© 2013 Boise State University1 What the Shifts in the Standards Mean for Learning and Instruction Michele Carney, PhD Spring 2014

© 2013 Boise State University 1

What the Shifts in the Standards Mean for Learning and InstructionMichele Carney, PhD

Spring 2014


Agenda• What does it mean to engage students in the

practice of mathematics?• Examine assessment items and categorize the

type of cognitive demand that are required from students

• What does this mean for instruction?

What does it mean to say students need to engage in the ‘Practice of ELA/Mathematics’Language Arts Mathematics• We teach phonics,

grammar, punctuation, spelling, etc. for the purpose of students’ engaging in the practice of language arts: – Reading – Writing

• Focused on teaching skills, facts, algorithms, procedures, etc.

• Now we are asking that students be able to put these into the practice of mathematics:– Problem solve– Model situations– Reason quantitatively– Critique the reasoning of

others


Claim 1:Concepts & Procedures

Claim 2:Problem Solving

Claim 3:Communicate

Reasoning

Claim 4:Modeling & Data

Analysis

DOK 1

DOK 2

DOK 3

DOK 4

SBAC Assessment & Reporting Areas

Areas assessed by the ISAT

Areas assessed by SBAC


If we are going to ask students to meaningfully engage in the practice of mathematics:

Then we must vary the type and depth of cognitive demand we are asking from students in classroom tasks, activities and assessments.

Level of Cognitive Demand

Rote, Skill or Recall

Concepts

Problem Solving

Reasoning & Justification

Modeling and Data Analysis

Mathematics Practices

Problem Solve

Model Situations

Reason Quantitatively

Critique the reasoning of others


TYPES OF COGNITIVE DEMAND


Porter (2002)

Memorize

Perform Procedures

Communicate Understanding

Solve Nonroutine Problems

Conjecture, Generalize, or

Prove

Webb (2007)

Recall

Skill/Concept

Strategic Thinking

Extended Thinking

SBAC Claims

Concepts and Procedures

Problem Solving

Communicate Reasoning

Model with Mathematics

Type DMT Description Example

Claim 1


Rote, Skill, Recall items require students to produce a response by following a set of rote procedures, demonstrating procedural skills or recalling information (Webb, 2002).

Typically procedural or algorithm focused problems

ConceptsConcept items require students to respond by producing models and diagrams or demonstrate an understanding of mathematical properties and their applications (Webb, 2002)

Often involves asking for visual or iconic representation of a topic

Claim 2

Problem Solving

Problem Solving items require students to produce a response to a given problem for which there can be a variety of answers or problem-solving strategies. Solution methods are not readily apparent and require students to make decisions about how to solve the problem (Hiebert et al, 1992; Porter, 2002).

Typically multi-part, contextual questions but must go beyond skill level applications

Claim 3


Reasoning and Justification items require students to justify their own reasoning or critique the reasoning of others through careful analysis and by explaining and modeling how a response is either correct or incorrect (de Lange, 1999)

Identifying the incorrect solution strategy from two examples and how to correct it

Claim 4


Modeling and Data Analysis performance tasks require students to analyze complex, real-world scenarios and/or use mathematics models to interpret and solve problems (SBAC, 2011).


Type of Cognitive Demand• As a group:– Solve each problem– Identify the type of cognitive demand required by

each item

Type of Cognitive Demand: __________________________________

https://sat2.sbacpt.tds.airast.org/Student/Pages/TestShellModern.aspx






http://www.smarterbalanced.org/smarter-balanced-assessments/



http://www.smarterbalanced.org/wordpress/wp-content/uploads/2012/09/performance-tasks/tulips.pdf

Type of Cognitive Demand: ___________________________

p.5

p.6


• Reflect upon the different types of cognitive demand:– How should these be integrated into classroom

practice?– How do they promote different aspects of the

mathematical practice standards?– Is there a particular order in which tasks with

different cognitive demands should be sequenced?

Discuss in your small groups and select one to two items to share with the whole group.


FOCUSING ON COGNITIVE DEMAND IN YOUR SCHOOL OR DISTRICT

6th Grade Focus Areas

Rate and ratio

Dividing fractions and understanding rational (e.g.,

negative) numbers

Writing, interpreting, and using expressions and equations

Statistical thinking

6th Grade Math Topics # of Days

Expectations for Students

Rote, Skill or Recall Concepts Problem

SolvingReasoning & Justification


Rate and ratio A B C D A B C D A B C D A B C D A B C D

Dividing fractions and understanding rational (e.g., negative) numbers

A B C D A B C D A B C D A B C D A B C D

Writing, interpreting, and using expressions and equations

A B C D A B C D A B C D A B C D A B C D

Statistical thinking A B C D A B C D A B C D A B C D A B C D

Other A B C D A B C D A B C D A B C D A B C D

(A) no emphasis; (B) slight emphasis (less than 25% of time spent on this topic); (C) moderate emphasis (accounts for 25–33% of time spent on this topic); and (D) sustained emphasis

Adapted from Porter, A. C. (2002). Measuring the content of instruction: Uses in research and practice. Educational Researcher, 31(7), 3-14.


Sample ISAT/NWEA MAP item Sample SBAC item

Is the level of cognitive demand in the CCSS and assessed on the Smarter Balanced test what Idaho students need?


Describe the relationship you see between the mathematical practice standards and the levels of cognitive demand.Level of Cognitive Demand


Concepts

Problem Solving



Mathematics Practices

Problem Solve

Model Situations

Reason Quantitatively

Critique the reasoning of others

Documents

© 2013 Boise State University1 What the Shifts in the Standards Mean for Learning and Instruction Michele Carney, PhD Spring 2014