1. For Use by DPS and Blueprint Only. Standards of Mathematical Practices 1 & 3 Math Fellow Training 2013

2. SMP 1 & 3 Objectives: F/CWBAT explain why it is important for students to demonstrate proficiency in SMP 1 and 3, citing real world connections. F/CWBAT explain how the techniques Ratio and Wait Time can affect student achievement, citing the Framework for Fellow Effectiveness indicators for SMP 1 and 3.

3. Do Now 1. Give a real world example from your life of a time when you had to, “make sense of a problem, and persevere in solving it.” 2. Give a real world example from your life of a time when you had to, “construct a viable argument and critique the reasoning of others.”

4. SMP 1 Standards of Mathematical Practice 1: Make sense of problems and persevere in solving them Student Indicators  Students ask probing questions to clarify conceptual understandings  Students respond appropriately to problems, despite the difficulty level  Students describe possible approaches to a solution  Students identify connections to prior learning  Students are able to identify specific steps they will take to accomplish weekly goals, as well as long-term SMI and TCAP goals  Students persist in making multiple attempts to solve, and avoid asking for the solution  Students check their answers using different methods  Students monitor their progress and change strat egies when needed  Students utilize reading comprehension strategies

5. SMP 1 Standards of Mathematical Practice 1: Make sense of problems and persevere in solving them Framework for Fellow Effectiveness: Instructional Practice 1: Ask clarifying questions and extend student thinking Fellow Indicators  Fellow asks “how and why” questions  Fellow explains and emphasizes the understanding of a concept, before teaching a procedure or algorithms  Fellow links lesson objective to prior learning  Fellow links daily work to students’ lives, as a means to motivate and encourage perseverance  Fellow gives students appropriate wait time  Fellow does not allow students to opt out of a response  Fellow scaffolds instruction effectively  Fellow celebrates resilient problem solving efforts  Fellow models, and empowers students to utilize, reading comprehension strategies

6. SMP 1 Standards of Mathematical Practice 1: Make sense of problems and persevere in solving them Framework for Fellow Effectiveness: Instructional Practice 1: Ask clarifying questions and extend student thinking Evidence Implementations Strategies and Resources  Student or Fellow work samples with written explanations and key academic language  Example problems with multiple approaches for solving  Current data trackers, utilized for self-monitoring by students  Wait Time Teach Like a Champion pg. 134

7. SMP 3 Standards of Mathematical Practice 3: Construct viable arguments and critique the reasoning of others Student Indicators  Students use assumptions, definitions, and previous results to explain or justify solutions  Students use logic to articulate conjectures  Students use examples and counterexamples in constructing viable arguments  Students justify conclusions in a way that is understandable to teachers and peers  Students compare two possible arguments for strengths and weaknesses  Students use academic language appropriately  Students write viable arguments in their work  Students write precise and reasonable critiques of others’ work

8. SMP 3 Standards of Mathematical Practice 3: Construct viable arguments and critique the reasoning of others Framework for Fellow Effectiveness: Instructional Practice 3: Encourage student discourse Fellow Indicators  Fellow asks “how and why” questions  Fellow provides opportunities for students to analyze other students’ work to try to understand the thought process behind the work  Fellow explains and emphasizes the understanding of a concept, before teaching a procedure or algorithms  Fellow has students make and test conjectures to communicate their mathematical thinking  Fellow encourages productive student discourse around viable arguments and critique of reasoning by: ○ Providing a positive, respectful environment: Error is normalized, all students have equal opportunity to share, students receive precise praise, questions are encouraged ○ Modeling productive discourse: Proper language usage, active listening skills, turn-taking, utilizing wait time, questioning, respectful disagreement ○ Scaffolding to support dialogue: Providing sentence starters for questioning and disagreement ○ Upholding high expectations ○ Emphasizing that reasoning is more important than the final answer

9. SMP 3 Evidence Implementations Strategies and Resources  Sentence starters and discussion points posted  Student work demonstrating arguments that justify reasoning, with specific feedback from Fellow and/or peers  Ratio Teach Like a Champion pg. 92 Standards of Mathematical Practice 3: Construct viable arguments and critique the reasoning of others Framework for Fellow Effectiveness: Instructional Practice 3: Encourage student discourse

10. Video - Christina For Use by DPS and Blueprint Only. Christina Dehning 02 - http://vimeo.com/album/232324 0/video/62896858 http://vimeo.com/album/232324 0/video/62896858 Password = mindthegap (start time 10:00 – end time 12:00) Look for… SMP 1 & 3 indicators What are students doing? What is the Fellow doing? What other evidence do you see? I noticed examples of SMP1/3 when…”

11. Ratio and Wait Time For Use by DPS and Blueprint Only. Ratio: The proportion of cognitive work your students do 1.Unbundle 2.Half-statement 3.What’s next? 4.Feign ignorance 5.Repeated examples 6.Rephrase or add on 7.Whys and Hows 8.Supporting evidence 9.Batch process 10.Discussion objectives WaitTime Strategically delaying a few seconds after answering a question Narration

12. Video - Christina For Use by DPS and Blueprint Only. Christina Dehning 02 - http://vimeo.com/album/232324 0/video/62896858 http://vimeo.com/album/232324 0/video/62896858 Password = mindthegap (start time 10:00 – end time 12:00) Look for… Ratio &Wait Time techniques I noticed examples ratio when…”

13. Exit Ticket 1. Explain how the techniques Ratio and Wait Time connect to student achievement, citing the Framework for Fellow Effectiveness indicators for SMP 1 and 3. 2. Explain why it is important for students to demonstrate proficiency in SMP 1 and 3, citing real world connections.