1. Learning Power Institute
TRU Math
by Marcia Torgrude

2. Where are your teammates?
Who is on your team?
Find others who have the other pieces of the same graph and your recorder. 
As a team, come up with a story that could be represented by your team’s graph.  Think carefully about each part of the graph. 
Once your team agrees on a story, make sure every member of the team can describe each part of the story.  You should also be able to explain its connection to the corresponding part of the graph.
Where are your teammates?

3. Agenda Build an understanding of TRU Math
Connect lessons and tasks to the 5 Dimensions of TRU Math
Assess the thinking in the lesson or task using the 5 Dimensions rubric
Build your questioning capacity to support the 5 Dimensions and improve learning
Focus on working collaboratively to improve learning
Unconstruct a constructed lesson
Develop a lesson using the lesson plan template

4. Norms
Speak with the possibility of being heard and listen with the possibility of being changed.
Be present, and be your best self.
Everyone has something to learn.  Everyone has expertise to offer.
We need each other.
You have the right to ask for help, and the duty to assist.
Be willing to experience discomfort.
Make a poster

5. What Does Learning Look Like?
Watch the video and record:
What is the important mathematics content and practices taking place in the video?
How are students building their understanding of the math?
What is the teacher doing?
Handout in binder

6. What important mathematics is happening?
Teaching Channel Presents – Bridge to Geometry
Post your notes on chart paper
Put all notes on Chart Paper
Teaching Channel Presents – 30:30 start
What mathematics concepts are evident in this video?
How are students building their understandings of mathematics?
What is the teacher doing?

7. TRU Math Suite Teaching For Robust Understanding of Mathematics
Research-based tools for studying and improving mathematics teaching, with a specific emphasis on helping students understand and solve contextually rich problems.
Schoenfeld, A. H., Floden, R. E., & the Algebra Teaching Study and Mathematics Assessment Project. (2014). An introduction to the TRU Math document suite. Berkeley, CA & E. Lansing, MI: Graduate School of Education, University of California, Berkeley & College of Education, Michigan State University. Retrieved from: and/or

8. TRU Math
“Teachers’ work is remarkably complex – in particular when the goal is not just for students to master facts and procedures, but to Teach for the Robust Understanding of Mathematics. Because of this, there is always room for learning and growth, for every teacher regardless of prior training, years of experience, or current successes. Indeed, ongoing learning is the essence of teaching.”
is always room for learning and growth, for every teacher regardless of prior training, years of experience, or current successes. Ongoing learning is the essence of teaching.

9. TRU Math Continues the Learning Through:
Conversations grounded in classroom observations
Shared experiences from your classrooms and your students

10. TRU Math Suite Teaching for Robust Understanding of Mathematics
Analytic framework for characterizing important dimensions of mathematics classroom activity
A scoring rubric for capturing their presence in instruction.
Five minimally overlapping dimensions of mathematics classroom activity.
captures an essential aspect of productive mathematics classrooms — classrooms that produce powerful mathematical thinkers.
This document provides the theoretical rationale underlying the Teaching for Robust Understanding in Mathematics (TRU Math) analytic scheme. The TRU Math scheme consists of an analytic framework for characterizing important dimensions of mathematics classroom activity and a scoring rubric for capturing their presence in instruction. The scheme has two parts: a general frame that applies to all mathematical classrooms, and a content-specific component that applies to solving contextual algebraic problems. The general part of TRU Math delineates a measurement scheme that focuses on five minimally overlapping dimensions of mathematics classroom activity. Each of these five dimensions captures an essential aspect of productive mathematics classrooms — classrooms that produce powerful mathematical thinkers.

11. TRU Math Suite Teaching Robust Understanding of Mathematics
Next page of your binder

12. Five Dimensions
Connect the Five Dimensions to our notes from the videos
Find the dimension that connects to the content on the charts
Place the dimension dot color next to the words and be ready to explain why
Make a set of sticky notes with the headings of the 5 dimensions

13. Propane tanks Work individually to solve the task.
Work together as a group to analyze work done by each of you.
Compare what students did with what you did.
Review your initial work and score it based on the rubric.
Score the student work – compare at your table.
Share out Whole Group

14. Propane tanks Tour of Website - http://map.mathshell.org
This is the pre – assessment – learn where your students are but don’t grade them. Provide feedback for them to consider what they would do differently.

15. Dimension Study- Propane Tank
Group by Dimension
Read your specific Dimension pages
Create a poster
Your dimension
Core question
Your summary- where does it appear in the teaching and learning?
Provide connections to the lesson
Have them count off 1-5. Group by number.

16. Improving Learning through Questioning
Thinking about why we ask questions
Private think time – handout 1
Table talk – handout 1
Group work-Round Robin – handout 2
Read handout 3 – Five Principles for effective questioning
Questioning handouts 1-6

17. Improving Learning through Questioning
Read and try the “Sharing Gas Costs” problem individually.
Compare your method to methods 1 and 2 and determine which method is better.
Round Robin share your selected method defending your answer.
Handout 4

18. Improving Learning through Questioning
Gwen’s Lesson – Look for the Five Principals – shifting one dimension to the left at your table
What were the findings?
How does questioning fit into our 5 Dimensions?
Principals document to fill in

19. Important Mathematical Ideas
Our intention is to support discussions and questions about “Important Mathematical Ideas”. “It is more important to work together to push our students and ourselves as educators toward more interconnected and fundamental understandings of mathematics than to decide exactly which ideas are most important.”

20. TRU Math Scoring Rubrics
Using the rubrics where would you place Gwen’s class and why? Focus on your dimension in all rubrics – then discuss at your tables.
Whole group discussion after the table talk.

21. Scoring Gwen’s Lesson with Your dimension
Whole Class
Small Group
Individual Work
Student Presentations
Summary
Share whole group – What was the focus dimension for this lesson?
Divide into 5 groups – groups number off 1-4 – begin with your group number video and each person in the group study the video using a specific rubric –Whole class, individual, small group, presentation - some videos may not have your rubric information to discuss
Be prepared to share what you scored each video based on the rubrics.

22. Always, Sometimes, or Never True?
(x + 2)(y + 2) = xy + 4

23. Always, Sometimes, or Never True?
In your groups, take turns to place a card in a column and justify your answer to your partner.
If you think the equation is ‘sometimes true’, find values of x for which it is true and values of x for which it is not true.
If you think the equation is ‘always true’ or ‘never true’, explain how we can be sure that this is the case.
Another member of the group should then either explain that reasoning again in his or her own words, or challenge the reasons you gave.
When everyone in the group agrees, write the reason for your choice or draw an example as I did next to the card.

24. Always, Sometimes, or Never True?
Sorting Equations and Identities
Shift one dimension to your left – how does this dimension fit the lesson?

25. Students Working Collaboratively
Private think time – write your response to your assigned question
With your team, compare your responses and try to refine the answer until you feel you have reached a consensus.

26. Students Working Collaboratively
Take a few moments to reflect on the experience you have just had:
What are the implications of this activity for your classroom?
Reflection handout

27. Students Working Collaboratively
Analyzing the Discussions
Role-play each of the transcripts
Using Handout 3, determine the characteristics of each transcript
What strategies would you use that would help students to discuss more meaningfully?
Share out whole group
Read handouts 5-7
Highlight your focuses for your classroom
Reflection handout
Either have students help you make discussion ground rules or possible make handout 5 with samples for students to consider in the discussion

28. Students Working Collaboratively on Skeleton Tower
Private Think Time to work through the problem on your own.
Work in pairs at your table to discuss how you solved the problem or to ask questions where you are struggling.
Table talk about your strategies to solve the problem and discuss how you came to your solutions.
Which strategy would you like to share?
Who in your group will share?
Keep your readings in mind as you work through the Skeleton Tower
Reflection handout
Whole group share out with discussion about the strategies shared

29. 5-D Scoring of Skeleton TOwer
Whole Class
Small Group
Individual Work
Student Presentations
Summary
Share with your table
Share whole group – What was the focus dimension for this lesson?
Each person in group select one of the 5 areas on the screen to evaluate the skeleton tower – be ready to share evidence of your choice.

30. Modeling Motion: Rolling Cups
Which of these objects do you think will roll the largest circle? Why?
How might you order the objects from smallest circle to largest?

31. Modeling Motion: Rolling Cups
You will be working in threes for this task.
Discuss your predictions prior to beginning the task
What do you need to prove or disprove your predictions?
Work individually first, then as a trio.

32. Modeling Motion: Rolling Cups
Team Work Reflection
The lesson online
What did you notice as differences from what they offered as a lesson and what I provided you?
This is the first introduction to unstructuring structured lessons. Students are provided to much information thus aren’t truly being asked to be problem solvers and critical thinkers.

33. 5-D Scoring of Rolling Cups
Whole Class
Small Group
Individual Work
Student Presentations
Summary
Share with your table
Share whole group – What was the focus dimension for this lesson?
Each person in group select one of the 5 areas on the screen to evaluate the skeleton tower – be ready to share evidence of your choice. Make sue you have a different rubric than the previous task.

34. Intro to Problem Solving Lessons
Discuss the problem
List all the decisions that are being made for students
Revise the structured problem
Hand back some of the decisions to the students
Divide into 3 groups
Group 1 – Table Tennis
Group 2 – Designing a box for 18 Sweet
Group 3 – calculating Body Mass Index

35. Intro to Problem Solving Lessons
Compare structured and unstructured problems
What decisions have been left for the students?
What pedagogical issues will arise when you start to use unstructured problems like this?
How will the questioning and discourse support these unstructured problems?
Handout 2, 3, and 4

36. Your Lesson Locate a lesson in your materials or at the MARS site.
Unstructure the lesson
Consider the questioning that will need to take place
Give thought to the collaborative discourse process

37. Your Lesson Template

38. Closure What value do you see in the 5 Dimensions of TRU Math?
What value do you find in the 5 Dimensions rubrics of TRU Math?
What are your thoughts or concerns as you begin to develop your unstructured task or lesson?
What questions do you still have?
Please complete the Survey at:
Note Cards