1. Assistant Principals’ Meeting March, 2014 CFN 204 Focus: Problem Solving in Mathematics

2. Food For Thought
“… twenty-first-century citizens need mathematics. But the mathematics that people need is not the sort of math learned in most classrooms.
People do not need to regurgitate hundreds of standard methods.
They need to reason and problem solve, flexibly applying new methods in new situations.”
- Jo Boaler, 2008.
Jo Boaler is a British education author, and is Professor of Mathematics Education at the Stanford Graduate School of Education.
Common core standards align with this philosophy. (thoughts & response)

3. Today’s Agenda Introduction: Classroom visits- 9:00 a.m. to 10:00 a.m.
Debrief session
Lunch: 11:30-12:30
Math Professional Development
Navigate CFN204 website for math resources

4. Essential Questions/Session Objectives
How can we engage students in productive struggle, and provide meaningful experiences so our students become problem solvers?
How can we adapt our teaching practices, to show/accept multiple solution pathways to a problem? How can we help students make connections between the flexible ways and the traditional ways of computing?
How can teachers facilitate purposeful math discussion in their classroom?
How can the teacher provide entry points for the ELLs and the SWDs?

5. Norms for Classroom Visits
Please make sure that there are no more than 6 visitors in a classroom.
Please do not interact with the students. You can listen in, but do not ask any questions.
You may take pictures of the classroom environment if you like.
Please do not ask any questions from the teachers, because it may take them away from the instruction. If you have any questions, write them down, and I’ll try and get the answers for you during lunch.

6. Focus Questions for Classroom Visits
Was the task and instruction designed to engage students, and advance them through the content? (1e)
Were the activities cognitively challenging for the students? (3c)
How did the teacher foster an environment of respect and rapport? (2a)
What assessment practices and tools were used by students and teachers? (1f and 3d)
How did the teacher facilitate genuine student discussion? (3b)
How did the teacher allow for multiple entry points? (1b)

7. Debrief
Was the task and instruction designed to engage students, and advance them through the content? (1e)
Were the activities cognitively challenging for the students? (3c)
How did the teacher foster an environment of respect and rapport? (2a)
What assessment practices and tools were used by students and teachers? (1f and 3d)
How did the teacher facilitate genuine student discussion? (3b)
How did the teacher allow for multiple entry points? (1b)

8. ICT Classrooms
Are co-teachers working to ensure that their instructional strategies engage all students in ways that are possible when only one teacher is present?
Are the teachers working to ensure that they can bridge the learning of all students to the next level?

9. Components of Problem Solving Lessons
Mathematical Power
Explore
Conjecture
Reason Logically
Use a Variety of Mathematical Methods
Effectively Solve Problems
Components of Problem Solving Lessons

11. Problem of the Day
Take a few minutes to solve the following problem. Please make your thinking visible.
Use models, numbers and words to show your mathematical thinking.
Sheila is painting one of the walls in her bedroom. She has ½ of the wall left to paint when 3 of her friends offer to finish the painting for her. What fraction of the wall will each friend need to paint to finish painting that wall?
Try and solve it as many ways as possible.
5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

13. Why is it important to ask the students to make their thinking visible?
This practice allows students to:
By making students’ thinking visible,
a teacher can:
determine what students know, believe, feel
identify preconceptions and misconceptions
assess the quality of conceptual understanding
assess the ability of students to transfer learning to new situations
evaluate and improve instruction
refine their thinking and reflect on their own thought
use opportunities for metacognition and self regulation
engage in self and peer assessment
learn from others in the classroom
Making student thinking visible is beneficial for both teachers and students. When a classroom culture is conducive to learning and the inquiry process, where responsibility is shared, and relationships are supportive and collaborative, the benefits are spread to all stakeholders.

14. Assessments
When using an assessment provided by the program, teachers should think about…
Is the question assessing the standard or a strategy?
Do we need to modify the assessment, and make the questions open ended, so we can tap into the students’ thinking?
How can the teachers collect data at different points of the lesson?
Why is it important to incorporate performance tasks along with multiple choice exams/tests?
Are the assessments truly helping us identify our level 4 students?

15. How can we provide multiple entry point in math?
Tiered tasks: Students are presented with problems with different levels of complexity, aligned to the same standard
Students are presented with an open ended rigorous task that has multiple solution pathways. Their entry point may be an attempt to solve the task using pictures, manipulatives etc. They may not be able to complete the task, but they can start their thought process using concrete models.  Even if it’s just drawing a diagram, if every student can make an initial attempt at a Project or Problem, then the task allows for multiple entry points.

16. 5 Key Practices for Orchestrating Productive Mathematical Discussions
Anticipating likely student responses to challenging mathematical tasks
Monitoring students’ actual responses to the tasks (while students work on the tasks in pairs or small groups)
Selecting particular students to present their mathematical work during the whole-class discussion
Sequencing the student responses that will be displayed in a specific order
Connecting different students’ responses and connecting the responses to key mathematical ideas.

17. Learning Activity #1
by-whole-numbers-lesson?fd=1.
Transcript for the lesson is included in the hand-outs if needed.

18. An Example of Effective Teaching

19. CFN204 Website
Please visit my page on the CFN website to access the resources.

20. Learning Activity #2
Please read the article “How to Leverage the Potential of Mathematical Errors”
While reading, think about…
How did the teacher use an open ended task to assess student understanding?
Why is the selection of the task important for problem solving lessons?
How did the teacher anticipate student errors, and how did she maximize the use of errors to foster student learning?
20 minutes to read quietly; 20 minutes to discuss using the evidence for the questions from the “Three Questions for Purposeful Work”

21. Questions and Feedback
Please fill out the feedback forms before you leave. Thank you so much for coming!