WORKSHOP 1 - A HANDS-ON APPROACH TO ARITHMETIC AND ALGEBRA IN DIFFERENT LEARNING SPACES: PHYSICAL, VIRTUAL, AND HYBRID MODELS
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Common Core Basic Education (CCBE)
MICHELINE AMMAR, Pedagogical Consultant
Martin Francoeur, Pedagogical Consultant
Louise Roy, Pedagogical Consultant Recit MST
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Welcome!
Please go to
https://www.wooclap.com/AGEMATH
and write your name, school board, and what level of math do you teach?
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Housekeeping
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AGENDA
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Introduction
Micheline Ammar, Louise Roy, Julie Bourcier Nicole Martin
Martin Francoeur, Richard Painchaud
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By the end of the workshop you will:
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Our teaching realities
Students’ Evaluation criterion have changed from knowledge based to competency based
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Complex situation
The city of Montreal has an extensive highway network. Large sums of money must be set aside each year for maintenance.
In this city, a 6-lane highway (3 lanes in each direction) with a width of 3.5 m/lane, a length of 2 km and a thickness of 10 cm, costs $800,000 of asphalt. To asphalt a highway, 5 employees work at a salary of $50/hour each.
Task 1: The city wants you to produce an algebraic model that will allow the mayor to determine the cost of paving a highway based on the volume of asphalt required and the number of hours worked by city employees.
Task 2: The City Hall office would now like you to determine the price of a future 3.5 km long, 4-lane road that would be the same thickness as the previous one and would take 35 hours to pave?
Author: Marc-André Poirier, Centre l’Avenir, CSA, juin 2015
Source : http://reussirpermis.com/depasser-sur-autoroute
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Learning Situation vs. Situational Problem
Learning situation | Situational Problem |
-Guided -Divided into activities that aim to strength the problem solving skills required to solve the learning situation | -Not guided -Student only receive a description of the problem, the task, and relevant information |
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Competencies
In adult education as you may all know we have 3 competencies.
C1: Interpretation (decoding) & Representation
C2: Planification strategies and carrying out of the chosen strategy to resolve the problem
C3: Communication of results
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Resolution of problems:What is student is evaluated on
Problem solving | Steps | Questions |
Interpretation & Representation | Identify , gather, and organize information | How well can I gather and organize information when solving a problem? |
Model | Model the problem (manipulative, drawings, diagrams, writing out equations, creating a graph…) | How well can I model the problem? Do i need math manipulative to represent the problem? |
Planification | Strategize: choose a math strategy ( or several different strategies) | Did i use different ways to illustrate the problem? Did I pick a math strategy A and Math strategy B to solve? |
Resolution | Use the chosen math strategy to create and test a solution to see if it makes sense ( you can try other strategies too) | How well can I choose and apply one or more problem solving strategies? Did i answer the question? Does the answer make sense? |
Reflection | Reflect on the process | What did we try, how did it work out? What would you do same/different next time?Could we have solved it with fewer steps? What did we learn? |
Slight adaptation from https://building21.org/open_resources/math-competencies-and-continua/
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Math Strategy?
It is an approach to finding a solution to a problem. It is similar to choosing the right tool for the job.
If you are a plumber and you’re trying to unscrew a bolt, which tool will you use?
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Math Strategy?
The tool you choose depends on the problem you’re trying to solve. Sometimes we need multiple tools to get the job done. It’s the same way with math strategies.
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Example of Math Strategies
https://garyhall.org.uk/maths-problem-solving-strategies.html
Visualize | Manipulate materials to connect to the problem. Draw a picture. Many pictures might lead to correct solution. Label your steps as you resolve. |
Experiment | Trial and error (Guess and check)! |
Use a table/make a list | Sort and group relevant information, list all possibilities. |
Logical reasoning | Examine and generalize relationship. |
Find pattern | Look for patterns, regularities, symmetry in the problem and in the solution (s). Use pattern to find the missing information. |
Working backwards | Start at the end of a problem, and work step by step toward the beginning to get a solution. Make a list of what you know and what you don’t know. Write down each step as you get closer to the answer the last step will verify that the solution works. |
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Math manipulatives and math representation strategies are important tools to fortify and deepen math understanding.
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Do you currently use any math manipulative?
What kind?
To answer Go to https://www.wooclap.com/AGEMATH
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What are math manipulatives?
WORKSHOP 1 - A HANDS-ON APPROACH TO ARITHMETIC AND ALGEBRA IN DIFFERENT LEARNING SPACES: PHYSICAL, VIRTUAL, AND HYBRID MODELS
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Why use manipulatives
Which would You rather do? To answer go to https://www.wooclap.com/AGEMATH
A B
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Why Use Manipulatives?
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Why Use Manipulatives?
P78 Principals to Actions, NCTM, 2014
Beliefs on tools and technology in learning mathematics | |
Unproductive beliefs | Productive beliefs |
Physical and virtual manipulatives should be used only with very young children who need visuals and opportunities to explore by moving objects | Students at all grade levels can benefit from the use of physical and virtual manipulative materials to provide visual models of a range of mathematical ideas. |
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Why Use Manipulatives?
I hear and I forget.
I see and I remember.
I do and I understand.
-Confucious
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Big idea behind the use of manipulatives
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4 effective math teaching elements are:
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Suggested reading: https://www.edutopia.org/article/math-manipulatives-hiding-junk-drawer
Research publication https://www.jstor.org/stable/749423?seq=1
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C-R-A
Concrete: Math manipulatives (physical/virtual)
Representational: Use of Drawing, diagram, tally marks, Venn Diagram…
Abstract: The use numbers and symbols
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Benefit of CRA
-Remove language barriers
-Show the student’s understanding or not
-Add tools to their toolbox
-Stimulate discussions and exchanges
-Stimulate Creativity
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Any questions so far?
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In Class Hands-on Activities Examples
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Example1: Comparing fractions
Task 1: Make 2 different fractions with the same denominators but different numerators.
Using the CRA model
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Example1: Fraction
C: Use Fraction sticks
R: Sketch it on a Paper
A: Use numbers and symbols to communicate 2/4 > 1/4
Discussion
Two fourths is larger than one quarter because ¼ is less in size
If the denominators are the same, than the larger the numerator the greater is the fraction
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Ex2: Compare fractions
Task 2: Make 2 different fractions with the same numerators but different denominators.
Using the CRA model
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Example2: Fraction
C: Use Fraction sticks
R: Sketch it on a Paper
A: Use numbers and symbols to communicate 3/4 > 3/5
Discussion
Three quarters is larger than three fifth because ⅗ is less in size
If the numerators are the same, than the larger the denominator the smaller is the fraction
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Ex3: Variables
Play a game of cards (21) including the Joker cards in the deck. Take a picture of three hands with the joker in them.
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Example3: variable
C:
R: Sketch it on in your notebook
J=10 J=8 J=4
A: Discussion:
Joker is the same card in all hands yet it has a different value therefore the Joker is a space holder. It takes the value of the missing card in the game. In math The joke is like X or variable J.
J
J
J
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Examples of
Virtual Math Manipulatives & Activities
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Virtual Platform Graspable math
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The Hybrid Model
Hybrid learning model is when some students are being taught remotely while others are being taught in class at the same time.
Teachers can animate the same activity in class or virtually using math manipulative to deepen their math learning.
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The Blended Model
Often Blended learning gets confused with Hybrid learning.
Blended learning combines in-person teaching with asynchronous learning methods, where students work on online exercises and watch instructional videos during their own time.
Teachers can plan some in class activities and some
online activities and choose whatever in class math tool or virtually math tool to deepen the math understanding.
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How to use Manipulatives
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Use Blooms taxonomy as your guide in the choice of the Hands-on activity
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Effective Pedagogical Tool: The Art of Questioning
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Food for Thought
In play
We lose, we win, we are ok. It is fun! It is part of the game.
We keep trying, we observe, we ask questions and we continue to play the game.
In math
We win --> we pass!
We lose --> we fail!
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Resources available to you:
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Take away:
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Invitation to Action
your liking
couple of weeks.
We are inviting you to meet with us (Nicole and I) on Feb 12 at 12:00 to share your feedback on what worked and what didn’t.
https://sites.google.com/cssmi.qc.ca/fnm/english-sector
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Q&A
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