Assignment 4-1 Pre-assessment Polygraphs (5 points) Note You need a partner to play Polygraph. If you don’t have someone who is willing to go to the Desmos activity at the same time as you (a family member, friend, co-worker, etc.), and I will match you with someone from the class. (If you happen to have a flexible schedule this week and are willing

Module 4: Polygraph

Learning Goals:

• I can use the Mathematics Teaching Practices to plan and enact lessons:
  • Elicit and use evidence of student thinking.

Access a list of all assignments for this module at this location.

Assignment 4-1: Pre-assessment Polygraphs (5 points)

Note: You need a partner to play Polygraph. If you don’t have someone who is willing to go to the Desmos activity at the same time as you (a family member, friend, co-worker, etc.), and I will match you with someone from the class. (If you happen to have a flexible schedule this week and are willing to be matched with someone who needs help, let me know!)

• If you and your partner are in the same location, I encourage you to not look at each other’s screens. But also note that you and your partner don’t have to be in the same location to connect and play a round.
• I hope that between the two activities you will get to be the asker and the guesser at least one round each, but if that doesn’t work out randomly, I hope you will consider playing an additional round.
• If someone else from the class and their willing partner decide to play a round at the same time as you and your willing partner, it is possible that you will be matched with one of them instead of your own willing partner. I hope that this is okay with you. Be flexible and try to work it out, but don’t hesitate to let me know if you run into any problems.

1. Complete the following Desmos activity.

Hey, students!

Go to student.desmos.com

and type in:

26ZTGC

(You are not required to login to an account to participate in an activity, but if you choose to create an account or login through a Google account, then you’ll have a record of the activities that we use throughout the course.)

This activity came from Desmos. Here is the original, if you’d like to look at it from a teacher’s perspective. Polygraph: Hexagons

1. Complete the following Desmos activity.

Hey, students!

Go to student.desmos.com

and type in:

V29SPA

(You are not required to login to an account to participate in an activity, but if you choose to create an account or login through a Google account, then you’ll have a record of the activities that we use throughout the course.)

This activity came from Desmos. Here is the original, if you’d like to look at it from a teacher’s perspective. Polygraph: Exponentials

Always abide by and include the following on turn-in assignments: I pledge that I am turning in my own work. For this assignment, type the pledge in the text once you have completed both Polygraphs, along with the name of the person(s) with whom you played each round.

Assignment 4-2: Planning an already-created Polygraph for a lesson (10 points)

Make a copy of the Routine Planning Guide. Go to teacher.desmos.com and type Polygraph in the search box at the top left of the page. Select a Polygraph that you could use for a warm-up for a lesson you teach, and then complete the routine planning guide based on the Polygraph that you have selected.

Note: The planning guide for a Polygraph is on page 2 of the document. You can delete the warm-up planning guide from your copy.

Provide a link to your planning guide or upload it as a Word document or PDF. (If you provide a link to your google document when you submit the assignment be sure to change the sharing settings so that ­­­­­________ can comment.)

Assignment 4-3: Principles to Actions in action (5 points – discussion)

1. Read the Executive Summary of Principles to Actions, published by NCTM in 2014, which is linked from this informational page about Principles to Actions from NCTM (right above the “purchase” button).
2. Write a short reflection using the slightly altered Compass Points visible thinking routine on what you’ve read and how you have and/or might use the Mathematics Teaching Practices, the Guiding Principles for School Mathematics, and the Actions in your classroom:

1. E = Excited
   What excites you about the Mathematics Teaching Practices or Guiding Principles for School Mathematics? What’s the upside? Which is a strength is your own practice?
2. W = Worrisome
   What do you find worrisome about the Mathematics Teaching Practices or Guiding Principles for School Mathematics? What’s the downside? Which could use more attention in your own practice?
3. N = Need to Know
   What else do you need to know or find out about the Mathematics Teaching Practices or Guiding Principles for School Mathematics? What additional information would help you to evaluate things?
4. S = Stance or Suggestion for Moving Forward
   What is your current stance or opinion on the Actions that are listed in the Executive Summary? How might you move forward in your own Actions?

Assignment 4-4: 5 Practices reading (5 points)

Read the first part of Chapter 3 of 5 Practices for Orchestrating Productive Mathematics Discussions, Second Edition (pages 29-35).  I WILL UPLOAD THESE PAGES TO YOU IN A FEW DAYS.

1. (from Active Engagement 3.1 on page 29) Read the vignette Tiling a Patio: The Case of Darcy Dunn and identify places in the lesson where Ms. Dunn appears to be engaging in the five practices. Use the line numbers to help you keep track of the places where you think she used each practice. (List the line numbers for each practice in your response.)
   1. Anticipate
   2. Monitor
   3. Select
   4. Sequence
   5. Connect
2. Select at least two Mathematics Teaching Practices. What evidence do you find of Ms. Dunn enacting the practice? (List the line numbers along with why this is evidence of the Mathematics Teaching Practice.)

1. Establish mathematics goals to focus learning.
2. Implement tasks that promote reasoning and problem solving.
3. Use and connect mathematical representations.
4. Facilitate meaningful mathematical discourse.
5. Pose purposeful questions.
6. Build procedural fluency from conceptual understanding.
7. Support productive struggle in learning mathematics.
8. Elicit and use evidence of student thinking.

1. Read the second part of Chapter 3 of 5 Practices for Orchestrating Productive Mathematics Discussions, Second Edition (pages 35-40).
   1. What differences do you see in what the authors called out for the five practices and the Mathematics Teaching Practices and your own responses in #1-2?

Always abide by and include the following on turn-in assignments: I pledge that I am turning in my own work.

Assignment 4-5: Reflecting on student work for your Polygraph (5 points)

Suppose the student learning target for an upcoming lesson is: I can describe characteristics of quadrilaterals such as regular, rotational symmetry, reflectional symmetry, convex, concave.

You are going to assign Polygraph: Hexagons to see what mathematical vocabulary students are using and to determine what mathematical knowledge they are bringing to the lesson.

1. Anticipate the mathematical terms high school geometry students in your school/district might use. Include mathematical terms that students might use incorrectly.
2. Open this compilation of some student work from the Hexagons polygraph. Consider the round between Daina Taimina and José Sofia Kovaleskaya.
   1. What misconceptions arise?
   2. What questions might you ask to find out more about what these students know about polygons?
3. Consider the round between Alicia Boole Stott and José Ádem Chaín?
   1. What misconceptions arise?
   2. What questions might you ask to find out more about what these students know about polygons?

Always abide by and include the following on turn-in assignments: I pledge that I am turning in my own work.

Assignment 4-6: Creating a Polygraph for a lesson (10 points)

Create your own Polygraph for a lesson that you teach. You will need to create a teacher account at teacher.desmos.com if you don’t already have one. If you are unfamiliar with how to create your own, see this video from David Petro. David’s instructions are for uploading 16 images for the “suspects”. If you prefer to use graphs that you can graph in Desmos, this video from Daniel Kaufmann will be helpful.

Once you have created your Polygraph, go back to teacher.desmos.com, click on Custom, and then click on the three dots at the end of the box with your Polygraph and select Share activity. That will open a window where you can copy the URL for your activity. Upload the URL for this assignment, and include your pledge in a comment.

Always abide by and include the following on turn-in assignments: I pledge that I am turning in my own work.

Assignment 4-7: Giving and receiving feedback for your Polygraph (5 points – discussion)

1. Create a class code for the polygraph you have made. When you are logged in to teacher.desmos.com, go to Custom, then click on your Polygraph, then click on Create Class Code. For your initial post to this discussion board, post the following.
   1. The number of student you are to post. So the first person who posts will type #1, the second #2. You should be able to look at the post before yours and add 1 to their number to know what number you should post.
   2. Hey, students!

Go to student.desmos.com

and type in:

######

(Replace ###### with the class code you generated in Desmos.)

1. 1. Your mathematical learning goal for the polygraph.
2. Find a willing partner to play the polygraph of the person who posted before you and the person who posts after you. (The person who posts first will play the polygraph of the person who posts second and also twelfth. The person who posts second will play the polygraph of the person who posts first and third.)
3. Respond to both of your classmates’ posts with feedback on their Polygraph using I like …, I wonder …, What if …

I recognize that the first person who posts is going to have to wait until the last person posts (#12) in order to complete this assignment. It’s also possible that the last two or three people might be delayed in completing as well, depending on the timing of submissions. You do not have to keep checking back to figure out when the next person has posted – do so by Tuesday at noon if possible after the assignment is due, and if that is impossible with your schedule, send me an email, and we will work out a different way for you to complete the assignment.

Assignment 4-8: Reflection (5 points)

Our goals for this module:

I can use the Mathematics Teaching Practices to plan and enact lessons:

• Elicit and use evidence of student thinking.

1. Read through the blog post I can elicit and use evidence of student thinking. Where are you in being able to say confidently “I can elicit and use evidence of student thinking”? Use the leveled learning progressions for I can elicit and use evidence of student thinking and I can elicit and use evidence of student thinking to reflect on your own practice in the classroom.
2. Complete the following statements, based on your work in this module:

I have learned …

I still need to know …