SVMI Network Meeting
April 10, 2013
Formative Assessment
Assessing and
Using Prior
Learning to Adapt
Teaching to the
Needs of Students
Network Meeting, April 10, 2013
Silicon Valley Mathematics Initiative
www.svmimac.org
Welcome
Please sign in,
 help yourselves to
refreshments,
 find a seat, and
 introduce yourself to your
tablemates.

Agenda
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Welcome
Announcements, Norms and
Introductions
Re-visiting Formative Assessment with
a MAP Module
Doing Collaborative Mathematics: A
Problem Solving Task
Announcements
SVMI is …


still accepting applications for the SCVMP
Leadership Institute: 5 Tuesdays in May
and a week in June. The application is on
our website: www.svmimac.org. Each
member of SVMI is entitled to one
scholarship.
holding two Summer Institutes: Peninsula
location is Sequoia HS July 29-August 2
and East Bay is Sunset HS August 5August 9. The application is on our
SVMI is …
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
offering Lesson Study mini-grants again
this year. The mini-grants are for teams of
5 to 7 teachers; the stipend is for $3,000.
The application will be out May 1, 2013.
presenting the preliminary results of the
2013 MAC assessment at our General
Meeting on May 15, 2013. We encourage
everyone to attend.
SVMI Calendar for 2013/2014

Please be sure to pick one up.
Field Testing K-3 Tasks
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SVMI needs at least two classes for
each task.
A teacher may only do one task;
there is no need to do all five.
If possible, the field testing should
be done as soon as possible.
Field testing to be done in the
stated Grade Level
Kinder Tasks

Alphabet Count:
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Classroom Helpers:
Counting and
Cardinality/Op. and Alg. Thinking
Op. and Alg.
Thinking
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Kinder Measurement:
Measurement/Geometry
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Dog Park:
Counting and Cardinality
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Crayons:
Op. and Algebraic Thinking
First Grade Tasks
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Field Day:
Op. and Alg. Thinking/ Number Ops.
In Base 10
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Number Puzzles:
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Recess Equipment:
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Weather:
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Shapes, Shapes, Shapes:
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School Garden:
Op. and Alg.
Thinking/Number Ops. in Base 10
Op. and Alg. Thinking
Data/Op. and Alg. Thinking
Geometry
Measurement/Geometry
Second Grade Tasks
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Seasons:
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Quilt Designs:
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Town Zoo:
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Can You Tell?:
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Our Gardens:
Data
Geometry
Linear Measurement
Op. and Alg.
Thinking/Number Ops. In Base 10
Op. and Alg. Thinking – Mult.
and Div.

Favorite Planets:
Data
Third Grade Tasks

Dinosaur Museum:
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Tamiko’s Puzzles:
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That’s Entertainment:
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The Queen and her Pears:
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Mowing for Money:
Measurement - Time
Fractions
Op. and Alg.
Thinking/Number Ops. In Base 10 using 4
operations
Measurement
Fractions
Geometric
Norms
The Social Culture of our Network
Seek to Understand
Respectfully Speak your
Truth
Monitor your Airtime
Getting Acquainted or Re-Acquainted
Goals and Outcomes
Goals and Outcomes
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Explore Social Norms and Socio/Mathematical
Norms in the context of experiencing a formative
assessment problem solving lesson
Strengthen and enhance participants’ leadership
abilities by experiencing a high-quality professional
development module to support teachers in their
classrooms
Deepen participants’ understanding of the
effectiveness of Formative Assessment in the
classroom for teachers and students
Lenses to Consider During Professional
Development Sessions
Learner Lens
Coach/Admin Lens
Mathematical
Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving
them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning
of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Socio-Mathematical Norms
Harold Asturias
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Errors are gifts…they promote discussion and
learning
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The math is important…not just the answer
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Ask questions…until it makes sense
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Think with language…use language to think
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Use multiple strategies…multiple
representations
Setting the Stage
Questioning
A Look at
Module 4 and an
Alpha FAL
Network Meeting, September 5, 2012
Silicon Valley Mathematics Initiative
www.svmimac.org
Collaboration
A Look at
Module 5 and
Collaborative
Tasks
Network Meeting, October 31, 2012
Silicon Valley Mathematics Initiative
www.svmimac.org
A Look at Addressing Curriculum
Needs
Exploring
Cognitive Demand
Network Meeting, January 9, 2013
Silicon Valley Mathematics Initiative
www.svmimac.org
Formative Assessment
How can I respond to students in ways that
improve their learning?
Assessing and
Using Prior
Learning to Adapt
Teaching to the
Needs of Students
Network Meeting, April 10, 2013
Silicon Valley Mathematics Initiative
www.svmimac.org
Introduction
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Students do not arrive in classrooms as
“blank slates.”
Students come with a wide variety of
skills and conceptions.
Research shows that teaching is more
effective when it assess and uses prior
learning so that teaching may be
adapted to the needs of students.
Assessing and Using Prior Learning to Adapt
Teaching to the Needs of Students
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Prior learning may be uncovered through
any activity that offers students
opportunities to express their
understanding and reasoning.
It does not require testing.
It can take the form of a single written
question given at the beginning of a
session to elicit a range of explanations
that may then be discussed.
Assessing and Using Prior Learning to Adapt
Teaching to the Needs of Students
Defining Formative Assessment: Black and
Wiliam, 1998
…all those activities undertaken by
teachers, and their students in assessing
themselves, which provide information to
be used as feedback to modify the
teaching and learning activities in which
they are engaged. Such assessment
becomes ‘formative assessment’ when the
evidence is actually used to adapt the
Assessing and Using Prior Learning to Adapt
Teaching to the Needs of Students –Our
Focus
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How can problems be used to assess
performance?
How can this assessment be used to
promote learning?
What kinds of feedback are most helpful
for students and which are unhelpful?
How can students become engaged in the
assessment process?
Research on Formative Assessment

Inside the Black Box: Raising Standards
through Classroom Assessment Black and
Wiliam, 1998

Working Inside the Black Box:
Assessment for Learning in the Classroom
Black and Harrison, 2002
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Assessment for Learning: Putting it into
Practice Black, Harrison Lee, Marshall & Wiliam 2003
Mathematics Inside the Black Box Hodgen &
Activity A
Introducing Formative Assessment

We begin with the following questions:

Why does one assess students?

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What different purposes do
assessments serve? Make a list.
Protocol:
 Individual SOLO Think Time-1 minute
 Pair/Share-2 minutes
 Whole Group Sharing -3 minutes
Activity A
Introducing Formative Assessment

To summarize, there are two main purposes of assessments:


Summative Assessment: to summarize and record
overall achievement at the end of a course, for
promotion or certification. Most ‘high stakes’ tests
and external examinations are designed for this
purpose. It is also used to evaluate the relative
effectiveness of a particular course, teaching
method, or even an institution.
Formative Assessment: to recognize achievements
and difficulties at the beginning or during a course
so that teachers and students can take appropriate
action. This type of assessment forms an integral
Activity A
Introducing Formative Assessment

The potential of formative assessment to improve learning:

Setting the Case: “We checked many books and
nine years’ worth of more than 160 journals, and
earlier reviews of research. This process yielded
580 articles or chapters to study. We prepared a
review using material from 250 of these sources.
All…studies show that…strengthening…formative
assessment produces significant, and often
substantial, learning gains. These studies range
over ages, across several school subjects, and over
several countries… Black and Wiliam, 1998
Activity B
Teachers’ Own Experiences of Formative Assessment
We begin with the following situation:
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Think of two students, one who is particularly strong
and one who is finding the work very difficult. Using a
dyad format, describe the students’ strengths and
difficulties in as much detail as possible to your
partner.
Protocol:
 Individual Solo Think Time-30 seconds
 Dyad-1 minute per partner
Activity B
Teachers’ Own Experiences of Formative Assessment
We begin with the following situation:

How did you become aware of these strengths and
difficulties?

On what evidence do you base your judgments? Test results?
Memories of oral responses during lessons? Observations of the
student working? Written work?

Protocol:
 Individual Solo Think Time-1/2 minute
 Dyad -1 minute per partner
Activity B
Teachers’ Own Experiences of Formative Assessment
The third part of the situation:
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
In what ways do assessments of these students affect
lesson planning? Give examples.
Protocol:
 Individual Solo Think Time-1 minute
 Dyad-1 minute per partner
Activity B
Teachers’ Own Experiences of Formative Assessment
What difficulties do teachers encounter?


Handout #1: Difficulties in Formative Assessment
Protocol:
 Individual Reading Time-1 minute
 Think about these questions:



How far are the criticisms on the handout valid
in your context as a coach/admin/teacher?
If any are, then what may be done about them?
We leave these questions to ponder as we
explore this module in more depth.
Activity C
Principles for Formative Assessment

Handout #2
Keeping in mind the difficulties discussed in
Activity B, please read Principles for Formative
Assessment.


1 minute
Please discuss these principles with your
partner.


Which of these principles do you see implemented
in classrooms?
Which of these do you or teachers you know find
most difficult to implement? Why?
Activity C
Principles for Formative Assessment
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“It’s all very well telling us to assess our students, but
how can a busy teacher know what is going on inside
30 individual heads?”
 How would you answer this teacher?
 What strategies do you have for finding out what
students are thinking in your lessons or the ones
you observe?
 1 minute for individual think time
Please discuss these strategies with your partner.
 2 minutes
Popcorn Sharing with Whole group
 1 minute
Activity C
Principles for Formative Assessment

Handout #3
Please read Making Reasoning Visible.


1/2 minute
Please discuss these strategies with your
partner.


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
Why are these tools an indispensable resource for
teachers?
1 minute
Watch two Video Clips with students in
action. 6 min
Suggest some further strategies for making
MAP
http://map.mathshell.org/materials/index.php
Activity C
Principles for Formative Assessment
Handout #3
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Whole group sharing on the video clips. 2 minutes
Comments from the module.
Teachers can see at a glance with every student
thinks.
Allows teachers to ask new kinds of questions, e.g.,
“Show me an example of….”
Posters allow students to externalize their thinkingarticulate their reasoning and justification.
Posters can be used to show what they already know
not necessarily what they have just worked on.
Whole group sharing on additional strategies for
Doing Mathematics
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A purposeful shift
Engaging in one of three selected
problem solving lessons addressed
and used in this module
Lenses to Consider During Professional
Development Sessions
Learner Lens
Coach/Admin Lens
PROBLEM SOLVING LESSONS
LET’S DO SOME
MATHEMATICS
Optimizing: Security Cameras
Assessment Task: Solo
Assessment Task


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What are the big mathematical
ideas in this task?
What strategies might students use
in completing this task?
Please anticipate what students will
understand about this task.
Please anticipate where students
may have difficulty with this task.
Protocol


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Discuss these questions and
anticipations with a neighbor. 2
min
Share with members in your table
group. 2 min
Popcorn share with whole group. 2
min
Assessment Task




What are the big mathematical
ideas in this task?
What strategies might students use
in completing this task?
Please anticipate what students will
understand about this task.
Please anticipate where students
may have difficulty with this task.
Feedback Questions/Prompts
Feedback Questions/Prompts
Collaborative Activity: Improving the Solution
Sharing Work and Learning From Each Other
Collaborative Work:
Planning a Joint Solution
1.
1.
1.
1.
1.
Take turns to explain your work and how you think it could be
improved.
Listen carefully to each other and ask questions if you don’t
understand or agree.
Once everyone in the group has explained their method, plan
a joint method that is better than each of your separate ideas.
Make sure that everyone in the group can explain the reasons
for your chosen method.
Write a brief outline of your planned method on your large
sheet of paper.
Break
Collaborative Analysis of Sample Responses
Analyzing Sample Responses to
Discuss
1. Simon
2. Ellie
3. Rhianna
P-62
Sample Responses to Discuss:
Simon
P-63
Sample Responses to Discuss: Ellie
P-64
Sample Responses to Discuss:
Rhianna
P-65
Whole Class Discussion
Whole Class Discussion




Compare the different solution methods and
comment on their strengths and weaknesses.
How is this work similar/different to what you
did?
Did analyzing the responses enable anyone to
see errors in their own work?
Of the three sample pieces of work, which do
you think has the most complete and accurate
solution? Why? In what ways could it be
improved further?
Individual Reflection
Sample Responses to Discuss:
Rhianna
P-69
Returning to the Module
Activity D
Analyze Students’ Responses to Pb Solving Tasks

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
The three tasks in this Activity, Counting Trees, Cats
and Kittens, and Security Cameras have a variety of
mathematical content, but all focus on problem solving
and the modeling skills described in the SMP.
Students are required to choose and combine
techniques in non-routine ways.
Traditional summative assessment often focus on
isolated content standards and fail to test these
‘process skills’.
Formative Assessment is an effective way to
ensure that students are developing these
Activity D
Four Phases of Problem Solving: A Useful Tool to
Analyze Students’ Work on These Tasks


Formulate questions, choose appropriate
representations and techniques.
Reason logically, construct hypotheses and
arguments, compute accurately.

Interpret and evaluate results obtained.

Communicate and reflect.

Teacher Discussion of Sample Student
Responses
What does each sample student’s response
[Simon, Ellie, and Rhiana] tell you about his or
her capacity to use each of the phases of
problem solving:

Formulate

Reason

Interpret and Evaluate

Communicate and Reflect

Discuss with your shoulder partner. 5 minutes

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Questions for Feedback
H-17 and H-19 [Handout #6]
If you were the teacher of these students, what
feedback would you give them to help them
improve their responses?
Frame this help in the form of oral questions
you could ask in the classroom.
You may find it helpful to refer to the generic
questions on Handout #6.
Discuss with your shoulder partner. 5 minutes
Whole group share out-Round Robin Protocol.
Watching 3 Teachers Discuss
Feedback Questions to Students

Were these questions similar or
different to the ones you and your
partner discussed?
MAP
http://map.mathshell.org/materials/index.php
Watching 3 Teachers Discuss
Feedback Questions to Students



Were these questions similar or
different to the ones you and your
partner discussed?
What have you learned from this
video clip?
Popcorn Whole Group Sharing
Activity E
Observe Formative Assessment in Action



In an earlier lesson, these teachers had asked
students to sit in different places and attempt one of
the tasks individually, with no help.
They then collected their students’ responses,
assessed the work qualitatively and prepared
written feedback in the form of questions.
The film clips you are about to see are taken from the
follow-up lesson. Students have returned to their
normal seats and most have solutions that are
different than their partners.
Activity E
Observe Formative Assessment in Action

As you watch the video clips, consider these
questions:



What different kinds of assessment can you see?
What is the purpose of each kind of
assessment?
What do both the teachers and the students learn?
MAP
http://map.mathshell.org/materials/index.php
Activity E
Observe Formative Assessment in Action

Debrief in your table groups:



What different kinds of assessment can you see?
What is the purpose of each kind of
assessment?
What do both the teachers and the students learn?
Activity G
Consider the Effects of Feedback on Student Learning
So far we have focused on the teachers’ role in providing
assessment feedback to students. In Activity G, we will
consider the use students make of different types of feedback
and the impact this has on their learning.

As you watch the video clip consider these
questions:


Which of their comments strike you as
particularly perceptive and important?
What are the implications of their comments?
MAP
http://map.mathshell.org/materials/index.php
Activity G
Consider the Effects of Feedback on Student Learning
So far we have focused on the teachers’ role in providing
assessment feedback to students. In Activity G, we will
consider the use students make of different types of feedback
and the impact this has on their learning.

As you watch the video clip consider these
questions:


Which of their comments strike you as
particularly perceptive and important?
What are the implications of their comments?

Give yourselves ½ minute to gather your thoughts
and then have a 2 minute dyad with a partner.
Activity G
Consider the Effects of Feedback on Student Learning
Handout #8


Please read The Effects of Feedback on
Students’ Learning. 1 minute
Have a discussion with your table group and
compare the students’ comments with the
research quotes in this handout. 3 minutes





Activity G
Consider the Effects of Feedback on Student Learning
Handout #8
Consider the following questions individually:
The dangers of giving marks, levels,
rewards, and rankings
What are the implications of this for your practice?
What would happen if you stopped giving marks or
levels on your pupils’ work?
Why are so many teachers resistant to making this
change?
Discuss in your table groups.




Activity G
Consider the Effects of Feedback on Student Learning
Handout #8
Consider the following questions individually:
The advantages of giving clear, specific,
content-focused feedback
What are the implications of this for your practice?
Does this kind of feedback necessarily take much
longer to give?
Discuss in your table groups.

Activity G
Consider the Effects of Feedback on Student Learning
Research shows that students benefit most
from feedback that:








Focuses on the task, not on grades or scores
Is detailed rather than general
Explains why something is right or wrong
Is related to objectives
Makes clear what has been achieved and what has
not
Suggests what the student may do next
Offers specific strategies for improvement
How could you involve students in improving your
MAP
Mathematics Assessment Project
Lunch