tools for teachers linking assessment and learning “assessment should be an integral part of...

Tools for TeachersLinking Assessment and Learning

“Assessment should be an integral part of teaching. It is the mechanism whereby teachers can learn how students think about mathematics as well as what students are able to accomplish.”

Everybody Counts

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7th Grade Pizza Crust 2006



7th Grade – Task 3: Pizza CrustsWork the task and examine the rubric.What do you think are the key mathematics the task is trying to assess?

Look at student work in part 1a and 1b. How many of your students are confusingarea and perimeter?

Now look at student work for 2a.• How many of your students confused 36 sq. in. for the perimeter instead of the area? What would their answer have been?• How many of your students put the length of one edge instead of the total length of the crust?

Look at the work for designing a rectangle.• How many of your students gave dimensions that would yield an area different than 36 sq. inches?• How many of your students gave dimensions that would yield a perimeter of 36 inches?• How many of your students gave dimensions that would not create a rectangle?• What other types of errors did you find?

Student G makes the common error of confusing area and perimeter in part 2a.





Student H draws in the units to find the perimeter in part 2b. However, for both rectangles the area is 32 sq. in. instead of 36 square in.

While we predict tests will measure one core standard, the tasks are rich and allow other ideas to surface. This means that less tasks need to be used, but many standards are covered.

TOOTHPICK SHAPESTom uses toothpicks to make the shapes in thediagram below.

shape 1

6 toothpicks

shape 2

9 toothpicks

shape 3 shape 4

1. How many toothpicks make shape 3?_________________

2. Draw shape 4 next to shape 3 in th e diagramabove .

5. Tom says, “I need 36 toothp icks to make shape 12.”Tom is not correct. Explain wh y he is n ot correct.How many toothpicks are needed to make shape 12?

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Cycle of Formative Assessment to Inform and Improve Learning

Leads to improved teaching and learning in the classroom (re-engagement lessons)

Administer high-quality assessment tasks

Collectively score and analyze student work

Document student thinking to inform instruction.

Drives the professional development experiences of the teachers to plan experiences focused on their students.

Opportunity to Analyze Student Work

Design a Re-engagement Lesson

• Do the task and identify the mathematics.• Consider how the students might approach the math. Where and

how would they be successful? What challenges or misconceptions may arise?

• Look through the student work. Categorize solution strategies, approaches and where students struggled. What is the story of the task?

• Use the Tools for Teachers to compare your findings with the history of the tasks.

MARS Task Anticipation Sheet Task Name:__________________ Grade:_____ Year:______ Tot Pts. _____ Core Pts._____ In anticipating the student work where will students show success? What parts of the task will students be successful?

In terms of knowing and doing mathematics what does this indicate?

In anticipating the student work where will students struggle? What parts of the task will students be unsuccessful?

In terms of knowing and doing mathematics what does this indicate? What understandings or skills do the students need to learn?

Considering strengths and weaknesses from students, what are plans for future teaching? What are the implications for future instruction?

What specific instruction or lesson experiences will you design students?

Viewing a Re-engagement Lessons

The Mathematics Assessment Collaborative uses a process of formative assessment that examines student work and assessment results to inform instruction and design lessons to re-engage students in learning the mathematics.

Re-engagement Happens “Live”

• The heart of the process is in the discussion, controversy, and convincing of the big mathematical ideas.

• This is where students have the opportunity to clarify their own thinking, confront their misconceptions to see the errors in logic, use mathematical vocabulary for a purpose, and make generalizations and connections.

The design of a Re-engagement lesson

may mirror a MARS task

Access Core Ramp

Re-engagement• Makes use of actual student work - including

unique thinking, misconceptions and strategies.• Has all students re-work a task from different

perspectives.• Confronts misconceptions so that they can be dealt

with and let go.• Gives some students strategies for solving

problem• Helps other students solidify, connect, and clarify

their ideas.

Video Clip 1

How was the re-engagement lesson designed to provide access?

What were the basic concepts the students needed to learn and understand?

How were the students making sense of the mathematics?

What did the students communicate? What did the teachers emphasize?

Small Group Discussions

Re-engagement

• Use student work and their thinking to surface understanding and misconceptions.

• Use student work to address access into basic concepts and foundational understanding.

Video Clip 2

What is the core mathematics of the task?

What experiences in the lesson focused learning around the core mathematics?

How was student work used to promote understanding of the core mathematics?

Describe evidence of students demonstrating that understanding. Where are students still struggling?


Re-engagement

• Use student work to confront common misconceptions.

• Use student work to apply or adapt new or unfamiliar strategies.

• Use student work to “debug” unsuccessful approaches or flawed reasoning.

This process promotes learning core concepts.

Video Clip 3


Describe the components of the lesson that supported students to work at high cognitive levels.

What aspects of the lesson encouraged students to make connections?

How did students demonstrate deeper understanding of the mathematical concepts?

What did the teacher do to facilitate deeper student thinking?

Re-engagement

• Use student work to critique other students’ solutions and processes in order to deepen understanding and ramp up the cognitive load of the task.

Effective Formative Assessment Strategies

• Clarifying learning intentions and sharing criteria for success.

• Engineering effective classroom discussions.• Providing feedback that moves learners forward.• Activating students as the owners of their own

learning.• Activating students as instructional resources for

one another.

Dylan Wiliam, University of London

Formative Assessment Tools

• Common Core Standards

• MARS Tasks

• Scoring Materials and Protocols

• Tools For Teachers (Toolkits)

• Student Works Analysis Tools

• Re-engagement Lesson Videos

Option 1: Intensive Implementation Strategy

Training on the Formative Assessment

Cycle to Teams of Teachers

4-days SeptemberCentralized Location conducted by MAC

Facilitators

Local Formative Assessment

Session

6 days for Teams led by MAC Facilitator

Re-engagement

lessons taught


Session

6 days for Teams led by Teachers

Next Generation

Assessments Taught


Session


Next Generation

Assessments Taught

Training for Next Generation Assessments

to Teams of Teachers

4-days Aug/SepCentralized Location conducted by MAC

Facilitators

Year 1:

Induction to the Formative Assessment Cycle

Year 2:

Next Generation Assessments

Year 3:

Sustaining and Going Deeper

Option 2: : Introductory Training with Gradual Support Strategy

Training on the Formative Assessment

Cycle to Teams of Teachers

3-days SeptemberCentralized Location conducted by MAC

Facilitators


Session


Year 1:

Induction to the Formative Assessment Cycle


Session


Next Generation

Assessments Taught

Training for Next Generation Assessments

to Teams of Teachers

3-days Aug/SepCentralized Location conducted by MAC

Facilitators

Year 2:

Next Generation Assessments

Option 3: Leader Training and Indirect Support Strategy

One Year Option

For District Math Leaders (DML)

Trainer of Trainers Model to Support Target Teachers (TT)

Follow-up Training for District Math Leaders

2-days Oct/NovCentralized Location Conducted by MAC


2-days Jan.Centralized Location Conducted by MAC


2-days Mar.Centralized Location Conducted by MAC

Intensive Training for District Math Leaders

4-days SeptemberCentralized Location Conducted by MAC


Session

1 day for TT conducted by DML


Session



Session



Session


tools for teachers linking assessment and learning “assessment should be an integral part of...

Documents

student work slide

learning assessment

student g

assessment results

highquality assessment

student h draws

cycle of formative assessment

th grade task