For Use by DPS and Blueprint Only.

Standards of Mathematical Practices 1 & 3

Math Fellow TrainingMath Fellow Training20132013

SMP 1 & 3SMP 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.

Do NowDo 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.”

SMP 1SMP 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 strategies when needed Students utilize reading comprehension strategies

SMP 1SMP 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 thinkingFellow 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

SMP 1SMP 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 thinkingEvidence 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 Championpg. 134

SMP 3SMP 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

SMP 3SMP 3

Standards of Mathematical Practice 3:Construct viable arguments and critique the reasoning of others

Framework for Fellow Effectiveness: Instructional Practice 3:

Encourage student discourseFellow 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

SMP 3SMP 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

RatioTeach Like a Championpg. 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

Video - ChristinaVideo - Christina

For Use by DPS and Blueprint Only.

Christina Dehning 02 - http://vimeo.com/album/2323240/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…”

Ratio and Wait TimeRatio and Wait Time

For Use by DPS and Blueprint Only.

Ratio:Ratio:The proportion of cognitive work your students do

1.Unbundle2.Half-statement3.What’s next?4.Feign ignorance5.Repeated examples6.Rephrase or add on7.Whys and Hows8.Supporting evidence9.Batch process10.Discussion objectives

Wait Wait TimeTimeStrategically delaying a few seconds after answering a question

Narration

Video - ChristinaVideo - Christina

For Use by DPS and Blueprint Only.

Christina Dehning 02 - http://vimeo.com/album/2323240/video/62896858

Password = mindthegap (start time 10:00 – end time

12:00)

Look for…

Ratio &Wait Time techniques

I noticed examples ratio when…”

Exit TicketExit 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.