Day 1 Day 3 Day 4

Day 2: Tasks

To Print:
Circles and Squares.pdf
DOK chart.pdf

Cognitive Demand.docx
Continuum of Mathematical Understanding.pdf

Essential Questions:
What experiences do students need to successfully transfer their understanding to novel situations?
How do levels of cognitive demand influence the development of a learning cycle?

Focus and Goals
Morning Debrief

Session 3
Circles and Squares - An Assessment Task
1. Tell participants that there are several groups creating assessments for the core. The state has been associated most closely with the Smarter Balance Assessment Consortium, which is creating a range of assessments, multiple choice, performance, and formative. The task that we have selected is an example of the type of performance task that Smarter Balance is working on.
2. Give participants the task and ask them to work on it individually.
3. After participants have worked the task, ask participants to describe the knowledge that students would need to have to work the problem.
4. Hand out the "Cognitive Rigor Matrix" and ask participants to work together to identify where this task falls on the matrix.
5. In the whole group ask students for the levels they selected and justify why they selected those levels.
6. Hand out the DOK Levels circle chart. Ask groups to work together to write descriptors for each of the four levels.
7. Ask how the changing assessments will require a change in pedagogy.
Focus: Assessment for the Pythagorean Theorem
Goal: Participants will understand the changing assessment requirements and that these assessments will necessarily drive a change in the kind of work the student do in class.
Circles and Squares.pdf


Levels of Cognitive Demand
1. Remind participants of the reading that they did for homework in chapters 1 and 2 of "Five Practices". Refer to the task analysis guide on page 16. Go through each of the levels with the idea that there is a place for each of the types of task.
2. Hand out the Cognitive Demand document. Ask participants to go through each task and identify the level of cognitive demand. Remind participants that they may have done a similar cognitive demand task before, but this is something that teachers should consider for everything that they do in their classrooms. Remember that content level does not imply cognitive level. It is the nature of the questions being asked and the work that needs to be done.
3. Have a brief discussion of a few of the more controversial tasks.
4. Ask participants to consider the learning cycles that they have just work with. Their job is create tasks based on the Kung Fu Panda context for each level of cognitive demand. Suggest that participants start by writing a "procedures without connections" task and then move up to a "procedures with connections" and then "doing mathematics". If they don't write a memorization task, it is ok.
Focus: Identifying the levels of cognitive demand.
Goal: That participants understand the mathematical opportunities that are available to students in a particular task.
Cognitive Demand.docx

Session 4
Sequencing Tasks in a Learning Cycle
1. Refer participants back to the set of tasks on the Cognitive Demand handout.
2. Ask them to build a learning cycle from the set of the tasks. Identify which task would be the develop understanding, which would be the solidify understanding tasks, and which would be the practice task.
3. When participants have completed their work, ask them to share their learning cycle.
4. Discuss the following questions in the whole group:
How does the level of cognitive demand of the task that you chose support the part of the learning cycle? How do they work together?
5. Go back and look at the core and find the standards that you just addressed in the learning cycle you developed. Are there ideas that you need to develop further in your learning cycle? How might you refine this cycle so that you can use it in your class?
Focus: Building a learning cycle
Goal: Participants will build a learning cycle and consider that there is a place for various levels of cognitive demand within the learning cycle.


Session 4 (cont.)
Building a learning cycle
Start with the mathematics identified on the previous planning session. Work on putting the ideas in order to build a learning cycle. Remember to start by developing the concepts and representations needed to understand the skills. Work towards the practices tasks being the skills. Look at the progression of ideas, representations, and strategies from CMI Framework. Participants may need to add some mathematical ideas to their learning cycles. They will also want to consider how many learning cycles there will be in the unit.

Progression of ideas, representations and strategies from CMI Framework.
This document is a sample to show participants what their work might look like. (Don't distribute it)
Designing a Unit

Identify and sequence a group of tasks that could be used to achieve the mathematical goals you chose on Day 1.
Daily Reflection

5 Practices:
Read chapters 3, 4, 5
DOK chart.pdf