Primary / Junior

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Primary / Junior Mathematics
Mathematical Development in the Early Years
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David Watson

• Teacher for 41 years (Toronto and London)
• Rewired in teaching / software development
• 3 children (all teachers) - 2 are graduates of
  Althouse programs
• Contact
• dwatson3_at_uwo.ca
• Course Resources Preservice Web Pages
• Home 519453-4161
• Althouse Room 2045
• Office Hours to fit your needs

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Sam
Alli
Gillian
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Course Text

• Becoming A Mathematics Teacher
• Dr. George Gadanidis Althouse College, UWO

Curriculum Guide
The Ontario Curriculum - Grade 18 Mathematics
Career texts
Teaching Developmentally Elementary and Middle
School Mathematics (Pearson) John Van de
Walle Making Math Meaningful (Nelson) Marian
Small
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The Mathematics CurriculumTreasure Hunt
With a partner

• 1. Note Grade Designations
• 2. Find and highlight the 5 strands
• 3. Locate Overall / Specific Expectations and
  note differences
• 4. Check the glossary at the back
• 5. Where does curriculum come from?
• 6. Who determines what is valued?
• 7. Make yourself a simple look-up code.

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Skill Categories (Pages 11-17) The Mathematical
Processes

• Problem Solving

• Reasoning and Proving

• Reflecting

• Selecting Tools and Computational Strategies

Important Reading!

• Connecting

• Representing

• Communicating

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Course Outline

• Workshop Dates see Journal Page
• Assignments essential skills for teachers
• Exemplary Mathematics Resources - (50 value)
• Lesson Plan and Rubric 20
• Unit Plan 30
• Mathematics Essay - 20 value
• Reflection and Participation - 30 value
• Classroom work - 10
• Online work - 10
• Journal - 10

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Assignment 1 Exemplary Mathematics Resources
Lesson Plan - due before second
practicum Reference a. Template handout (web
page assignments) b. Rubric a frame for
evaluation
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Assignment 2 Exemplary Mathematics Resources
Unit Plan due second term Teaching Teams
random draw Teams posted on web
pages Reference a. How would you teach that? b.
Rubric a frame for evaluation
Template on web
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Assignment 3 Math Essay
Final class 30 minutes Reference Math4Teachers
problem solving exercises Essay content a. the
math found in the problems b. Pedagogy -
implications for teachers using the problem
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Assignment 4 Reflection and Participation
1. Journal entries evidence of personal and
professional growth 2. Classroom and online
presence 3. Postings that reflect the required
readings
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Web Pages

• http//preservice.edu.uwo.ca
• Use these to get
• PowerPoint Files
• Additional course resources
• Copies of handouts (Word.doc format)
• Access to content discussion areas (online)
• Communication tools

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Mathematics Survey Test
No Calculators
15 Minutes
How do most people feel about Mathematics?

• 1. Anxiety / Math Phobia / Panic
• 2. Badge of Honour
• 3. Teacher Actions / Responses
• 4. Routine of Math Handcuffed to a textbook
• 5. The easiest subject to teach . Poorly

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Math
The Science of Mathematics

• Collection of rules to memorize / follow
  directions
• Arithmetic computations
• Mysterious algebraic equations
• Geometric proofs

• Making sense and deeply understand mathematical
  objects
• Data / Form
• Change / Patterns
• How to Think not What to Think (Burns)

But to master these bits and pieces is no more
doing Mathematics than playing scales on a piano
is making music. Van de Walle 2002
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"Young children enter school mathematically
curious, imaginative and capable. They have to
learn to be otherwise. "
Papert 1980
7 year range
Ability in Mathematics
3 year range
0 5
13
Years
Prime Study Ohio State 2005
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Many grades . Many levels of achievement
Every teacher has a split grade every year.
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Teacher Notes
1. New teachers . being stretched.. 2. Primary
teachers need more than a primary math
background 3. Math4Teachers 4. Activities
initiate classroom ideas . seldom completed 5.
Stay aware of how you feel about changes.
(frustration) 6. Be patient with yourself . 7.
Learning is social / mistakes are opportunities
to learn.
Our Goals
1. Pedagogical content knowledge. 2.
Methodologies built on an understanding of how
children develop and think Mathematically.
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English / Language / Literacy and Mathematics /
Numeracy / Mathematical Literacy are not
subjects but sets of tools.
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Design Tasks to promote Mathematical Thinking
1. A farmer buys a horse for 50.00
2. Later, he sells it for 60.00
3. He buys the horse back for 70.00
4. He sells it a second time, but now for 80.00
Did he make or lose money? If so, how much?
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Constructivism
Children dont absorb ideas as the teacher
presents
"AHA" moment
Children are creators of their own knowledge
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I "learn" it ... but do I own it?
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3 groups of 5, no matter what the groups are.
Depth of conceptual understanding and use in
problem solving create ownership.
5 5 5
3 shirts
5 pants

15 outfits
3 x 5 15
5 more than 2 x 5
Half of 6 x 5
Rate
5 less than 4 x 5
5 km/hr for 3 hours
5 units
Area model
3 units
5 5 5
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"AHA"
Learning Objects
Manipulatives
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Roberto is shopping with his mother in a
large department store with many floors. They
enter the store on the middle floor from a skyway
and go to the credit department. They go up three
floors to house wares and then down five floors
to the childrens department. Then they go up six
floors to the TV department. Finally, they go
down ten floors to the main entrance, which is on
the first floor and leave to go to another store
down the street. How many floors does
the department store have?
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Active vs. Passive Classrooms
Mathematical ideas cant be poured into a
learner. Indeed, passive learning is an
oxymoron. The student needs to be mentally active.
List 5 indicators that might suggest an active
learning environment during a Math lesson.
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Solving Math Problems
Ultimately the reason for doing Mathematics in
the first place.
An activity for which students have no prescribed
or memorized rules / methods.
There is no perception by students that there is
a specific / correct solution.
An on-ramp exists for all learners.
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1 2 3 4
How many blocks will we need to make 10 shapes in
this pattern?
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The young Mathematician ..
Concrete- Operational
Abstract Thinker
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Problem Solving Strategies
1. Draw a picture (make a model) 2. Simplify 3.
Elimination 4. Make a table 5. Find a pattern 6.
Guess (Estimate) and Check
There is a need to formally teach these.
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Pattern Searching
4PA9
Term 1
2
5
3
4
How many toothpicks are used to make any given
number of squares?
How will you lead students to resolve this
pattern? Try a table of values.
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Growing Patterns Perimeter and Pattern Blocks
1.
4.
2.
3.
1.
2.
3.
4.
3M13
2.
1.
3.
4.
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What else might pattern here?
Term No. of White No. of Red
1
2
3
4
5
6

10
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This weekOnline Module 1Mathematical
Developmentin the Early YearsThinking
MathematicallyComplete Content/ Reference pages
/ and make 1 group posting