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Core Academy Level 1 Day 2 Cognitive Demand and Problem Based Learning Time 8:30 – 10:00 10:00 – 10:30 Activity Activity (part 1) Take a couple of minutes to write your personal definition of “going deeper” as it relates to instruction/learning/assessment. Our focus for today is looking at the concept of cognitive rigor. We are going to examine some questions and think of a solution paths, these are questions that you may see on a test, or that you have written for a test. Let’s look and discuss (in your groups) what do you notice about the different difficulty levels of the questions? What makes them easy for you or more difficult? First group of questions – These are examples of fluency types of questions, they lend themselves to strategies for speed and accuracy Discussion Points Easily solved with an understanding of basic math facts, count by 5’s, time on a clock, flashing 5 on their fingers Understanding of equal groups – 8 x 9 is 9 groups of 8, 80 is 10 groups of 8, and you subtract one group of 8, making it 9 groups of 8 Understanding that 49 is 7 groups of 7 and 56 is 8 groups of 7, understand repeated addition or subtraction to solve multiplication and/or division This conceptual understanding makes the fluency faster in all 3 examples Relate to Concrete-Representation-Abstract instruction model Connections to Make Relate to Blooms Taxonomy/Hess Cognitive Demand Matrix (Hand out Matrix) Have participants place the problems on the matrix Connection to Core – which standards by grade ask for fluency? Examine critical areas of different grade levels. What does mastery look like at each grade level BREAK Core Academy 2014 1 Materials Needed Power point Hand out with different types of questions or include in power point See Appendix for questions Blooms Taxonomy/Hess Cognitive Demand Handout Activity (part 2) Show second set of problems Let’s look and discuss (in your groups) what do you notice about the different difficulty levels of the questions Discussion Points Mental math strategy is embedded with the +1 You would need to compensate (take 1 away from 35) to compute mentally (1000 x 200) + (1 x 20) [distributive property, you distributed the 20] Connections to make Connect that the 3 points for discussion above are instructional strategies that can be used in your classroom to lead to better conceptual understanding and fluency. Different strategies will make these a different cognitive level. Have participants place these problems on the matrix Activity (part 3) Show third set of problems – these are examples of conceptual understanding types of questions, how and why math works Let’s look and discuss (in your groups) what do you notice about the different difficulty levels of the questions Discussion Points Can you use drawings to show combining groups 2/1; 4/2….. Importance of a number line, useful for comparing denominators, differentiation – use a ruler to help guide students 12:00 – 12:45 LUNCH 12:45 – 2:15 Activity (part 4) Show fourth set of problems – these are examples of application types of problems Let’s look and discuss (in your groups) what do you notice about the different difficulty levels of the questions Discussion Points Missing addend problems changes the difficulty of the problem, it is also a fraction problem, which doesn’t lend itself to always an increase in cognitive demand. Core Academy 2014 2 Second set of questions Third Set of questions Fourth Set of Questions Multi-step problem, with multiple entry points. Lends itself to a drawing or algorithm, multiple solution paths, and opportunities for student explanation. Good discussion for order of operation at any grade level (work with manipulative, draw a picture, write an equation) Critical thinking problem. Opportunity for proving and justifying answer/solution path. Good problem for generalization. Also good problem for discussion of potential misconceptions and assumptions. SAGE and Depth of Knowledge. What do the DOK levels mean? Connections to make Important to have all, but also to know when to use which level How to change any problem from textbook from one level to another Creative doesn’t mean a greater depth of knowledge What existing curriculum or assessment materials could you re-examine to increase the range of cognitive rigor? What gaps will need to be filled? Revisit your definition of Rigor- has it changed? Assessing only at the highest DOK level will miss opportunities to know what students do & don’t know – go for a range; end “high” in selected/prioritized content Performance assessments can offer varying levels of DOK embedded in larger, more complex tasks Planned formative assessment strategies and tools can focus on differing DOK levels (Karen Hess) Activity (Practice Standards) Review Practice Standards with participants 2:15 – 3:15 Core Standards from Day 1 Chart Paper Activity – Depth of Knowledge Articles Read articles and discuss, use Chalk Talk Protocol Activity – Textbook Participants will go through one unit in their textbook and count how many of each level they find. Where is it strong? Where is it weak? Complete template End of Day 2 Write what you learned about, an ah-ha moment, something you want to do differently, etc. using the vocabulary words: Cognitive Rigor and Depth of Knowledge, each of the four levels Core Academy 2014 Journal DOK Wheel 3 DOK article Chalk Talk Protocol Template Reflection Questions Core Academy 2014 4