1. Task Selection PARTNERS for Mathematics Learning1
PARTNERS
for Mathematics Learning
Formative Assessment to Support Student Learning
Module 2
Grades 6 – 8
Questioning
and
Task Selection
Partners
for Mathematics Learning

2. On the paper provided, list… 2
Putting It To Practice
On the paper provided, list…
 The lesson(s) and learning targets shared
 The methods of sharing with students and
parents
 Any impact you noticed within your students,
yourself, and/or your classroom from this
sharing
Be sure to look at your colleagues
pages at the break
Partners
for Mathematics Learning

3.  Module 1: Learning Targets 3
Overview of Modules
 Module 1: Learning Targets
 Module 2: Questioning and Task Selection
 Module 3: Inferences and Feedback
 Module 4: Making Students Active Partners
 Module 5: Decisions about Next Steps
 Module 6: Collaboration Around Assessment
Partners
for Mathematics Learning

4. Teaching-Learning Cycle
Clear
Learning
Targets
Decisions
About
Next Steps
Student Self-
Assessment &
Responsibility
Questioning &
Instructional
Tasks
Making
Inferences
& Giving
Feedback
Partners
for Mathematics Learning
Collaboration
Around
Assessment

5. Why Focus on Tasks?  Classroom instruction should be organized5
Why Focus on Tasks?
 Classroom instruction should be organized
around mathematical tasks
 The tasks in which students engage
determine what they learn about
mathematics and how they learn it
 “Not all tasks are created equal, and
different tasks provoke different levels and
kinds of student thinking.”
(Stein, Smith, Henningsen & Silver, 2000)
Partners
for Mathematics Learning

6. Why Focus on Tasks?  How do you use mathematical tasks in your class?6
Why Focus on Tasks?
 How do you use mathematical tasks in
your class?
 Currently, how do you
decide on the tasks
for your class?
Partners
for Mathematics Learning

7. Task Selection “One of the most important and yet difficult7
Task Selection
“One of the most important and yet difficult
aspects of designing a lesson is choosing or
creating the worthwhile mathematical task a
teacher wants students to engage in.”
Lappan & Friel, 1993
Partners
for Mathematics Learning

8.  To learn how to select tasks that allow for8
Module Learning Targets
 To learn how to select tasks that allow for
the greatest opportunity for student learning,
while being aligned with lesson learning
targets
 To ask questions at higher levels to support
those tasks in order to engage, deepen, and
assess mathematical understanding in our
students
Partners
for Mathematics Learning

9. C haracteristics of M athematical T asks9
C haracteristics of M athematical T asks
 Look at the two tasks on the
next slides and think about:
 How would you go about solving them?
 What would be a possible learning target you
would have for selecting these tasks?
Which of the two tasks requires students to
do more in-depth thinking and causes them
to be more intellectually engaged?
Partners
for Mathematics Learning

10. Task 1  You are carpeting a room that is 3 yards10
Task 1
 You are carpeting a room that is 3 yards
long and 4 yards wide. How many square
yards of carpeting do you need to
purchase?
Partners
for Mathematics Learning

11.  Our class will raise chickens for the11
Task 2
 Our class will raise chickens for the
science fair and can use 24 feet of fencing
to build a rectangular pen
 How long are the sides that give the chickens
as much room as possible?
 How long are the sides if only 16 feet of
fencing is used?
 How would you determine the pen with the
most room for any amount of fencing?
Partners
for Mathematics Learning

12. Comparisons  How are the two tasks alike?  How are they different?12
Comparisons
 How are the two tasks alike?
 How are they different?
 For each task…
 How/when would you implement this task?
 What is the role of the teacher and students?
 What skills were employed during the task?
 What kinds of information about a student’s
thinking can be gathered through each task?
Partners
for Mathematics Learning

13. 1 2 4 5 Difficulty vs. Intellectual Engagement13
Difficulty vs. Intellectual Engagement
+ =
 This problem would be difficult for a first
grader to solve but not for a sixth grader that
has the mathematical understanding
 The math is the same and the intellectual
engagement is the same for any grade level
 The level of difficulty changes depending on
the student’s mathematical understanding
Partners
for Mathematics Learning

14. NAEP Levels Of Complexity14
NAEP Levels Of Complexity
 Low Complexity- recall, recognition, calls
for some procedure or algorithm
 Moderate Complexity- more flexibility of
thinking than the low-complexity, beyond the
habitual, more than a single step, methods
of reasoning and problem-solving strategies
 High Complexity- more abstract reasoning,
planning, analysis, judgment, and creative
thought
Partners
for Mathematics Learning

15. Task Sort  Sort the task cards into piles15
Task Sort
 Sort the task cards into piles
 One pile you consider to contain low
complexity tasks
 One pile you consider to contain moderate
 One pile you consider to contain high
 Remember:
Difficulty ≠ intellectual engagement!
Partners
for Mathematics Learning

16.  When is the appropriate time and place for16
Turn and Talk
 When is the appropriate time and place for
lower complexity tasks?
 How should tasks relate to learning targets?
Partners
for Mathematics Learning

17.  Sufficient time allowed for exploration – not 17
Maintaining Higher Complexity Tasks
 Sufficient time allowed for exploration – not
too much or too little
 High level performance modeled by teacher
or capable students
 Task builds on prior knowledge
 Teacher draws on frequent connections
 Teacher presses for justifications, explanations,
and meaning through questioning, comments,
and feedback
Partners
for Mathematics Learning

18. Good Math Questions  Good math questions engage students18
Good Math Questions
 Good math questions engage students
 Students do more than recall known facts
 Students have opportunities to make
connections
 Good math questions promote
development of higher levels of thinking
and reasoning in students
Partners
for Mathematics Learning

19. Good Math Questions  Requires more than remembering a fact or19
Good Math Questions
 Requires more than remembering a fact or
reproducing a skill
 Students can learn from answering the
question and teachers learn about each
student from their attempts at solutions
 There may be several possible answers
Relate good questions to tasks that
require greater intellectual engagement
Partners
for Mathematics Learning

20. Math Task, Question, or Problem?20
Math Task, Question, or Problem?
 These terms are being used
interchangeably throughout our modules,
though different authors may use different
definitions
 Sometimes a task has only one question,
and other times, it’s a scenario with
multiple questions
Partners
for Mathematics Learning

21.  Explain why the first question is routine21
Recognizing “Good” Questions
 Explain why the first question is routine
 What is the mean of 6, 7, 5, 8, and 4?
 The average of five different numbers is 6. What
might the numbers be?
 After five games, the goalie had averaged
blocking 6 goals per game. What might be the
number of goals he blocked in each game?
 How do the 2 nd and 3 rd questions challenge
student thinking of the same learning target?
Partners
for Mathematics Learning

22. Transforming a Routine Question22
Transforming a Routine Question
 Learning Target: Solve multi-step
inequalities
 Routine Question: Solve 3 x + 1 < 28
NOW…
 Write a possible non-routine question
that is likely to stimulate student
interest and encourage a greater depth
of understanding
Partners
for Mathematics Learning

23. Transforming a Routine Question23
Transforming a Routine Question
Learning Target 1: Add and subtract integers
Learning Target 2: Use ratios to solve a problem
 Write a routine question
 Write 2 new non-routine questions
 Record your examples in your journals
and be ready to share with others
Partners
for Mathematics Learning

24. Talk at Your Tables  Why is it okay for students to struggle with24
Talk at Your Tables
 Why is it okay for students to struggle with
a task or a good question?
 Write your response in
your journal
Partners
for Mathematics Learning

25. The Role of Questioning25
The Role of Questioning
“During the course of a school day,
teachers ask many questions. In fact,
something like 60% of the things said by
teachers are questions and most of these
are not planned.”
Good Questions for Math Teaching , Sullivan & Lilburn, 2002
 Discuss with a partner kinds of questions
you routinely ask and write examples in
your journal
Partners
for Mathematics Learning

26. Ways Teachers Use Questions26
Ways Teachers Use Questions
 Engaging Questions
 Refocusing Questions
 Clarifying Questions
Dynamic Classroom Assessment , Bright and Joyner, 2005
Partners
for Mathematics Learning

27.  Invite students into a discussion, 27
Engaging Questions
 Invite students into a discussion,
 Keep students engaged in conversations
 Invite them to share their work or get
answers “on the table”
Examples:
What strategies might we use to solve this
problem?
What do you know that will help you answer
this question?
Partners
for Mathematics Learning

28. Find The Perimeter  Engaging  “How can we find 3 cm 4 cm 1 cm28
Find The Perimeter
 Engaging
questions are
questions that
invite students into
a conversation
4 cm
3 cm
1 cm
 “How can we find
the missing
measurements?”
Modified from Dynamic Classroom Assessment , Bright and Joyner, 2005
Partners
for Mathematics Learning

29. Refocusing Questions  Helps students get back on track or walk29
Refocusing Questions
 Helps students get back on track or walk
away from “dead end” strategies
 Reopens conversation to the group if only
one or two students are answering
Examples:
How is this problem similar to the one
we just did?
What quantities are you comparing?
Partners
for Mathematics Learning

30. Find The Perimeter  Refocusing questions  “If the figure is a large30
Find The Perimeter
 Refocusing questions
help students get back
on track or move away
from a dead-end
strategy
4 cm
3 cm
1 cm
 “If the figure is a large
rectangle with a piece
cut out, what do you
know about the large
rectangle?”
Partners
for Mathematics Learning

31. Clarifying and Probing Questions31
Clarifying and Probing Questions
 Help students clarify their own thinking
 Help teachers understand students’
thinking
 Help students understand each other’s
ideas
Example Questions
How did you figure out your answer?
Why did you start with that number?
Nika, can you explain, in own words what
Maria just shared?
Partners
for Mathematics Learning

32. Find The Perimeter  Bob said that the missing 3 cm 4 cm 1 cm32
Find The Perimeter
 Clarifying questions help
students explain &
teachers understand their
thinking
 Bob said that the missing
measurements are 1 cm
and 2 cm, and the teacher
asks, “Bob, can you
explain to Mary how you
got those answers?”
Partners
for Mathematics Learning
4 cm
3 cm
1 cm

33. Integrating Purposes of Questions33
Integrating Purposes of Questions
 Engaging questions can help thread a
discussion by involving many students in
the conversation
 Refocusing questions can help keep a
discussion from going off on a tangent
 Clarifying or probing questions can help
others understand student responses and
can help students self-check the relevance
of their contributions
Partners
for Mathematics Learning

34. How to Ask Good Questions34
How to Ask Good Questions
 From research on questioning we know
 Waiting for answers is important
 Questions may need to be rephrased for
clarity
 More probing questions need to be asked, not
just factual questions
 Ask only one question at a time
 Be flexible with expected answers
 So much of questioning is contextual
Partners
for Mathematics Learning

35.  Once your learning targets have been35
Making It A Habit
 Once your learning targets have been
determined and the appropriate tasks have
been chosen, think about important
questions to ask students during the lesson
 Engaging, Refocusing, Clarifying and Probing •
Specific to the content
For students who are struggling
For students who are on track
For students ready for more
 Copy them on index cards to keep with you
throughout the lesson
Partners
for Mathematics Learning

36. When selecting tasks, think about…  What are your learning targets? 36
In Summary
When selecting tasks, think about…
 What are your learning targets?
 What background knowledge is needed for the
task?
 What are ways the task can be solved?
(misconceptions/errors students may have)
 What are your expectations for students?
 How will you communicate and assess your
expectations?
 Are there any challenges for EC/ELL students?
Partners
for Mathematics Learning

37. Selecting and Supporting Tasks37
Selecting and Supporting Tasks
 What questions will you ask – engaging,
refocusing, and clarifying?
 How will you orchestrate a
classroom/group discussion around a
task?
 How will you assess student mastery of
the learning target?
 What will you do tomorrow to build on this
lesson?
Partners
for Mathematics Learning

38. Why Focus on Tasks?  Revisiting journal questions:38
Why Focus on Tasks?
 Revisiting journal questions:
 What questions do you still need answered
on mathematical tasks from your list from
earlier in this module?
 In summary, what makes a good
mathematical task?
Partners
for Mathematics Learning

39. Homework: Putting It To Practice39
Homework: Putting It To Practice
 Take a task you have used frequently in
class and change it to increase the level of
complexity associated with that task
 Create a list of questions - engaging,
refocusing, and clarifying and probing -
you might ask about this altered task
Partners
for Mathematics Learning

40. Partners for Mathematics Learning is a Mathematics-Science 40
DPI Mathematics Staff
Chief Consultant
Renee Cunningham Kitty Rutherford
Robin Barbour Mary H. Russell
Carmella Fair Johannah Maynor
Amy Scrinzi
Partners for Mathematics Learning is a Mathematics-Science
Partnership Project funded by the NC Department of Public
Instruction. Permission is granted for the use of these materials in
professional development in North Carolina Partner school districts.
Partners
for Mathematics Learning

41. PML Dissemination Consultants41
PML Dissemination Consultants
Julia Cazin
Ruafika Cobb
Anna Corbett
Gail Cotton
Jeanette Cox
Lisa Davis
Ryan Dougherty
Tricia Essick
Tery Gunter
Barbara Hardy
Kathy Harris
Rendy King
Rene Lemons-M atney
Tina McSwain
Marilyn Michue
Kayonna Pitchford
Ron Powell
Susan Riddle
Alisan Royster
Judith Rucker
P enny S hockley
Pat Sickles
Nancy Teague
Jan Wessell
Dan Wicks
Carol Williams
Stacy Wozny
Partners
for Mathematics Learning

42. 2010 Writers Ana Floyd Katie Mawhinney Kayonna Pitchford Wendy Rich42
Partners Staff
Jeane M. Joyner, Co-PI & Project Director
Freda Ballard, Webmaster
Anita Bowman, Outside Evaluator
Meghan Griffith, Administrative Assistant
Tim Hendrix, Co-PI and Higher Ed
Ben Klein , Higher Education
Katie Mawhinney, Co-PI and Higher Ed
Catherine Schwartz, Higher Education
2010 Writers
Ana Floyd
Katie Mawhinney
Kayonna Pitchford
Wendy Rich
Nancy Teague
Stacy Wozny
Please give appropriate credit to the Partners for Mathematics Learning project when
using the materials. Permission is granted for their use in professional development in
North Carolina Partner school districts.
Partners
for Mathematics Learning

43. Task Selection PARTNERS for Mathematics Learning43
PARTNERS
for Mathematics Learning
Formative Assessment to Support Student Learning
Module 2
Grades 6 – 8
Questioning
and
Task Selection
Partners
for Mathematics Learning