High School Teachers

December 12, 2013

Tell me everything you know about

Warm-Up

42 xy

1. Trial and Error/ Guess and Check2. Look for a Pattern3. Make a Model4. Draw a Picture5. Make a Table6. Write a Number Sentence7. Work Backwards8. Solve a Simpler (related) Problem

Problem Solving Strategies

• Participants will explore open ended problems and the use of problem solving strategies.

• Participants will focus on effective feedback and assessment practices.

• Participants will apply their knowledge and understanding to develop a lesson.

Outcomes

• Welcome and introductions• Problem solving strategies in a

mathematics classroom• Exploring a fixed versus growth mindset• Investigating effective assessment

practices• Looking at student work• Designing a lesson

Agenda

Design an open ended warm-up.• What problem solving strategies could

students use?• What key questions could you ask to

deepen the thinking in the classroom?• Record it on a half sheet of paper• Prepare to share

Tomorrow’s Lesson

Line Up - Line up according to a pre-established

criteria. - Can be used to make small groups (fold

the line, count off by 4's, etc.)- Promote communication and maximize

student-to-student discourse.

Fixed vs Growth MindsetFixed Vs Growth

At your table, construct a Venn Diagram that compares a Fixed Mindset to a Growth Mindset.

Fixed vs Growth Mindset

• Fixed Mindset – you have the qualities you were born with and they are fixed in stone– So if you have to work hard, then you’re

not smart enough.

• Growth Mindset – you can develop qualities through effort and experience over time– Challenges are fun and exciting.

Building a Growth Mindset

• Hear a fixed mindset voice and recognize it as self-defeating.

• Respond to it with a growth mindset voice and a growth mindset action.

Listen for a fixed mindset voice

“Are you sure you can do it?”

“We went over that yesterday. Weren’t you listening?”

“This work/problem will be so easy. ”

“I don’t know what to do.”

“Is my answer right?”

How we help students interpret challenges, failures, and feedback or criticism is a choice.

Take on challenge wholeheartedlyLearn from setbacks/mistakes and try

againHear the criticism and act on it

Growth Mindset Voice

“I’m not sure that I can do it but I can learn with time and effort. I can’t do this YET.”

“Many successful people have had failures along the way and still do.”

“If I don’t try, then I automatically fail.”

Feedback to avoid

“You did that so quickly. You are really smart!”

“This is easier for you than for other people. I’m really proud of you.”

“You are a natural at this.”

Praise to give…effective feedback

“You put in a lot of work on that. You used several strategies before you found one that worked. That’s great!”

“I like how you took that challenge and tackled it.”

“After working hard in this unit, look at the progress you’ve made.”

Task Level• Provides correction, clarification, cues, correct or incorrect

information, etc.

Process Level• Direct attention to the processes to accomplish the task • Provide students with different cognitive

processes/strategies • Point to directions that the students could pursue

Self-regulation Level• Be motivational so that students invest more effort or skill

in the task • Enable restructuring understandings

Hattie and Timperley 2007

3 Levels of Feedback

Value Wrong Answers

My Favorite NoConsider:• How does the teacher select her example?

• How does this strategy contribute to a growth mindset?

• How does this strategy provide for re-teaching?

Create a Culture of Risk Taking• Provide for productive challenge and

struggle

• Praise students on their process, not on results/success– Choices, effort, persistence, resilience, grit…

• It’s not about how quickly you get there

What is something that you struggled with but now you are great at? How did you get there?

Objective of this Lesson: Students will understand the Exterior Angle Theorem and use it to find the degree measure of an angle.

Looking at a Task

Do it/ Practice

Give its Use

Give the Theorem

Fixed Mindset Descriptors

• Lack of deep understanding• Lack of opportunity for productive

struggle• Often, no discovery = no ownership

Results of Fixed Mindset

• Your goal… Find the value of every angle in this figure

• Take 3-5 min to explore this problem individually

Our Take on this Task

• Compare your work with a partner• Did you both take the same approach or

did you approach this problem differently?

• If the same: Work with your partner to try to play with the math and find another pathway

• If different: 1. teach your approach to your partner and 2. write a brief description of the pathway your partner took.

Are there any other ways????

• CCSS.Math.Content.HSG-CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Let’s look at the standard….

Is the exterior angle theorem in this standard????

As the grade level/band teacher leader at your school –1. Fixed/Growth Mindset

Discuss with Principal:Who? What? When? Where? How?

Taking It Back

Break

Warm-Up

Choose distinct values for a, b, and c such that .

Explain how you know your values satisfy the equation.

The Task:Take a few minutes to individually reflect on assessment in your classroom and jot down as many examples as you can think of.

Use one post-it for each assessment

Assessment

The three overarching types of assessment are:

1) Assessment OF learning – occurs when teachers use evidence of student learning to make judgments on student achievement against goals and standards

2) Assessment FOR learning (formative) – occurs when teachers use inferences about student progress to inform their teaching and provide feedback to students to inform their learning – while it is still going on.

3) Assessment AS learning – occurs when students reflect on and monitor their progress to inform their future learning goals

Assessment

• Is there an assessment type that is predominant in our practice?

• Is there an assessment type you would consider to be under represented? Overrepresented?

Assessment

Summative - Assessment OF learning • Determining the degree to which a

student has mastered an extended body of content at a concluding point in a sequence of learning.

Assessment – Why? What? When?

Assessment – Why?, What?, When?Formative – Assessment FOR learning:

• Emphasizes a teacher’s use of information to do instructional planning that can effectively and efficiently move students ahead

• Includes pre-assessment

• Useful in understanding and addressing students’ interests and approaches to learning

• Rarely graded

• Provides opportunity for meaningful feedback that helps students understand areas of proficiency and areas that need additional attention which is more useful than grading because students are still practicing and refining their competencies

“Students taught by teachers developing the use of assessment for learning outscored comparable students in the same schools by approximately 0.3 standard deviations, both on teachers produced and external state-mandated tests. Since one year’s growth as measured in the TIMSS is 0.36 standards deviations, the effects of the intervention [formative assessment] can be seen to almost double the rate of student learning.”

Dylan Wiliam, 2007, 2011

Assessment – Why? What? When?

“Recent reviews of more than 4000 research investigations show clearly that when the [formative assessment] process is well implemented in the classroom, it can essentially double the speed of student learning producing large gains in students’ achievement, and at the same time, it is sufficiently robust so different teachers can use it in diverse ways and still get great results with their students.”

James Popham, 2011

Assessment AS instruction:

• Ensuring that assessment is a key part of teaching and learning

• Assisting students in self-analysis and becoming more aware of their own growth relative to learning targets

Assessment – Why?, What?, When?

• Of learning• For learning• As learning

Which type(s) of assessment have the greatest potential to increase student achievement? Why?

Assessment

Text Based Protocol:

1. What information was most compelling from the article?

2. Which elements of formative assessment, if any, are habitual in your work?

3. Which elements of formative assessment do you still have to be deliberate and intentional about?

4. In the conclusion it states, “the support of colleagues is essential”. How can we support colleagues with this transition?

Strategies for Effective Formative Assessment

CCSSM Instructional Shifts

•Focus•Coherence •Procedural Skill/Fluency •Conceptual Understanding•Application with equal intensity

Rigor

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique

the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make us of structure.8. Look for and express regularity in

repeated reasoning.

Standards For Mathematical Practice

SBAC Math Assessment Claims • “Students can explain and apply mathematical

concepts and interpret and carry out mathematical procedures with precision and fluency.”

Concepts & Procedures

Problem Solving

Communicating Reasoning

Modeling & Data Analysis

• “Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies.”

• Mathematics Preliminary Summative Assessment Blueprint

- Target Sampling High School (11)

• Claim Column – Assessment Targets• DOK Column – Hess Cognitive Rigor

Matrix• What do you notice? Wonder?

Next Generation Assessment

• Examine the sample assessment items. - connections to the claims and Standards for Mathematical Practice and Instructional Shifts - implications for instructional practice, lesson design and delivery

www.smarterbalanced.org- Smarter balanced assessments- Sample items and performance tasks- Mathematics- Items and About this item

Smarter Balanced Assessment

Work with a partner to:

- Provide feedback that moves learning forward by forcing students to engage cognitively with their work.

Examining Student Work

There are 3 main features to developing good questions:1. They require more than remembering a fact

or reproducing a skill.

2. Students learn by answering the questions, and the teacher learns about each student from the attempt.

3. There may be several acceptable answers.

Sullivan & Lillburn 1997

Developing Good Questions

Working in a group of 2 or 3

1. Select a chapter test or quiz from your textbook2. Choose 3 items to revise3. Display 1 of the items on chart paper - Show original item - Show revised item4. Gallery Walk with Praise/Question/Polish

Open the question up…

As the grade level/band teacher leader at your school –1. Fixed/Growth Mindset2. Changes in Assessment/Implications

for lesson design/instructional practice

Discuss with Principal:Who? What? When? Where? How?

Taking It Back

LUNCH

Collegial Sharing - Wikispace

1. Select an upcoming lesson from text resource

2. Unpack the standard(s)3. Develop/create a common assessment4. Identify key checkpoints for

understanding5. Select rich task and create 3-5 high

quality questions6. Record on chart paper 7. Gallery Walk – Praise/Question/Polish

Backward Lesson Design Process

As the grade level/band teacher leader at your school –1. Fixed/Growth Mindset2. Changes in Assessment/Implications

for lesson design/instructional practice3. Backward Lesson Design Process

Discuss with Principal:Who? What? When? Where? How?

Taking It Back

“An assessment functions formatively to the extent that evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers to make decision about the next steps in instruction that are likely to be better, or better founded, than the decisions they would have made in the absence of that evidence.” Dylan Wiliam 2011