Teaching mathematics what the research says a sample or three
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Teaching Mathematics What the Research Says: A Sample or Three. Expert Panel Reports. 30 Years of Research The Same Message at all levels: K-12 Drives the training, the resources Summary provided (by me). Teaching Through Problem Solving. the reason for math to exist

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Teaching mathematics what the research says a sample or three
Teaching MathematicsWhat the Research Says:A Sample or Three


Expert panel reports
Expert Panel Reports

  • 30 Years of Research

  • The Same Message at all levels:

    K-12

  • Drives the training, the resources

  • Summary provided (by me)


Teaching

Through

Problem Solving

  • the reason for math to exist

  • nobody does a sheet of math for fun

  • 3 part lesson

    • pose & discuss problem

    • students solve the problem

    • debrief

  • See New Curriculum Sample



Creating

a

Learning

Environment

  • 50% of the population suffer from math anxiety or math avoidance

  • teachers teach as they have been taught

  • mistakes are opportunities to discuss & learn (see communication)

  • take risks (see above)

  • arithmetic has one answer but mathematics has multiple solutions


Creating

a

Learning

Environment

  • children come to school as natural mathematicians – we beat it out of them

  • equity means each child has the right to be taught with methods that are most effective for them

  • at risk students learn best in a problem solving environment full of talk and communication


Promoting

Communication

  • students must speak to learn

  • a predominately silent math classroom is one where learning has been minimized

  • students can only write if they have been in a classroom where they have talked and listened

  • a math problem is the most complex text to read

  • math is where hands-on learners are successful – the perfect place to start reading & writing


Establishing the

Big Ideas

of

Mathematics

  • teaching mathematics around central concepts – not as a checklist of skills

  • understanding to create proficiency

  • Big Ideas of Number Sense

    counting

    quantity

    operational sense

    (relationships)

    (representation)

    proportional reasoning (Junior +)

  • See New Curriculum Sample


Using

Manipulatives

  • modeling mathematics through concrete materials and digital technology

  • an effective method to create understanding for all students – nothing to do with ability

  • essential for some learners

  • count the references to concrete materials in the Grade 3 number sense


Assessing

Effectively

  • main purpose of assessment to create learning (formative & feedback)

  • focused observation is the most effective tool and is the predominate tool for assessment and evaluation in the primary division

  • variety of tools (observations, performance tasks, journals, portfolios, investigations, self-assessment, tests (Gr. 3 & up)

  • only assign a grade or mark for summative tasks – grades do not increase learning


Expert panel reports summary

Positive Learning Environment

the learner

the classroom environment

equity

home connections

special needs/at risk

scheduling

teachers

Problem Solving Process

problem solving

making connections

lesson design

Expert Panel Reports Summary

  • All Learning Involves Communication

    • communication

    • language

  • The Big Ideas of Math

    • Big Ideas

    • Algorithms & Formulas

  • Learning Tools

    • concrete material

    • digital technology

  • Assessment for Learning

    • assessment


Sample Lesson

Think-Pair-Share

Think: How would you add these numbers?

24

36

48

72

Pair: 1. With your partner (group), discuss how you added the numbers.

2. Record the different methods in your group journal. (Pictures, numbers, words)


Sample Lesson

Think-Pair-Share

Share: Go to the front and share your groups solutions with the class.

In you journal:

Describe your favourite method and one other person’s method of adding these numbers.



Early Primary

Samples


Tell me what you know about 5 diagnostic week 1 grade 1
Tell me what you know about 5.(Diagnostic – Week 1 Grade 1)

5



One more than two more than facts
One More Than/Two More Than Facts

This strategy covers 36 basic facts.

They have either an addend of 1 or 2.

8 + 2 more

3 + 1 more









One more than

5

One More Than


Two more than
Two More Than

Let’s try two more for the following dot plates.


One more than two more than 36 facts

+

0

1

2

3

4

5

6

7

8

9

0

0

1

2

3

4

5

6

7

8

9

1

1

2

3

4

5

6

7

8

9

10

2

2

3

4

5

6

7

8

9

10

11

3

3

4

5

6

7

8

9

10

11

12

4

4

5

6

7

8

9

10

11

12

13

5

5

6

7

8

9

10

11

12

13

14

6

6

7

8

9

10

11

12

13

14

15

7

7

8

9

10

11

12

13

14

15

16

8

8

9

10

11

12

13

14

15

16

17

9

9

10

11

12

13

14

15

16

17

18

One-More Than/Two-More Than *36 Facts*


Facts to 10
Facts to 10

  • Use 10 Two-Colour Counters

  • Shake them in your hand

  • Drop them

  • Place them on the 10-Frame

  • Write a number sentence to represent this

  • remove the reds from yours and your partner’s. Add the yellows using the frames

  • You can do this for any number


How Would You Add These?How Would You Subtract These?

How many dots in all?What is the difference between the number of dots on these two plates?


Morgan has 7 apples jesse has 9 apples how da ya like dem apples
Morgan has 7 apples. Jesse has 9 apples. How da ya like dem apples?

  • show using counters and no frames

  • show using counters with frames

  • show using a numberless number line

  • show using abstract numbers

  • show using distributive property to demonstrate strategies

  • Why did I choose 7 and 9?




De brief grade 2
De-Brief – Grade 2 apples?

Last time for Pizza Day we ordered 37 slices of pizza. This time we need to order 13 more slices. How many pieces of pizza do we need to order?


Late Primary/ apples?

Early Junior

Samples


Race to 100
Race to 100 apples?

Race to 0



How do you teach apples?“Long Division”



Find a way to represent 13 x 12 using the base ten materials

10 x 3 apples?

10 x 10

2 x 3

2 x 10

Find a way to represent13 x 12Using the base ten materials

13

x12

100

30

20

6


Open arrays doubling halving
Open Arrays apples?doubling & halving

  • 10 X 13

  • 2 X 13

  • 12 X 13

  • 6 X 26


Open arrays doubling halving1
Open Arrays apples?doubling & halving

  • 6 x 8

  • 12 x 8

  • 12 x 16

  • 24 x 16

  • 12 x 32

  • 6 x 64


Open arrays doubling halving x2 2
Open Arrays apples?doubling & halving(x2,/2)

  • 7 x 7

  • 3½ x 14

  • a similar strategy (no paper allowed)

  • 8 x 4

  • 0.08 x 400


Late Junior apples?


The lesson takes place in a Grade 5 classroom towards the end of the school year. Ms. H teaches a class with a wide range of abilities, both in mathematics and literacy. In the first phase of the lesson Ms. H poses an opening problem for a unit on division: “I have a problem. I have a jar which I know held 317 marbles when it was full. As you can see, it is empty, and I want to fill it full of marbles again. At my corner store I can buy small bags of marbles, with 23 marbles in a bag.” She holds up the jar and the small bag of marbles. “I want to go to the store and buy enough bags but no extras. How many bags should I buy?”


Ms. H has not yet taught a standard algorithm for division, although a few students have seen it at home. Rather than going through the steps of division, students talk about the problem and look at the jar and the small bag of marbles.

Then they return to their seats to work in pairs. Each pair has a jar and a small bag of 23 marbles.


Math Quiz although a few students have seen it at home. Rather than going through the steps of division, students talk about the problem and look at the jar and the small bag of marbles.


Math Quiz although a few students have seen it at home. Rather than going through the steps of division, students talk about the problem and look at the jar and the small bag of marbles.

8

1


There are 134 different subtraction algorithms internationally
There are 134 different subtraction algorithms internationally

  • Research clearly shows that effective math instruction has students creating their own “algorithms” (see Grade 3 Number Sense)

  • Discussing and listening to others algorithms

  • Examining “standard’ algorithms

  • When professional mathematicians are given computation questions: 95% do not use standard algorithms.

  • Look to the numbers & use strategies!


Fractions internationally

(Proportional Reasoning)


Tangram exploration
Tangram Exploration internationally


Tangram peanut brittle
Tangram Peanut Brittle internationally

The “Dentists Love Us” candy company has decided to produce “top-of-the-line” peanut brittle. A full square of brittle costs $3.20. But you can buy a tangram piece for a proportional amount. How much would you pay for each type of tangram piece. Be prepared to explain whether you used fractions, decimals, division, or some other method.


Hypothesis: internationally

The formula for area of a trapezoid is in fact a generalized formula for the area of all triangles and quadrilaterals.

Demonstrate this for all triangles and quadrilaterals. (or determine how many cases it holds true for)

Prove algebraically. (Or prove for as many cases as it holds true for)

Area of Trap = (a + b) h

2


Area of Trap = (a + b) h internationally

2

a

h

b


Forward to the new basics
Forward to the New Basics internationally

There is a difference between being a dedicated caring teaching and being an effective teachers.

Dedication and care is the prerequisite that is necessary to be a teacher.

Effective starts with caring but only progresses with research-based methods and techniques.


Forward to the new basics1
Forward to the New Basics internationally

We are the only profession where a practitioner of 100 years ago would recognize most of what goes on in most situations today.

This is a major cultural shift. (Remember that term “Paradigm Shift”?


Forward to the new basics2
Forward to the New Basics internationally

Drive by in-service will not create the shift.


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