questions: Great Ways to Differentiate Mathematics Instruction. New York: Teachers College Press, 2009. Print.

  10. 1) Turn Around A Question • Instead of asking what is the median of this set of data: 3, 5, 6, 8, 10, 11, 11 • Ask, “I have a data set with 7 numbers and median of 8. What is the data set?”

  11. 2) Ask for Similarities and Differences How are lines in standard form and lines in slope intercept form similar? How are they different?

  12. 3) Replace a number with a blank • Traditional Percent question: • 72 is 75% of what number? • Replace it with: • Fill in values for the blanks to make this statement true • 72 is _____ % of _____

  13. Replacing a Number with a Blank If s=4 and t=5, these statements are true. 3(s+t)=27 2s+3t=23 2t-2s=2 Choose values for p and q. Write three true statements using those variables. See if a partner can figure out what your values are.

  14. 4) Asking for a number sentence • Students are asked to create a number sentence that includes certain words or numbers • Example: Create a question involving multiplication or division of decimals where the digit 9, 4, and 2 appear somewhere • Example: Create a question involving the height of a triangle using the numbers 3 and 6

  15. 5) Change an existing question • Old: • A cookie has a diameter of 1.75 inches. Express the diameter as a fraction in simplest form. • New: • A cookie has a diameter between 1 and 2 inches. Express the diameter as a fraction in two different ways.

  16. Open Ended Question Strategies • Turn Around A Question • Ask for similarities and differences • Replace a number with a blank • Asking for a number sentence • Change an existing question Take 5 minutes and write your own open ended question that you could use in the next 2 weeks. Be ready to share with the group.

  17. More Guidelines • Make the question meaningful—focused on curricular goals • Have just the right amount of ambiguity • Students should have a general idea what you’re looking for • Open enough so all students can engage with the question and have an answer • Follow up discussion • Call on those with simpler answers first • Value all answers • Build connections between answers

  18. Wrapping Things Up How do you think open-ended questions can fit with your curriculum? How can you structure it so that students can share their responses?

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