Making Math Contextual, Visual, and Interconnected Using Technology

Making Math Contextual,
Visual, and Interconnected
with Technology
@MathletePearce
tapintoteenminds.com

@MathletePearcewww.tapintoteenminds.com

Noob

Effective
Instructional Practice
Embedding
Technology
SAMR Model
Progression
MYCI

SAMR Model
Progression
Effective
Instructional Practice
Embedding
Technology

STUDENT
LEARNING
NEEDS

Math

Math Class

1. Take Up Homework
Math Class

2. Deﬁnitions, Formulae, Procedures/Algorithms
1. Take Up Homework
Math Class

3. Examples
1. Take Up Homework
Math Class

4. Homework
3. Examples
1. Take Up Homework
Math Class

Example 1
(a) List all combinations of three out of
the four colours: red, blue, white, and
green.

Example 1
(a) List all combinations of three out of
the four colours: red, blue, white, and
green.
(b) Considering the colour combinations
as arrangements with indistinguishable
elements, check the number of
combinations of three out of four items.

Result

Two Groups of
Students
Result

Two Groups of Students
Good at
Math

Good at
Math
Not
Good at
Math

Good at
Math
Not
Good at
Math
Know:

Good at
Math
Not
Good at
Math
Know:
terminology

Good at
Math
Not
Good at
Math
Know:
terminology
procedures

Good at
Math
Not
Good at
Math
Know: Know:
terminology
procedures
terminology
procedures

Good at
Memorization

Good at
Memorization
Not Good at
Memorization

Good at
Memorization
Not Good at
Memorization
Struggle with
unfamiliar
problems

TEST QUESTION

TEST QUESTION
=

TEST QUESTION
=
EXAMPLE

TEST QUESTION
=
HOMEWORK

TEST QUESTION
=
TEXTBOOK

UNFAIR

Good at
Memorization
Not Good at
Memorization
Struggle with
unfamiliar
problems
UNFAIR

Kyle Pearce

Good at
Math
Not
Good at
Math
Kyle Pearce

New Knowledge

New Knowledge
Prior Knowledge

MATH

MATH
SILO
1
SILO
2
SILO
3
SILO
4

A VISION FOR
MATHEMATICS
EDUCATION
VISION

VISION

Contextual
VISION

Visual and Concrete
Contextual
VISION

Interconnected
Visual and Concrete
Contextual
VISION

Interconnected
Visual and Concrete
Contextual
CONFIDENCE

Interconnected
Visual and Concrete
Contextual
PERCEPTION

Interconnected
Visual and Concrete
Contextual
STUDENT
SUCCESS

“He’s Crazy”

Change

Immune to
Change

1. Take Up Homework
3. Examples
4. Homework
trend in mathematics

trend

trend
unnoticed

trendunnoticed

1. Content of Interest to Teacher
trendunnoticed

2. Introduce skills today to solve
a problem tomorrow
trendunnoticed

a problem tomorrow
3. Dedicate time creating a resource
trendunnoticed

a problem tomorrow
4. Homework rather than “real work”
trendunnoticed

not just math…

Reﬂecting

how I learned…

a problem tomorrow
how I learned…

How it ends…

Eva Rinaldi from Sydney Australia [CC BY-SA 2.0]

Not quite.

creative
=

memorize

meaning.
memorize
without

“a natural”

how he learned…

1. Content of Interest to Teacher1. Content of Interest to
how he learned…

how he learned…
1. Content of Interest to STUDENT

a problem tomorrow
how he learned…
1. Content of Interest to STUDENT

a problem tomorrow
how he learned…
1. Content of Interest to
a problem
STUDENT

how he learned…
STUDENT1. Content of Interest to
a problem TODAY

how he learned…
a problem TODAY

how he learned…
a problem TODAY
3. Dedicate time

how he learned…
a problem TODAY
3. Dedicate time PRACTICING

how he learned…
a problem TODAY

vs.

http://www.vancouversun.com/life/From+geek+chic/6296707/story.html
Photograph by: Maggie Wong

http://www.wykamath.com/

@MathletePearcewww.tapintoteenminds.com https://mathstrategies.wordpress.com/tag/numb3rs/

algorithm

what’s
this?

algorithm

algorithm
s
engagement
=

algorithm
s
understanding
=

Workﬂow

“Which math apps
should I use?”

EVERGREEN

GoodNotes 4

Google Drive

Doceri

Effective Teaching
Practice

Transformational
Technology Use
Effective Teaching Practice
BEFORE

QUESTION

QUESTION
Mr. Pearce stacks reams of paper vertically
against a wall. If the height of 5 reams is
24.75 cm and the height of the room is
273 cm, how many reams of paper would
he need to reach the ceiling?

QUESTION
he need to reach the ceiling?FUN, RIGHT?

How many packs of paper would
it take to reach the ceiling?
Stacking Paper

PREDICTIONS

REQUEST
INFORMATION

How many packs of paper would
it take to reach the ceiling?
Stacking Paper
273cm
24.75cm

AnswerKey:55.15
QUESTION
he need to reach the ceiling?

How many packs of paper would it
take to reach the ceiling?
Stacking Paper
24.75cm

24.75 cm

24.75 cm
5 reams

24.75 cm
5 reams
= 4.95 cm

4.95 cm273cm

4.95 cm
273 cm

4.95 cm
=
273 cm 55.15
reams

How many packs of paper would it
take to reach the ceiling?
How many packs of paper
will it take to reach a
height of 273 cm?
packs of paper
height
273cm
4.95 cm

@MathletePearcewww.tapintoteenminds.com @MathletePearcewww.tapintoteenminds.com
A
B
short way
long
way

Understand how to get there the long
way before taking shortcuts.

Making Connections

packs of paper height
Independent Dependent
273cm
4.95 cm

0 0
1 4.95
2 9.9
4 19.8
40 198

packs of paper height:

packs of paper
height

packs of paper
height
24.75 cm
5 reams
=

24.75 cm
5 reams
=
273 cm
How Many?

5 reams
=
x
24.75 cm 273 cm
x ??

5 reams
=
x24.75 cm
273 cm
x ??

5 reams
=
x24.75 cm
273 cm
x ??
11.03

24.75 cm
5 reams
=
273 cm
11.03x
x

24.75 cm
5 reams
=
273 cm
55.15 reams
11.03
x 11.03
x

The Next Day…

How tall is the table?
130.75cm
4.95 cm

How tall is the table?130.75cm
5
packs130.75 5
4.95 cm

5
packs130.75 5
4.95 cm
Slope

5
packs
130.755
4.95 cm
Slope
)x y
(

3. Connections

In the past…

4. Consolidate

Consolidation

5
packs
130.755( )x y4.95 cm
Slope
2 1515
130.75cm

packs
( )x y
2 15151

packs
( )x y
2 1515
1
5
1
52
y = m x + b
2
( )
1 pack

packs
( )x y
2 15151 55
2 2( )
1
1y = m + b( )
5
1 pack

packs
( )x y
2 15151
5
5
2 2( )
1
1y = m + b( )5
1 pack

1pack
packs
( )x y
2 15151
5
5
2 2()
1
1y = + b()5 2

1pack
packs
( )x y
2 15151
5
5
2()
1
1y = + b()5 2
-2-2
2

1pack
packs
( )x y
2 15151
5
5
2()
1
1y = +b()5 2-2-22
3
3

1pack
packs
( )x y
2 15151
5
5
2()
1
1y = +b()5 2-2-2
2
3
3
y = 2x + 3

Struggle with
unfamiliar
problems
Good at
Math
Not Good
at Math

Good at
Math
Not Good
at Math
Struggle with
unfamiliar
problems

Interconnected
Visual and Concrete
Contextual
MATH

Interconnected
Visual and Concrete
Contextual
TASKS
CONNECTIONS
MATH

Interconnected
Visual and Concrete
Contextual
MATH
TASKS
INQUIRY
CONNECTIONS

Interconnected
Visual and Concrete
Contextual
MATH
TASKS
CONNECTIONS
INQUIRYCONSOLIDATE

3 ACT TASKS
/3act-math@MathletePearce www.tapintoteenminds.com @JustinLevack
iTunes U
kylep.ca/curiousmath1p

@MathletePearce
EVERGREEN
kylep.ca/curiousmath1p

MATH APPS
@MathletePearcekylep.ca/curiousmath1p

Interconnected
Visual and Concrete
Contextual
MATH
TASKS
CONNECTIONS
INQUIRYCONSOLIDATE
@MathletePearcekylep.ca/curiousmath1p

2x - 4 = 8
Solve for x:

2x - 4 = 8
Solve for x:
+ 4 + 4

2x - 4 = 8
Solve for x:
+ 4 + 4
2x = 12

2x - 4 = 8
Solve for x:
+ 4 + 4
2x = 12
2 2

2x - 4 = 8Solve for x:
+ 4 + 4
2x = 12
2 2
x = 6

GAMIFICATION

0
0

0
0
-
+

0
0
-
+
-
+

0
0
0
0

0
0
0 = 0
xx

0
0
x
0 = 0x+
-aa-
a
-
+

0
0
x
-a
+a
= 00 x a a+ -
b
b
+
-
+

0
0
x
-a
+a
-b
+b
=0 x a a+ - + 0 b b+ -
c
d
+
+

0
0
-a
+a
-b
+b
x
+c
+d
0 x a a = 0 b b c d+ - + + - + +

-a
+a
-b
+b
x
x a a = b b c d- + - + +
+c
+d
+0 +

+c
+d
-a+a
-b
+b
x
x aa = b b c d-+ - + +
0
0

+c
+d
-a+a
-b+b
x
x aa = bb c d-+ - + +
0
0
0
0

+c
+d
x
xaa = bbc d- - ++0 0

x = bbc d+

VISUALIZATION

VISUALIZATION
without an
APP

Find the area of a rectangle with
a length of 6 and a width of 2.
2
6

What is the area of the egg carton?

Area = lw

Area = 2w

Area = 2 6( )

Area = 12 eggs-squared2 6 =( )

ASSESSMENT

GRADE BOOK

ASSESSMENT
by
STANDARD

STANDARD
BASED
GRADING

ASSESSMENT GAMIFIED
WITH BADGES

Products
Assessment

Products
Conversations
Assessment

Products
Conversations
Observations
Assessment

Products
Conversations
Observations
AssessmentPROFESSIONAL
JUDGEMENT

Accurate Assessment
Assessment Day (Feb 10)
I can solve with pythagorean theorem visually

90%
Accurate Assessment

Assessment Day (Apr 7)
Accurate Assessment
90%

90%
60%
Accurate Assessment

90%
60%
YOU submit a screencast of a task: (May 5)
Accurate Assessment

90%
60%
88%
YOU submit a screencast of a task: (May 5)
Accurate Assessment

TEACHERS

iTunes U iBooks Author

iTunes U iBooks Author
kylep.ca/pythagorean-itunesu

@MathletePearce
STUDENTS
CREATIVE
are
kylep.ca/pythagorean-itunesu

Desmos
@MathletePearcekylep.ca/pythagorean-itunesu

@MathletePearcekylep.ca/pythagorean-itunesu

STUDENT

STUDENT
VISIBLE
thinking

DIFFERENTIATE

Good at
Math
Not Good
at Math
24.75cm
ASSESSMENT GAMIFIED
WITH BADGES

thing.every

Transformation
Enhancement

Enhancement
Transformation

thingevery .

one thing.

step.one

one vision.

thing.
one

AMAZING
thing .s

BIGGERand
better

?
thing
NEXT
what is your
AMAZING

Making Math Contextual, Visual, and Interconnected Using Technology

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