1. Grades K-2 Formative Assessment to Support Student Learning PARTNERS1
PARTNERS
for Mathematics Learning
Formative Assessment to Support Student Learning
Module 3
Grades K-2
Inferences
and
Feedback
Partners
for Mathematics Learning

2. Overview of Modules   Module 6: Decisions and Collaboration2
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: Student Self-Assessment and 
Responsibility
 Module 6: Decisions and Collaboration
Around Assessment
Partners
for Mathematics Learning

3.  Identifying what we know from student 3
Goals of Module 3
 Identifying what we know from student
conversations and student work
 Recording assessment information
 Identifying occasions for student interviews
 Identifying, discussing,
and writing helpful
feedback for moving
students forward
Partners
for Mathematics Learning

4. Teaching-Learning Cycle4
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

5. Learning from Conversations5
Learning from Conversations
 Conversation is a powerful formative
assessment resource
 As students explain their thinking
 As students talk in their groups
 As teachers talk with individuals
 Learning from conversations
means that we become better
at listening to our students
Partners
for Mathematics Learning

6. Learning from Conversations6
Learning from Conversations
Respond in your journal…
 How do you use conversations with your
students to learn about their work and
thinking?
As you watch the video, list in your journal…
 What are the different ways the teachers
are using conversations to learn about
their students’ thinking?
Partners
for Mathematics Learning

7. Listening to Students Teacher: What is your answer and7
Listening to Students
 Prompt: A boy looked
through the fence and
saw three horses. How
many legs were there?
 What can we infer about
these students’ thinking?
 What “next questions”
might you ask?
Teacher: What is
your answer and
how did you get it?
Jaylan: 13. I drew a
picture and counted
the legs.
Tricia: 12. I used
my counters.
Raya: 12. Horses
have 4 legs. There
are three horses. I
added
Partners
for Mathematics Learning

8. Knowing and Inferring  How can these additional8
Knowing and Inferring
 What can we infer about
what Sammy knows?
Teacher: Rick is
first in line. Who is
sixth in line?
Sammy: Mary is.
(correct answer)
 How can these additional
questions convince you
that Sammy can use
ordinal numbers?
 Why is it important to ask
additional questions?
ADDITIONAL QUESTIONS
Teacher: Sammy,
if Queen is eighth
in line, who is
third?
Teacher: Can you
get in line so you
are sixth?
Partners
for Mathematics Learning

9. Learning By Listening  Record an example of something you9
Learning By Listening
 Record an example of something you
learned about a student’s understanding or
thinking during a class discussion
 Explain why “wait time” is critical in order
to find out what students know
 Describe how probing questions asked in a
group setting can give valuable information
about individuals
Partners
for Mathematics Learning

10. Examining Student Work10
Examining Student Work
 Applying formative assessment strategies
means looking at student work through a
“different lens”
 “Scoring” is not the primary purpose
 Looking for evidence of thinking, identifying
misconceptions, and noting unusual
responses is the primary purpose
 “Tweaking” instructional plans helps to
address individual needs
Partners
for Mathematics Learning

11. “Tweaking” Lesson Plans11
“Tweaking” Lesson Plans
 Means responding to information gleaned
from assessments
 Adjust textbook lessons based on students’
needs and what they reveal they know
 Plan questions to continue assessing as you
teach
 Use pacing guides and textbook lessons
but do not allow students to practice using
mathematics incorrectly
Partners
for Mathematics Learning

12. A Different Lens  Identifying student misconceptions early12
A Different Lens
 Identifying student misconceptions early
helps us “tweak” instructional plans to
correct incomplete understanding and
misconceptions
 Identifying when students are ready to
“move on” or delve more deeply into the
content leads to greater student
achievement
Partners
for Mathematics Learning

13. Examining Student Work13
Examining Student Work
 For any set of papers, look for
 Students who get everything correct
 Common errors
 Careless errors
 Mistakes in computation
 Conceptual misunderstandings
 Any answer you do not understand
 Make notes of any students you need to
talk with in order to target their instruction
Partners
for Mathematics Learning

14.  With your partner examine the set of14
Examining Student Work
 With your partner examine the set of
student papers from your classroom
and make notes as directed
 Compare your notes with
others at your table
Partners
for Mathematics Learning

15. Methods of Assessment  Different assessment methods reveal15
Methods of Assessment
 Different assessment methods reveal
different aspects of mathematical thinking
 Selected Response
 Constructed Response
 Performances
 Personal Communications
 Assessment methods
should match learning targets
Partners
for Mathematics Learning

16.  Constructed Response16
Methods of Assessment
 Selected Response
 Multiple-choice, matching, true-false
 Constructed Response
 Short answer, fill-in items, open-ended questions
that require an original, written answer
 Performance Assessment
 Presentations, observations, or performances
 Personal Communication
 Interviews, conferences, conversations,
class discussions
Partners
for Mathematics Learning

17. Examining Student Work17
Examining Student Work
Does a student understand just because
they got it right?
 Why do we often need
more information than
just the answer?
 What are the implications
for your own classroom?
Partners
for Mathematics Learning

18.  Identifying what we know from student 18
Goals of Module 3
 Identifying what we know from student
conversations and student work
 Recording assessment information
 Identifying occasions for student interviews
 Identifying, discussing,
and writing helpful
feedback for moving
students forward
Partners
for Mathematics Learning

19. Rationale for Anecdotal Records19
Rationale for Anecdotal Records
 Primary students are not able to put in writing all
that they know and understand
 Anecdotal records document teacher
observations, class conversations, and
information from individual interviews
 Documentation is necessary for special
placement and accommodations, parent
conferences, and promotion/retention
 It is difficult to remember specific examples of
student responses and understanding
Partners
for Mathematics Learning

20. Recording Anecdotal Information20
Recording Anecdotal Information
 Multiple possible methods
 Class rosters
 Clipboards
 Photos/video
 Post-it notes
 Calendar grids
 Mailing labels
 Index cards
 Teacher logs
 No one “right way” to record information
 Note: Anecdotal notes can be reviewed
by parents and school personnel
Partners
for Mathematics Learning

21. Recording Anecdotal Information21
Recording Anecdotal Information
 Class Rosters
 Post-it Notes
11/4
Sali
Applies algorithms correctly
still does not know facts -
*suggest to parents that he
drill with flash cards for facts
he keeps missing
Partners
for Mathematics Learning

22. Recording Anecdotal Information22
Recording Anecdotal Information
 Class Grid
 Mailing Labels
Partners
for Mathematics Learning

23. Recording Anecdotal Information23
Recording Anecdotal Information
 Clipboard
 Index Cards
Angel
Cara
Alonzo
Maya
Will
Warren
Tony
Luc
Aubry
9/ identifies patterns, can continue simple
ones but has difficulty creating an original one
10/ counts orally to 50; inconsistent in
crossing decades
10/24
finds sums usually by counting on;
sometimes still counts all
Sonia
Joseph
Evan
Mattie
Rusfika
Jose
Marika
Jimmy
Kaneka
Enrico
Meg
Cole
Ben
Lucia
Tinamarie
Mike
Partners
for Mathematics Learning

24. Recording Anecdotal Information24
Recording Anecdotal Information
 Teacher Logs 
Photos
Partners
for Mathematics Learning

25. Recording Anecdotal Information25
Recording Anecdotal Information
 Flip Video
Partners
for Mathematics Learning

26. Recording Anecdotal Information26
Recording Anecdotal Information
 Look at the forms in the handout
 What has been your
most successful way
to keep anecdotal
records?
Partners
for Mathematics Learning

27. Respond in Your Journal27
Respond in Your Journal
 Is there a record keeping idea that you
have not tried that appeals to you?
 How can anecdotal records help you guide
individual students’ learning and/or seek
interventions?
 How will anecdotal records improve your
conversations at parent conferences?
Partners
for Mathematics Learning

28. Goals of Module 3  Identifying what we know from student28
Goals of Module 3
 Identifying what we know from student
conversations and student work
 Recording assessment information
 Identifying occasions for student
interviews
 Identifying, discussing,
and writing helpful
feedback for moving
students forward
Partners
for Mathematics Learning

29. Rationale for Student Interviews29
Rationale for Student Interviews
Through conversations and interviews…
 Teachers learn more about each child’s
thinking and learning needs
 Teachers can “tweak” lessons to meet
individual needs within the structure of
lessons from their math program
 Teachers have better information for
providing interventions and differentiation
Partners
for Mathematics Learning

30. Student Interviews  Can be scheduled with individuals30
Student Interviews
 Can be scheduled with individuals
throughout the week
 Can be a brief conversation with students
as they are waiting in line
 Can be a focused small group discussion
 Can be conversations during center time,
as students play games or complete
seatwork
Partners
for Mathematics Learning

31.  Teacher: What does infinity mean? 31
Importance of Clear Evidence
 Teacher: What does infinity mean?
 Student (who has behavior problems):
I think it is the back of the Cream of Wheat
Box
 Teacher’s impression: (Student does not
know)
Does the individual that answers make a
difference in our inferences or the follow-
up questions we ask?
Partners
for Mathematics Learning

32. Importance of Clear Evidence32
Importance of Clear Evidence
 Student explains: The picture on the back of
the Cream of Wheat box is of a man holding
the same box, and this picture showed the
same picture of the man holding the box and
the same smaller man holding the box
 Notice that the answer was not clear or
adequate to define infinity, but the issue is
that we might not have asked for the
explanation
Partners
for Mathematics Learning

33.  Identifying what we know from student 33
Goals of Module 3
 Identifying what we know from student
conversations and student work
 Recording assessment information
 Identifying occasions for student interviews
 Identifying, discussing,
and writing helpful
feedback for moving
students forward
Partners
for Mathematics Learning

34. Providing Feedback  What types of feedback do teachers34
Providing Feedback
 What types of feedback do teachers
provide students?
 What is the purpose
of providing feedback?
Partners
for Mathematics Learning

35. Feedback Informs Learning35
Feedback Informs Learning
 “Actionable” feedback tells students what
they are doing right or what they need to
rethink or correct
 Can be given to the class as a whole, small
groups, or to individual students
 Can be written or oral
 Should relate to the mathematics of the tasks
 Should be timely
 Is based on observations or student work
Partners
for Mathematics Learning

36.  In table groups, sort the feedback cards36
Providing Feedback
 In table groups, sort the feedback cards
into categories
 Talk at your table
 How did you sort your cards?
 Would you change any of the feedback?
Partners
for Mathematics Learning

37. Praise as Feedback  Motivational feedback may encourage or37
Praise as Feedback
 Motivational feedback may encourage or
support the learner, but it does not offer
suggestions for improvement
 How might the comments “Good Work” or
“Excellent” discourage a strong student
from continuing to improve?
 How are struggling students affected when
others get praise and they never get this
feedback?
Partners
for Mathematics Learning

38. Grades as Feedback  Research says that if teachers give38
Grades as Feedback
 Research says that if teachers give
students feedback and a grade on work,
students ignore the feedback and focus
on the grades
 What does a grade tell students or parents
about what the child knows and what the
child still needs to learn?
 How do grades (as opposed to feedback)
provide information about student growth?
Partners
for Mathematics Learning

39. Descriptive/Actionable Feedback39
Descriptive/Actionable Feedback 
Is specific to the learning targets
Describes learning
Points students in a productive direction
Makes students aware of errors or areas
for more thought
 Provides next steps for specific action
(Guskey, T., 2009)
Partners
for Mathematics Learning

40. * Basic ideas for student involvement in learning40
Feedback That is “Actionable”
 Helps students answer these questions:*
 Where am I going?
 Where am I now?
 How can I close the gap?
 Provides opportunities for students to have
ownership of their learning
* Basic ideas for student involvement in learning
from the majority of formative assessment literature
Partners
for Mathematics Learning

41. Summarizing Feedback  Feedback is formative only if the41
Summarizing Feedback
 Feedback is formative only if the
information given back to the learner
is used by the learner in improving
performance
 The bottom line is that teachers need to
reflect on what students are saying and
putting on paper so that they are able to
give their pupils feedback that they know
in advance is going to be useful
Black and Wiliam, 2009
Partners
for Mathematics Learning

42. Homework for Module 4  This module addressed both student42
Homework for Module 4
 This module addressed both student
interviews and providing helpful feedback
to students…
 Select one new practice addressed in Module
3 to try in your classroom
 In your journal, describe the practice you
tried and how it impacted the assessment
in your classroom
Partners
for Mathematics Learning

43. Reflection  Identify times in your day and throughout43
Reflection
 Identify times in your day and throughout
your mathematics program when you can
 Gather information about student thinking
through conversations and looking at student
work
 Schedule student interviews
 Provide actionable feedback
Partners
for Mathematics Learning

44. Partners for Mathematics Learning is a Mathematics-Science 44
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

45. PML Dissemination Consultants45
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

46. 2010 Writers Ana Floyd Katie Mawhinney Kayonna Pitchford Wendy Rich46
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

47. Grades K-2 Formative Assessment to Support Student Learning PARTNERS47
PARTNERS
for Mathematics Learning
Formative Assessment to Support Student Learning
Module 3
Grades K-2
Inferences
and
Feedback
Partners
for Mathematics Learning