Summer Leadership 2015
Elementary Math
Elementary Preview and Planning Day
Math
Key Question #5:
How can leaders focus on supporting teachers to
impact student success in math?
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Math (Grades 3-5)
On p. 141, you will find the “Top Teacher Training Take-Aways”.
Let’s take a few moments to read through these before we view just a small
portion of the content your teachers are experiencing.
We will follow-up each overview section with a short reflection time on p. 165
of your manual. We will be using this notes later as we complete a planning
document for each key area.
pp. 141, 165 in your manual
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Math (Grades 3-5)
Look at the overarching theme of this set of trainings:
“Task predicts performance.”
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Learning Leaders Modules
Let’s take a look over the contents of the modules that your teachers are
experiencing in math.
The overview of the math training modules found on pp. 142-143. Mark any
topics that you think will be important during the redelivery phase for your
teachers.
pp. 142-143 in your manual
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Assessing the Current ‘Math
Mindset’
All of us who are stakeholders have a role to play and important
actions to take if we finally are to recognize our critical need for a
world where the mathematics education of our students draws
from research, is informed by common sense and good judgment,
and is driven by a non-negotiable belief that we must develop
mathematical understanding and self confidence in all students.
NCTM Principles to Action
Somehow it’s okay for people to
chuckle about not being good at
math. Yet if I said, ‘I never
learned to read,’ they’d say I was
an illiterate dolt.
Neil deGrasse Tyson
I don’t like to be negative about
math because it really teaches you
a lot of great things. You kind of
use math every day.
Madison Davenport
If you stop at general math, you’re only going to
make general math money.
Snoop Dogg
p. 144 in your manual
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What is the Overwhelming Public Perception of
‘Math’?
Emily Calandrelli
MIT Graduate
NASA Intern
Xploration Outer Space Host/Producer
Passionate about STEM
Emily’s TEDx Talk on the dangers of
negative STEM stereotypes and how we
can promote a positive attitude toward
STEM literacy
Play Video: idontdomath.mp4
NASA – Bill Stafford
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Discussion Activity: What is my school’s
‘Math Mindset’?
Instructions: First, complete each question individually on p. 144.
Then, share at your table.
1. What are my personal math biases? Have I ever said ‘I’m not good at
math’?
2. What ‘math mindset’ am I hearing in the halls and classrooms from
students?
3. What ‘math mindset’ am I hearing from my math faculty? Non-math
Faculty?
p. 144 in your manual
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NCTM Productive and Unproductive
Beliefs
UNPRODUCTIVE BELIEFS
PRODUCTIVE BELIEFS
Students possess different innate levels of abilities
in mathematics, and these cannot be changed by
effective instruction.
Mathematics ability is a function of opportunity,
experience, and effort. All students are capable of
participating and achieving in rigorous mathematics.
ELL students are less able to learn mathematics and
must be in a separate track.
ELL students can learn the language of mathematics
at or beyond grade level at the same time they learn
English with appropriate instruction
Students living in poverty lack the cognitive,
emotional, and behavioral characteristics to
participate and achieve in rigorous mathematics.
Effective teacher practices (e.g. using high level
tasks, Accountable Talk) provide greater
opportunities to higher-order thinking and raising
achievement of all students.
Only high-achieving or gifted students can reason
about, make sense of, and persevere in challenging
mathematics.
All students are capable of making sense of and
persevering in challenging mathematics given
opportunities, support, and confidence.
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PLC Resource
On p. 145 of your manual, you will find a “Math
Mindset” PLC Guide that can walk your fellow
administrators and faculty through current attitudes on
mathematics education, common misconceptions, and
fostering ideas on improving the ‘math mindset’ of a
school.
p. 145 in your manual
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Characteristics of Excellent Math
Instruction
• One of the activities that your teachers will be involved in will be to identify
the characteristics of high-level math instruction. Let’s do this as leaders.
• Turn to page p. 146 and independently complete the Frayer Model
entitled, “Characteristics of high-level math instruction and student
engagement”.
• How should these characteristics impact what we look for in classroom
instruction as leaders focused on helping our teachers improve?
p. 146 in your manual
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NCTM Mathematics Teaching Practices
• Turn to p. 147 in your manual. Read through the document
entitled, “NCTM Mathematics Teaching Practices.”
• Be sure to UNDERLINE those characteristics that are similar to
your Frayer Model.
• Circle those characteristics that you would like to add to your
Frayer Model.
p. 147 in your manual
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NCTM Mathematics Teaching
Practices
• After reading the “NCTM Mathematics Teaching Practices”,
work as a group to complete the center rectangle of your Frayer
Model.
• In the center write your group’s best summary of what excellent
math instruction should encompass.
• Prepare to share out whole group.
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Supporting Mathematics Teaching
Practices
• Throughout our journey in our leadership courses, we have talked about
several key teacher actions that will support excellent instruction in our
math classes, such as:
• Accountable Talk
• Assessing and Advancing Questions
• Task Selection and Modification
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Supporting Mathematics Teaching
Practices
• Turn to p. 148 in your manual and read over the “Assessing and
Advancing Student Understanding Rationale”. Underline key
ideas as you read.
• Turn and talk with a shoulder partner about some of the
different ways you see evidence of these key ideas in your math
classrooms.
p. 148 in your manual
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Assessing and Advancing
Questions
Assessing Questions
Advancing Questions
Are based closely on the work students
students have produced.
Use what students have produced as a
produced as a basis for making progress
progress toward the target goal.
Clarify what students have done and
and what students understand about
about what they have done.
Move students beyond their current
current thinking by pressing students to
students to extend what they know to a
know to a new situation.
Provide information to the teacher about Press students to think about something
teacher about what students
something they are not currently thinking
understand.
thinking about.
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NCTM Mathematics Teaching
Practices
• The NCTM Mathematics Teaching Practices come from a
document entitled “Principles to Action – Executive Summary”
which can be found in the appendix on p. 152.
• There is a PLC Guide available online to accompany this
section that will help schools focus examine the current
teaching practices for mathematics classes.
p. 152 in your manual
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Math Tasks
Back to our big idea: “Task predicts performance.” Let’s read this
quote together:
There is no decision that teachers make that has a greater impact
on students’ opportunities to learn and on their perceptions about
what mathematics is than the selection or creation of the tasks
with which the teacher engages students in studying
mathematics.
Lappan & Briars, 1995
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Math Tasks
Let’s review what we’ve talked about many times. A mathematical
task is a problem or set of problems that focuses students’
attention on a particular mathematical idea.
p. 160 in your manual
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Math Task Arc
• On p. 158 in your manual you will see an overview of Mathematics Task
Arcs.
• On p. 160 in your manual you will see a table of contents for a task arc for
Grade 4. On pp. 162-163 you will see an overview for the same task arc.
• Are task arcs being used in your school for mathematics instruction?
What can you as a leader do to support the use of task arcs in your
school?
pp. 158, 160, 162-163 in your manual
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Structures and Routines of a
Lesson
Remember
this?
What power
is there in
encouraging
your teachers
to utilize this
model?
p. 150 in your manual
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Math Tasks
Teachers must be able to choose appropriate mathematical tasks, judge the
advantages of particular representations of a mathematical concept, help students
make connections among mathematical ideas, and grasp and respond to students’
mathematical arguments and solutions.
A lack of mathematical content knowledge can impede teachers’ abilities to notice
and analyze students’ mathematical thinking, design actions that respond to
students’ understanding, or engage in productive professional conversations.
Doerr, H. M., & English, L. D. (2006); Hunting, R. P., & Doig, B. A. (1997); Britt, M.
S., Irwin, K. C., & Ritchie, G. (2001)
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Task Selection
• True or False? (Discuss your answer with a partner)
1. All tasks must be high-level.
2. Accountable talk is only used during a high-level task.
3. The main purpose of tasks is for assessment purposes only.
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Computational Fluency
Let’s change gears a bit. Our teachers will spend time this
summer talking more about computational fluency, which refers
to having efficient and accurate methods for computing.
Fluency is not meant to come at the expense of conceptual
understanding. Rather, it should result from a progression of
learning and thoughtful practice. It is important for fluency to
have students build conceptual understanding with skills.
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Fluency Expectations
p. 151 in your manual
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Reflection
As we close out our overview of the math content, let’s think about how we, as
leaders, can best:
– Support redelivery
– Support our teachers’ ongoing implementation of strategies during the next school
year
Turn to p. 165 in your manual and complete the take-aways and key actions
portions of the planning form.
After completion, let’s take a few moments to share out from each table any
key actions you know you will prioritize as a leader to support teachers.
p. 165 in your manual
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