1. Questioning Formative Assessment to Support Student Learning PARTNERS1
PARTNERS
for Mathematics Learning
Formative Assessment to Support Student Learning
Module 2
Grades K-2
Questioning
and Task
Selection
All Aboard for Learning!
Partners
for Mathematics Learning

2. Teaching-Learning Cycle2
Teaching-Learning Cycle
Clear
Learning
Targets
Decisions
About
Next Steps
Questioning &
Instructional
Tasks
Collaboration
Around
Assessment
Student Self-
Assessment &
Responsibility
Making
Inferences
& Giving
Feedback
Partners
for Mathematics Learning

3. Overview of Modules  Module 1: Module 2: Module 3: Module 5:
Learning Targets
Questioning and Task Selection
Inferences and Feedback
Making Students Active Partners
Student Self-Assessment and
Responsibility
 Module 6: Decisions and Collaboration
Around Assessment
Partners
for Mathematics Learning

4.  Consider different ways to use questions in4
Goals of Module 2
 Consider different ways to use questions in
order to engage and deepen mathematical
understanding in our students
 Learn how to select tasks that allow for the
greatest opportunity for student learning
 Utilize the information gleaned from these
tasks to guide our instruction
Partners
for Mathematics Learning

5. Current Practice Respond in your journal:  How do you decide on the5
Current Practice
Respond in your journal:
 How do you decide on the
questions that you ask during lessons?
 How do you select the tasks to use in
your class?
Partners
for Mathematics Learning

6. Ways Teachers Use Questions6
Ways Teachers Use Questions
Teachers use questions for many different
purposes
 To engage students in discussions
 To refocus class discussions
 To probe students’ thinking
Dynamic Classroom Assessment , Bright and Joyner, 2005
Partners
for Mathematics Learning

7. Engaging Questions  Invite all students into a discussion7
Engaging Questions
 Invite all students into a discussion
 Keep students involved in the class’s
conversations
 Invite them to share their work or to get
answers “on the table”
Examples of engaging questions:
What strategies might we use to solve this problem?
What do you know that will help you answer this
question?
Partners
for Mathematics Learning

8. K-2 Context: Engaging Question8
K-2 Context: Engaging Question
What would be the 15 th shape in the pattern?
Engaging Question Examples:
What do you notice about the pattern?
Why do you think this could be called a
pattern?
Partners
for Mathematics Learning

9. Refocusing Questions  Helps students get back on track or move9
Refocusing Questions
 Helps students get back on track or move
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

10. K-2 Context: Refocusing Question10
K-2 Context: Refocusing Question
What would be the 15 th shape in the pattern?
If a student says the pattern is star, heart, star,
heart, star, heart
Refocusing Question Example:
What do you notice about the hearts?
Is there a difference in the hearts and stars?
Partners
for Mathematics Learning

11. Clarifying and Probing Questions11
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 your own words
what Maria just shared?
Partners
for Mathematics Learning

12. K-2 Context: Clarifying Question12
K-2 Context: Clarifying Question
What would be the 15 th shape in the pattern?
Clarifying Question Example:
What makes you say a star would come
next in the pattern?
Why do you say the pattern will use a lot
more hearts than stars?
Partners
for Mathematics Learning

13. Integrating Purposes of Questions13
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

14. Purposes for Questions14
Purposes for Questions
Mary has 4 nickels. Will has 3 dimes, and Carley has
6 pennies. Together how much money do they have?
 Possible engaging questions:
 What do you have to know to solve this problem?
 What do you know about the value of the coins?
 One student tells about finding a quarter; other
students then want to tell their stories about finding
money
 Teacher refocuses the discussion:
 How much money do these children have?
Partners
for Mathematics Learning

15. Purposes for Questions15
Purposes for Questions
Mary has 4 nickels. Will has 3 dimes, and Carley has 6
pennies. Together how much money do they have?
 Student writes on paper:
30 40
/ / / / / / 46
 Teacher asks child to clarify:
 Tell me how you figured out how much money
they have
 What other questions might the teacher ask to
probe this child’s thinking?
Partners
for Mathematics Learning

16. Purposes for Questions16
Purposes for Questions
Three children are having a parade. One child rides a
tricycle. Two children ride bicycles. How many wheels
are in the parade?
 Teacher: What is happening in the story?
 Child 1: They are having a parade
 Teacher: Who is in the parade?
 Child 2: Three children-two boys on their
bicycles and their little sister on her tricycle
Partners
for Mathematics Learning

17. Purposes for Questions17
Purposes for Questions
Three children are having a parade. One child rides a
tricycle. Two children ride bicycles. How many wheels
are in the parade?
 Teacher: What are we trying to find out in this
problem?
 Child 3: How many wheels - um, 7 wheels
 Teacher: How did you figure this out?
 Child 3: I counted the wheels
 Teacher: Tell me how you counted the wheels
Partners
for Mathematics Learning

18.  Let’s practice generating some engaging18
Let’s Try It!
 Let’s practice generating some engaging
questions to introduce the task of sorting
the shapes into groups
Partners
for Mathematics Learning

19. Let’s Try It!  Let’s practice generating some clarifying19
Let’s Try It!
 Let’s practice generating some clarifying
questions around this geometry sorting task:
 Suppose a child has completed this geometry
sort
 What might be some clarifying questions you
could ask?
Partners
for Mathematics Learning

20. The Role of Questioning20
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
Partners
for Mathematics Learning

21.  Good questions engage students21
What are Good Questions?
 Good questions engage students
 Students do more than recall known facts
 Students have opportunities to make
connections
 Good questions promote development of
higher levels of thinking and reasoning in
students
Partners
for Mathematics Learning

22.  Requires more than remembering a fact 22
Features of Good 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
How do questions relate to tasks?
Partners
for Mathematics Learning

23.  From research on questioning we know23
Asking 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

24. Routine vs Non-routine Questions24
Routine vs Non-routine Questions
 Routine questions ask a student to give an
answer from memory or apply simple
procedural or conceptual understandings
 What number is in the tens place: 136?
 Non-routine questions require a student to
think more deeply about a topic
 How many groups of 10 could you make if you
had 136 toothpicks?
Partners
for Mathematics Learning

25. Recognizing “Good Questions”25
Recognizing “Good Questions”
 Explain why the first question is routine and
the second one is non-routine
 What is the average of 6, 7, 5, 8, and 4?
 Identify 5 numbers whose average is 6
 Which of the set of numbers are even?
 Tom has an odd number of cookies. Can he
share them fairly with a friend and himself?
Explain your thinking
 How do the 2nd questions challenge students?
Partners
for Mathematics Learning

26. Transforming a Routine Question26
Transforming a Routine Question
 Learning Target: Use numbers to record
the value of a group of coins
 Routine Question: What is the value of
two quarters, two dimes, and a nickel?
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

27. Transform a Kindergarten Question27
Transform a Kindergarten Question
 Learning Target: Classify 2-dimensional
shapes
 Routine Question: Which shapes are
triangles?
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

28.  Consider different ways to use questions in28
Goals of Module 2
 Consider different ways to use questions in
order to engage and deepen mathematical
understanding in our students
 Learn how to select tasks that allow for the
greatest opportunity for student learning
 Utilize the information gleaned from these
tasks to guide our instruction
Partners
for Mathematics Learning

29. Why Focus on Questions and Tasks ?29
Why Focus on Questions and Tasks ?
 Classroom instruction is generally
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

30. “One of the most important and yet difficult 30
“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

31. Characteristics of Mathematical Tasks31
Characteristics of Mathematical Tasks
 Look at the tasks on the next slides:
 How would you go about solving them?
 What are the essential characteristics of
each task?
 What would be a possible learning target
you would have for selecting these tasks?
Which of the two tasks requires more
in-depth thinking and causes them to be
more intellectually engaged?
Partners
for Mathematics Learning

32. Task 1  You are carpeting a room that is 15 feet32
Task 1
 You are carpeting a room that is 15 feet
long and 10 feet wide
 How many square feet of carpeting do you
need to purchase?
Partners
for Mathematics Learning

33.  Our class will raise chickens for the science33
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

34.  How are the two tasks alike?  How are they different? 34
Comparisons
 How are the two tasks alike?
 How are they different?
 For each task…
 Discuss the flow and progression for
supporting each 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

35. Task 3  Mrs. Wilson has 3 green  How many candles does she have?35
Task 3
 Mrs. Wilson has 3 green
birthday candles and 4 yellow ones
 How many candles does she have?
 What is the mathematics in this task?
 What action is required of students ?
Partners
for Mathematics Learning

36. Task 4  Mrs. Wilson has 7 birthday candles36
Task 4
 Mrs. Wilson has 7 birthday candles
 Some candles are green and some candles
are yellow
 How many of each color could she have?
 In what ways is this problem like the
previous one? How is it different?
 Why is this task more engaging
intellectually?
Partners
for Mathematics Learning

37. Task Sort  Sort the task cards into piles  Remember:37
Task Sort
 Sort the task cards into piles
 One pile you consider to contain higher
intellectually engaging tasks
 The other pile that you consider to contain lower
intellectually engaging tasks
 Remember:
 Think about intellectual engagement, not
difficulty
Partners
for Mathematics Learning

38.  What is an appropriate time and place for38
Turn and Talk
 What is an appropriate time and place for
lower level tasks?
Partners
for Mathematics Learning

39.  Sufficient time allowed for exploration – not 39
Intellectually Demanding 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

40.  What are your learning targets? 40
Selecting and Supporting Tasks
 What are your learning targets?
 What background knowledge is needed
for the task?
 What are ways it can be solved?
(misconceptions/errors students may have)
 Any challenges to EC/ELL students?
 What are your expectations for students? –
how will you communicate and assess them?
Partners
for Mathematics Learning

41. Selecting and Supporting Tasks41
Selecting and Supporting Tasks
 What questions will you ask – engaging,
refocusing, and clarifying?
 How will you orchestrate a classroom
discussion so you can accomplish your
learning target?
How will you assess student understanding
of the learning target?
 What will you do tomorrow to build on this
lesson?
Partners
for Mathematics Learning

42.  Why is it okay for students to struggle42
Talk at Your Tables
 Why is it okay for students to struggle
with a task or a good question?
Partners
for Mathematics Learning

43. I nstruction and F ormative A ssessment43
I nstruction and F ormative A ssessment
Partners
for Mathematics Learning

44. Homework for Module 3  Bring a set of class papers to analyze in44
Homework for Module 3
 Bring a set of class papers to analyze in
Module 3
 Try to decide on the same task as a grade
level and bring a class set of papers to be
discussed and analyzed during module 3
Partners
for Mathematics Learning

45. Reflection Respond in your journal:  How will you decide on the45
Reflection
Respond in your journal:
 How will you decide on the
questions that you ask during lessons?
 What are three things you will consider
as you select tasks for your class?
Partners
for Mathematics Learning

46. Partners for Mathematics Learning is a Mathematics-Science 46
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

47. PML Dissemination Consultants47
PML Dissemination Consultants
Julia Cazin
Ruafika Cobb
Anna Corbett
Gail Cotton
Jeanette Cox
Lisa Davis
R yan D ougherty
Tricia Essick
Tery Gunter
Barbara Hardy
Kathy Harris
Rendy King
R ene L emons- 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

48. 2010 Writers Ana Floyd Katie Mawhinney Kayonna Pitchford Wendy Rich48
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

49. Questioning Formative Assessment to Support Student Learning PARTNERS49
PARTNERS
for Mathematics Learning
Formative Assessment to Support Student Learning
Module 2
Grades K-2
Questioning
and Task
Selection
All Aboard for Learning!
Partners
for Mathematics Learning