Leveraging Student Representations and Discourse to Advance Learning

through Progressions

LEUSD Middle and High SchoolSeptember 23, 2015

Ryan Dent, LEUSD

How long is the song I Got You?

Ryan Dent, LEUSD

What should kids be doing while they’re

learning mathematics?

Ryan Dent, LEUSD

Ryan Dent, LEUSD

According to the CA Math Framework…

Ryan Dent, LEUSD

Ryan Dent, LEUSD

What do you notice? What do you wonder?

Rachel

Ryan Dent, LEUSD

Pre/Post Reflection

What can I do to get every student to engage in the SMP’s? What challenges – that I can control - have been keeping me from doing so?

Write down initial thoughts, and then you will revise at the end of the day.

Ryan Dent, LEUSD

CLAIM

When teachers use tasks that promote reasoning and problem-solving, use and connect multiple representations, and facilitate meaningful discourse through posing purposeful questions, students will engage in the SMP’s.

Ryan Dent, LEUSD

Ryan Dent, LEUSD

Phil Daro on Principles to Actions

https://www.youtube.com/watch?v=o2MgrECf9Xo

Ryan Dent, LEUSD

“They would have to learn to be tenacious, to probe their own and others’ ideas and interpretations, to doubt and be skeptical. And they would have to learn to combine intellectual aggressiveness and a willingness to take risks with a humility about the incompleteness and uncertainty of their own ideas.”

Ryan Dent, LEUSD

Which one doesn’t belong?

Ryan Dent, LEUSD

Which one doesn’t belong?

Ryan Dent, LEUSD

While watching the video…

Students• What were the kids doing?• What SMP’s were they

engaged in?• What big mathematical

ideas showed up in what they did/said?

• How would the kids describe their role in “math”?

Teacher• What was he doing?• What was the purpose of

his questions?• What big mathematical

ideas did he draw out?• How would the teacher

describe his role?

Ryan Dent, LEUSD

“Line of Best Fit” Lesson

Scatter Plots

Ryan Dent, LEUSD

Ryan Dent, LEUSD

Ryan Dent, LEUSD

Talking Points Round 3 TallyAgree/Disagree/Unsure

Because of the abstract nature of mathematics, people have access to mathematical ideas only through the representations of those ideas.

An effective teacher makes the mathematics easy for students by guiding them step by step through problem-solving to ensure that they are not frustrated or confused.

Mathematics learning should focus on developing understanding of concepts and procedures through problem-solving, reasoning and discourse.

Ryan Dent, LEUSD

Representations

Contextual

Physical

Visual

Symbolic

Verbal

Ryan Dent, LEUSD

Ryan Dent, LEUSD

Talking Points

Ryan Dent, LEUSD

Today’s Meet

What is “depth of understanding?”

Ryan Dent, LEUSD

What do you notice?

Ryan Dent, LEUSD

How many blocks would be in the 7th step?How many blocks would be in the 43rd step?How many blocks would be in the n th step?

Ryan Dent, LEUSD

Is this useful for anything?

Ryan Dent, LEUSD

Could you use this student’s

work to engage all kids in the SMP’s?

Ryan Dent, LEUSD

What’s the difference?

Ryan Dent, LEUSD

What is “depth of understanding?”

How does connecting

student representations

promote depth?

Ryan Dent, LEUSD

Pre/Post Reflection

What can I do to get every student to

engage in the SMP’s?

Ryan Dent, LEUSD

Task

http://youtu.be/5JCm5FY-dEY

Ryan Dent, LEUSD

Orchestrating Productive Discussions

What you read

What we did

Ryan Dent, LEUSD

What is “depth of understanding?”

How does connecting

student representations

promote depth?

Ryan Dent, LEUSD

Pre/Post Reflection

What can I do to get every student to engage in the SMP’s?

Ryan Dent, LEUSD

Hot Dogs and Buns Task

http://robertkaplinsky.com/work/how-many-hot-dogs-and-buns-should-he-buy

/

Ryan Dent, LEUSD

While watching the video…

Students• What were the kids doing?• What SMP’s were they

engaged in?• What big mathematical

ideas showed up in what they did/said?

• How would the kids describe their role in “math”?

Teacher• What was he doing?• What was the purpose of

his questions?• What big mathematical

ideas did he draw out?• How would the teacher

describe his role?

Ryan Dent, LEUSD

Contextual

Physical

Visual

Symbolic

Verbal

Ryan Dent, LEUSD

Talking PointsTalking Points Round 3 Tally

Agree/Disagree/Unsure

Students’ understanding is deepened through discussion of similarities among representationsthat reveal underlying mathematical structures or essential features of mathematical ideas that persist regardless of the form.

Using these different representations is like examining a concept through a variety of lenses, with each lens providing a different perspective that makes the concept richer and deeper.

Multiple representations should be done and presented by the teacher so that students of a variety of learning styles will see the mathematics.

Ryan Dent, LEUSD

Phil Daro says, “If I were teaching today…”

Types of tasks

Open-Ended

Closed

Open Middle

Ryan Dent, LEUSD

Rachel

What do you notice?What do you wonder?

video 1 (post)video 2 (pre)

But first, think about a procedure that kids are expected to be proficient with before the end of

this year.

Ryan Dent, LEUSD

Ryan Dent, LEUSD

Would you rather…

Ryan Dent, LEUSD

Ryan Dent, LEUSD

Pre/Post Reflection

What can I do to get every student to

engage in the SMP’s?

Ryan Dent, LEUSD

Tough Reflection Questions

• Compare the percent of time that students are talking in your classroom to the percent of time that you’re talking. Does that need to change?

• Of the time that you are talking, what percent of what you say is a statement? What percent of what you say is a question?

• Do your questions strive for what you want them to say, or to make their thinking visible?

• Who’s engaging in the SMP’s in your classroom…your students or you?

Ryan Dent, LEUSD

What is my PLAN to get every student to engage in the SMP’s?

Using Adobe Voice, create a compilation of the things you’ve heard, seen, captured, and/or experienced to illustrate a specific plan for what you are going to do to engage every student in the SMP’s.

Think about the potential for using similar tools for students in your classroom.

Ryan Dent, LEUSD

Explore the MTBOS

1. Spend some time exploring the MTBOS for a task that you could use in the next week to promote reasoning and problem-solving. http://bit.ly/1hIr6bP

2. Identify a goal that would you would strive for in using that task that will keep you focused throughout the task.

3. Anticipate the strategies/representations students will use, and the sequence you will display them in

Ryan Dent, LEUSD

I hope…

• You will launch rich, open-middle problems to kids to solve on their own.

• You will use their representations in a sequence for universal access.

• You will ask at least 3 times as many questions as you make statements.

• You will make kids’ thinking visible through discourse during at least 60% of your classroom time.