This is the slide deck from the Greater Essex County District School Board (GECDSB) Mathematics Learning Teams (MLT) Session #1 held during the week of October 17th to 21st, 2016.
3. TODAY’S LEARNING
We are:
• Extending our understanding of the GECDSB:
Mathematics Vision and Mathematical Proficiencies
• Building an understanding of number sense concepts
from K-10
• Developing an understanding of Pedagogical Systems
• Planning a math task
• Learning to lead math in our schools
Math
Pedagogy
Math
Content
Leadership
&
Professional
Capital
4. THE MATHEMATICS JOURNEY
• Mathematics journey is unlike many others
• It is not an implementation of a program or process
• It is the enaction of the GECDSB Vision
5. The Work: Ambitious and Necessary
Enact the Vision
“The GECDSB provides mathematics education that engages and
empowers students through collaboration, communication, inquiry,
critical thinking and problem-solving, to support each student’s
learning and nurture a positive attitude towards mathematics.”
Table Talk…
Why is this work both ambitious and necessary?
6. SCHOOL MATH TEAM
Click to
add text
Session 1 October
Session 2 November
Session 3 January
Session 4 & 5 February and March
Session 6 April
Table Talk...
What is the role (possible role) of the school math team at your school?
Where are some professional learning spaces in your school?
8. What does it mean to be good at math?
Enjoy learning math
Develop persistence and tenacity
Learn to use math to solve problems
Develop logic and reasoning skills
See the value for mathematics in their world
Learn their facts and mathematical procedures
Understand the ‘whys’ of math
9. GECDSB: A Vision for Mathematics
Strategic Competence
Procedural Fluency
Conceptual Understanding
Adaptive Reasoning
Productive Disposition
This is a vision for mathematics that
is both ambitious and necessary.
10. Math Task Force Data
What does it mean to be good at math?
Math as a functional skill
Math as applied to a profession
Math as a way of thinking and seeing the world
14. Does this change your definition of what it
means to be good at math?
15. The Work: Guided By Our Questions
We have many questions about mathematics education.
Table Talk…
With the learners at your table, brainstorm some of the
questions you have or yourstaff may have about mathematics
education.
Share them with the larger group.
28. Stable-Order
The list of words used to count must be in a repeatable
order.
This “stable list” must be at least as long as the number of
itemsto be counted.
1
2
3
4
5
6
7 8 9 10
32. … the quantityof five large things is the samecount as a
quantityof five small things or a mixed group of fivesmall
and large things.
Abstraction
…we can count any collection of objects, whether tangible
or not.
1 2
3 4
5
1 2 3 4 5
33. Understanding thateach object being counted must be
given one count and only one count. It is useful in the early
stages for children to actually tag each item being counted
and to movean it out of the way as it is counted.
One-to-One Correspondence
1
2
3
4
5
34. Understanding thatthe last count of a group of objects
represents how many are in the group. A child who
recounts when asked how many candies are in the set that
they just counted, has not understood the cardinality
principle.
Cardinality
1 2 3 4 5 6
35. The ability to 'see' a small amount of objects and know how
many there are without counting.
Subitizing
“5”
36. Understanding thatas you move up the counting sequence
(or forwards), the quantityincreases by one and as you
move down (or backwards), the quantitydecreases by one
or whatever quantityyou are going up/down by.
Movement is Magnitude
1 2 3
37. Understanding thatas you move up the counting sequence
(or forwards), the quantityincreases by one and as you
move down (or backwards), the quantitydecreases by one
or whatever quantityyou are going up/down by.
Movement is Magnitude
1 2 3 4
38. Understanding thatas you move up the counting sequence
(or forwards), the quantityincreases by one and as you
move down (or backwards), the quantitydecreases by one
or whatever quantityyou are going up/down by.
Movement is Magnitude
1 2 3 4 5
39. Understanding thatas you move up the counting sequence
(or forwards), the quantityincreases by one and as you
move down (or backwards), the quantitydecreases by one
or whatever quantityyou are going up/down by.
Movement is Magnitude
1 2 3 4
40. Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when it exceeds 99) and that thisis indicated by a 1
in the tens place of a number.
Unitizing
tens ones
41. Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when it exceeds 99) and that thisis indicated by a 1
in the tens place of a number.
Unitizing
tens ones
42. Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when it exceeds 99) and that thisis indicated by a 1
in the tens place of a number.
Unitizing
tens ones
43. Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when it exceeds 99) and that thisis indicated by a 1
in the tens place of a number.
Unitizing
tens ones
44. Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when it exceeds 99) and that thisis indicated by a 1
in the tens place of a number.
Unitizing
tens ones
1 0
45. Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when it exceeds 99) and that thisis indicated by a 1
in the tens place of a number.
Unitizing
tens ones
1 9
46. Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when it exceeds 99) and that thisis indicated by a 1
in the tens place of a number.
Unitizing
tens ones
2 0
48. PRODUCTIVE
DISPOSITION
Ability to formulate, represent & solve
mathematical problems using an effective strategy
STRATEGIC
COMPETENCE
PROCEDURAL
FLUENCY
Understanding and using a variety of
mathematical procedures
ADAPTIVE REASONING
Capacity for logical thought, reflection,
explanation, and justification
Inclination to see mathematics as
useful and valuable.
Ability to understand mathematical concepts,
operations, and relationships
CONCEPTUAL
UNDERSTANDING
116. “Spatial thinking, or reasoning,
involves the location and
movement of objects and
ourselves, either mentally or
physically, in space. It is not a
single ability or process but actually
refers to a considerable number of
concepts, tools and processes.”
(National Research Council, 2006)
117. “The relation between spatial
ability and mathematics is so
well established that it no longer
makes sense to ask whether
they are related…”
“…moreover, spatial thinking
was a better predictor of
mathematics success than either
verbal or mathematical skills.”
285. PRODUCTIVE
DISPOSITION
Ability to formulate, represent & solve
mathematical problems using an effective strategy
STRATEGIC
COMPETENCE
PROCEDURAL
FLUENCY
Understanding and using a variety of
mathematical procedures
ADAPTIVE REASONING
Capacity for logical thought, reflection,
explanation, and justification
Inclination to see mathematics as
useful and valuable.
Ability to understand mathematical concepts,
operations, and relationships
CONCEPTUAL
UNDERSTANDING
287. In Math Class
Table Talk…
What would we see, hear and feel in an exemplary
math class?
Write one idea per sticky note.
Identify the groups with a heading/theme/category.
289. In Math Class
Table Talk…
Fold the chart paper into quarters to reflect the
4 aspects of the pedagogical system.
Do your ideas fit/match these categories?
What other ideas can you add?
Instructional
Task
Non-
threatening
Classroom
Environment
Tools and
Representations
Classroom
Discourse
290. Pedagogical System: Understanding
Task
What is a Math Task?
Anyproblem or set of problemsthat focuses students'attention on a
particular mathematical ideaand/or providesan opportunitytodevelopor
use a particular mathematical habit of mind.
High or Low CognitiveDemand
The cognitive demandof a task is the levelof cognitive engagement needed
to completethe task (Stein et al. 2009).
291. A task by itself is not rich;
it is what we do with the task and
how it connects to the pedagogical
system that makes it rich.
Understanding Task
292. Bump It Up
Bump up a task as an Assessmentfor Learning
• Use the Task Cards at your table
• Grade, Topic, Overall Expectation and a Task
• Use the Mathematics Curriculum and find
the specific expectations
• Re-write the task
293. Task: Assessment for Learning
Tom Schimmer’s (Grading From the Inside Out, 2016) premise is that
all assessment practices should be put through two filters:
1. Is it accurate?
2. Does it promote confidence/optimism in students?
“School is no longer about the completion of a series of activities,
but rather the pursuit of proficiency as a set of outcomes that
students achieve through the instructional experience”
296. Understanding Math Tasks
If you deny students the opportunity to
engage in this activity – to pose their own
problems, to make their own conjectures and
discoveries, to be wrong, to be creatively
frustrated, to have an inspiration, to cobble
together their own explanations and proofs –
you deny them mathematics itself.
Paul Lockhart, A Mathematician’s Lament, 2009
Mathematics Learning