2013 Mathematics Standards of Learning Institutes

Analyzing and Modifying AssessmentsExamining How We Assess in K-2

Learning Outcomes

Participants will be able to

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• analyze a variety of assessments• modify existing assessments to raise the level of

cognitive demand• modify existing resources to promote problem

solving

Learning Outcomes

Participants will be able to

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• examine how we assess• explore when we assess• determine the relationship between instruction

and assessment

Assessment

• How do we assess?

• What does assessment look like in a K-2 setting?

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When our students leave us they might be asked to…

Problem 1 Problem 2

8 x 5 =

Use pictures, numbers, and words to tell how you would solve the following problem.

Lucy buys 8 packs of gum. Each pack of gum has 5

pieces in it. How many pieces of gum does she have?

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Characteristics of Rich Mathematical Tasks• High cognitive demand (Stein et. al, 1996; Boaler & Staples, 2008)

• Significant content (Heibert et. al, 1997)

• Require justification or explanation (Boaler & Staples, in press)

• Make connections between two or more representations (Lesh, Post & Behr, 1988)

• Open-ended (Lotan, 2003; Borasi &Fonzi, 2002)

• Allow entry to students with a range of skills and abilities

• Multiple ways to show competence (Lotan, 2003)

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So, who is responsible?

Math 3.5 The student will recall multiplication facts through the twelves table, and the

corresponding division facts.

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Problem 1 Problem 2

8 x 5 =

Use pictures, numbers, and words to tell how you would solve the following problem.

Lucy buys 8 packs of gum. Each pack of gum has 5 pieces in it. How many pieces of gum does

she have?

We ALL are! So how do we get there?

• What mathematics do you teach to support SOL 3.5?

• What did you write for K?

Kindergarten First Second

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GarbageHow to play… 1-3 player game Materials: Count by 5 cards - 5 to 50 or 55 to 100 Directions:

• Each person picks 10 cards from the pile and lays them face down to look like a ten frame.

• The rest of the cards stay in the stack. • Player 1 draws another card from the pile and figures out

where it would go in the 10 frame. Say it to Play It! Player must tell how they know where it goes. Play continues until player has a repeat. Player then says “Garbage” and places card in the discard pile face up.

• Player 2 begins.• The goal is to be the first player to have all your cards face up

and in sequence. 9

Garbage

• How does this activity connect to the standards?

• How would you assess your students’ understanding?

• What does it tell us?

PLAY!

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Math Instruction

Everything you do in mathematics needs to be deliberate and purposeful.

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Garbage

Share and Reflect• How does this activity connect back to the

standards?– K.4– 1.2– 2.4– 3.5

• Does it address all the Essential Knowledge and Skills of each of these standards?

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Garbage

Complete our assessment

• How did we assess your understanding?• What does it tell us?• How can we make it better?

5 10 40 50

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When did we assess?When should assessment take place?

Before During After

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Assessment

Does assessment always have to look the same?

Observations Think about the behaviors you are looking to see…

Questions What am I asking?Why am I asking it?What do I hope to learn from the answers?

Paper/ Pencil Problems/Tasks (problem solving)Journal promptPictures/ Symbols (representations)Multiple choice/ Fill in the blank

Other

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Observations

Questions

Paper/ Pencil

Other

Assessment Template

Before During After

Observations

Questions

Paper/ Pencil

Other

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Break

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Bears in Caves 2 players Materials

– Counting bears (6-10)– Cave - upside down cup or bowl

Directions:• Players agree on the number of bears to use. • Player 2 closes their eyes.• Player 1 hides “some” of the bears in the cave (under the cup) and puts the

others in his/ her hand.• Player 2 open there eyes, looks at the bears NOT in the cave, and uses that

information to tell how many bears are in the cave. • Player 1 lifts the cave and the two players see how many bears are in the cave.• Students state a math sentence to tell about the bears. 5 in the cave and 2 out

make 7, 5+2=7 or 7 bears in all, 2 were out of the cave so 5 are in the cave. • Switch jobs and repeat.

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Assessment Template

Before During After

Observations

Questions

Paper/ Pencil

Other

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Assessment

Recap and Reflection• What have we done today?

• How will this change what you do in your classroom?• How will you share what you’ve learned?

• examine how we assess• explore when we assess• determine the relationship between instruction

and assessment

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2013 Mathematics Standards of Learning Institutes

Modifying Mathematical Tasks to Promote Problem Solving

Dan Meyer: Math class needs a makeover (12 min)

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Many thanks to the Shell Center, UC Berkeley, and the University of Nottingham for their extraordinary work with quality mathematics assessment and for providing these free resources. LINK

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Promoting Problem Solving and Critical Thinking

Do the Task• Solve the task – “Organizing a Table Tennis Tournament” individually• While you are solving, list the mathematical or problem-

solving decisions that are being made for students.

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Reflect on the task• Discuss your methods for solving• Discuss the decisions that are being made for

students

Promoting Problem Solving and Critical Thinking

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Promoting Problem Solving and Critical Thinking

Revise the Task• With your group, discuss how the task could

be revised to return decision-making to students.

• Record your group’s revisions. Be able to justify.

• Share your group’s revisions and why individual revisions were made

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Break

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Decisions being made for students

Students are told• How to code the players (A, B, C, D, etc.)• To list all the matches that need to be played• How to systematically organize these matches• How to tabulate the order of play• To remember that players cannot play on two

tables at once

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Structured vs. Unstructured

Compare and Contrast• Compare and contrast your group’s less-

structured version of the task with the version on the next slide.

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Less-structured version

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Promoting Problem Solving and Critical Thinking

Video Analysis• Watch the video.

– How did the teacher introduce the task?– Why were students asked to work in small groups?– How did the teacher support struggling students?– How did the teacher encourage sharing of

approaches and strategies?

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Remodeling at K-2

Joey had 50 cents in his piggy bank. He had fewer than 10 coins. What are 3 possible combinations of coins that Joey could have?

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Quarters Dimes Nickels Pennies

Promoting Problem Solving and Critical Thinking

Reflect• What would be the benefits of using more

unstructured tasks?• What challenges might teachers and students

face when using unstructured tasks?

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Promoting Problem Solving and Critical Thinking

Reflect• Review Handout – “Practical advice for

teaching problem solving”• What do you notice? • What do you wonder?• What would you add to this list?

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Learning Outcomes

Participants will be able to• analyze assessments for:

– SOL alignment– Level of cognitive demand– Format

• modify existing assessments to raise the level of cognitive demand

• modify existing resources to promote problem solving

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Connecting Assessment to Instruction

Group Discussion• How will the assessment analysis and

modification work today impact planning, instruction, and assessment?

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Professional Development Resources

• Online professional development modules will be provided on the VDOE Mathematics Web site– 2 modules with 7 parts total, broken into 45-min

segments– Facilitators guide, all necessary documents

• Options for delivery– grade-level/subject area teams to work through

professional development in their learning community meetings

– division-wide professional development37