Task Analysis Guide (TAG). Framework for Viewing What does the teacher do to foster learning? What...
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Transcript of Task Analysis Guide (TAG). Framework for Viewing What does the teacher do to foster learning? What...
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
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
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.
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 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
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
1. Make sense of problems and persevere in solving them.
Questioning
plan a solution pathway rather than simply
jumping into a solution attempt
1. Make sense of problems and persevere in solving them.
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?
1. Make sense of problems and persevere in solving them.
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
1. Make sense of problems and persevere in solving them.
Thinking
analyze givens, constraints,
relationships, and goals
1. Make sense of problems and persevere in solving them.
Problem Solving
make conjectures about the form and meaning of
the solution
1. Make sense of problems and persevere in solving them.
Problem Solving
make conjectures about the form and
meaning of the solution
try special cases and
simpler forms of the original
problem
1. Make sense of problems and persevere in solving them.
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
make sense of quantities and their relationshipsin problem situations
2. Reason abstractly and quantitatively.
Thinking
make sense of quantities and
their relationshipsin problem situations
creating a coherent
representation of
the problem at hand
2. Reason abstractly and quantitatively.
Problem Solving
abstracta given situation and
represent it symbolically
2. Reason abstractly and quantitatively.
Problem Solving
abstracta given
situation and represent it
symbolically
considering the units involved;
attending to the meaning of quantities
2. Reason abstractly and quantitatively.
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
Making plausible arguments
3. Construct viable arguments and critique the reasoning of others.
Questioning
Making plausible
arguments
listen or read the
arguments of others
3. Construct viable arguments and critique the reasoning of others.
Questioning
Making plausible argument
s
listen or read the
arguments of
others
ask useful
questions to clarify
or improve
the argument
s
3. Construct viable arguments and critique the reasoning of others.
Academic Feedback
communicate them to others, and respond to
the arguments of others
3. Construct viable arguments and critique the reasoning 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
3. Construct viable arguments and critique the reasoning of others.
Thinking
analyze situations by breaking them into cases
3. Construct viable arguments and critique the reasoning of others.
Thinking
analyze situations by
breaking them into
cases
compare the effectivenes
s of two plausible
arguments
3. Construct viable arguments and critique the reasoning of others.
Problem Solving
can recognize and use counter examples
3. Construct viable arguments and critique the reasoning of others.
Problem Solving
can recognize and use counter
examples
justify their conclusions
3. Construct viable arguments and critique the reasoning of others.
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.
Thinking
making assumptions and approximations to simplify a complicated situation, realizing that these may
need revision later
4. Model with mathematics.
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
4. Model with mathematics.
Problem Solving
identify important
quantities in a practical situation
draw conclusions
4. Model with mathematics.
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
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
notice if calculations are repeated
8. Look for and express regularity in repeated reasoning.
Thinking
notice if calculations are repeated
lookboth for general
methods and for shortcuts