Materials
Beliefs
• Cut-up beliefs
• Answer key
Adjusting support tool
Tasks activity
• Martha’s carpeting problem (on
ppt)
• Fencing problem (labels)
• 3-5 tasks (6-8 tasks)
• Levels of cognitive demand
• Answer key
• Factors affecting copies
Supporting Implementation of
Mathematics Standards
RSD Principals
October 22 and 23, 2014
Sue Larson
Nora Ramirez
Outcomes
• Become familiar with a tool to adjust support by self
assessing mathematics instruction at a school site
• Increased ability to affect teachers’ beliefs regarding the
teaching and learning of mathematics
• Raise awareness of how mathematical tasks differ with
respect to their levels of cognitive demand
• Increased understanding of an administrator’s role in
supporting teachers as they implement math standards
• Consider expectations of teachers as they implement
problem solving (related to the October 31 RSD Professional
Development Day)
A Data Collection Tool
Adjusting Professional Support
A Data Collection Tool
Adjusting Professional Support
Outcome
Become familiar with a tool to adjust support
by self assessing mathematics instruction at a
school site
Beliefs about Teaching and Learning Mathematics
• Pass out slips of paper in each group
• Sort beliefs as either productive and
unproductive beliefs with each person taking a
turn to read and determine if the belief is
productive or not. The group then reaches
consensus on each decision.
• Check answers.
Principles to Actions: Ensuring Mathematical Success for All, NCTM 2014
Beliefs about Teaching and Learning Mathematics
• Count off 1-6. Get into numbered group taking
the list of Productive and Unproductive Beliefs
with you.
• How might you coach a teacher to address
this unproductive belief?
Principles to Actions: Ensuring Mathematical Success for All, NCTM 2014
Reflection
• What unproductive beliefs do you find more
prevalent in your school?
• What moves might you make to begin to
overcome these unproductive beliefs?
Beliefs about Teaching and Learning
Outcome
Increased ability to affect teachers’ beliefs
regarding the teaching and learning of
mathematics
Mathematical Tasks
Oct 31 Professional
Development Outcomes
To reinforce the foundations of teaching and
learning mathematics by enhancing teachers’
ability to:
– Use problem solving as a vehicle to teach in a
balanced approach
– Select/modify/create tasks with high levels of
thinking
Agenda
• Activate Prior Knowledge
• Problem Solving Introduction
• Tasks and Mathematical Practices
• Problem Solving #1
• Tools for Problem Solving
• Problem Solving #2
• Balanced Approach
• Stations
Independent Work
Begin to solve these two problems individually.
Record your work in your packet.
•Martha’s Carpeting
•Fencing
Martha’s Carpeting Task
Martha is recarpeting
her bedroom, which is
15 feet long and 10 feet
wide. How many square
feet of carpeting will she
need to purchase?
Fencing Task
Ms. Brown’s class will raise rabbits for their
spring science fair. They have 24 feet of
fencing with which to build a rectangular
rabbit pen to keep the rabbits.
1.
If Ms. Brown’s students want their rabbits
to have as much room as possible, how
long would each of the sides of the pen be?
2.
How long would each of the sides of the
pen be if they had only 16 feet of fencing?
3.
How would you go abut determining the
pen with the most room for any amount of
fencing? Organize your work so that
someone else who reads it will understand
it.
Partner Work
Continue to work on the two problems
with your partner.
•Martha’s Carpeting
•Fencing
Presentations
.
Group Discussion
How are Martha’s Carpeting Task and the Fencing Task
the same and how are they different? Do the
differences matter?
Consider your own experience in solving the tasks, the
“mathematical possibilities” of the tasks, and/or the complexity
of the tasks.
Analyzing Mathematical Tasks
“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 and Briars, 1995
Math & Science Collaborative
DIGGING INTO TASKS
- Categorizing
- Characterizing
Categorizing
Tasks
• Sort Tasks A – P into two categories
[high-level and low-level]
• Develop a list of criteria that describe the
tasks in each category
Categorizing Tasks
Low
High
A, D, E, G, L, O
B, C, F, H, I,
J, K, M, N, P
Discussion
• What are the characteristics of the tasks you
categorized as “low” level?
• What are the characteristics of the tasks you
categorized as “high” level?
Math & Science Collaborative
Discussion
• Are all high-level tasks the same?
Is there an important difference between
Tasks J and B?
• Are all procedural tasks the same?
Is there an important difference between
Tasks I and O?
Math & Science Collaborative
Categorizing
Tasks, Part Two
Further sort the mathematical tasks into four
categories:
–
–
–
–
Memorization tasks
Procedural tasks without connections
Procedural tasks with connections
Doing mathematics tasks
Reflection & Share
• What information can we add to our initial
brainstorm:
– What are characteristics of high levels of
mathematical thinking and reasoning?
Categorizing Tasks
“If we want students to develop the
capacity to think, reason, and problem
solve then we need to start with highlevel, cognitively complex tasks.”
Stein & Lane, 1996
Math & Science Collaborative
Patterns of Set up, Implementation, & Student
Learning
Task
Set Up
Task
Implementation
Student
Learning
High
High
High
Low
Low
Low
High
Low
Moderate
A.
B.
C.
Stein & Lane, 2012
Reflect and share
• What do you now understand about the
levels of demands of tasks?
Problem Solving
• Select task considering
– Level of cognitive demand
– The mathematics students will apply and learn
– The accessibility of the task to students
• Anticipate student responses
– Possible student misconceptions
– Different strategies and tools students might use
– Language that indicates understanding
Adapted from Principles to Actions
Problem Solving
• Teacher presents problem, facilitates the KFA process and does not
model or suggest a solution process.
• Teacher has tools available for student use.
• Students work individually, then in pairs/groups while the teacher
– Monitors,
– asks guiding questions that promote the SMP,
– assesses students’ understanding, and
– chooses students to present and sequence of presentations.
• Teacher facilitates discourse requiring students to explain, defend,
ask questions, clarify, model with equations, use representations
and appropriate tools, use precise language, make connections, etc.
• Teacher facilitates a class summary and an individual reflection.
Adapted from Principles to Actions
Supporting Teachers
What is your role in supporting teachers as they implement problem solving?
Think about
• what you can do to help teachers implement problem solving
• how you might help them learn what problem solving looks like and sounds
like
• how you will scaffold their learning and implementation
What might you tell your teachers that you expect to see in their classrooms?
Think about
• how often you expect to see problem solving
• the type of problems teachers use
• how you might help them persevere
• what student engagement might look like
• acceptance and acknowledgment of the learning process
Outcomes
• Become familiar with a tool to adjust support by self
assessing mathematics instruction at a school site
• Increased ability to affect teachers’ beliefs regarding the
teaching and learning of mathematics
• Raise awareness of how mathematical tasks differ with
respect to their levels of cognitive demand
• Increased understanding of an administrator’s role in
supporting teachers as they implement math standards and
specifically problem solving
• Consider expectations of teachers as they implement
problem solving (related to the October 31 RSD Professional
Development Day)
Evaluation, Feedback and Input
• Complete the project’s evaluation form
• Complete the + / Δ form.