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A Purposeful Ice-Breaker, Hopefully…

Kentaro Iwasaki, Associate Director for Pathway & Curriculum Development

ConnectEd: The California Center for College and Career

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Ice Breaker for Norm BuildingGoals: 1. Use an Ice Breaker to Get to Know Other People (and Ourselves) Better2. Build Norms—an Essential Element in

any Social Setting, Especially the Classroom

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Norm Building

Marshmallow ChallengeEACH TEAM BUILDS A FREE-STANDING STRUCTURE (NO TAPE ON TABLE) IN 15 MINUTES WITH THE INTACT MARSHMALLOW REACHING THE HIGHEST POINT POSSIBLE 20 sticks of spaghetti + one yard tape + one yard string + one intact marshmallow

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Norm Building

Marshmallow Challenge DebriefDiscuss what your group found out about:

the Marshmallow Challenge itselfmembers in your group (who did what?)how your group worked together (what went

well and what could be done better?)anything else interesting

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Norm Building

Marshmallow Challenge Video

Think about:

1. Debrief the video. 2. What is your experience with norms in and out of the classroom ?3. What norms would be helpful to make the Marshmallow Challenge better?

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Norm Building

Students will not automatically know how to work collaboratively without explicit directions, norms, and “ground rules.”

My Personal Examples

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Norm Building

Norms for this PD:1. Stay together on agreed-upon topic2. Work to maintain equity of voice

(“Step Up, Step Back”)

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Norm Building

Teachers themselves also need to abide by norms when they ask students to work collaboratively.

Which of these teacher roles is most challenging for teachers and why?

How can we help teachers with these roles and help them establish and maintain group norms?

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Frame of Reference

Please participate during this PD as a learner and as a teacher leader who will lead others in the formative assessment lesson process.

Jot down the names or people you will have in mind during the PD with whom you will share the formative assessment lessons and strategies.

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Agenda1. Norm Building Task and Debrief2. Background and Components of a Formative

Assessment Lesson3. Model, Participate In, and Analyze a Formative

Assessment Lesson4. CCSS-M Standards and Practices5. Formative Feedback and Questioning6. Formative Assessment Lesson #27. Homework: Email Reflection Questions from

Day 1

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OK, Who is this Guy?

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Formative Assessment and 5 Strategies

1. Please first read the “Big Idea of Formative Assessment” and then “Five Strategies of Formative Assessment,” and answer the questions individually (5 minutes) and then think-pair-share your reflections (5 minutes).

2. Please be ready to share out!

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Classroom Specific Strategies

1. Avoid cold-calling by giving opportunities for think-pair-share or think-group-share

2. Record the discussion thread with names and contribution

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Formative Assessment Lessons (FALs)

Part 1: Pre-Assessment : Give Students Feedback and Teachers a Qualitative Sense of Students’ Grasp of Targeted Mathematics (15 minutes)

Part 2: Brief Class Discussion (10 minutes) and Collaborative Activity : Focus on Guided Inquiry to Address Student Misconceptions (45-90 minutes)

• Part 3: Post Assessment and Revision: Give Students a Chance to Reflect on Their Learning and Offer Teachers Perspective on Next Steps and Their Teaching Effectiveness

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“Interpreting Algebraic Expressions” Formative Assessment Lesson

Math Goal: Translate between words,symbols, tables, and area representations of algebraic expressions. • Recognize the order of algebraic operations.• Recognize equivalent expressions.• Understand the distributive laws of multiplication and division over addition

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“Interpreting Algebraic Expressions” Formative Assessment Lesson

COMMON CORE STATE STANDARDSA-SSE: Interpret the structure of expressions.A-APR: Rewrite rational expressions.

Math Practices:2. Reason abstractly and quantitatively.7. Look for and make use of structure.

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“Interpreting Algebraic Expressions” Formative Assessment Lesson

Part 1: Individual Pre-Assessment

Please read through or do the pre-assessment individually.

What areas of student understanding or misconceptions can you gather from this?

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Part 2: Brief Classroom Discussion

1. Class questions based on pre-assessment

2. Not intended to address every misconception3. For example, write an algebraic expression that means

a. Multiply n by n, and then multiply your answer by 5.

b. Multiply n by 5, and then square your answer.

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1. Take out the pink and green cards. Match the corresponding pink card to the green card. Leave these cards out.

2. Take out the blue cards next and place the blue cards next to the corresponding pink and green cards.

3. Do the same with the yellow cards. 4. Please fill in any blanks on the cards.5. How you might make extensions and/or modifications

to this task if needed.6. How does this task address student misconceptions

and further student understanding?

Part 3: Collaborative Activity

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Part 4: Revision and Post-Assessment

1. Pre-Assessment and a New Sheet are given back to students for revision.

2. Students might respond to a prompt such as, “What did you learn from this lesson that helps you improve your work?”

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Part 5: Teacher Decisions about Next Steps

1. Based on revisions and post-assessment, a teacher decides what next steps are best to address existing misconceptions.

2. The Formative Assessment Lesson, if taught 2/3 of the way through a unit, allows time in the unit for a teacher to direct where he/she will lead the class.

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DEBRIEF

1. What aspects of the formative assessment lesson allow for deeper student engagement and learning?

2. What challenges arise around the formative assessment lessons for teachers and students? How will you address these challenges?

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VIDEO

Please observe the video and be ready to share out thoughts or observations.

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QUALITATIVE FEEDBACK

Based on a study by Ruth Butler (1988), which type of feedback improves student work quality the most from a first lesson to a similar second lesson? Why?

A. Numerical score/grade onlyB. Written feedback onlyC. Numerical score/grade and written

feedbackD. No feedback

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QUALITATIVE FEEDBACK

1. What type of feedback did you or other math teachers typically give to students? How did you (or others) provide feedback?

2. How effective did you find your feedback to be? Why?

3. How would you think the feedback could be more effective? Why?

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QUALITATIVE FEEDBACK

1. Evaluate the feedback suggestions given. How effective do you find them to be?

2. How might you make them more effective?

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QUALITATIVE FEEDBACK

Read the sheet on qualitative feedback.

Discuss in a small group.

How can we improve the feedback we and other teachers give to students?

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Concept Development Lessons and Problem Solving LessonsConcept Development lessons are intended to assess and develop students’ understanding of fundamental concepts through activities that engage them in classifying and defining, representing concepts in multiple ways/representations, testing and challenging common misconceptions, and exploring the structure of a problem.

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Concept Development Lessons and Problem Solving LessonsProblem Solving lessons are intended to assess and develop students’ capacity to select and deploy their mathematical knowledge in non-routine contexts and typically involve students in comparing and critiquing alternative approaches to solving a problem.

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Problem Solving Lessons’ Structure

1. Students individually work on a “less structured” task (pre-assessment)

2. Brief Class Lesson Drawing Out Misconceptions

3. Students Collaborate on the Task4. Students Examine sample student work

and asked to critique and improve these5. Students then revise their initial attempts

and/or try an alternative approach.

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Security Cameras

Mathematical goals

This lesson unit is intended to help you assess how well students are able to:

• Analyze a realistic situation mathematically.

• Construct sight lines to decide which areas of a room are visible or hidden from a camera.

• Find and compare areas of triangles and quadrilaterals.

• Calculate and compare percentages and/or fractions of areas.

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Security Cameras

Mathematical Content6.RP: Understand ratio concepts and use ratio reasoning to solve problems. 6.G: Solve real-world and mathematical problems involving area, surface area, and volume.

Mathematical PracticesMP1: Make sense of problems and persevere in solving them MP2: Reason abstractly and quantitatively MP3: Construct viable arguments and critique the reasoning of others MP4: Model with mathematics

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Security Cameras

1. What misconceptions do you think students will have?2. What questions would you ask for a BRIEF

class discussion?3. What type of feedback would you give or

be prepared to give?

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Making Matchsticks

1. What misconceptions do you think students will have?2. What questions would you ask for a BRIEF

class discussion?3. What type of feedback would you give or

be prepared to give?

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Agenda

1. Feedback—thanks!2. Re-Norming3. Formative Assessment Lesson #3 with EL

Support4. Questioning5. Feedback6. Formative Assessment #47. Planning/Next Steps, Evaluation

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Re-Norming

1. Debrief the String Geometry Activity.2. Discuss how and when teachers would

use re-norming

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Bruce Tuckman’s Stages of Group Development1. Form2. Storm3. Norm4. Perform5. Our addition—Re-Norm

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EL Support ell.stanford.edu

1. Focus on students’ mathematical reasoning and not on their accuracy in using language

2. Focus on mathematical practices and not on language as single words or definitions

3. Treat everyday and home languages as resources and not as obstacles

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EL Support

How would you scaffold this lesson for EL students?What would you add? What would you keep the same? Describe your rationale.

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EL Support--Instructions

One suggestion is to change the instructions in the activity to be clear, direct, and concise. How would you suggest writing the instructions?

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EL Support--Instructions

“Estimate how many matches can be made from the wood in this tree. Use the relevant information on the formula sheet. It will helpyou find some answers. Read the task, and show all your work. Showing your workhelps me understand your reasoning (thinking). It is important that your work is organized and presented in a clear manner (way).”

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QUESTIONING

Please spend a few minutes individually reflecting on these questions.

Then we will share in small groups and in a large group.

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VIDEO

295 Students in a school.A bus holds 25 students.How many buses are needed to hold all the students?

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QUESTIONING

Fill in the blanks:Based on large study of elementary school classrooms, Ted Wragg analyzed 1000 teacher questions._____% Managerial Questions_____% Recall Questions_____% Questions that Require Students to Analyze, Make Inferences, Generalize__________________________________Less than _____% resulted in new learning

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QUESTIONING

1. Which questions do you find most effective? Why?

2. Which questions can be improved? How so?

3. What challenges around questioning do math teachers face?

4. How do we support math teachers in asking good questions?

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Planning to Work With Teachers

1.Local, Organic, Sustainable

2.It’s a Long Road…3.Do Math Together in Your

PLC/Dept/Team

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Planning to Work With Teachers

Strategize with your district teachers or instructional specialists to determine what needs and next steps you have in working with teachers on the formative assessment lessons and strategies.1. What do you need?2. What do the teachers need?3. How will you work with the

teachers on what they need?

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Planning to Work With Teachers

3 webinars throughout the school year to support your work with teachers:

1. Norm Building2. FAL enactment3. FAL issues? EL Issues?

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Planning to Work With Teachers

3 webinars throughout the school year to support your work with teachers:

1. Norm Building2. FAL enactment3. FAL issues? EL Issues?

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Math Design Collaborative (MDC)

“Mathematically proficient students continually ask themselves, “Does this make

sense?” and change course if necessary. They justify their conclusions, communicate

them to others, and respond to the arguments of others. They can apply the mathematics they know to solve problems

arising in everyday life, society, and the workplace. They continually evaluate the

reasonableness of their intermediate results, realizing that these may need revision

later.”

—Common Core State Standards for mathematics

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The Need for Formative Assessment

CST Algebra Question

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The Need for Formative Assessment

Smarter Balanced Performance Task

In the task, a new water tank or water tower for a town needs to be built, and your job is to recommend the best solution for the town.

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The Need for Formative Assessment

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Thank you!

Please contact me with any feedback or questions:

kiwasaki@connectedcalifornia.org

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