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Leveraging Student Representations and Discourse to Advance Learning
through Progressions
LEUSD Middle and High SchoolSeptember 23, 2015
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Ryan Dent, LEUSD
How long is the song I Got You?
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Ryan Dent, LEUSD
What should kids be doing while they’re
learning mathematics?
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Ryan Dent, LEUSD
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Ryan Dent, LEUSD
According to the CA Math Framework…
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Ryan Dent, LEUSD
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Ryan Dent, LEUSD
What do you notice? What do you wonder?
Rachel
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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.
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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.
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Ryan Dent, LEUSD
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Ryan Dent, LEUSD
Phil Daro on Principles to Actions
https://www.youtube.com/watch?v=o2MgrECf9Xo
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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.”
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Ryan Dent, LEUSD
Which one doesn’t belong?
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Ryan Dent, LEUSD
Which one doesn’t belong?
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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?
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Ryan Dent, LEUSD
“Line of Best Fit” Lesson
Scatter Plots
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Ryan Dent, LEUSD
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Ryan Dent, LEUSD
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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.
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Ryan Dent, LEUSD
Representations
Contextual
Physical
Visual
Symbolic
Verbal
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Ryan Dent, LEUSD
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Ryan Dent, LEUSD
Talking Points
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Ryan Dent, LEUSD
Today’s Meet
What is “depth of understanding?”
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Ryan Dent, LEUSD
What do you notice?
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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?
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Ryan Dent, LEUSD
Is this useful for anything?
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Ryan Dent, LEUSD
Could you use this student’s
work to engage all kids in the SMP’s?
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Ryan Dent, LEUSD
What’s the difference?
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Ryan Dent, LEUSD
What is “depth of understanding?”
How does connecting
student representations
promote depth?
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Ryan Dent, LEUSD
Pre/Post Reflection
What can I do to get every student to
engage in the SMP’s?
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Ryan Dent, LEUSD
Task
http://youtu.be/5JCm5FY-dEY
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Ryan Dent, LEUSD
Orchestrating Productive Discussions
What you read
What we did
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Ryan Dent, LEUSD
What is “depth of understanding?”
How does connecting
student representations
promote depth?
![Page 34: Leveraging Student Representations and Discourse to Advance Learning through Progressions LEUSD Middle and High School September 23, 2015](https://reader035.vdocuments.net/reader035/viewer/2022081520/56649f175503460f94c2d7fb/html5/thumbnails/34.jpg)
Ryan Dent, LEUSD
Pre/Post Reflection
What can I do to get every student to engage in the SMP’s?
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Ryan Dent, LEUSD
Hot Dogs and Buns Task
http://robertkaplinsky.com/work/how-many-hot-dogs-and-buns-should-he-buy
/
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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?
![Page 37: Leveraging Student Representations and Discourse to Advance Learning through Progressions LEUSD Middle and High School September 23, 2015](https://reader035.vdocuments.net/reader035/viewer/2022081520/56649f175503460f94c2d7fb/html5/thumbnails/37.jpg)
Ryan Dent, LEUSD
Contextual
Physical
Visual
Symbolic
Verbal
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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.
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Ryan Dent, LEUSD
Phil Daro says, “If I were teaching today…”
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Types of tasks
Open-Ended
Closed
Open Middle
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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.
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Ryan Dent, LEUSD
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Ryan Dent, LEUSD
Would you rather…
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Ryan Dent, LEUSD
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Ryan Dent, LEUSD
Pre/Post Reflection
What can I do to get every student to
engage in the SMP’s?
![Page 46: Leveraging Student Representations and Discourse to Advance Learning through Progressions LEUSD Middle and High School September 23, 2015](https://reader035.vdocuments.net/reader035/viewer/2022081520/56649f175503460f94c2d7fb/html5/thumbnails/46.jpg)
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?
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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.
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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
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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.