as an educator and a technological
innovator I’m always looking for
practical and purposeful ways to use
technology to enhance teaching and
learning and today I would like to share
with you some of my ideas as to how
technology can be used as a pedagogical
tool in order to aid in math literacy
now when it comes to the subject of math
at least if internet memes are any
indication at all the subject is met by
students with feelings of confusion
frustration and downright dread so why
is this well some people might surmise
that these negative feelings associate
at a company students when it comes to
math is due to difficulties they might
be having in grasping the concepts that
are associated with math and assumptions
aside this notion that students have
difficulty with math concepts is
actually substantiated by data according
to the pro according to data gathered
from the program of international
student assessments students in the u.s.
ranked 40th in math 40th out of in the
world out of 70 tested countries so we
have 15 year olds in the u.s. that are
being outperformed out ranked in math by
their international counterparts and
teachers the nation over our bemoaning
the fact that students just tend to lose
interest in math after the fifth grade
so why is this even an issue
well lack of affinity and aptitude for
math equals lack of affinity and
aptitude for STEM fields and in a world
that is becoming increasingly technical
where technological innovations are
being made at exponential rates where
occupations in STEM fields are projected
to grow
this is a disconcerting statistic and
even though the m4 math comes last in
stem the acronym for science technology
engineering and math it is the most
essential because conceptual
understanding of math is a requisite for
STEM fields in order to resolve this
issue one must first understand why it
exists and why persists some people
accredit this lack of conceptual
understanding to archaic methods of
teaching from the past in which teachers
simply write equations on the board
posit so that the students start to
solve for X go over a step-by-step
procedure demonstrating how to solve for
X while students sit silently and copy
notes only to the repeat this process
later on in a problem that they are
likely encountering in a textbook such a
mode of teaching is not conducive to
conceptual understanding and this is
because the concepts that are being
thoughts are very far removed from the
actual context in which they’re
applicable that is to say even if
somebody remembers how and when to use a
formula the practical use of that
formula might be lost upon them still
because their only interaction with that
concepts was relegated to a problem that
they encountered in the textbook and the
only reason that they interacted with
that concept in the first place is
because their teacher told them to do so
and when it comes to teaching you cannot
teach anything outside of the context in
which they are applicable for instance
I’m a language arts teacher right so one
thing that students constantly do in
language arts class is generate a claim
cite sex evidence and generate a claim
cite sex evidence but I always like to
provide students when I go over the
skill the various contexts in which
someone would generate a claim and cite
sex evidence I might bring up law for
instance so if you’re a lawyer if you’re
a public defender or a prosecutor you
will likely be charged with with the
duty of proving someone’s innocence or
guilt and in order to do this you would
have to
reference illegal documents sites text
evidence from this legal documents in
order to lend credence to your claim
regarding this individuals innocence or
guilt and by conceptualizing the skill
in that way I allow my students to
realize how the concepts that we learn
in language arts class how they are
relevant in the real world how they are
relevant in a context outside of I have
to do this assignment because of my
teacher told me to and the same has to
be done with math math concepts have to
be contextualized in a similar fashion
otherwise students will not see the
utility of those concepts outside of
school and therefore creating a
disconnect between them and that
concepts there but thereby causing them
to lose interest now some people might
say word problems word problems
conceptualize math concepts right and
maybe they do okay you might have word
problems that try to implicate math
concepts into familiar routines that one
might encounter on a day to day basis
and they might read something like this
so three coffees and two muffins cost a
total of seven dollars two coffees and
for muffins cost eight dollars what is
the individual price for a single coffee
and a single muffin now I’m assuming
that the actual context in this
hypothetical scenario where this
hypothetical problem takes place would
be and say like a cafe when someone’s
getting their morning coffee
I would also imagine that in this actual
context there would be easier ways to
divine the price of a single muffin and
a single coffee I mean I personally
would just look at the menu so the point
is I’m not actually engaging in all this
computational thinking when I’m in that
context and that is what math is about
math is about using computational
thinking to solve a very specific
problem by applying math concepts and
those problems are encountered in very
specific contexts so in what context
could what engage in computational
thinking to solve problems using math
concepts and how can technology help
teachers to replicate those concepts
contexts inside the classroom well one
thing that comes to mind is game design
and coding now in the past when
technology was scarce replicating this
type of authentic context in which one
would apply math concepts would not have
been possible but today with platforms
such as scratch such a replication of
these contexts is made possible for
those who don’t know what scratch is
scratch is an online community in which
individuals are able to create and share
interactive media and the interactive
media that they’re creating may take the
form of an animation or it may take the
form of a game and the way that those
animations and games are created is by
using a block based coding language that
now what you have here what you’re
looking at is a game of pong that I
created
I hope we’re all familiar with the game
of pong think of it like table tennis
there’s a ball you have a paddle when
the ball comes towards you you have to
make sure you hit it with the paddle in
the opposite direction now when I was
creating this game I was actually
engaging in computational thinking to
solve problems and applying my knowledge
of math concepts so how was I doing this
well there are many different elements
in the game and I had some manipulates
all of the elements of the game take the
element of the ball for instance this is
the code that I wrote the script
essentially that tells the ball what to
do and by applying my knowledge of
obtuse angles right angles acute angles
I was able to convey what I wanted to
what I wanted the ball to do given
specific circumstances so I had to
express
my commands in mathematical terms so you
see I give the ball a condition says
when touching the paddle so when it
comes to the contact with the paddle
I want it to turn and move in the
opposite direction anywhere from 90 to
180 degrees so within the scope of a
right angle and because I programmed it
like that the movement of the ball when
it comes into contact with the paddle
will be as erratic as possible because
the ball’s movements will go anywhere
along the directional arrows or in
between them and the more complex your
game dynamics are the greater the
chances that more complex math concepts
will become involved but this is just a
very simple incomprehensible way to
demonstrates how how application of math
concepts can be used in a context like
coding and game design
now other contexts other realms in which
math concepts are applicable might
include that of civil engineering and
among the duties of a civil engineer
would be maybe the mapping out various
the dimensions of various structures
like houses or buildings using
computer-aided design software how many
of you guys have heard of 3d printing
before all right cool how many of you
guys have heard of computer-aided design
software before okay so less hands came
up for that so basically the
computer-aided design is what you would
use to create an objects that would
later on be 3d printed so essentially my
point is that this type of activity
would culminate in a tangible final
product which would allow students to
see how the math concepts that they use
to create that product how they manifest
themselves in a real-life thing now
constructionist principles of Education
put forth the notion that students learn
by doing
now think if we actually had students do
math and I don’t mean do problems in a
textbook I mean actually use do math use
the concepts to create actual things
that they could interact with it would
it would make them it would make the
concepts more tangible thereby
invariably enhancing conceptual
understand
and also a raising awareness of
relevance thus promoting interest and in
a world where there is growing concern
over the lack of interest in math which
corresponds to a lack of interest in
STEM fields I want to leave you with
this
think about how teaching math in such a
way by harnessing the power of
technology so replicates actual
authentic contexts in which these math
concepts could be used
how would that address these concerns
moving forward into the future thank you [Applause]
innovator I’m always looking for
practical and purposeful ways to use
technology to enhance teaching and
learning and today I would like to share
with you some of my ideas as to how
technology can be used as a pedagogical
tool in order to aid in math literacy
now when it comes to the subject of math
at least if internet memes are any
indication at all the subject is met by
students with feelings of confusion
frustration and downright dread so why
is this well some people might surmise
that these negative feelings associate
at a company students when it comes to
math is due to difficulties they might
be having in grasping the concepts that
are associated with math and assumptions
aside this notion that students have
difficulty with math concepts is
actually substantiated by data according
to the pro according to data gathered
from the program of international
student assessments students in the u.s.
ranked 40th in math 40th out of in the
world out of 70 tested countries so we
have 15 year olds in the u.s. that are
being outperformed out ranked in math by
their international counterparts and
teachers the nation over our bemoaning
the fact that students just tend to lose
interest in math after the fifth grade
so why is this even an issue
well lack of affinity and aptitude for
math equals lack of affinity and
aptitude for STEM fields and in a world
that is becoming increasingly technical
where technological innovations are
being made at exponential rates where
occupations in STEM fields are projected
to grow
this is a disconcerting statistic and
even though the m4 math comes last in
stem the acronym for science technology
engineering and math it is the most
essential because conceptual
understanding of math is a requisite for
STEM fields in order to resolve this
issue one must first understand why it
exists and why persists some people
accredit this lack of conceptual
understanding to archaic methods of
teaching from the past in which teachers
simply write equations on the board
posit so that the students start to
solve for X go over a step-by-step
procedure demonstrating how to solve for
X while students sit silently and copy
notes only to the repeat this process
later on in a problem that they are
likely encountering in a textbook such a
mode of teaching is not conducive to
conceptual understanding and this is
because the concepts that are being
thoughts are very far removed from the
actual context in which they’re
applicable that is to say even if
somebody remembers how and when to use a
formula the practical use of that
formula might be lost upon them still
because their only interaction with that
concepts was relegated to a problem that
they encountered in the textbook and the
only reason that they interacted with
that concept in the first place is
because their teacher told them to do so
and when it comes to teaching you cannot
teach anything outside of the context in
which they are applicable for instance
I’m a language arts teacher right so one
thing that students constantly do in
language arts class is generate a claim
cite sex evidence and generate a claim
cite sex evidence but I always like to
provide students when I go over the
skill the various contexts in which
someone would generate a claim and cite
sex evidence I might bring up law for
instance so if you’re a lawyer if you’re
a public defender or a prosecutor you
will likely be charged with with the
duty of proving someone’s innocence or
guilt and in order to do this you would
have to
reference illegal documents sites text
evidence from this legal documents in
order to lend credence to your claim
regarding this individuals innocence or
guilt and by conceptualizing the skill
in that way I allow my students to
realize how the concepts that we learn
in language arts class how they are
relevant in the real world how they are
relevant in a context outside of I have
to do this assignment because of my
teacher told me to and the same has to
be done with math math concepts have to
be contextualized in a similar fashion
otherwise students will not see the
utility of those concepts outside of
school and therefore creating a
disconnect between them and that
concepts there but thereby causing them
to lose interest now some people might
say word problems word problems
conceptualize math concepts right and
maybe they do okay you might have word
problems that try to implicate math
concepts into familiar routines that one
might encounter on a day to day basis
and they might read something like this
so three coffees and two muffins cost a
total of seven dollars two coffees and
for muffins cost eight dollars what is
the individual price for a single coffee
and a single muffin now I’m assuming
that the actual context in this
hypothetical scenario where this
hypothetical problem takes place would
be and say like a cafe when someone’s
getting their morning coffee
I would also imagine that in this actual
context there would be easier ways to
divine the price of a single muffin and
a single coffee I mean I personally
would just look at the menu so the point
is I’m not actually engaging in all this
computational thinking when I’m in that
context and that is what math is about
math is about using computational
thinking to solve a very specific
problem by applying math concepts and
those problems are encountered in very
specific contexts so in what context
could what engage in computational
thinking to solve problems using math
concepts and how can technology help
teachers to replicate those concepts
contexts inside the classroom well one
thing that comes to mind is game design
and coding now in the past when
technology was scarce replicating this
type of authentic context in which one
would apply math concepts would not have
been possible but today with platforms
such as scratch such a replication of
these contexts is made possible for
those who don’t know what scratch is
scratch is an online community in which
individuals are able to create and share
interactive media and the interactive
media that they’re creating may take the
form of an animation or it may take the
form of a game and the way that those
animations and games are created is by
using a block based coding language that
now what you have here what you’re
looking at is a game of pong that I
created
I hope we’re all familiar with the game
of pong think of it like table tennis
there’s a ball you have a paddle when
the ball comes towards you you have to
make sure you hit it with the paddle in
the opposite direction now when I was
creating this game I was actually
engaging in computational thinking to
solve problems and applying my knowledge
of math concepts so how was I doing this
well there are many different elements
in the game and I had some manipulates
all of the elements of the game take the
element of the ball for instance this is
the code that I wrote the script
essentially that tells the ball what to
do and by applying my knowledge of
obtuse angles right angles acute angles
I was able to convey what I wanted to
what I wanted the ball to do given
specific circumstances so I had to
express
my commands in mathematical terms so you
see I give the ball a condition says
when touching the paddle so when it
comes to the contact with the paddle
I want it to turn and move in the
opposite direction anywhere from 90 to
180 degrees so within the scope of a
right angle and because I programmed it
like that the movement of the ball when
it comes into contact with the paddle
will be as erratic as possible because
the ball’s movements will go anywhere
along the directional arrows or in
between them and the more complex your
game dynamics are the greater the
chances that more complex math concepts
will become involved but this is just a
very simple incomprehensible way to
demonstrates how how application of math
concepts can be used in a context like
coding and game design
now other contexts other realms in which
math concepts are applicable might
include that of civil engineering and
among the duties of a civil engineer
would be maybe the mapping out various
the dimensions of various structures
like houses or buildings using
computer-aided design software how many
of you guys have heard of 3d printing
before all right cool how many of you
guys have heard of computer-aided design
software before okay so less hands came
up for that so basically the
computer-aided design is what you would
use to create an objects that would
later on be 3d printed so essentially my
point is that this type of activity
would culminate in a tangible final
product which would allow students to
see how the math concepts that they use
to create that product how they manifest
themselves in a real-life thing now
constructionist principles of Education
put forth the notion that students learn
by doing
now think if we actually had students do
math and I don’t mean do problems in a
textbook I mean actually use do math use
the concepts to create actual things
that they could interact with it would
it would make them it would make the
concepts more tangible thereby
invariably enhancing conceptual
understand
and also a raising awareness of
relevance thus promoting interest and in
a world where there is growing concern
over the lack of interest in math which
corresponds to a lack of interest in
STEM fields I want to leave you with
this
think about how teaching math in such a
way by harnessing the power of
technology so replicates actual
authentic contexts in which these math
concepts could be used
how would that address these concerns
moving forward into the future thank you [Applause]
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