CFN 204 · Diane Foley · Network Leader Assistant Principals’ Meeting March, 2014 CFN 204 Focus: Problem Solving in Mathematics 1

CFN 204 · Diane Foley · Network Leader

Assistant Principals’ Meeting

March, 2014

CFN 204

Focus: Problem Solving in Mathematics

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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.


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

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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?

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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.

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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)

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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)

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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?

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Mathematical

Power

Explore

Conjecture

Reason Logically

Use a Variety of

Mathematical Methods

Effectively Solve

Problems

Components of Problem Solving Lessons

CFN 204 · Diane Foley · Network Leader 10


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.

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Why is it important to ask the students to make their thinking visible?

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

This practice allows students to:

- 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

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AssessmentsWhen 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?

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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.

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5 Key Practices for Orchestrating Productive Mathematical Discussions

1. Anticipating likely student responses to challenging mathematical tasks

2. Monitoring students’ actual responses to the tasks (while students work on the tasks in pairs or small groups)

3. Selecting particular students to present their mathematical work during the whole-class discussion

4. Sequencing the student responses that will be displayed in a specific order

5. Connecting different students’ responses and connecting the responses to key mathematical ideas.

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Learning Activity #1

https://www.teachingchannel.org/videos/multiplying-fractions-by-whole-numbers-lesson?fd=1. https://www.teachingchannel.org/video

Transcript for the lesson is included in the hand-outs if needed.

https://www.teachingchannel.org/videos/multiplying-fractions-by-whole-numbers-lesson?fd=1



https://www.teachingchannel.org/video




An Example of Effective Teaching


CFN204 Website

http://www.cfn204.com/simi-minhas/

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

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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?


Questions and Feedback

Please fill out the feedback forms before you leave.

Thank you so much for coming!

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Documents

CFN 204 · Diane Foley · Network Leader Assistant Principals’ Meeting March, 2014 CFN 204 Focus: Problem Solving in Mathematics 1