Task Analysis Guide (TAG). Framework for Viewing What does the teacher do to foster learning? What is the impact on student learning?

Task Analysis Guide (TAG)

Framework for Viewing

What does the teacher do to foster learning?

What is the impact on student learning?

What Are Mathematical Tasks?

Mathematical tasks are a set of problems or a single complex problem the purpose of which is to focus students’ attention on a particular mathematical idea.

Why Focus on Mathematical Tasks?

Tasks form the basis for students’ opportunities to learn what mathematics is and how one does it.

Tasks influence learners by directing their attention to particular aspects of content and by specifying ways to process information.

Why Focus on Mathematical Tasks?

The level and kind of thinking required by mathematical instructional tasks influences what students learn.

Differences in the level and kind of thinking of tasks used by different teachers, schools, and districts, is a major source of inequity in students’ opportunities to learn mathematics.

“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”

Stein, Smith, Henningsen, & Silver, 2000

“The level and kind of thinking in which students engage determines what they will learn.”

Hiebert et al., 1997

Pag

e 54

The Cognitive Level of Tasks

• Lower-Level Tasks Memorization Procedures without connections

• Higher-Level Tasks Procedures with connections Doing mathematics

Task Analysis Guide

Read over the Task Analysis Guide and highlight important words, phrases or ideas for each level.

Discuss at your table.

Page 54

Memorization Tasks

Involves either producing previously learned facts, rules, formulae, or definitions OR committing facts, rules, formulae, or definitions to memory.

Cannot be solved using procedures because a procedure does not exist or because the time frame in which the task is being completed is too short to use a procedure.

Are not ambiguous – such tasks involve exact reproduction of previously seen material and what is to be reproduced is clearly and directly stated.

Have no connection to the concepts or meaning that underlie the facts, rules, formulae, or definitions being learned or reproduced.

Procedures Without Connections Tasks

Are algorithmic. Use of the procedure is either specifically called for or its use is evident based on prior instruction, experience, or placement of the task.

Require limited cognitive demand for successful completion. There is little ambiguity about what needs to be done and how to do it.

Have no connection to the concepts or meaning that underlie the procedure being used.

Are focused on producing correct answers rather than developing mathematical understanding.

Require no explanations, or explanations that focus solely on describing the procedure that was used.

Procedures With Connections Tasks

Focus students’ attention on the use of procedures for the purpose of developing deeper levels of understanding of mathematical concepts and ideas.

Suggest pathways to follow (explicitly or implicitly) that are broad general procedures that have close connections to underlying conceptual ideas as opposed to narrow algorithms that are opaque with respect to underlying concepts.

Usually are represented in multiple ways (e.g., visual diagrams, manipulatives, symbols, problem situations). Making connections among multiple representations helps to develop meaning.

Require some degree of cognitive effort. Although general procedures may be followed, they cannot be followed mindlessly. Students need to engage with the conceptual ideas that underlie the procedures in order to successfully complete the task and develop understanding.

Doing Mathematics Tasks

Requires complex and non-algorithmic thinking (i.e., there is not a predictable, well-rehearsed approach or pathway explicitly suggested by the task, task instructions, or a worked-out example).

Requires students to explore and to understand the nature of mathematical concepts, processes, or relationships.

Demands self-monitoring or self-regulation of one’s own cognitive processes.

Requires students to access relevant knowledge and experiences and make appropriate use of them in working through the task.

Requires students to analyze the task and actively examine task constraints that may limit possible solution strategies and solutions.

Requires considerable cognitive effort and may involve some level of anxiety for the student due to the unpredictable nature of the solution process required.

Task Analysis Guide

What type of task was the “Percentage Task and the “Sweater Task?” Why?

Take 3 minutes to discuss this at your table.

Page 55

You Decide…

Use your TAG on page 54.

As a group, categorize each task by the cognitive levels• Lower-Level Tasks

Memorization Procedures without connections

• Higher-Level Tasks Procedures with connections Doing mathematics

There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics.

Lappan & Briars, 1995

Structure and Practicality

Pag

e 56

The importance of the start

Low

LowLow

High

High

Low

High

Moderate

High

Task Set – UP

Task Implementatio

n

Student Learning

The Explore Phase:Private Work (Think) Time

Generate Solutions

Teacher monitors: Variety of representations Errors Misconceptions

The Explore Phase:Small Group – Problem Solving

Generate and Compare Solutions Small groups work to find best

solution

Assess and Advance Student Learning

Share Discuss and Analyze the Lesson

Share and Model

Compare Solutions

Focus the Discussion on Key Mathematical Ideas

Engage in a Quick Write

25

We will narrow the focus of the TCAP and expand use of Constructed Response Assessments

NAEP

PA

RC

C

NAEP

2011-2012 2012-2013 2013-2014 2014-2015

TCAP

We will remove 15-25% of SPIs that are not reflected in Common Core State Standards from the TCAP NEXT year.

The specific list of SPI’s will be shared on May 1.

Constructed Response

We will expand the constructed response assessment for all grades 3-8, focused on the TNCore focus standards for math.

26

2012-2013 assessment plan, math 3-8

• Official Constructed Response Assessment

• (paper-based only, scored by state, results reported in July)

May

• CRA 2 • (paper and

online option, scored by teachers in Field Service Center region, reported by school team)

February

• CRA 1• (paper and online

option, scored by teachers in Field Service Center region, reported by school team)

October

Small Field Test,

May 2012

Student performance on the Constructed Response Assessments will not affect teacher, school, or district accountability for the next two years.

Where will your students be in 2014-2015?

Moral Obligation

The time is always right to do what is right.

Martin Luther King Jr.

Be sure you put your feet in the right place, then stand firm.

Abraham Lincoln

Questioning

Questioning Resources

DOK Question Stems Page 58

Pearson Ring (Assessing & Advancing) Page 50-60

Pearson Effective Question Stem Cards Page 61-65

Qu

est

ion

ing

Qu

est

ion

ing

Assessing

Advancing

Qu

est

ion

ing

Assessing

What students know

What students understand

Advancing

Qu

est

ion

ing

Assessing

What students know

What students understand

AdvancingMove the student

toward target

Assessing Questions

Based closely on the work the student has produced.

Clarify what the student has done and what the student understands about what s/he has done.

Provide information to the teacher about what the student understands.

Advancing Questions

Use what students have produced as a basis for making progress toward the target goal.

Move students beyond their current thinking by pressing students to extend what they know to a new situation.

Press students to think about something they are not currently thinking about.

Marking

Function Direct

attention to the value and importance of a student’s contribution.

Example “That’s an

important point.”

Challenging students

Function Redirect a

question back to the students or use student’s contributions as a source for a further challenge or inquiry.

Example “What do YOU

think?”

Modeling

Function Make one’s

thinking public and demonstrate expert forms or reasoning through talk.

Example “Here’s what

good readers do...”

Recapping

Function Make public in a

concise, coherent form, the group’s achievement at creating a shared understanding of the phenomenon under discussion.

Example “What have we

discovered?”

Keeping the channels open

Function Ensure that

students can hear each other, and remind them that they must hear what others have said.

Example “Did everyone

hear that?”

Keeping everyone together

Function Ensure that

everyone not only heard, but also understood what a speaker said.

Example “Who can

repeat...?

Linking contributions

Function Make explicit the

relationship between a new contribution and what has gone before.

Example “Who wants to

add on...?

Verifying and clarifying

Function Revoice a student’s

contribution, thereby helping both speakers and listeners to engage more profitably in the conversation.

Example “So, are you

saying...?

Pressing for accuracy

Function Hold students

accountable for the accuracy, credibility, and clarity of their contributions.

Example “Where can we

find that...?

Building on prior knowledge

Function Tie a current

contribution back to knowledge accumulated by the class at a previous time.

Example “How does this

connect...?

Pressing for reasoning

Function Elicit evidence and

establish what contribution a student’s utterance is intended to make within the group’s larger enterprise.

Example “Why do you

think that...?

Expanding reasoning

Function Open up extra

time and space in the conversation for student reasoning.

Example “Take your

time... say more.”

49

Reflection

•What have you learned about assessing and advancing questions that you can use in your classroom?

•Turn and Talk

Common Core and TEAM Model

TEAM Evaluatio

n

Common Core

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

Questioning


Questioning

plan a solution pathway rather than simply

jumping into a solution attempt


Questioning

plan a solution pathway rather

than simply jumping into a

solution attempt

check their answers to

problems using a different method,

and they continually ask

themselves, “Does this make

sense?


Academic Feedback


Academic Feedback

explain correspondences between equations, verbal descriptions,

tables, and graphs or draw diagrams of important features

and relationships, graph data, and search for regularity or trends


Thinking


Thinking

analyze givens, constraints,

relationships, and goals


Problem Solving


Problem Solving

make conjectures about the form and meaning of

the solution


Problem Solving

make conjectures about the form and

meaning of the solution

try special cases and

simpler forms of the original

problem


Problem Solving

make conjectures about the form and

meaning of the solution

try special cases and

simpler forms of the

original problem

understand the

approaches of others to

solving complex

problems

2. Reason abstractly and quantitatively.

Thinking


Thinking

make sense of quantities and their relationshipsin problem situations


Thinking

make sense of quantities and

their relationshipsin problem situations

creating a coherent

representation of

the problem at hand


Problem Solving


Problem Solving

abstracta given situation and

represent it symbolically


Problem Solving

abstracta given

situation and represent it

symbolically

considering the units involved;

attending to the meaning of quantities


Problem Solving abstracta given

situation and

represent it

symbolically

considering the units involved; attending

to the meaning of quantities

knowing and

flexibly using

different properties

of operations

and objects

3. Construct viable arguments and critique the reasoning of others.

Questioning


Questioning

Making plausible arguments


Questioning

Making plausible

arguments

listen or read the

arguments of others


Questioning

Making plausible argument

s

listen or read the

arguments of

others

ask useful

questions to clarify

or improve

the argument

s


Academic Feedback


Academic Feedback

communicate them to others, and respond to

the arguments of others


Academic Feedback

communicate them to

others, and respond to the arguments of

others

if there is a flaw in an

argument—explain what it

is


Thinking


Thinking

analyze situations by breaking them into cases


Thinking

analyze situations by

breaking them into

cases

compare the effectivenes

s of two plausible

arguments


Problem Solving


Problem Solving

can recognize and use counter examples


Problem Solving

can recognize and use counter

examples

justify their conclusions


Problem Solving

can recognize and use counter

examples

justify their conclusion

s

distinguish correct logic or

reasoning from that which is flawed

4. Model with mathematics.

Questioning


Questioning

reflect on whether the results make sense


Thinking


Thinking

making assumptions and approximations to simplify a complicated situation, realizing that these may

need revision later


Thinking making

assumptions and approximations to

simplify a complicated

situation, realizing that these may

need revision later

interpret their mathematical results in the context of the

situation


Problem Solving


Problem Solving

identify important quantities in a practical

situation


Problem Solving

identify important

quantities in a practical situation

draw conclusions


Problem Solving

identify important quantities

in a practical situation

draw conclusion

s

possibly improving the model if it has not served its purpose

6. Attend to precision.

Academic Feedback


Academic Feedback

communicate precisely to others


Academic Feedback

communicate precisely to

others

use clear definitions in

discussion with others and in their

own reasoning

8. Look for and express regularity in repeated reasoning.

Thinking


Thinking

notice if calculations are repeated


Thinking

notice if calculations are repeated

lookboth for general

methods and for shortcuts

ResourcesBeth Gilbert

Documents

Task Analysis Guide (TAG). Framework for Viewing What does the teacher do to foster learning? What is the impact on student learning?