+ Improving Student Problem Solving Through Reasoning & Revision Jessica Murk, Windsor High School Math Teacher February 19, 2015 Sonoma County Leadership Network
+ A Case for Revision The definition of mathematical proficiency has changed
+ A Case for Revision Previous definition: CALIFORNIA HIGH SCHOOL EXIT EXAM
+ A Case for Revision New Definition: SMARTER BALANCED ASSESSMENT CLAIMS
+ A Case for Revision The new expectations for students require new instructional strategies. Showing students exactly how to do a problem and then having them practice doing problems of the same type may work for Claim 1, but it will not work for Claims 3 and 4. Those require instructional strategies more like a writing class than a traditional math class.
+ A Case for Revision The new expectations for students requires new instructional strategies. One becomes a better writer by writing, getting feedback, and revising. One does not improve by only writing first drafts. Math class often is about getting a certain percentage of problems “correct” and then moving on. Communicating reasoning and mathematical modeling are processes that can always be improved.
+ The Target has Changed! NEW DEFINITION OLD DEFINITION OF PROFICENCY OF PROFICENCY Tools for Reasoning and Revision
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+ Overview of Our Time Together REASONING AND EXPLAINING OVERARCHING HABITS OF MIND 1. Make sense of problems and persevere in 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision solving them SEEING STRUCTURE & GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning
+ Goals Big Picture of CCSS Shifts Some specific strategies to use in your classroom that can help with these shifts Give your students opportunities to engage in the SMPs using our current curriculum
+ Tools for Reasoning & Revision Bongard Problems Developing Definitions Peer Feedback Template
+ Reasoning Revision Tool #1: Bongard Problems The Problem: Students struggle with abstract reasoning
+ Reasoning Revision Tool #1: Bongard Problems Students can test their rules on their own (Agency) The template allows them to write down their initial thoughts and then revise as they hear other ideas (Attend to precision) The “puzzle” element lowers fear and anxiety for students (Access/Equity)
+ Bongard Problems M.M. Bongard (1924 – 1971) was a Russion computer scientist interested in cognition and artificial intelligence. He introduced a set of problems (now called Bongard Problems ) in his 1967 book Проблема Узнавания .
+ Let’s Try One The goal is to identify a simple rule or property that applies to each of the figures on the left hand side AND none of the figures on the right hand side.
+ I would like to add an option for their first draft and then a revised rule.
+ Bongard Problem #94
+ Student Responses
+ Student Responses
+ Student Responses
+ Challenge
+ Let’s Try Another One
+ Revising as a Class: A written record of revision
+ Reasoning Revision Tool #1: Bongard Problems Students can test their rules on their own (Agency) The template allows them to write down their initial thoughts and then revise as they hear other ideas (Attend to precision) The “puzzle” element lowers fear and anxiety for students (Access/Equity)
+ Reasoning Revision Tool #2: Developing Definitions The Problem: Students don’t understand the difference between a “mathematical” definition and a dictionary definition
+ Reasoning Revision Tool #2: Developing Definitions Access student prior knowledge in an authentic way (Use of assessment) They are not blank slates (Access/ Identity) Make connections between what they already know and the more precise, mathematically rigorous definition (Cognitive Demand)
+ Teaching Vocabulary
+ Developing Definitions: Old School Look terms up in a dictionary Provide students the formal definition from the textbook through direct instruction
+ Developing Definitions: New School Asking students what they already know Making connections between their prior knowledge and more precise, mathematically rigorous definitions
+ Access Prior Knowledge We know it’s a good idea (research and credential programs tell us so) But HOW?!? How can we access a student’s prior knowledge in an authentic way?
+ Geometry Vocabulary
+ Geometry Vocabulary
+ Geometry Vocabulary
+ Geometry Vocabulary Are these points collinear? Can we think of the freeway as a segment? Or is it more of a line? Which towns are the endpoints of the freeway?
+ Reasoning Revision Tool #2: Developing Definitions Access student prior knowledge in an authentic way (Use of assessment) They are not blank slates (Access/ Identity) Make connections between what they already know and the more precise, mathematically rigorous definition (Cognitive Demand)
+ Reasoning Revision Tool #3: Peer Feedback Template The Problem: Students lack experience in critiquing the reasoning of others
+ Reasoning Revision Tool #3: Peer Feedback Template The authority shifts from teacher to student (Authority) Developing mathematical definitions and constructing arguments (Mathematics) Revising their definitions based on feedback (Cognitive demand)
+ Peer Feedback with Revision Peer Feedback Template First Draft ≠ Final Draft Building on the ideas and conjectures that students have about reflections Goal is to help students move toward a more formal definition, which will ultimately be provided by the teacher
+ Giving Feedback… A Gentle Reminder Unnatural in a math class Students have very little experience Rarely receive this type of feedback in a math class It takes practice!!!
+ Giving Feedback
+ A Little Help
+ Let’s Try One
+ Peer Feedback: Our Purpose
+ Peer Feedback: Some Suggestions • Students write their argument individually • Each argument gets rotated to another table • Pairs work together on providing feedback to two arguments • This happens twice • Arguments are returned to original authors • Students read through feedback to consider where they might revise their original argument and write a second draft
+ Peer Feedback
+ Student Work – Lizbeth
+ Student Work – Emily
+ Student Work – Nicole
+ Reasoning Revision Tool #3: Peer Feedback Template The authority shifts from teacher to student (Authority) Developing mathematical definitions and constructing arguments (Mathematics) Revising their definitions based on feedback (Cognitive demand)
+ Tools for Reasoning & Revision Bongard Problems Developing Definitions Peer Feedback Template
+ Thank You!! Jessica Murk Email: jmurk@wusd.org Blog: themathymurk.blogspot.com Twitter: @JessicaMurk13
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