Impact of Programming on Primary Mathematics Learning
In this episode I unpack Laurent et al.’s (2022) publication titled “Impact of programming on primary mathematics learning,” which describes a randomized control study that compared the impacts of learning mathematics with an integrated CS and mathematics class.
-
quote in summary the present RCT study
shows that the use of computational
thinking via programming as a vehicle
for learning mathematics in grades 4 and
where math is taught for itself the
transfer of learning although critical
is difficult to achieve even when the
presumed best conditions are met to
facilitate it by relying on a near
mathematics in both situations and high
road transfer optimized by an explicit
guidance of the teacher thus visual
programming languages should be
introduced with caution if they are
intended to replace regular mathematics
teaching the presented results are a
strong indicator that this might be
deleterious to mathematics acquisition
end quote that's from page 8 of the
publication titled impact of programming
on primary mathematics learning which
was written by Manon Laurent rosemaria
Christie Pascal braceu amid cha chawa
Sicily nura Erica DeVries and Pierre
chonikai I most likely butchered all
those names my apologies for that here's
the abstract for this paper quote the
AIM of the study is to investigate
whether programming activity might serve
as a learning vehicle for mathematics
acquisition in grades 4 and 5. for this
purpose the effects of a programming
activity an essential component of
computational thinking were evaluated on
learning outcomes of three mathematical
Notions euclidean division n equals 1880
additive decomposition n equals 1763 and
fractions n equals 644. classes were
randomly assigned to the programming
with scratch and control conditions
multi-level analyzes indicate negative
effects effect size range negative 0.16
to negative 0.21 of the programming
condition for the three mathematical
Notions a potential explanation of these
results is the difficulties in the
transfer of learning from programming to
mathematics end quote biota summarizes
this study into a single sentence I say
that this randomized control study
compared the impacts of learning
mathematics with an integrated Cs and
Mathematics course you can find a link
to this paper in the show notes which is
linked in the description of whatever
app let you're listening to the Sun or
you can visit jaredoleery.com where
you'll find hundreds if not thousands of
free computer science education
resources including well over 180 other
podcast episodes at the date of this
recording which has solo episodes like
this one as well as many interviews with
some awesome folks in computer science
education and outside of the field
talking about education in general and
if you don't know who I am my CV is
linked on my website but I've worked
with evergrade kindergarten through
drill students in a variety of contexts
from music education to Computer Science
Education if you've listened to this
podcast for a while you know that I've
had a very strong interest in exploring
integration having previously developed
professional development used by
hundreds if not thousands of teachers
around the country as well as writing
curriculum that's been used by a few
hundred thousand students around the
world I'm well aware that many people
are very interested in the idea of
integration however as I've mentioned in
many of the episodes on integration it's
not really clear what people mean by it
kind of like how computational thinking
is a very vague term where like if you
say to one person they might have a
different understanding than a different
person same thing with integrating there
are many ways that you can integrate
I've mentioned this on many episodes
says but I personally don't think the
approach of just kind of like inserting
or crowbarring computer science
computational thinking into the
classroom like a math class or a science
class or Ela or whatever is going to
improve both that subject area and
computer science or computational
thinking if anything I think it might
lead to overwhelm but there's not a lot
of studies that actually look at how the
two kind of work together or don't in
those kind of contexts so this study
kind of actually explores that in terms
of what does it look like if we take
computer science Concepts and teach
mathematics with it in comparison to a
class that is only focusing on math
without computational thinking or
computer science now the authors in the
introduction mentioned that there's not
really any kind of conclusion on whether
or not mathematics and CS integration
has a positive negative or neutral
effect if it were positive great then we
can see that hey if you incorporate
these two or integrate these two
different subject areas they'll have a
better result than if you do not do that
and that better is kind of like
depending on what you're looking at
maybe it's more motivation or higher
test scores or whatever ever there's
many factors in there but another good
result could be hey it has no negative
impact it has a neutral impact on there
even though you might be taking away
some time from the subject area by
incorporating another domain you're
learning two things without at the cost
of the first one but we also don't
really have enough research to find out
whether or not it actually has a
negative impact which is what I would
guess might happen depending on how
things are integrated now the author's
note in their introduction that of the
studies that do look at integration it's
usually looking at it from a computer
science standpoint to see like hey if we
integrate computer science into Ela
classes what kind of computer science
Concepts and practices can you learn in
those settings not necessarily what kind
of an impact does it have on Ela when it
does look at that kind of impact it
doesn't necessarily do it in a
randomized control study which is
admittedly difficult to get without lots
of funding like NSF grants things like
that now when it comes to computational
thinking many people talk about how well
this like pattern recognition and
abstraction and Etc is all going to be
helpful for understanding X Y or Z
subject areas and while that might sound
fancy those claims aren't always backed
by Empirical research it's like for
music educators like there was this like
music makes you smarter campaign that
was going on I believe that was the
wording that was going on like a decade
or two ago and that was actually based
off of faulty research like the whole
so-called Mozart effect basically any
stimulant is going to make it so that
you're going to perform better on a test
whether you do jumping jacks or listen
to Mozart and it's only going to have an
effect size depending on how you listen
to it and for a short period afterwards
and the same can be said with some of
the studies on computational thinking or
not necessarily studies but some of the
research it might be a hypothesis that
hey this skill of abstraction is useful
it would probably be useful in this
other setting that would be called
transfer of the transfer effect and we
don't really have a lot of studies that
look to see does this impact
understanding of abstraction and does it
actually transfer over into another
domain a lot of the studies that do look
at transfer find that the skills do not
necessarily transfer over or the
understanding don't transfer over and
this is just from like integration
studies in general and like different
transfer effects and things that I've
looked at in like sports psychology and
educational psychology
Etc everything that I was just saying
you can find a study or two that is
going to say actually Jared this says
the other way and that's great but it
all comes down to we don't really have a
conclusion on this yet we're still kind
of figuring things out I happen to be in
the camp where I'm very skeptical about
it not only from a learning standpoint
but also from like a power structure
standpoint and whatnot in terms of like
are we putting domains and subservient
relationships to other domains and I've
talked about that in other episodes that
I link in the show notes but I keep
bringing up these integration studies
because again I think it's important for
us to explore these now here's a quote
from page three that is kind of like a
little bow on what I was just kind of
saying quote moreover results on the
effect of programming to learn
mathematics should be viewed with
caution because among the majority of
studies interested in the effects of the
use of programming through mathematics
lots are targeting the effects of
computational thinking skills and not on
mathematical learning among the few that
are targeting mathematical learning few
are randomized controlled trials based
on empirical measures of learning
outcomes in mathematics end quote okay
so why is it so important to have
randomized control trials well you might
have a study where you you're looking at
case studies multiple case studies doing
some qualitative research or even like
looking in a specific District or class
or school or whatever those are great I
love those studies in terms of being
able to understand perspectives and
whatnot and to understand how does this
very specific population respond to a
treatment or whatever but a randomized
control study makes it so you can
actually make some generalizable
statements to say using the statistics
that we've went through we found that
this would likely have an effect outside
of this population for X Y and Z
characteristics or situations context
Etc so if we had more randomized control
studies and specifically more
longitudinal randomized control studies
in education not just like something
that happens in like a six week period
or something like that but maybe a six
year period and then we can actually
start to look at cause and effect in
education and that's something that we
talked about with like many other people
like Andrea steffic in our interview
which is all the way in episode 27 which
is titled accessible CS education
through evidence-based programming
languages with Andrea stefek so I highly
recommend checking out that one as well
as all the other interviews because
there's some awesome guests on this
podcast okay so now we've kind of talked
about the introduction like abroad or
overview of things so let's take a look
at well what was actually happening in
this particular study so in this study
they looked at three different
mathematical Concepts so these were
euclidean division additive
decomposition and fractions each of
these had a pretest and a post-test that
were administered by teachers to an
entire class in total there were 107
classes from 46 different schools and
each one of the schools was assigned to
a treatment and control group the
treatment group would receive
mathematics instruction integrated with
computer science whereas the control
group would only do mathematics like by
writing algebraic equations Etc and this
was with grades four and five so this is
like ages 9 through 11 with a total of
really interesting tables and a lot of
interesting details that are kind of
explored in terms of like what are the
means and standard deviations between
the treatment and controls Etc I highly
recommend taking a look at that I'm
going to skip through a lot of this
because I don't think it'd be very
interesting in an audio podcast I'm
going to read for you a quote on the
bottom of page six quote the effect of
the programming group is systematically
significant and negative for all final
models belonging to the programming
group leads to a significant decrease in
final performance for each Concepts in
comparison to the control group this
decrease is 0.16 standard deviations for
euclidean division 0.19 standard
deviations for additive decomposition
and 0.21 standard deviations for
fractions all other things being equals
it explains 10 percent of the between
Class variants of the final score for
euclidean division 6.3 percent of the
same variance for additive decomposition
and 17 percent of this same variance for
fractions end quote against from page
six so in other words the group that was
doing math and CS performed worse than
the group that just did math now in page
seven in the discussion section the
authors have three potential
explanations for this so let's explore
each one of those alright so the first
reason that they may have scored lowers
because as teachers are spending more
time teaching scratch or teaching
students how to use scratch than they
were actually teaching mathematics so a
question that might be explored is over
time like an extended period of time
several years let's see what happens in
these treatment and control groups does
the mathematics group only perform
better than the mathematics integrated
with computer science or computer
science integrated with mathematics what
about some of the other approaches that
we've talked about in other integration
episodes where they're going in parallel
so we have mathematics teaching a
concept which is then reinforced by
computer science class which teaches the
similar concept from a different
perspective or different angle which
approach to integration work better or
worse again we need longitudinal studies
to figure out okay how does this
actually have an impact down the road
but this is an important thing to
consider maybe if this was a longer
study and it was lasting for like at
least a year the teachers had more
experience with it or students had more
experience with scratch maybe they would
have spent more time on mathematics in
the class and maybe they would have
scored just as well as the class that
only did mathematics or maybe they would
have been more motivated to want to
continue to learn mathematics like that
in and of itself even if it had a lower
score I would argue is going to make it
so that students would want to stick
with it longer have more grit and
actually enjoy the subject area in the
long run as opposed to someone like
myself who scored well on math classes
but I never pursued it Beyond any of the
requirements that I was mandated to take
maybe if I had an integrated computer
science and math class maybe I would
have found a passion in it another
explanation is the amount of time that
was on task so having worked with
scratch with a variety of students from
second grade all the way up through like
college students there can be a lot of
off task time if we might think of it
that way where you are just exploring
the different features and functions
like well what happens if I reverse the
sound effect or what happens if I change
the different costumes as opposed to
like focusing on mathematics and
computer science integration you're
focusing on all the little neat things
that you can do in scratch which is
great it gets people interested in the
platform wanting to learn things maybe
they'll create more stuff at home
Express themselves blah blah blah blah
huge fan of that but if we're just
trying to figure out whether or not in
integration with scratch and math is
going to have any kind of an effect
positive negative or neutral the amount
of time that students spent like
exploring those different features would
have potentially taken away time from
them actually exploring the mathematics
concept skills understandings or
whatever so that's a good second
potential explanation for this the third
potential explanation that the authors
mentioned it has to do with like memory
management so cognitive load Theory
which is an idea that you can hold I
believe seven plus or minus two things
at any given moment so like if I ask you
to memorize a phone number you might be
able to do that hold on to that in your
memory but if I ask you to do that while
walking on a tightrope while reciting
the alphabet backwards and like doing
that well I don't know scratching your
head while patting your tummy the odds
of you being able to remember that phone
number significantly decreased the more
cognitive load that you have which is
why the theory I believe was seven plus
or minus two things it depends on like
how complicated it is or whatever the
task is ETC you can maybe do five and
hold on to it or maybe do nine but
usually it's around seven so going back
to what the authors were visiting here
is maybe with cognitive load Theory the
idea of holding and learning a new
mathematics concept while holding and
learning a new computer science platform
maybe combining those two is too much
cognitive load on a student which is one
of the things that we've talked about in
many of the other integration episodes
that I've done is that if you're going
to teach students two new things
simultaneously they're going to have to
try and split their attention on
something rather than teaching one
either before you learn the other or in
parallel with but disconnected so for
example one of the things I've talked
about quite frequently is if you're
going to teach music and computer
science it can be very difficult to
learn music concept skills practices Etc
while learning computer science one at
the same time ask me how I know I've got
a drum set right behind me have a PhD
music education and I've taught Computer
Science Education for almost a decade
I'm very grateful I learned one before
the other because I was able to apply my
understanding with better ease than some
of the students that I've seen try and
do both simultaneously it certainly can
be done but it can can be a little more
frustrating which I've seen some
research on that talks about how this
can be very difficult for students when
they are asked to learn two things
simultaneously and it can lead to
burnout or frustration faster than if
they learn each of them sequentially or
in parallel with each other rather than
simultaneously but again other episodes
kind of explore different approaches
where you're learning stuff in parallel
rather than simultaneously and that's
kind of a very quick summary and
introduction to the paper itself I do
recommend taking a look at it it's very
interesting and I do appreciate the
three explanations that they provided at
the end but at the end of these
unpacking scholarship episodes I like to
talk about some of my lingering
questions and thoughts so one of them is
what approaches to integration do you
think work better than others we've
talked about integration quite a bit and
different approaches that you can take
when you're integrating CS with another
subject area Etc which of those
approaches do you think would work
better than others and why and if you're
working with somebody who wanted to
integrate CS with another subject area
what advice would you give them would
you warn them or would you encourage
them why would you do one over the other
and when would you do one over the other
for example if the teacher is is an
expert in both computer science and
another domain that they are teaching
would you encourage them to integrate
the two if the teacher was novice to
both computer science and another domain
that they were being forced to integrate
with would you encourage them to do that
or would you talk to admin and go I
don't know if we should be doing that in
that way it might actually turn students
away from both domains because maybe
it's going to be taught in a way that
would be discouraging or frustrating for
students I pose these questions and I've
certainly shared my own opinions on
these in the different podcast episodes
but there's not a right or wrong way to
do this with education everything is
great there are many different contexts
and different nuances that would inform
one District Source teacher's decision
to do something different than another I
just think it's important for us to
think through these things and kind of
share our discussions on it I also think
it's important that we have more
research studies like this that are
actually looking at randomized control
studies but also looking at it from a
longitudinal standpoint like several
years ideally unfortunately we don't
really have a lot of those at least not
in the field of Computer Science
Education like in the NSF grants that
I've worked on in terms of applications
and stuff they often ask you to use like
the what works Clearinghouse which
usually has a bunch of like longitudinal
studies like talking about here's the
effects of this type of professional
development on blah blah blah right but
it's all on subject areas other than
computer science so we often have to
look at and say Well it worked this way
in this other subject area so we think
it would work this way in computer
science professional development or
curriculum or whatever and so it's just
kind of a big guess we need more of this
kind of research I enjoy studies like
these and if you did too and you know
somebody who might enjoy this as well
please consider sharing this episode
with them just helps more people find
the free resources on my website
jodaly.com thank you so much for
listening stay tuned next week for
another episode until then I hope you're
staying safe and are having a wonderful
week
Article
Laurent, M., Crisci, R., Bressoux, P., Chaachoua, H., Nurra, C., de Vries, E., & Tchounikine, P. (2022). Impact of programming on primary mathematics learning. Learning and Instrucction (82), 1-9.
Abstract
“The aim of this study is to investigate whether a programming activity might serve as a learning vehicle for mathematics acquisition in grades four and five. For this purpose, the effects of a programming activity, an essential component of computational thinking, were evaluated on learning outcomes of three mathematical notions: Euclidean division (N = 1,880), additive decomposition (N = 1,763) and fractions (N = 644). Classes were randomly assigned to the programming (with Scratch) and control conditions. Multilevel analyses indicate negative effects (effect size range -0.16 to -0.21) of the programming condition for the three mathematical notions. A potential explanation of these results is the difficulties in the transfer of learning from programming to mathematics.”
Author Keywords
Computatinal thinking, programming activity, mathematics learning, primary school, randomized trial, learning transfer
My One Sentence Summary
This randomized control study compared the impacts of learning mathematics with an integrated CS and mathematics class.
Some Of My Lingering Questions/Thoughts
What approaches to integration do you think work better than others?
If you were working with someone who wanted to integrated CS with another subject area, what advice would you give them?
Resources/Links Relevant to This Episode
Other podcast episodes that were mentioned or are relevant to this episode
Accessible CS Education through Evidence-based Programming Languages with Andreas Stefik
In this interview with Andreas Stefik, we discuss the importance of using evidence-based programming languages, problems with the lack of replication in CS education scholarship and academia in general, the importance of designing for accessibility and disabilities, lessons learned designing Quorum (an accessible programming language and platform), and much more.
Contemporary Venues of Curriculum Inquiry
In this episode I unpack an excerpt from Schubert’s (2008) publication titled “Curriculum inquiry,” which describes different venues or types of curriculum that educators and education researchers should consider.
Educational Aims, Objectives, and Other Aspirations
In this episode I unpack Eisner’s (2002) publication titled “Educational aims, objectives, and other aspirations,” which problematizes behavioral education objectives and discuss two alternative approaches.
In this episode I unpack an excerpt from Schubert’s (1986) book titled “Curriculum: Perspective, paradigm, and possibility,” which describes different examples, intents, and criticisms of “images” or “characterizations” of curriculum.
The Centrality of Curriculum and the Function of Standards: The Curriculum is a Mind-altering Device
In this episode I unpack Eisner’s (2002) publication titled “The centrality of curriculum and the function of standards: The curriculum is a mind-altering device,” which problematizes curricula and standards by discussing how both can deprofessionalize the field of education.
The Role of Deliberate Practice in the Acquisition of Expert Performance
In this episode I unpack Ericsson, Krampe, and Tesch-Römer’s (1993) publication titled “The role of deliberate practice in the acquisition of expert performance,” which debunks the notion of innate abilities within a domain and describes the role of deliberate practice in achieving expert performance.
In this episode I unpack Bresler’s (1995) publication titled “The subservient, co-equal, affective, and social integration styles and their implications for the arts,” which “examines the different manifestations of arts integration in the operational, day-to-day curriculum in ordinary schools, focusing on the how, the what, and the toward what” (p. 33).
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