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welcome to liquid margins and today's guest is matt salamoni from bridgewater state university and then
our moderator today is nate angel he's the director of marketing at hypothesis so with that um matt would you like to introduce yourself and tell us where you're from what you do
no problem so i'm matt salamoni i'm a mathematician associate professor at bridgewater state university bridgewater is kind of equidistant from boston cape cod and providence rhode island so we're kind of in southern massachusetts we're the largest
of the state university system in massachusetts we have about 10 and a half thousand students mostly undergraduates and one of the things that really drew me to bsu in the first place
is that the mission of our institution is largely wrapped up in teacher training so we're the largest producer of k-12 of math and stem in particular educators in the commonwealth of massachusetts
um and you know we began as a normal school in the 1800s with that specific sort of mission and purpose we were a horus man institution and that's still kind of in our dna and
i've always had a passion for education and and teaching and um bridgewater is the kind of place where we have a very large lever uh with which to influence the next generation of teaching and learning
um both at the college level and also at the k-12 level um and so i'm coming into my 11th year here in the in the math department at bsu i've been the chair of our department for four years which reduces my teaching but also
increases my engagement with other kinds of work on campus and i'm getting to work with students in different ways and participating in conversations that are larger than the institution such as we're having today so okay great thank you um and
nate would you like to say a few words and introduce yourself and then we'll just i'll hand it over to you and we can get started great yeah thanks frannie um and thanks for coming on the show matt it's really
an honor to have you here we've been um we've been really looking forward to this because um a lot of the use of hypothesis and collaborative annotation has been there's been a lot of noise made about its use in the humanities people doing
close readings you know and things things like english and composition and history and disciplines like that but we know that there's really vibrant possibilities and use in in stem fields and in math
and we know that you're one of the people who's really taking that the farthest and so we're super glad to have you today so i'm nate angel i'm calling from sunny portland oregon where it's actually not sunny today oddly but uh i
work at hypothesis along with my colleagues who are here today on the call um and um i myself am a humanities person and so i don't uh necessarily have the the background so you really give this a
um a full look so i'm going to be relying on you matt to kind of help steer some math but i did have a part of my career where i was focused on helping to produce open educational resources
and we produced a lot of math oriented resources including even print textbooks which is boy talk about a pesky problem getting math to print is uh as i'm sure you probably don't see
this tricky absolutely um and so i definitely have had some professional experience with it and but before we get started on all that i mean we were talking a little bit before the show started you know this is probably um
there's never probably been a start of a fall term that's been exactly like this in in higher education in the united states or anywhere really and i'm just before we get started i thought i might just check in you know how are you feeling matt are you
are you feeling okay are you ready for this well i don't think any of us can say that we're truly ready for the beginning of this fall i think you know to the extent to which i've always
been i've been kind of a technology fan my entire life and so i did a lot of things in my own teaching with technology that i've been doing for you know 5 10 in some cases 15 years um and the extent to which i'd already
integrated a lot of technological and online tools into my even into my face-to-face teaching practices that when we made the shift to remote learning in february of this past year we moved 100
online it was an easy transition for me and so i could really focus on helping out my colleagues in the department across campus some of whom were not using any instructional technology to speak of with their teaching
to try to help them to make the pivot so i've been really more concerned lately with making sure that the people around me have everything that they need and access to the technology resources and training and the actual physical devices there was
such a run on webcams in february that we had trouble even just getting people the hardware that they needed so we're looking for workarounds so yeah i think my own readiness is at a place right now
or about a week out from the beginning of the semester and my usual week out anxiety that's usually at about a five or six is it about a 15 or 16 right now but that's just because of how much we don't know about what beginning of fall term like
this is going to look like yeah well i again i really appreciate you coming on at a time when your anxiety levels at a 15 so this is a highlight of my week okay all right well let's make it as as good as possible then
you know one you talked a little bit about uh bridgewater's history and i didn't know that i i actually lived in providence for a while so i'm familiar with the area um but i didn't know bridgewater's history and i'm sounds like you know the teacher education
is a big part of the school's dna like you said could you describe a little bit the kinds of classes that you do normally teach and you know what kind of students you have what levels they're at sure me personally i've kind of seen it all
every corner of our curriculum at bridgewater when i first came to bsu i came in as the coordinator for our developmental math program so the math course is taken by students who we as an institution in one way or
another assess you might not be ready to thrive in a college-level full-on full-bore you know calculus or you know college level math class um and so from the beginning you know i was really working with that population
of students who are coming in with a lot of what i like to think of as unhelpful habits and beliefs and attitudes about mathematics and their own role in their own agency within the subject
and really a lot of you know students come to college with a lot of trauma around mathematics that they're bringing in from experiences that they had as children coming up through the grades sometimes at home um
and so you know my first priority when i got to my institution was well how can we do better by those students both in the classroom with our feet on the ground teaching them you know pedagogically and then also kind of institutionally are
other ways that we can be thinking differently about how to give students the support that they need to actually kind of find their voice in mathematics understand that they have a voice within mathematics
because to be honest that's a voice that too often gets taken away from them at some point along their journey from early childhood into college and so to the extent that we can try and undo some of that
trauma in a semester or two of developmental courses i've always tried to do that in one way or another but even though that was my sort of main purview my my research
as a phd student was in sort of mathematics straight up mathematics i did research in celestial mechanics the intersection of kind of physics and and higher mathematical techniques
and so you know i always have also had an interest in just teaching anywhere across the curriculum one of the places i've taught a lot in the past few years is i've taught a lot of our abstract algebra course so this is the course
where math majors kind of open up the hood of the algebra that you learn in high school and figure out well what is really the essence of algebra if we take the numbers away what are the important questions that we
can still ask and answer what does that look like and then sort of rebuild up to the algebra that was familiar in high school so that's one of the courses where when i first started teaching it face-to-face i taught it in a flipped classroom
and so i generated a lot of video content that i sort of unthinkingly really shared out online via youtube so i have these entire sort of course length playlists of 70 or 80 hours
a piece that constitute this sort of semester's worth of 10 and 15 minute individual lectures that i used for my flipped classroom and those materials have lived on um past my teaching of those courses in ways that
when the open education conversation came along and i hope we'll get a chance to talk more about this that i realize oh i'm kind of doing this already you know sort of teaching with open educational resources that i created
and open pedagogy and you know that's been a really nice set of resources that not only can i reuse in my own teaching but that i know that other folks out there are using particularly now
during our remote learning uh environment um but you know so i kind of teach in all different segments of the curriculum this semester coming up i have a class of graduate students in our in our master
of arts and teaching program so these are practicing high school math educators working on their final licensure master's degree so i'll be teaching a course in the theory of algebra and knots k n ots
the actual strings tied up into various figures there's a rich mathematical study around them that also connects into algebra which fascinates me and i'm also on the other hand teaching a course of business mathematics
so marketing and business management and accounting majors taking their last required math course for their degree which is also the one that scares them the most in their degree program so i kind of get really two sides of the
spectrum of math comfort and carried trauma this semester that's really a lot a lot was packed in while you were saying there it's a so much interesting stuff i'm imagining now a class in
the math of knots and sailing that would be a good good class for your area there and absolutely you know there's a great mathematician's name is colin adams he teaches at williams college um and he's a he's a really performative guy
one of one of his routines that he does actually is a kind of a lesson on not theory where he assumes the persona of a sailor telling the audience here's why here's why i'm interested in knots here's here's how they work and here's some of
the mathematics behind them and he really he's one of those really gifted mathematicians that treads that line between scholar and entertainer and really has figured out how to speak to broader audiences about
mathematical ideas that have a pretty low floor because everyone's tied a knot at some point in their life but they also have a very high ceiling that there's a lot of active research going on in the math community around nuts and what they can tell us about
algebra what they can tell us about topology and geometry combinatorics they have these connections in all different subfields of our discipline so i'm imagining him talking like a pirate during those classes
because indeed yes yes fact to follow yeah really um so um one thing you know since i'm we could just talk about math all day that's fascinating but um one thing that you know the purpose of this show liquid margins
is to talk a little bit about how you might have related to collaborative annotation and so well maybe to get started like how did you first learn about collaborative annotation and it might not even been in the
digital space right it may have been an analog practice or something how did and how did you learn about hypothesis and and get started with hypothesis yeah so i don't think that the concept of collaborative annotation
was much on my radar screen as an entity until the open education conversation came along so um it probably was probably five or so years ago that our our faculty development
teaching and learning center on our campus brought in robin derosa from plymouth state um to come and give a presentation on open educational resources and open pedagogy um and it was one of those presentations robin is also one of these really
talented almost evangelists right for open education and open pedagogy and it was in that presentation that really sort of it's one of these what's it called a threshold concept once you grab hold of
that concept cognitively your entire frame on things changes um in the course of one hour my frame kind of changed with i'm so i've been doing all of these different practices in my own teaching and i have these sort of tacit beliefs about education that i wasn't able to
articulate and then i kind of realized in that moment hey you know i what i the way that i want to interact with my students and the way that i want myself and my students interact with the broader community beyond our institution
really is informed by the mission of public education as a public good and the mission of sort of open resources you know because the information that my students are learning also is a public
good and particularly at a large public university you know i understood in ways that i couldn't really put to words until then that you know the mission of our institution is to make information
accessible and transparent both to our students but also to the the community beyond our borders and so you know she sort of was talking about all those things and showing us you know impressing us with the various digital
tools that she had used with her students to really sort of collaboratively author a compilation of works for an interdisciplinary studies course but i remember that the social annotation piece of it was the piece
that stuck out to me the most because um one of the things that is almost a truism about math majors which are primarily the students i was teaching at the time is sort of the the inverse of what you
hear from a lot of english majors a lot of english majors will tell you well i chose the humanities because i like reading and writing and i don't like quantitative analysis right math but i hear the opposite thing from a lot of our math majors like well
i didn't want to be an english major because i don't really like reading or writing i just like crunching numbers i like solving a problem that i know has a solution and i know that someone will tell me if that solution is right or not
and i can move on to the next question and so i always felt like both sides of that debate were missing something and the thing that my math majors were in my opinion missing the most is i didn't see them engaging with
text both writing but also reading right and not being able to be there present while my students were trying to read about a math concept
um i was missing out on a lot of the the sort of that formative thought process that that wrestling match that we have with a new text that my students were going through or maybe they weren't maybe they were just blowing it off
because i think what we find a lot in math is the way that students use and interact with text is very different than the way that folks in the humanities do because a math student
will often come to their textbook because they have a problem set to work on right you have to do all the even numbers from 2 to 20 by tomorrow so they open the textbook the night before they look first at the
problems and then it's only if they get stuck on those problems not knowing how to solve them but then they might go back and flip through the text and try and get into a paragraph or two maybe look for a formula in a big blue
box on the page somewhere find me the magic tool that will help me to get this done and that's not the way that i wanted my students to interact with text
but i wasn't there wasn't really a way for me to know how they were interacting with text unless we could create a social annotation context around it um so that's what sort of you know when i saw that there were tools
like hypothesis allowing one to do this with open resources as the backbone and nate as you mentioned there's a lot of really high quality open educational resources and mathematics out there
but that was one of those aha moments for me that that we could kind of have that experience in a virtual space of all sort of gathering around a text and kind of do the work of teaching math students how to read about
math because math is also written about in ways that are not congruous with the way other subjects are written about i mean mathematical writing tends to prize uh brevity over clarity in a lot of ways like well
why should i write a whole paragraph when i can just write a single algebraic formula and it should speak for itself well they don't speak for themselves formulas and numbers don't have a voice until we give them one
um and a lot of students don't arrive in college knowing how to do that with a math text and so having the social context in which to do that with my students and watch their developing interactions with the text and their developing
understanding um really that for me is the niche that social annotation could fill in my teaching wow that's that's really great stuff i keep hearing that you talk about voice and agency and
um that's that's such a refreshing refreshing language to hear from uh folks focused on math um so not that i've uh you know done a some sort of like great study of math teachers and whether or not they
talk about that but i really love i love hearing those words um you i i want to actually even take a minute to get into the actual nitty gritty and so like it's really
easy for people like me to imagine you know how one might um collaboratively or socially annotate a poem right but but when it comes to math can you kind of
show us around what some actual annotation looks like in the math context sure um so one of the exciting things for me is that there are a lot of different angles that you can take to annotating a
math text because mathematical exposition tends to take various forms right one of the things that we reprise in math education is sort of the ability to communicate a concept graphically
through for example using a graph or a or a diagram or something but also numerically using a table of data verbally using your written vernacular language and then also algebraically using formulas and symbols which is kind of the really
unique language to my discipline and so one of the things i'm going to share my screen with you here real quick one of the things i try to use social annotation to do is to help students to translate between those different modes
so one of the problems i'll sometimes give students is you know point out a formula somewhere in in the text and try and put into words what that formula actually means why
somebody should care about that right or if you had to explain this to somebody who's not currently taking our math class you know what would that explanation look like so this is an example of an open text called active prelude to calculus um
it's part of a sort of a three volume open uh educational resource written by matt balkins at grand valley state university that i recommend anyone teaching in the calculus sequence has to check this out um it's designed
not only as an open resource but also is aligned to kind of principles of inquiry-based learning um so it doesn't feed it doesn't sort of spoon feed students the right answers and concepts upfront but sort of leads them through a series of
activities that they can do with one another in which the important concepts emerge from those activities so um that too kind of jives with my own sort of values pedagogically
and so here's an example of a sort of a sentence that has some mathematical notation in it it's asking about a specific you know word what is the domain of this function which is written as h equals g composed with d what is its range um and
so you know i asked my students to not only kind of address the question but also kind of tell us about the thinking that led them to their answer so this student is probably not super visible but they're saying well for this
domain here's the answer that i got for this i was wondering if somebody can check my work which to me that's that's much better than asking the sort of closed-ended question hey solve this question in an annotation
right um instead this person got an answer and then they're inviting further conversation for which then i have a couple of students who jump in and they verify oh yeah i also got this and here's how i did it oh this person
says it took me a couple of tries before i figured this out but i did get the same answer right so i think the first one of the first context in which students will find it natural to kind of have conversations in the margins of the
math textbook is just in the sort of problem-solving context here's the answer that i got does anyone agree with this can you check me what's what's your process like um but then the more
the more that i have students working in this space the more that i also invite them to contribute other resources to the the formative process of understanding what's there so this is from a pre-calculus course that
i taught in this past spring semester and i invited students to you know if you if you would like if you find a helpful resource elsewhere on the web that helped you to understand this thing that's being written in the
text share it here and the ability to embed there's a lot of great youtube content to explain math ideas the ability to embed a youtube video directly into the annotation is an
option that students took that option a lot if i look through this whole page it's probably you know six or seven additional videos that they contributed in the annotation stream in addition to the videos that are already embedded within the text
as well so um sort of making the annotation space a place where students can not only bring in their own ideas and their own experiences but also hey here's some additional resources i found
online that helped me to understand this concept there's also kind of an information literacy aspect to it because i want my students not to rely upon me or to rely on a single textbook
for understanding what they're learning but to build those skills to reach out and and assess other sources as well and bring those into the conversation yeah that's ah that really makes sense
um and can i just ask what's um so it looks like you're in canvas there you're the learning management system for bridgewater probably and then embedded in that is this math text is that is that just a website
or whatever this is just a website yeah so um i guess the first first thing to note is that canvas actually is not my university's main lms wow you're actually a blackboard campus i'm using a canvas
free for teachers account uh in this we won't tell yeah right no one will know um but the one of the main reasons why i chose to use canvas free for teacher rather than blackboard um
is that i feel like it integrated tools like this in a much friendlier way for students it had more flexibility for different pedagogical styles i found than blackboard did my grading system is a bit unorthodox my
grade based on standards-based grading system rather than points and percentages so you clearly define learning targets and give students opportunities to revise their work and improve it over the semester and their final grade reflects
the number of those topics on which they were able to demonstrate mastery full stop um and that includes all the revisions and resubmissions and those conversations that happened so um canvas also was a place that was much
it was much more natural to embed that grading structure within that lms but yeah so the this particular uh open textbook it just resides on the web it's authored using a system called
pretext which is gaining a lot more sort of purchase in the mathematical open textbook authoring community because it's got this really sort of friendly structure um to it with you know the
sections and subsections and it has math type as you were saying and you know typing up math in the first place is a challenge but um pretext is friendly to all of those things um and so you know it creates these really
nice looking pages but also has the opportunity the option to export as a pdf in a friendly fashion so you create this central uh xml source code that then compiles into html that becomes a web page that we're seeing here
but also can compile into pdf and other e-reader formats and stuff so the same same source material gets can get processed in different formats so yeah what we're seeing here in canvas is just
the uh the uh basically a a hypothesis web page embedded within a canvas assignment um and i noticed by the way in the in the chat the question was the course
that i used this with an online course or was it an in-person course and actually in my case this past spring the answer is that it was both i was teaching one section of face-to-face students and one section of 100 online students and from the very
beginning of the semester my intention was to blend those classes together so that i created some small groups that were mixed so three students from the web section two students from the face-to-face section had an online discussion group that they
worked with inside of the lms and so the course was a little bit of both but then when we made the pivot to fully remote learning um my face-to-face students all became online students overnight
but they were already working with students that were in the web section to begin with we were already doing a lot of interactions for the course in the online space even with face-to-face students so it was kind of one of those lucky choices
that i made in january that turned out to make my life a lot easier in february but i i'll say that even even before this past spring um i've used these tools with face-to-face students just as
here is here are your here what your reading assignments for the course will look like and you'll do these assignments virtually in this space outside of the classroom yeah that's uh so that you're sort of um you got
lucky you say but it sounds to me more like you uh were anticipating a pedagogical strategy that is actually a valuable one to carry forward this idea of blending the face-to-face and online experience i
mean even just to bring those two student populations together seems like a really valuable thing yeah and i think particularly thinking about the challenges that 100 web students face a lot of students opt for online
courses not for pedagogically sound reasons but because of you know scheduling and expedience and they don't always you know the attrition rates for students taking web only courses are much higher than face to
face and if nothing else blending the two student populations i had hoped would create a cohorting effect where they are sort of connected more to campus life because they're interacting with students in the face-to-face course
i don't know if it worked but again it seemed to have been a lucky choice it seems like a really good idea that should be experimented with further at least um of course we don't have the face-to-face aspect as much anymore right now um fingers crossed that we'll come back
so um one thing i'm curious about like i see a lot of um you know annotation going on on the actual language around the equations and so forth but two things i was interested to hear your you're thinking about
was are people annotating equations themselves and then as a follow-up um are your students making use of the ability to put equations into the annotations
themselves so the short answer is sometimes the the longer answer is that that i found depends a lot on my population of students so precalculus is a course where most of
my students were not majors in math or computer science um and so i didn't really they generally did not make too much use out of type setting their own equations within the annotation
space on the other hand when i've used this as a tool with my math majors and my more advanced students who are already come in with a little bit more comfort typing equations they don't always do a ton of it in their previous courses to
mine but they find it easier to pick up on usually to be able to write out the the latex codes that actually create the math type within the the annotation margin but i do see it happening more
with my students who are already in the math space and have already had some experience with doing that in the past yeah it makes sense i mean um typing latex is not like a common skill for every student nope
yeah um you know i wanted to get back to this idea that you um you kind of raised before about uh you know building people's sense of agency and addressing the
trauma that people you know kind of experience uh in learning about math especially in the context that you were saying at bridgewater state being such a an institution that focuses so much on teacher training i'm curious
have you um i bet you have but have you worked in the idea of helping people that are themselves going to become teachers bring that kind of um set of practices to try to you know
improve agency and lessen trauma into their work with presumably k-12 students that they'll go on to teach sure so i haven't so in in our department at least for the courses that are
mainly populated by by future teachers i guess they fall into two categories so in massachusetts our future elementary teachers and early childhood teachers and our future middle and high school teachers have sort of different different curricula
different expectations for getting their initial license and going forward so for the most part most of the future teachers that i see in my upper level courses in the math major most of them but not all of them are
planning on secondary education as as their target middle or high school our future elementary teachers in fact every future elementary teacher at bridgewater has to take three semesters of a math
course for future elementary educators um and i haven't had too much experience teaching those students um but they have so they have a very different sort of they come in because they haven't selected to be math majors in
the way that our future middle and high school teachers have um and so i think again we're seeing the difference in the two populations um but definitely one thing that i do hope is happening with my math majors
and and also with my in-service teachers who are my graduate students that i've taught before so i think it's important to model these practices with students who are pre-service educators and sort of be
intentional and explain to them up front hey here's a here's a pedagogical choice that i'm making with our class right now you my pre-service teachers and me here's why i'm making that choice here's why i think that's important here are ways in which that's
connected to sort of current research in how students learn and how they thrive in education and just sort of you know talking through that with students and making them aware that this is a choice that i'm making that maybe your previous teachers
made different choices why might they have made those different choices how what and just sort of you know giving them the language to talk about such things um one of the things that the common core state standards
do for states that are that are adopting those of which massachusetts is one is in the math arena they define not just what are the content skills that we expect students to be building in their math classrooms
but they also develop these standards of mathematical practice they call them which are kind of describe a set of habits attitudes and beliefs that we want students to demonstrate about mathematics and about themselves
that actually lead to this thing that we sometimes call productive persistence right we want students to be able to persist through the solving of a new and difficult problem by applying sort of strategies and
and developing cultivating a mindset and a habit of mind that makes that persistence productive um and so i think that you know when i talk to my future teachers and
even my current in-service teachers about this um that everything is kind of i'm trying to point everything towards that goal of helping students to develop those those skills that are not just about solving equations but about knowing that they are
mathematical themselves that there's no such thing as a math person um and that we can kind of you know unpack some of that trauma that they don't realize as trauma uh that they've
developed coming up through through their early grades and just help them to become more comfortable talking about mathematics and mathematizing questions and mathematizing problems from their life
and doing that in their own voice and in in a community because what the practice of mathematics looks like not just at the teaching and learning level but at the professional sort of research mathematics level
is that mathematics is an inherently social enterprise how we figure out whether a mathematical idea is even true in the first place is we don't submit it to some all-knowing all-seeing oracle in the sky
somewhere right is we submit it to one another and we engage in a conversation and we assess you know the success of a new argument or even the success of a very definition
in community with one another and that's what it looks like to sort of practice mathematics i think one of the things that's telling about math is that other disciplines get different
verbs out in front of them we can practice in art we can conduct a science experiment we can investigate a question in social science but what is the thing that gets attached to math what's the verb that gets attached to math we
do math and the reason that we do math is that it can be done and we can then do something else with the rest of our day right just the choices of words that we use there
um and it sort of glosses right over the fact that we don't do math as individuals most of the time in math classes that's what it looks like um in the field of math we are sort of plagued
with this myth of individual genius right we celebrate these individuals who have made contributions to our field who are almost invariably young white and male and so there's this this folklore that
builds up around math that's what doing math for the sake of having it done looks like is one person that's brilliant um usually a white guy sitting in front of a piece of paper almost monastically and sort of elucidating it all on paper
but that's not what real math looks like it's not what it looks like for professional research mathematicians it shouldn't be what it looks like for first graders you know learning basic facts in their classroom um and so even just the ability to come
together and decide whether or not an argument is sufficient or decide whether or not even a definition of a term is the right definition one of my favorite moments over the past couple of years has been the debate in
math social media about whether a hot dog is a sandwich this is something that caught on in not just the math sphere but uh i i point the finger at john warner's book why they can't write um as one of the places that popularized
this as what he called sort of an unwinnable argument is a hot dog a sandwich um but to a mathematician it's it's not that that argument is winnable or unwinnable it's what does that argument tell us about the definitions that we care about
um why do i believe a hot dog is a sandwich where somebody else might not is one of our definitions better than the other um and so that's become an activity that i do at the beginning of the semester with all my math students
tell me about whether you think a hot dog is a sandwich and why more importantly and try and argue with the person next to you over why your definition is superior to theirs where is where does ura's definition potentially break down um and those are
the conversations that mathematicians have is the number one a prime number you can make an argument for a definition one way and a definition the other way and the definition that prevails tends to be the one that makes the rest of the the work that
we do more comfortable and easy right it's not because it's right it's because mathematicians have decided it's more convenient so just getting students to understand that we all have that role to play in the development of
mathematical knowledge is something that necessarily happens in a social context oh that's really powerful stuff and i love that that hot dog practice i've been in that with myself
plus the uh is zero a uh is there an even or odd number question is always going to um i had a professor shout out to arnie langberg uh well a teacher back in high school who said that math was taught backwards
and that we did all the boring stuff first and so people had to slog through arithmetic and algebra and so forth until they got to the really interesting kind of math questions that happened in the more theoretical end
um and he proposed the idea of reversing it and like let's do the interesting stuff first even if people can't do the equation part of it that and then build toward uh you know the sort of more
um kind of specialized ability to actually work with complex equations and so forth later on when you have a reason to curious if that kind of resonates with your practices that definitely i think that resonates
with most of our mathematical community in a lot of powerful ways because one of the things that the k-12 curriculum kind of does is it it trains us to believe that what math is is arithmetic algebra geometry
trigonometry calculus right when in reality that's a very narrow segment of what mathematicians study there are all sorts of fields that have very little if anything to do
with school mathematics that are yet still mathematical enterprises in the ways in which we construct knowledge and assess one another's work around them and a lot of those topics do have very low floor like
we've talked about not theory before if you've tied a knot you've done something mathematical right um so just figuring out what that sentence even means what it means to do something mathematical and then trying to unpack that into something that resembles a
mathematical theory that is something that students that a lot of different levels can do um and so uh there's this one of the more famous sort of writings about this is a paper called lockhart's lament it's the sort of
article written by a mathematician looking at the k-12 curriculum and saying the thing that we're not doing well in k-12 is we're not allowing students to express their creativity in their math education we're sort of
stomping the creative juices out of our students in the process of their math education and standard curriculum and a lot of mathematicians and math educators i think have taken that to heart over the years and said
well how do we teach math in a way that we're teaching it to the whole person right where they are able to bring their authentic selves and their voices and their creativity into the math classroom and instead of funneling them all to the one correct
technique and answer how do we help them to focus instead of to funnel and to and to do math as themselves instead of having to put on sort of an artificial mathematical
formal persona in order to fit in their classroom so how do we teach to the whole student in the math classroom i love that um and i kind of wanted to ask a like a follow-up it sort of dovetails
with that and also what you were just talking about earlier about voice and finding your voice and so what does that look like when you have diversity in the classroom or even for your female
students or your female students of color yes a lot of us are told we're not good at math so yes that's an important point right because to the extent that math anxiety is a social contagion right it's something that
passes person to person teacher to student sometimes parent to student sean bilock's research on math anxiety shows that the female young girls are more susceptible
to those messages from other female authority figures in their lives you know teachers and and female parents that that tends to be they tend to catch that social contagion more readily um through that route um and so
you're right first of all that you know more students of color students who are not white males are coming into college with the belief that i'm not a math person i'm not good at math this is not a field that's for me i need to find
something else to do right because that's who i am somehow um and so i think that we do have to do that work of kind of not just helping each student to understand that they
are mathematical right that they can mathematize a problem they can be successful in mathematical reasoning and it doesn't always have to look exactly like the mathematical reasoning that their high school math teacher showed
them right but there are many different routes to an answer and sometimes there are even many different answers which makes a lot of math majors uncomfortable but then we still do have to do that work to unpack the
really the the gendered and the racialized additional trauma that is picked up by students from sort of minoritized groups as they're coming up through their math education
and those students do disproportionately land in courses in college like remedial algebra right and so that's not just an individual mandate to help those students to come to grips with their own voice and agency in the math
classroom that's also you know kind of an artifact of an institutional bias that exists across higher education and that we're only now starting to figure out how to productively unpack um so you're right and to the extent
that any course in any discipline um has to create safety productivity and sort of norms around participation in conversation i think we have to do that in math as well maybe even more so because of the
additional weight that those students feel about having been stigmatized as non-math people for such a long time yeah and so like um and we should probably wrap up but this is such an interesting thing to me and so are there
ways that you have found that you can use collaborative annotation you know to that end to helping people find their voice or even being really transparent about all the biases that come in
that they're coming in with you know yeah i don't know how much that's really intentional around that that i've done in the social annotation space i mean one thing that i do uh the one thing that i do do um i'm
gonna actually share this on my screen again real quick is that i try especially with math students um i find that you have to be really kind of directive to say hey here's here's how here are some ideas for how to engage with this text
um and sort of one of the important things i think that has a disproportionate effect on students from minoritized backgrounds is just encouraging the asking of questions as the most important part of the
enterprise of doing math and not worrying ahead of time about whether it's the right question whether it's a smart question whether other people might have this question just setting the the norm in the course that what i want you to do
more than anything else is just to ask right and if we can lower the activation energy for doing that for all students i think that will it's one of those universal design principles that will have a disproportionately positive impact
on students who you know historically have not felt the agency to ask a question felt it wasn't their place that asking a question exhibits ignorance or or dumbness right that's that that that fixed mindset that i'm
not a math person so if i ask a question it's because i'm stupid that that sounds it sounds blunt and trite to say it that way but i really believe that that's what a lot of students are carrying with them out of high school
and so just to encourage that formulating of a question and then the sharing of resources around the answering of questions those are something that that everybody can do and so creating the space and the and sort of walking students through
the process of what that can look like without shutting down any of the discussion or saying oh well we you know why didn't you know this to begin with you know there's a lot of stigma that students feel coming into a math class and asking
what they perceive to be an elementary question that they should already have known and just training out of ourselves as instructors and then training out of our uh out of our syllabi in a lot of ways um that sort of belief that students
should already know whatever the body of contact the content might be um and then opening up the floor to ask anything i think is the most important thing that i do with annotation specifically
wow that's great i really love that um i wish i was taking your math class now i wish i could go back in time uh but anyway speaking of time we're pretty well out of it
um but i want to thank you so much for being here today and for everyone who joined and nate for all your really great great questions um and i feel i'm gonna walk away
sort of a different person with less math anxiety myself just because i feel really inspired by your word so perfect um and i would like at this time to give you an opportunity
to say goodbye and leave us with anything you want to leave us with so thank you first of all for having me on today i think that it's been
i don't know why but it surprises me that there aren't more math and science and engineering educators that have really sort of taken the leap into social annotation and really using
text as a way to to gather around with their students so i'm hoping that that some of this conversation has been helpful to connect people with the ideas and the philosophies and the resources that can help other stem educators to do that and i would just encourage people if you
have math and science educators on your on your campus so don't be shy to talk to them we're actually not we're not the prickly group uh we mathematicians that that we have a reputation of being um and there are there is i'm sure a
champion on your campus who would love to hear about how to do more sort of social active annotation activities with their math students so don't be shy to talk to them or send them to me you can find me on twitter
you can find my website on matthematics.com so spell mathematics with a doublet dot com you'll find my website um i'm happy to help connect you with any other resources from there as well so it was really a pleasure great
conversation today thank you thank you so much
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