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Language: en

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Hello my name is Ahsan and this is my 
presentation on "Why is this useful? A  

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search for meaning in mathematics education." 
So students will ask questions to this effect,  

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when is this ever going to be useful, why is this 
important, things of that nature all the time and  

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the way that I'm looking at this is or the focus 
of my research is how teachers respond to this  

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question and in particular like I'm treating 
important useful meaningful and kind of the same  

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way and so the way that I'm kind of seeing this 
play out then without I'm suspecting this will  

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play out is that teachers' goals beliefs and 
values will interact with their context and  

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background to influence well how they respond to 
this question instructionally if they choose to  

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but if I'm treating these 
words of like useful relevant  

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important meaningful all as synonymous then I'm 
particularly interested on an instructor's beliefs  

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on what's meaningful or important and how that 
influences what they how they end up teaching  

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and so if I'm looking at ways to construe 
meaning or meaningful or important  

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I'll set out this framework for kind of what I'm 
thinking or kind of like the glasses i'll use to  

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kind of frame the different ways that meaningful 
or important can be construed don't worry about  

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understanding it now i'll kind of explain it as 
i go. Brownell talks about two different senses  

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of meaning he talks about the meaning of something 
as being like the understanding of thing in itself  

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it talks about the meaning for something 
as understanding the relevance of something  

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so for instance he talks about not knowing the 
meaning of the atomic bomb because he doesn't know  

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the engineering and the physics beyond it but 
he does know the meaning for the atomic bomb  

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in terms of its implications for war and 
peace the destruction of society things of  

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that nature and so then extending that idea then 
to mathematics we can talk about the meaning of  

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mathematics as like understanding math itself um 
like connecting concepts things of that nature  

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or understanding like the relevance of math 
with the meaningful mathematics and there  

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that can be like procedural computations because 
physicists might need it or something like that  

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um or you know making critically informed citizens 
and promoting like critical thinking skills  

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but it doesn't always have to be as grandiose 
as that sometimes it can just be skills you need  

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for the next test or the next course um what's 
important in all of that though is that all of  

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those previous ideas kind of focus or all those 
previous ways of construing meaning talk about  

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meaning from the perspective of understanding and 
understanding is something that lives in our hands  

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um but we all go to grad school we've been to 
school we know the purpose of our education isn't  

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just for you know passing on information in a way 
our grad school is a way to kind of prepare us for  

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the careers that we'll end up being in so we can 
kind of think about it in terms of a bit of an  

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apprenticeship in a way and so a lot of uh i guess 
a lot of people who take a social perspective on  

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learning kind of take um kind of point to this 
aspect of education needing to be attended to  

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in terms of thinking about education not only as 
information but also just practices and from their  

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perspective um meaning or at least from some some 
social some people who take a social perspective  

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for them meaning is that experience of 
everyday life uh within particular communities  

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and so i can talk about like taking that 
conceptual understanding and taking the social  

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analog of that they'll be talking about like the 
social meaning of mathematics and that will be  

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like practices that mathematics uh mathematicians 
engage in so this could be like proving um  

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defining things of that nature doing mathematics 
and i can take that aspect of relevance and take  

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the social analog of that and that will be 
at least according to how i synthesize things  

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um talking about practices that 
non-mathematics communities engage in  

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um so this could be procedural computations or 
critical thinking skills like historically some of  

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the goals of our education system has been to push 
critical thinking skills on elites while pushing  

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uh procedural computations on lower class citizens 
as a way to kind of maintain social uh social  

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stratification and kind of maintain social order 
or maintained the status quo to say so to speak  

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um and so i'm using these uh kind of taking 
those initial like cognitive views of what's  

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meaningful and important and i can extend those 
socially um and i'm using this then to frame  

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how instructors answer this question of when is 
this ever going to be useful and why should i care  

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um and here are just some examples of kind of 
how each of these ways of construing meaning can  

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be demonstrated or can manifest so you know 
that conceptual understanding can be pushed  

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um by having teachers really focus on like 
connecting ideas or concepts um if you're  

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talking about relevance it could be just like 
you need to know how to do you need to know  

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how to do math to do your taxes or something 
like that um in terms of that social analog of  

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like conceptual understanding there's that 
functioning as mathematicians so i mentioned like  

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doing mathematics proofs things like that um 
and if we're taking that idea of relevance  

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and taking the social analog there um that would 
be things like critical thinking and procedural  

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skills for societal maintenance or even like 
being able to engage in routine calculations  

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as a to be a physicist and so then i'm focused 
on in this in response to this question of when  

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is this ever going to be useful i'm focused 
on like what do instructors understand to be  

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meaningful or important um and how do they focus 
on those in their classrooms and why um and i'm  

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thinking things like their background effective 
factors things like that might influence that  

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um so uh in terms of looking at actual instructors 
then um i talked about instructors in multiple  

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different courses just because there was more 
of a chance of seeing different ways of looking  

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or understanding meaning show up um and so yeah 
um in terms of my like i guess how i was kind  

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of getting a view of what instructors were doing 
um i did i took interviews with each instructor i  

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did classroom video recordings which i brought 
into interviews and asked instructors like you  

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know what were your goals in the moment how 
did those connect to your larger goals and  

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like now what are you trying to do here um and 
that was pretty much done through uh my analysis  

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process and i'll leave the details out um so in 
the discussion that i'll follow i'll talk about um  

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the background of each instructor and then how 
um each one of the ways that i'm framing or  

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construing meaning showed up in the instructor's 
goals um so the first instructor was a  

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uh was a math for liberal arts instructor 
um they had an identity kind of rooted in  

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mathematics like they were good in math they 
grew up good in it they made friends that way by  

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tutoring others in math and so it was kind of 
natural for them to go on and major in mathematics  

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um and they developed this view where mathematics 
they saw math as kind of like this pure thing like  

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you know you can get anything you can 
do anything with math you don't really  

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the other all the other subjects are subservient 
to that but as they grew older um they saw a lot  

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of inequalities in our society either through news 
their friends were realizing their own privileges  

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um and so they ended up kind of shifting away 
from that idealistic view of mathematics to  

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seeing mathematics as like a practical means of 
upliftment in a society that really values stem um  

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the next instructor was a stats instructor they 
had a lot of difficulty with math um because they  

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moved around a lot so they had no main intention 
of majoring in math when they gone to college  

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uh they went in as a business major and when 
they were doing that they went into a business  

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scout class where they were able to really see how 
math could be applied not really appeal to them  

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and so they decided to switch their major into 
mathematics despite a lot of gender stereotypes  

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and barriers that were up against them um 
then they ended up going into grad school  

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doing a master's in statistics they went into the 
business life a little while and then they decided  

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to come back to teaching where they really 
threw themselves into looking at education  

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research and how to teach better the 
next instructor was a calculus instructor  

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um he as he was growing up he was curious 
about why math rules were what they were um  

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but their family really wasn't well wasn't really 
able to answer those kinds of questions for him  

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but they were well off enough to be able to send 
him to a private school where he was able to get  

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ahead and so he really did well in math and he 
liked it um but once he was done with um k-12 he  

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kind of left school had no intention of going into 
math wandered a bit um after kind of traveling and  

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seeing he kind of seeing things he kind of came 
back to school um where he got a job as a tutor  

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and there um he ended up turning people in math 
and he was really he really enjoyed being able  

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to talk about mathematical details with his 
students and so he ended up deciding to or that  

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he wanted to end up teaching math um and because 
of kind of his own background he mentioned how he  

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mentioned having really strong beliefs about 
how math has its own kind of inherent beauty  

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and it doesn't need to be relevant the 
same way we don't talk about poetry or  

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playing the piano as being relevant those 
just kind of have their own natural beauty  

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the last instructor was a teacher educator um she 
had a very love-hate relationship with math like  

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she liked doing that and especially teaching it 
um but she didn't like being identified good at  

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math um and despite that though she had a lot of 
supportive individuals who kind of pushed her um  

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so that she ended up majoring in mathematics in 
college and when she was there she came across  

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a class where the teacher showed her how all the 
mathematical ideas that she was doing were just  

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particular cases of larger mathematical ideas um 
and that and being able to see those connections  

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really appealed to her and so that love hate 
relationship changed her pure love relationship  

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um and she decided to continue forward and 
go into teaching uh where she ended up uh  

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teaching a lot of underserved students and 
um kind of uh in really hard-hit areas and  

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she was really able to see how math could be 
a gatekeeper issue for a lot of those students  

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so in terms of the different ways 
that mathematics can be meaningful  

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if for looking at meaningful and important 
from that perspective of functioning as a  

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mathematician that actually barely showed up um 
and so like for instance with the calc instructor  

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um he knew some of his students would be math 
majors and so he felt like he needed to talk about  

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certain ways of doing mathematics like proving or 
like ways of approaching problems just because he  

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felt like some of them would need that in their 
future in their future careers um the national  

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liberal arts instructor um they they were trying 
to use math for actually applying it to things  

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but first they needed to kind of understand how 
mathematicians were communicating certain ideas  

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and so they really had to talk about notation 
a lot before they actually ended up using math  

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um in terms of that importance or meaningful 
in terms of like professional functioning or  

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societal functioning um or like you know practices 
that apply to nothing non-mathematics communities  

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um there's a lot of diversity here 
but all of them actually have like  

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an underlying trend of being influenced by 
their student demographics in various ways  

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um so for instance um like the count constructor 
they have stem measuring students so they were  

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trying to show like they tried showing a lot of 
stem applications of the calculus they're doing  

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um the uh the stats instructor um they the courses 
that their course fed into which were like health  

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science courses because their classes mainly 
for like health sciences and business majors  

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though the depart the departments of the courses 
that those that that stats course fed into they  

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really cared about their students kind of being 
able to interpret uh data and statistical results  

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but not so much on the mathematics itself um 
and so they put pressure on the instructor to  

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really focus on that and so she ended up doing 
showing a lot of like calculator shortcuts um  

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as opposed to like going into the mathematics 
and trying to understand it because of that  

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influence um in terms of the teacher educate 
or i know i'll talk about them after liberal  

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arts instructor first um the national liberal arts 
instructor he doesn't have stem measuring students  

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but in terms of projects that he kind of had 
his students engage in he had them engage in a  

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data collection project where they were just to 
figure out how many books in their library are  

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read and they had a whole debate over like what's 
considered red um and the point there was really  

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to focus on how like making his students really 
critical of things that they might hear news in  

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the news um and so really fostering that idea of 
being like critically informed democratic citizens  

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um the teacher educator they had their teaching 
teachers um so they spent a lot of time like  

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having their students like interpret other 
students thinking looking at student reasoning  

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and trying to understand that the one interesting 
case here was like this relevance outside math  

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um and the the the teacher actually tied this to 
her own background where she realized that not all  

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students are going to be engaged by mathematical 
activity itself and so they need to be teachers  

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need to be able to talk about relevance in various 
ways and so she was trying to prepare her uh  

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pre-service teachers for that in terms of that 
meaning uh in terms of meaning or importance in  

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terms of math for its own sake or like conceptual 
understanding the idea of connections was pretty  

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consistent across all the instructors or in 
terms of like different things that they tried to  

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emphasize um the one interesting case here was the 
stats instructor who talked about applications um  

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and she tied this to her own background of having 
struggled with math she felt like she learned  

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concepts best by seeing applications first and so 
she was trying to teach from that perspective of  

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um what she struggled with learning or how she 
struggled with learning so in terms of importance  

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or meaningful in that from that perspective of 
relevance outside math um there was this idea of  

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skills across all the instructors that showed up 
um the one interesting case here for me was the  

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relevance to non-math that showed up for the stats 
and the teacher educator um and the reason that  

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was interesting to me was the two instructors 
who hadn't mentioned it the math and the  

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math for liberal arts and the calc instructor both 
of them had actually expressed discomfort about  

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going about this kind of this way of understanding 
meaningful or important um and what stood out to  

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me there was that both of these instructors were 
instructors who had backgrounds of like really  

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appreciating math for its own sake um and liking 
and like being successful in math and so what that  

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might suggest for me then is that their background 
might have actually served as blinders in a way  

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it might have made answering that question 
of relevance or importance or meaningfulness  

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um and diversity very difficult for them just 
because their backgrounds might have made certain  

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ways of answering that question more accessible to 
them than others the one disconfirming case here  

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was the teacher educator who we'll talk about in 
the next slide kind of recapping i was i had these  

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four ways of kind of considering how meaningful 
or important can be understood and they and i was  

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using that then to kind of frame instructors goals 
about what they thought was important um and what  

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i found was that you know a lot of it a lot of the 
ways that those meanings or importances kind of  

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manifested depending on the student demographics 
but also the instructor's own background  

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um i mean there was like when i'm thinking 
background i'm thinking of the calc and the  

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latin math for liberal arts instructors who like 
their background in math might have made answering  

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that question of like relevance and diverse ways 
it might have made that difficult for them just  

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because their background might have made certain 
ways of thinking about meaningful or important  

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more applicable or relatable to them um the one 
disconfirming case here however was the teacher  

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educator who didn't care about math um or didn't 
care about relevance but she just liked math for  

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its own sake but because of her experience of like 
seeing disenfranchised students she realized that  

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being able to answer this question of importance 
in various ways was something that was needed the  

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same thing with the stats instructor she actually 
had that personal experience of struggling with  

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math and so kind of looking overall what stood 
out for me here was that if we want instructors  

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to be able to answer this question of when is 
this ever going to be useful in diverse ways  

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what this might suggest is that we need teachers 
who've had either that personal experience of  

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struggling with math like the stats instructor 
or have that experience of really seeing others  

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be disenfranchised by that and that can have a 
lot of really important consequences for equity  

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and also in terms of engaging our students if 
we want to really be able to engage our students  

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perhaps we need more instructors 
who have these diverse experiences  

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and are thus able to then answer 
this question in diverse ways

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and these are my references

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thank you