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District Math Night 2016
Dis
tric
t M
ath
Nig
ht
20
16
Alicia
Burd
ess &
Jessie
Shir
ley
Decem
ber
6,
2016
Cath
olic E
ducati
on C
entr
e
Who are these people?
Alicia Burdess Jessie Shirley
Alicia has taught mathematics to Jessie’s children.Jessie has fed Alicia’s children a great deal of sugar.**What fraction of time does Alicia spend shopping for groceries?
Jessie and Alicia have worked together since 2010, investigating: • math problems • how students learn• how teachers learn• how the human brain learns math
Our message….that numeracy is as important as literacy
It’s a balancing act
• Program of Studies• Subject Area• Know Thy Students• Pedagogy• Classroom Management
Our Society needs to “re-think” Mathematics
It is socially acceptable to hate math, or not be good at math
David Sousa states,
“Children often say, ‘I can’t do
math!’ But you never hear them
say, ‘I can’t do language!’ Why
the difference?”
Verizon YouTube video
http://www.youtube.com/watch?v=zN9LZ3ojnxY
Millionaire YouTube video
http://www.youtube.com/watch?v=BbX44YSsQ2I
Two Guiding Factors
1. Number Sense
Dr. James Tanton:
“I am not fast when it comes to
computing.”
“Mathematicians do not rely on
standard algorithms – they look
at the problem first, then make a
decision how to move forward.”
Program of Studies
Number Sense is “…the most important foundation of numeracy”
“Number Sense can be developed by producing rich mathematical tasks”
We want to develop “…students who are computationally fluent and flexible with numbers….”
Two Guiding Factors
2. Differentiation
“They (students) will be at varying developmental stages”
It is our job to ensure all students are moving forward with their learning.
Program of Studies
“Concepts should be introduced using manipulatives and be developed concretely, pictorially and symbolically”
PROBLEM SOLVING
BTW….this is meant to be FUN
1. Get yourselves into your groups according to your Toy Story Cards.
2. Make sure your group has a handout of the problem.3. Sit in SILENCE for a minute or two and think individually about
this problem.4. At the signal, TALK within your group about this problem.5. There is a whiteboard, a marker, and manipulatives at your
table.6. Can your group decide on a solution?7. Does everyone in your group understand the solution?8. Would everyone in your group be able to explain the solution to
someone else?
- The Man Who Counted by Malba Tahan
Is it possible to find a satisfactory answer to this problem?
The sheik addressed the three of them:
“Here are my three friends. They are sheep rearers from Damascus. They are facing one of the strangest problems I have come across.It is this: as payment for a small flock of sheep, they received, here in Baghdad, a quantity of excellent wine, in 21 identical casks: 7 full, 7 half full, 7 empty.
They now want to divide these casks so that each receives the same number of casks and the same quantity of wine.
Dividing up the casks is easy – each would receive 7.
The difficulty, as I understand it, is in dividing the wine without opening them, leaving them just as they are.
Learning Mathematics
Bloom’s Taxonomy isn’t always linear, and students can think at higher levels and solve problems, even at the start of their learning, or before they memorize computations.
Students need to solve problems, think about, discuss, and do mathematics.
As opposed to watching their teacher solve problems, think about, discuss, and do mathematics.
Our Program of Studies
emphasizes a varied approach
that accommodates ALL
learners.
The 2007 Math Curriculum
Does this occur in your classroom?
ConnectionsCommunication
VisualizationTechnology
Problem-solvingReasoning
Mental Math/Estimation
“Worksheets don’t grow Dendrites” – Marcia Tate
“The Program of Studies incorporatesseven interrelated mathematical processes that
are intended to permeate teaching and learning.”
For example:
Grade 8
NUMBER
General OutcomeDevelop Number Sense
3. Demonstrate an understanding of percents greater than or equal to 0%, including greater than 100%. [CN, PS, R, V]
Percentages are meant to HELP, not HINDER
100% 50% 25% 10% 5% 2% 1%
$80 $40 $20 $8 $4 $1.60 $0.80
30% of $80?90% of $80?35% of $80?40% of $80?125% of $80?
60% of $80?15% of $80?70% of $80?75% of $80?24% of $80?
100% 50% 25% 10% 5% 2% 1%
$80
What do the Experts Tell us?
John Van De Walle
“The standard algorithms, when introduced too early
and without number sense, can cause difficulty for
many students.”
“Most, if not all, mathematical concepts and
procedures can best be taught through problem-
solving.”
What do the Experts Tell us?
Marian Small
“….differentiating instruction in mathematics is a relatively new
idea….perhaps it is because teachers may never have been
trained to really understand how students differ mathematically”
“….provide tasks within each student’s zone of proximal
development”
What do the Experts Tell us?
Grayson Wheatley
“A curriculum that emphasizes computational methods at the expense
of mathematics concepts and relationships is no longer acceptable”
“Gone are the days when the teacher explains meaningless rules from
the textbook and students only practice computational methods”
Personal Strategies:
develop while students are engaged in mathematical activities
develop and become more efficient over time with multiple experiences
develop through problem solving, group work, number talks
develop thinking and understanding and vice versa
Cuisenaire Rods
Additive Thinking Multiplicative Thinking
Dot Collections
Dot Collections
5-frames
10-frames
10-frames
Balances
Balances
Math Squares
Math Squares
Math Squares
Two Ways
Two Ways
Fractions
Decimals
Examples of Personal Strategies for Addition
Examples of Personal Strategies for Subtraction
Examples of Personal Strategies for Multiplication
Examples of Personal Strategies for Division
(Seriously…..let’s stop torturing children)
Long Division is uselessand
Mad Minutes are cruel
Closing Points
Number Sense
Develop a STRONG foundation of number sense in students
Differentiation
Mathematics requires differentiation
Questions?
Websites
http://www.aliciaburdess.com/resources-and-websites.html
https://www.youcubed.org/week-of-inspirational-math/
http://learning.arpdc.ab.ca/course/view.php?id=351
http://www.peterliljedahl.com/
References
Alberta Education, Mathematics K-9 Program of Studies, 2007
Change the Equation website. http://changetheequation.org, 2013.
National Council for Teachers of Mathematics, Mathematics Assessment Sampler, 3-5, 6-8, 2005
Small, Marion, Good Questions and Great Ways to Differentiate Mathematics Instruction, 2009
Sousa, David, How the Brain Learns Mathematics, 2008
Van de Walle, John, Teaching Student-Centered Mathematics, K-3, 3-5, 5-8, 2006
Wheatley, Grayson, Developing Mathematical Fluency, 2007
Alicia Burdess, District Lead for Mathematics
Jessie Shirley, Asst. Superintendent, Teaching and Learning
Thank you for your time!
How about those Multiplication Tables?
Memorization should NOT be the main component of instruction
“The result is that as children spend their time memorizing arithmetic tables and facts, they become little calculators who can compute without having any idea of the underlying arithmetic principles involved.
When students attempt to carry out simple arithmetic computations using memorized facts, they often jump to conclusions without considering the relevant conditions of the problem. They become so skilled at the mechanics of computation that they arrive at answers that do not make sense” – Sousa, 2008, p. 57
6 x 4 = 24
Learning multiplication facts using arrays.
