A Purposeful Ice-Breaker,
Hopefully…
Kentaro Iwasaki, Associate Director for Pathway &
Curriculum Development
ConnectEd: The California Center for College and Career
1
Ice Breaker for Norm Building
Goals:
1. Use an Ice Breaker to Get to Know Other People
(and Ourselves) Better
2. Build Norms—an Essential Element in any Social
Setting, Especially the Classroom
2
Norm Building
Marshmallow Challenge
EACH TEAM BUILDS A FREESTANDING STRUCTURE (NO TAPE ON TABLE)
IN 15 MINUTES WITH THE INTACT
MARSHMALLOW REACHING THE HIGHEST
POINT POSSIBLE
20 sticks of spaghetti + one yard tape +
one yard string + one intact marshmallow
3
Norm Building
Marshmallow Challenge Debrief
Discuss what your group found out about:
the Marshmallow Challenge itself
members in your group (who did what?)
how your group worked together (what went well and
what could be done better?)
anything else interesting
4
Norm Building
Marshmallow Challenge Video
Think about:
1. Debrief the video.
2. What is your experience with norms in and out of
the classroom ?
3. What norms would be helpful to make the
Marshmallow Challenge better?
5
Norm Building
Students will not automatically know how to
work collaboratively without explicit directions,
norms, and “ground rules.”
My Personal Examples
6
Norm Building
Norms for this PD:
1. Stay together on agreed-upon topic
2. Work to maintain equity of voice (“Step Up,
Step Back”)
7
Norm Building
Teachers themselves also need to abide by
norms when they ask students to work
collaboratively.
Which of these teacher roles is most challenging
for teachers and why?
How can we help teachers with these roles and
help them establish and maintain group norms?
8
Frame of Reference
Please participate during this PD as a
learner and as a teacher leader who will
lead others in the formative
assessment lesson process.
Jot down the names or people you will
have in mind during the PD with whom
you will share the formative assessment
lessons and strategies.
9
Agenda
1. Norm Building Task and Debrief
2. Background and Components of a Formative
Assessment Lesson
3. Model, Participate In, and Analyze a Formative
Assessment Lesson
4. CCSS-M Standards and Practices
5. Formative Feedback and Questioning
6. Formative Assessment Lesson #2
7. Homework: Email Reflection Questions from
Day 1
10
OK, Who is this Guy?
11
Formative Assessment and 5 Strategies
1. Please first read the “Big Idea of
Formative Assessment” and then “Five
Strategies of Formative Assessment,” and
answer the questions individually (5
minutes) and then think-pair-share your
reflections (5 minutes).
2. Please be ready to share out!
12
Classroom Specific Strategies
1. Avoid cold-calling by giving
opportunities for think-pair-share or
think-group-share
2. Record the discussion thread with
names and contribution
13
Formative Assessment Lessons (FALs)
Part 1: Pre-Assessment : Give Students Feedback and
Teachers a Qualitative Sense of Students’ Grasp of
Targeted Mathematics (15 minutes)
Part 2: Brief Class Discussion (10 minutes) and
Collaborative Activity : Focus on Guided Inquiry to
Address Student Misconceptions (45-90 minutes)
•Part 3: Post Assessment and Revision: Give Students a
Chance to Reflect on Their Learning and Offer Teachers
Perspective on Next Steps and Their Teaching
Effectiveness
14
“Interpreting Algebraic Expressions”
Formative Assessment Lesson
Math Goal: Translate between words,
symbols, tables, and area representations of
algebraic expressions.
• Recognize the order of algebraic operations.
• Recognize equivalent expressions.
• Understand the distributive laws of
multiplication and division over addition
15
“Interpreting Algebraic Expressions”
Formative Assessment Lesson
COMMON CORE STATE STANDARDS
A-SSE: Interpret the structure of
expressions.
A-APR: Rewrite rational expressions.
Math Practices:
2. Reason abstractly and quantitatively.
7. Look for and make use of structure.
16
“Interpreting Algebraic Expressions”
Formative Assessment Lesson
Part 1: Individual Pre-Assessment
Please read through or do the pre-assessment
individually.
 What areas of student understanding or
misconceptions can you gather from this?
17
Part 2: Brief Classroom Discussion
1. Class questions based on pre-assessment
2. Not intended to address every
misconception
3. For example, write an algebraic
expression that means
a. Multiply n by n, and then multiply
your answer by 5.
b. Multiply n by 5, and then square your
answer.
18
Part 3: Collaborative Activity
1. Take out the pink and green cards. Match the
corresponding pink card to the green card. Leave
these cards out.
2. Take out the blue cards next and place the blue cards
next to the corresponding pink and green cards.
3. Do the same with the
cards.
4. Please fill in any blanks on the cards.
5. How you might make extensions and/or modifications
to this task if needed.
6. How does this task address student misconceptions
and further student understanding?
19
Part 4: Revision and Post-Assessment
1. Pre-Assessment and a New Sheet are
given back to students for revision.
2. Students might respond to a prompt
such as, “What did you learn from this
lesson that helps you improve your
work?”
20
Part 5: Teacher Decisions about Next
Steps
1. Based on revisions and postassessment, a teacher decides what
next steps are best to address existing
misconceptions.
2. The Formative Assessment Lesson, if
taught 2/3 of the way through a unit,
allows time in the unit for a teacher to
direct where he/she will lead the class.
21
DEBRIEF
1. What aspects of the formative
assessment lesson allow for deeper
student engagement and learning?
2. What challenges arise around the
formative assessment lessons for
teachers and students? How will you
address these challenges?
22
VIDEO
Please observe the video and be ready to
share out thoughts or observations.
23
QUALITATIVE FEEDBACK
Based on a study by Ruth Butler (1988),
which type of feedback improves student
work quality the most from a first lesson to
a similar second lesson? Why?
A. Numerical score/grade only
B. Written feedback only
C. Numerical score/grade and written
feedback
D. No feedback
24
QUALITATIVE FEEDBACK
1. What type of feedback did you or other
math teachers typically give to
students? How did you (or others)
provide feedback?
2. How effective did you find your feedback
to be? Why?
3. How would you think the feedback could
be more effective? Why?
25
QUALITATIVE FEEDBACK
1. Evaluate the feedback suggestions
given. How effective do you find them
to be?
2. How might you make them more
effective?
26
QUALITATIVE FEEDBACK
Read the sheet on qualitative feedback.
Discuss in a small group.
How can we improve the feedback we and
other teachers give to students?
27
Concept Development Lessons and
Problem Solving Lessons
Concept Development lessons are intended to
assess and develop students’ understanding of
fundamental concepts through activities that
engage them in classifying and defining,
representing concepts in multiple
ways/representations, testing and challenging
common misconceptions, and exploring the
structure of a problem.
28
Concept Development Lessons and
Problem Solving Lessons
Problem Solving lessons are intended to assess
and develop students’ capacity to select and
deploy their mathematical knowledge in nonroutine contexts and typically involve students in
comparing and critiquing alternative approaches to
solving a problem.
29
Problem Solving Lessons’ Structure
1. Students individually work on a “less
structured” task (pre-assessment)
2. Brief Class Lesson Drawing Out
Misconceptions
3. Students Collaborate on the Task
4. Students Examine sample student work and
asked to critique and improve these
5. Students then revise their initial attempts and/or
try an alternative approach.
30
Security Cameras
Mathematical goals
This lesson unit is intended to help you assess
how well students are able to:
• Analyze a realistic situation mathematically.
• Construct sight lines to decide which areas of a
room are visible or hidden from a camera.
• Find and compare areas of triangles and
quadrilaterals.
• Calculate and compare percentages and/or
fractions of areas.
31
Security Cameras
Mathematical Content
6.RP: Understand ratio concepts and use ratio
reasoning to solve problems.
6.G: Solve real-world and mathematical problems
involving area, surface area, and volume.
Mathematical Practices
MP1: Make sense of problems and persevere in
solving them
MP2: Reason abstractly and quantitatively
MP3: Construct viable arguments and critique the
reasoning of others
MP4: Model with mathematics
32
Security Cameras
1. What misconceptions do you think students will
have?
2. What questions would you ask for a BRIEF
class discussion?
3. What type of feedback would you give or be
prepared to give?
33
Making Matchsticks
1. What misconceptions do you think students will
have?
2. What questions would you ask for a BRIEF
class discussion?
3. What type of feedback would you give or be
prepared to give?
34
Agenda
1. Feedback—thanks!
2. Re-Norming
3. Formative Assessment Lesson #3 with EL
Support
4. Questioning
5. Feedback
6. Formative Assessment #4
7. Planning/Next Steps, Evaluation
35
Re-Norming
1. Debrief the String Geometry Activity.
2. Discuss how and when teachers would use renorming
36
Bruce Tuckman’s Stages of Group
Development
1.
2.
3.
4.
5.
Form
Storm
Norm
Perform
Our addition—Re-Norm
37
EL Support ell.stanford.edu
1. Focus on students’ mathematical
reasoning and not on their accuracy in
using language
2. Focus on mathematical practices and
not on language as single words or
definitions
3. Treat everyday and home languages as
resources and not as obstacles
38
EL Support
How would you scaffold this lesson for EL
students?
What would you add? What would you
keep the same? Describe your rationale.
39
EL Support--Instructions
One suggestion is to change the
instructions in the activity to be clear, direct,
and concise. How would you suggest
writing the instructions?
40
EL Support--Instructions
“Estimate how many matches can be made
from the wood in this tree. Use the relevant
information on the formula sheet. It will help
you find some answers. Read the task,
and show all your work. Showing your work
helps me understand your reasoning
(thinking). It is important that your work is
organized and presented in a clear manner
(way).”
41
QUESTIONING
Please spend a few minutes individually
reflecting on these questions.
Then we will share in small groups and in a
large group.
42
VIDEO
295 Students in a school.
A bus holds 25 students.
How many buses are needed to hold all the
students?
43
QUESTIONING
Fill in the blanks:
Based on large study of elementary school
classrooms, Ted Wragg analyzed 1000
teacher questions.
_____% Managerial Questions
_____% Recall Questions
_____% Questions that Require Students
to Analyze, Make Inferences, Generalize
__________________________________
Less than _____% resulted in new learning
44
QUESTIONING
1. Which questions do you find most
effective? Why?
2. Which questions can be improved?
How so?
3. What challenges around questioning do
math teachers face?
4. How do we support math teachers in
asking good questions?
45
Planning to Work With Teachers
1. Local, Organic, Sustainable
2. It’s a Long Road…
3. Do Math Together in Your
PLC/Dept/Team
46
Planning to Work With Teachers
Strategize with your district teachers or
instructional specialists to determine what
needs and next steps you have in working
with teachers on the formative assessment
lessons and strategies.
1. What do you need?
2. What do the teachers need?
3. How will you work with the teachers on
what they need?
47
Planning to Work With Teachers
3 webinars throughout the school year to
support your work with teachers:
1. Norm Building
2. FAL enactment
3. FAL issues? EL Issues?
48
Planning to Work With Teachers
3 webinars throughout the school year to
support your work with teachers:
1. Norm Building
2. FAL enactment
3. FAL issues? EL Issues?
49
Math Design Collaborative (MDC)
“Mathematically proficient students continually ask
themselves, “Does this make sense?” and change
course if necessary. They justify their conclusions,
communicate them to others, and respond to the
arguments of others. They can apply the
mathematics they know to solve problems arising
in everyday life, society, and the workplace. They
continually evaluate the reasonableness of their
intermediate results, realizing that these may need
revision later.”
—Common Core State Standards for mathematics
50
The Need for Formative Assessment
CST Algebra Question
51
The Need for Formative Assessment
Smarter Balanced Performance Task
In the task, a new water tank or water tower for
a town needs to be built, and your job is to
recommend the best solution for the town.
52
The Need for Formative Assessment
53
Thank you!
Please contact me with any feedback
or questions:
kiwasaki@connectedcalifornia.org
54
55