Common Core High School Mathematics: Transforming Instructional Practice for a New Era

Common Core High School Mathematics:Transforming Instructional Practice for a New Era

School Year Session 2: October 2, 2013

Tasks that Promote and Assess Thinking

1.1

Agenda

• Homework Discussion• Principles of Task Modification• Break• Assessment Based on Task Selection• District Planning Time• Homework and closing remarks

1.2

1.3

Homework Discussion

Sit with others teaching the same content as you this semester.• One person places his or her selected tasks face

up on the table• Other group members study them individually, in

silence, for 1 minute• Discuss the levels of cognitive demand of each

task• Repeat, until everyone has presented their tasks

Activity 1:

Learning Intentions & Success Criteria

Learning Intentions:

We are learning to identify the principles of task modification, and of assessment based on task selection

Success Criteria:

We will be successful when we can select and modify a task to meet the shifts of the Common Core, and build an assessment framework for that task based on the principles by which it was selected.

1.4

1.5

Principles of Task ModificationActivity 2:

For the original task:• Identify the mathematical

goal for the task• Identify the level of

cognitive demand and reasons for that categorization

• Identify any promising features

For each modification:• Identify the mathematical

goal for the task• Identify the level of

cognitive demand and reasons for that categorization

• Identify the ways in which the task has changed

Consider the set of five tasks, A-E, and their modifications in your group.

1.11

Principles of Task ModificationActivity 2:

• Ask students to create real world stories for “naked number” problems

• Use an additional representation and make connections between two (or more) representations

• Solve an “algebrafied” version of the task• Use a task “out of sequence” before students have memorized a

rule or have practiced a procedure that can be routinely applied • Eliminate components of the task that provide too much

scaffolding• Provide more opportunities for students to conjecture, think

and reason

Break

1.12

1.13

Assessment Based on Task SelectionActivity 3:

Two consortia of states have accepted the assessment challenge:• The Standards of Mathematical Practice are

STANDARDS that the participating states have signed on to implement.

• Placing attention and focus only on content standards is insufficient!

Smarter Balanced Assessment Consortium (SBAC)

• 27 states representing 43% of K-12 students

• 21 governing, 6 advisory states

• Washington state is fiscal agent

A Balanced Assessment System

1.16

Assessment Based on Task Selection

Smarter Balanced Assessment Consortium (SBAC) claims about student performance in each of the following categories:Claim 1: Concepts and ProceduresClaim 2: Problem SolvingClaim 3: Communicating and ReasoningClaim 4: Modeling and Data AnalysisWe will look at each of these in turn – with a realization of

overlap – particularly in classroom application.

Activity 3:

1.17

Assessment Based on Task Selection

SBAC Claim 1: Concepts and Procedures

Students can

• explain and apply mathematical concepts • interpret and carry out mathematical

procedures with precision and fluency

Activity 3:

1.18

Assessment Based on Task Selection

SBAC Claim 2: Problem SolvingStudents can

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

Note: this is closely related to MP1

Activity 3:

1.19

Assessment Based on Task Selection

Evidence sought in Claim 2:

• Seek evidence of student performing expected routines, etc.

Activity 3:

1.21

Assessment Based on Task Selection

SBAC Claim 3: Communicating and Reasoning

Students can

• clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

Note: this is an almost verbatim statement of MP3

Activity 3:

1.22

Assessment Based on Task Selection

SBAC Claim 4: Modeling and Data Analysis

Students can

• analyze complex, real-world scenarios

• construct and use mathematical models to interpret & solve problems

Note: this is strongly related to MP4

Activity 3:

1.23

Assessment Based on Task Selection

Evidence sought in Claims 3 & 4:

• Student artifacts show students recognize that the task is intended to assess their strategy development• Students demonstrate construction of a sequence of

mathematical reasoning, with justifications• Students self-assess their initiative and effort in

establishing a strategy, and monitor its effectiveness

Activity 3:

1.24

Assessment Based on Task Selection

In small groups, rotate through the stations around the room. At each station:

• Decide which SBAC claim the task(s) at that station are designed to assess•Write your answer on a post-it note and attach

it behind the task(s)

Activity 3:

1.25

Assessment Based on Task SelectionActivity 3:

1.26

Assessment Based on Task SelectionActivity 3:

1.27

Assessment Based on Task SelectionActivity 3:

1.28

Assessment Based on Task SelectionActivity 3:

1.29

Assessment Based on Task Selection

Analyze the “Shopping Carts” and “Supermarket Cart” tasks through the lens of the SBAC claims.

How might each of these tasks be used to provide evidence for one or more of the claims?

How are the two tasks similar? How do they differ?

Activity 3:

1.32

Assessment Based on Task Selection

Analyze the higher level task you brought for this week’s homework, through the lens of the SBAC claims.

How might that task be used to provide evidence for one or more of the claims?

Activity 3:

Learning Intentions & Success Criteria

Learning Intentions:

We are learning to identify the principles of task modification, and of assessment based on task selection

Success Criteria:

We will be successful when we can select and modify a task to meet the shifts of the Common Core, and build an assessment framework for that task based on the principles by which it was selected.

1.33

1.34

District Planning Time

Reorganize into your district teams. With them:

• Continue your discussion from last time around your chosen focal Standards for Mathematical Practice.

• Select one or two of the SMP that you would like to focus your reform efforts on across your district team this year.

• As you discuss, consider what you might collect as evidence of student mathematical engagement in your focal SMPs.

Activity 4:

1.35

Homework & Closing Remarks

Homework:• Read the article Responding to Students’ Work on a Rich

Task by Emily Kuper and Patrick Kimani.

• As part of your last homework, you selected two tasks (one low-level and one high-level) that you had used in one of your classes. Modify each of these tasks using the principles you discussed this evening, in order to raise the cognitive demand of each of them. (If you have already taught the 2 tasks you brought this week, you should choose 2 new tasks to modify.) Bring your original and your modified tasks to our next session (October 16).

• Select a lesson or unit that you will develop and implement as your major project this semester. This should be something you will teach between November 20 and December 4.

Activity 5: