1. Formative Assessment to Support Student Learning1
PARTNERS
for Mathematics Learning
Formative Assessment to Support Student Learning
Module 5
Grades 6-8
Decisions
about
Next Steps
Partners
for Mathematics Learning

2. Putting it to Practice  Turn and talk2
Putting it to Practice
 Turn and talk
 Describe the strategy you used to increase
student responsibility in your classroom
 Describe what worked and what didn’t
 Discuss possible ways of altering this practice and
how you implement the strategy a second time
Partners
for Mathematics Learning

3. Overview of Modules  Module 1: Learning Targets3
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. Making Decisions: Next Steps4
Making Decisions: Next Steps
Learning targets for this module
 Identify next steps for
meeting student’s needs
 Practice with various
strategies, in order to
implement them in
the classroom
Partners
for Mathematics Learning

5. Teaching-Learning Cycle5
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

6. Making Decisions: Next Steps6
Making Decisions: Next Steps
The quality and depth of student
learning is influenced by the decisions
teachers make
Partners
for Mathematics Learning

7.  Thus, formative assessment should7
Making Decisions: Next Steps
 Thus, formative assessment should
 Give information about students’ understanding
 Guide teachers in choosing interventions for
individual students
 Assist in planning next steps for the whole class
 Formative assessment data has value
according to how well we use it to plan
Partners
for Mathematics Learning

8. Information About Students8
Information About Students
 We gather information about students’
understanding in many ways…
 Students’ written work
 Conversations or interviews
with individuals
 Class discussions
 Pre-assessments for
learning targets
Partners
for Mathematics Learning

9. Making Decisions: Next Steps9
Making Decisions: Next Steps
 Whole Class Instruction
 Instruction for all levels– designing
instruction to meet needs of all students
across the spectrum of mastery
 Within the context of whole class instruction
 Instruction for all needs – specific strategies
to meet identified needs of students
 Individualized/small group instruction
 In this module, we focus on students who have
yet to meet the learning targets
Partners
for Mathematics Learning

10. Three Stars and a Wish  In your journal…10
Three Stars and a Wish
 In your journal…
 List ways you are using formative assessment
to inform your instructional planning
 List the ways you are currently addressing
differing levels of mastery in your classroom
differing needs in your classroom
 Star the 3 most effective of these
 Write one specific wish for ideas related
to these
Partners
for Mathematics Learning

11.  To effectively meet all students’ needs…11
Research Suggested Strategies
 To effectively meet all students’ needs…
 Keep focus on concepts and sense-making
 Use formative assessment strategies to
understand students’ thinking
 Maintain high expectations for achievement of
learning targets for all students
 Use ongoing assessments to identify students
who need additional support or extensions
 Involve students more in self-assessment
 Use assessment to make flexible groupings
Partners
for Mathematics Learning

12. Next Step: Flexible Groups12
Next Step: Flexible Groups
 Flexible grouping is a powerful strategy
that can be used to meet students needs
 Groups are not static but are ever-
changing based on a variety of criteria
 Responses to tasks
 Readiness
 Work habits
 Performance
 Student Interests and choices
Partners
for Mathematics Learning

13. Types of Groups  Learning styles  Student interests  Student choice13
Types of Groups
Whole class 
Work as individuals
Teacher designated
Random groups
Readiness for tasks
 Like readiness
 Different levels of
readiness
 Learning styles
 Similar
 Random
 Student interests
 Student choice
What other ways do
you group students?
Partners
for Mathematics Learning

14. Looking at Student Work14
Looking at Student Work
 Daily practice may be used to make
decisions about the needs of students
 Look at the student work and talk at your
table about what you know about these
students and their knowledge
 What would you do next in a whole class lesson?
 How might you group students based on the
work?
 Be prepared to share your ideas
Partners
for Mathematics Learning

15.  If, in reaction to student work, the groups15
Remember
 Groups should change
 If, in reaction to student work, the groups
are always the same, another strategy for
grouping or addressing student needs is
required
 Grouping should have a purpose and
enhance the lesson
 Students will need structure and practice
within their groups
Partners
for Mathematics Learning

16. Next Step: Whole Class Lesson16
Next Step: Whole Class Lesson
 Whole group lessons
 Provide common experiences
 Expose students to a variety of thinking
 Can support individual needs and strengths •
Use think/pair/share strategy
Allow wait time before responses
Encourage responses from several students
Connect comments to previous speakers
 We learn much more together than we
can alone
Partners
for Mathematics Learning

17. Next Step: Whole Class Lesson17
Next Step: Whole Class Lesson
 Have students look at examples and discuss
which are correct, which are not and why
 Put samples on an overhead, document camera,
or write on the board
 Be sure no student names are attached
 Let students - not teacher - discuss errors
 Teacher chooses 3 or 4 problems to discuss
with the class and then gives students an
opportunity to solve 3 or 4 similar problems
Partners
for Mathematics Learning

18. Classroom Discussion Tools18
Classroom Discussion Tools
 Teacher re-voices student’s statement
 “So you’re saying that…”
 Students restate another’s reasoning
 “ Can you put her idea into your own words?”
 Students share different strategies
 “Who solved the problem in a different way?”
 Apply own reasoning to another’s reasoning
 “Do you agree or disagree? Why?”
Partners
for Mathematics Learning

19.  Prompting further participation19
Classroom Discussions Tools
 Prompting further participation
 “Would anyone like to add to his idea?”
 Prompting a response from all students
 “Thumbs up if you understand the solution.”
 Prompting more from one student
 “Say more about what you are thinking.”
 Wait before and after responses
 “Take your time… We’ll wait for you to think.”
 Wait at least 5-10 seconds for students to think
Partners
for Mathematics Learning

20. 20
What Next? Making Plans
“…our job is to challenge students’ comfort level
and then to help them find their next boundaries.
…we try to identify evidence for what the child
knows or has mastered, areas where initial ideas
are formed but additional experience with them
is needed, and those concepts and skills that
require further scaffolding or additional readiness
development.”
Dacey and Lynch, Math for All: Differentiating Instruction, 2007
Partners
for Mathematics Learning

21. Keep in Mind… Zone of Proximal Development21
Keep in Mind…
Zone of Proximal Development
Vygotsky (1978), Fleer (1992), Jacobs (2001)
Student’s
Current
achievement
Partners
for Mathematics Learning

22. Next Step: Scaffolding Learning22
Next Step: Scaffolding Learning
 Scaffolds are structures put in place to
allow students to be successful learners
of mathematics
 Scaffolding gives students opportunities
to accomplish tasks that
they would be unable to
complete alone
Partners
for Mathematics Learning

23. Scaffolding Learning  Teacher becomes a coach –23
Scaffolding Learning
 Teacher becomes a coach –
helping all students reach their potential
 Scaffolding learning is guiding the student
toward the kind of thinking that is
necessary to do the task, not toward one
specific strategy or answer
 Scaffolding learning does not mean
replacing student thinking with teacher
thinking
Partners
for Mathematics Learning

24. Scaffolding Learning  Scaffolds may24
Scaffolding Learning
 Scaffolds may
 Include questions that lead students to be
more systematic or logical
 Encourage students to go beyond their
level of comfort and understanding
 Help develop strategies explicitly for
working with new mathematical content and
activities
 Connect new learning to prior knowledge
Partners
for Mathematics Learning

25. Scaffolding: Questions25
Scaffolding: Questions
 Task: Find the area of the triangle
Teacher: What is this
task asking you to do?
What do you already 13
know that will help? 12
Partners
for Mathematics Learning

26.  Task: Find the area of the triangle26
Scaffolding: Questions
 Task: Find the area of the triangle
Student responds by
calculating 1 " 12 " 13 2
Teacher: Tell me about 13
your calculation. How do
Partners
for Mathematics Learning 12
you know what to do?

27.  Task: Find the area of the triangle27
Scaffolding: Questions
 Task: Find the area of the triangle
The student responds
by finding the length
of the other leg 13
Teacher: Show me
how you found the
length 12
Partners
for Mathematics Learning

28.  Task: Find the area of the triangle28
Scaffolding: Questions
 Task: Find the area of the triangle
Student finds the area
Teacher: How do you
know that you have 13
the correct area?
Students describes
the steps she used 12
Partners
for Mathematics Learning

29. Scaffolding: Graphic Organizers29
Scaffolding: Graphic Organizers
 Can encourage organization of written work
for students not already developing their own
methods of organizing
 Can help students communicate their
thoughts and reasoning
Look at the handout for some examples
Discuss these ideas at your tables and share other
graphic organizers you have found useful for
students in your classroom
Partners
for Mathematics Learning

30. Scaffolding: Vary Problem Structures30
Scaffolding: Vary Problem Structures
 Sean invested $1,000 in a money market
account. How much interest would he earn
on his money after 2 years at a yearly simple
interest rate of 5%?
 What do we know?
 What are we trying to find out?
1000 × .05 × 2 = ?
Partners
for Mathematics Learning

31. Scaffolding: Vary Problem Structures31
Scaffolding: Vary Problem Structures
 Sean invested $1,000 in a money market
account. How much would he have in his
account, after 2 years at a yearly simple
interest rate of 5%?
 What do we know?
 What are we trying to find out?
× .05 × 2 = ?
Partners
for Mathematics Learning

32. Scaffolding: Vary Problem Structures32
Scaffolding: Vary Problem Structures
 If Sean earned $100 in interest on money
that he invested for 2 years at a simple
yearly interest rate of 5%, how much money
did Sean invest?
 What do we know?
 What are we trying to find out?
? × .05 × 2 = 100
Partners
for Mathematics Learning

33. Scaffolding: Vary Problem Structures33
Scaffolding: Vary Problem Structures
 If Sean earned $100 in interest on $1,000
that he invested at a simple yearly interest
rate, what are possible rate and time
combinations that would have earned him
this interest?
 What do we know?
 What are we trying to find out?
1000 × __ × __ = 100
Partners
for Mathematics Learning

34. Scaffolding: Vary Problem Structures34
Scaffolding: Vary Problem Structures
 In grade-level groups, write 3 restructured
problems from the list below
 Grade 6 : Each tablet in a box of allergy medicine
weighs 0.3 gram. Find the total weight of the
tablets in the box if there are 50 tablets.
 Grade 7 : A school population rose from 234 to
440 over a period of two years. What is the
percent increase in students, to the nearest tenth
of a percent?
 Grade 8 : One third of a number plus three times
the same number is sixty. Find the number.
Partners
for Mathematics Learning

35. Scaffolding: Vary Problem Difficulty35
Scaffolding: Vary Problem Difficulty
 Sean drove ( 60, 120, 3407 ) miles last year
on his vacation. He drove ( 93, 180, 2159 )
miles on this year’s vacation. How many
miles did Sean drive on both vacations?
 Teachers may direct which numbers to use
 Students may choose numbers to use
What conversations might students have
when you use this type of task?
Partners
for Mathematics Learning

36. Scaffolding Learning  All students - even our most advanced36
Scaffolding Learning
 All students - even our most advanced
ones - should be challenged to struggle
with tasks that require some support to
accomplish
 Support through teacher question
 Support by graphic organizers
 Support by varying problem structure
 Challenges should involve meaningful
mathematics to develop depth of thinking
Partners
for Mathematics Learning

37. Reacting to Student Responses37
Reacting to Student Responses
 When we assign tasks, whether to the
class as a whole or to groups of students,
we need to think ahead about
 What are we looking for in the students’
responses
 What misconceptions or incomplete
understandings do we need to watch for
 Formative assessment is about structuring
lessons for depth of knowledge and long-
term student success
Partners
for Mathematics Learning

38. Next Step: Tiered Assignments38
Next Step: Tiered Assignments
 Tiered activities or lessons
 A series of related tasks of varying complexity
 Relate to essential understandings and key
skills that students need to acquire
 Assigned as alternative ways of reaching the
same goals taking into account individual
student needs
 Teachers can utilize alternative tasks in
textbooks
Partners
for Mathematics Learning

39. Process of Tiered Assignments39
Process of Tiered Assignments
 Identify the learning target (same for all
tiers)
 Form groups based on prior assessments
 Plan a meaningful activity for each group
depending on the students’ needs
NeedsAttention
(Tier1-allstudents
shouldbeabletodo
this)
DevelopingMastery
(Tier2-studentswho
coulddoTier1task
butneedmore)
NeedsChallenge
(Tier3-studentswho
aredefinitelyready
formoredepth)
Partners
for Mathematics Learning

40.  Do the example, then discuss40
Linear Example
 Do the example, then discuss
 How are the tiers alike/different?
 How do they relate to the learning targets?
 Are there different questions that could be
asked at each tier?
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Partners
for Mathematics Learning
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41. Linear Example  What you do the next day?
 What would the learning targets be?
 What tasks might you plan for each tier?
 If students in the lower tiers are successful
with the tasks, would you assign them these
problems?
 Would you bring the groups back together,
keep the same tiers, or reconfigure the tiers?
Partners
for Mathematics Learning

42. Flexible Groups: Tiered Assignments42
Flexible Groups: Tiered Assignments
 Students work in assigned groups, so that
two groups can work independently while
the teacher works with one group
 If students have a question, and are not in
the group that the teacher is currently
working with, then they must
 Ask at least two other people in their group
before they can ask the teacher
 Or complete a “3 Before Me”; try 3 things
Partners
for Mathematics Learning

43. Next Step: Student Choice43
Next Step: Student Choice
 Anchors, Choice Boards, and Menus
 A collection of activities from which students
may choose while the teacher is working with
another individual or group (or whenever a
choice is appropriate)
 Activities are worthy of a student’s time, focus
on essential skills, and are appropriate to
learning needs
 Activities are meaningful tasks that provide
extensions or reinforcement of mathematics
Partners
for Mathematics Learning

44. Student Choice  Think-Tac-Toe O X44
Student Choice
 Think-Tac-Toe
 A grid of activity choices or problems
 Teacher tells students how to choose their
activities, ex. choose one from each row, or
complete one activity from each column, or
complete all tasks in any row or column X O
Partners
for Mathematics Learning

45. Assume classroom strategies and student 45
Next Step: Interventions
Assume classroom strategies and student
experiences are not enough…
 Strategic or Instructional Interventions are
modifications within the classroom
 Intensive Interventions are strategies
employed beyond the classroom
Partners
for Mathematics Learning

46. Interventions: Making the Time46
Interventions: Making the Time
 Share with the group ways that you have
found time to provide intensive interventions
for students
 As you listen to your colleagues,
list in your journal new ways that
you would like to try
Partners
for Mathematics Learning

47. Instructional Intervention is…47
Instructional Intervention is…
 Targeted instruction based on ongoing
assessments
 Additional instruction administered by the
teacher or a resource person
 Pre-teaching or mini-lessons on needed
skills
 Teaching additional strategies
 Modifications in curriculum
 Changes in types and methods of feedback
Partners
for Mathematics Learning

48. Instructional Intervention is…48
Instructional Intervention is…
 Modifications in
 Modes of task presentation
 Instructional time
 Group size
 Amount and kind of cues and prompts
 Task structure (increase)
 Task relevant practice (increase)
Partners
for Mathematics Learning

49. Instructional Intervention is NOT…49
Instructional Intervention is NOT… 
Preferential seating*
Shortened assignments*
Parent contacts*
Classroom observations*
Suspensions or retention
Doing more of the same assignment
*Helpful strategies for improved student
performance but are not intervention strategies
Partners
for Mathematics Learning

50. Meeting Student Needs  Keep focus on concepts, understanding,50
Meeting Student Needs
 Keep focus on concepts, understanding,
and sense-making
 Use ongoing assessments to find students
who need more support or extensions
 Make groupings flexible
 Be the guide and facilitator
 Assess based on growth and achievement
of learning targets
Partners
for Mathematics Learning

51.  Go back to the 3 Stars and a Wish in your 51
M eeting S tudent N eeds: R eflections
 Go back to the 3 Stars and a Wish in your
journal from the beginning of the module
 Would you write a different wish now?
 What new “star” would you want to identify
at the end of your next year
of teaching?
 Respond in your journal
Partners
for Mathematics Learning

52. Homework:Putting It To Practice
 Bring back to the next session a summary
in which you describe a way you have
used an idea from this module in your
classroom
 Be specific in your example
 Explain why you will continue (or not continue)
this practice
 Write a reflection on this experience
in your journal
Partners
for Mathematics Learning

53. Partners for Mathematics Learning is a Mathematics-Science 53
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

54. PML Dissemination Consultants54
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

55. 2010 Writers Ana Floyd Katie Mawhinney Kayonna Pitchford Wendy Rich55
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

56. Formative Assessment to Support Student Learning1
PARTNERS
for Mathematics Learning
Formative Assessment to Support Student Learning
Module 5
Grades 6-8
Decisions
about
Next Steps
Partners
for Mathematics Learning