Welcome to BCIU 14 District RolloutDay Two

Amy Martell, Intermediate Unit 17Created by: Dan Richards & Rebecca Chadwick

Berks County Intermediate Unit

Let’s get our Math Brains working!

• Complete Individually– Having Kittens or Security Camera

• As a table, discuss.• Prepare a poster to present your solution and

explanation.

http://goo.gl/YLdcVe

Welcome Back!

Goals for Day 2

• How does a Problem Solving FAL differ from a

Concept Development FAL?

• What are the benefits to non-routine problem solving?

• Develop an action plan and determine IU support.

Let’s Review

• As a table group, put the steps of a Concept Development Lesson in the correct order.

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Concept DevelopmentLesson

START: Pre

AssessmentAnalyze student

work - create questions - group

students

Whole Class Introduction

Collaborative Activity

Whole class discussion

Post Assessment

Analyze student work

for growth

Modify subsequent instruction

Two Types of FALs

Concept Development Lessons are meant to first reveal students’ prior knowledge, then develop students’ understanding of important mathematical ideas, connecting concepts to other mathematical knowledge.

Problem Solving Lessons are meant to assess, then develop students’ capacity to apply their mathematical thinking flexibly to non-routine, unstructured problems – within mathematics and with real world applications.

What makes this word problem so structured ?

Organizing a Table Tennis Tournament

Is this better? If so, why?

VIDEO Lets Watch the teacher from England organize her students for the Unstructured Tennis tournament

Now it is time to look more closely at the other FAL: Problem Solving

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Problem SolvingLesson

START: Pre

AssessmentAnalyze student

work - create questions - group

students

Students reflect

individually to questions

Collaborative Activity

Students evaluate, comment, compare sample responses

Whole Class Discussion

Self reflection

Modify subsequent instruction

Steps of a Problem Solving Lesson

• Frame the lesson and administer the pre-lesson assessment

• Analyze student responses and write feedback questions• Distribute the feedback questions and responses to the

pre-lesson assessment• Students reflect individually to questions• Facilitate students working collaboratively on the problem • Facilitate whole group discussion• Students evaluate, comment, and compare sample

responses• Administer the student reflection sheet• Modify subsequent instruction

Benefits of Problem Solving Lessons

• Students are sharing ideas, communicating/explaining methods

• Exposed to multiple approaches• Exposed to unique, non-routine problems• Required to analyze students’ work• Required to diagnose others’ errors and

misconceptions• Required to make decisions about best method

Some immediate issues that teachers raise are:• Unstructured problems are more difficult. • It is more difficult to plan a lesson with these problems.• Students may not even know how to get started on them.

Will we therefore need to structure them anyway?• Students will not necessarily use what we have taught them.• If we offer help too quickly, students will simply do what we

say and not think for themselves.• Students will generate a greater variety of approaches and

solutions.• Students may need reassurance that it is OK to try a different

approach or reach a different conclusion.

Framing the Lesson(Concept Development or Problem Solving)

• Give each student a copy of the assessment task.• It is important that, as far as possible, students are allowed to

answer the questions without your assistance.• Read through the questions and try to answer them as

carefully as you can. • Students should not worry too much if they cannot

understand or do everything, because in the next lesson they will work on a similar task, which should help them. Explain to students that by the end of the next lesson, they should be able to answer questions such as these confidently. This is their goal.

Gold Rush (Pre Lesson Assessment)

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Analyzing Student Work

• Choose 1 Misconception.• Write 1 Guiding Question.• Share Out.

• Groups

Data Analysis – Option 1

Data Analysis – Option 2• What misconceptions/issues did you observe from the

pre assessment class data?

• What strategies did you observe your class using to solve the problem?

• What needs will you address moving forward with this content or problem solving?

• How will I group the students?

Feedback Questions

• Based upon your work, I have developed some questions to help you improve your first efforts.

1. What does the rope represent, mathematically?2. Did you create several different size plots using the same rope?

– Is that enough to convince someone of your answer? – Show me how you represented this information.

3. Suppose 3/4/5/or more prospectors share land. What area of land would each prospector get? How do you know?4. How did you organize your efforts? Can someone who did not work the problem understand what you did?

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Why Ask Questions?

• To interest, engage, and challenge

• To assess prior knowledge

• To stimulate recall

• To focus on important concepts

• To help students extend their thinking

• To promote thinking, problem solving, hypothesizing

Questioning Mistakes We Make• Ask irrelevant questions• Ask and answer yourself• Simplify for immediate response• Ask only capable students• Ask only closed, one-answer questions• Judge every response• Not allowing time to think• Ignore incorrect answers and move on

Tips for Effective Questioning

• Remember wait time: Provide at least three seconds of thinking time after a question and after a response

• Utilize “think-pair-share.”

• Ask “follow-ups” (Why? Do you agree? Can you elaborate? Can you give an example?)

• Withhold judgment: Respond to student answers in a non-evaluative fashion.

• Require students to defend their reasoning against different points of view.

Tips continued …

• Ask for summary (to promote active listening) “Could you please summarize John’s point?”

• Survey the class “How many people agree?” (“thumbs up, thumbs down”)

• Allow for student selection: “Richard, will you please call on someone else to respond?”

• Call on students randomly. Not just those with raised hands.

• Play devil’s advocate

Collaborative ActivityPreparing a Joint Solution

• Review feedback questions individually and think about how you would possibly change your answers.– Discuss with your shoulder partner your

strategies/methods and reasoning for solving the problem.

• You and your partner will join two others to discuss and plan a presentation.– Create poster and share out.

Planning a Joint Method1. Take turns to explain your method and how you think your work could

be improved.

2. Listen carefully to each other.– Ask questions if you don’t understand.

3. Once everyone in the group has explained their method, plan a joint method that is better than each of your separate ideas.

4. Make sure that everyone in the group can explain the reasons for your chosen method.

5. Write a brief outline of your method on one side of your sheet of paper.

Approximately 35 minutes20 for teachers

P-28

Evaluating Student Sample Responses

1. Imagine you are the teacher and have to assess the student work.

2. Work through a students’ solution.

Write your answers on your mini-whiteboards.

3. Explain your answer to the rest of the group.

4. Listen carefully to explanations.– Ask questions if you don't understand.

5. Once everyone is satisfied with the explanations, write the answers below the student’s solution. - Make sure the student who writes the answers is not the

student who explained them.

P-29

6. Work through each response using this protocol.

Ann’s method

P-30

Jake’s method

P-31

Kodie’s method

P-32

Mark’s method

P-33

Problem Solving FALAlternate to Class Data Summary Spreadsheet

Creating Better Problems – Removing Structure - Dan Meyer

Let’s Compare the 2 Types of LessonsConcept Development / Problem Solving

• Read 2 page excerpt from “Guide”.

• When do you use them?• How often do you use them?• Are grouping strategies the same?• What are the typical activities used in each?• Are the post lesson assessments the same?• When are feedback questions provided?

MDC and Teacher Evaluation

• Focus on Domain 3 and highlight statements/areas that you feel FALs used under MDC would provide evidence to support a teacher meeting that criteria.

• What did you find?

Pilot Comments• Teacher

o “With MDC lessons, I almost feel like I’m cheating the system.”

• Administratoro “I did back to back observations one day with one

teacher using a MDC lesson and the other teaching another typical lesson per the curriculum. The differences noticed based on the rubric were remarkable. The teacher using the MDC lesson scored significantly higher.”

Goals for Day 2

• How does a Problem Solving FAL differ from a Concept Development FAL?

• What are the benefits to non-routine problem solving?

• Develop an action plan and determine IU support.

Challenges and Logistics

• Based on what you’ve seen in the training, discuss at your table what challenges you may face at your district.

• Discuss how you might overcome them.• Share out.

Things to Consider

• Time• Planning/Co-Planning• Acquiring Materials• Preparing Materials• Classroom Management• Physical Structure of Classroom• Curriculum Alignment

Expectations for Implementation

• Now to October 27– Plan and implement 1 lesson for 1 section/class.

• Materials Preparation• Invite to assist with planning or observation.• Other onsite assistance as needed.• Data Chart with 15+ students.• Student Samples

– Reflection Survey http://goo.gl/forms/tcdoLQ7r5x – On-Site Visit (structure) /

Sketching Out Possibilities

• Review MDC lessons and district curriculum to decide what lessons would fit in the near future.– Use Calendar Planner to sketch out upcoming

months– Use PA Core Alignment– Discuss with district team and/or grade level

groups in and out of district.

Choosing Your First Lesson• Select a lesson that you will implement prior

to the next group meeting.• Lesson Selection Form/Request for Materials

– http://goo.gl/forms/tcdoLQ7r5x

Preparing for Your Lesson• Pull copy of your lesson from binder or ask to

have it printed.• Read through the steps of the lesson.

– Questions for me?• Complete Pre Lesson Assessment.• Complete Formative Assessment Anticipation

Guide.• Determine copies needed.• Will any manipulatives assist in the lesson?

Workshop Evaluation

• Contact:– Amy Martell

• amartell@iu17.org• amartell1@nebpanthers.com• 570-506-4116 ©• 570-744-2521 ext 2214 (w)