December 16, 2024 • 29 mins
Join us for an engaging discussion with Kevin Dykema, past president of the National Council of Teachers of Mathematics, as he sheds light on the evolving landscape of math education. Kevin shares his transformation from excelling in rote memorization to prioritizing a deeper understanding of mathematical concepts. We explore the challenges educators face when adhering to procedural teaching methods and the pressing need for a student-centered approach. Listen in as we uncover the disconnect between teacher preparation and real classroom experiences, and why it's crucial to reimagine how we teach mathematics.
Together with Kevin, we confront the societal misconceptions that often surround mathematics, from adults' tendencies to downplay their math skills to the stereotypes of mathematicians. This episode presents a six-point action plan designed to foster a positive math identity, emphasizing perseverance and community support. Discover how these strategies can transform the perception of math from mere memorization to a field that encourages critical thinking and real-world application, thereby helping students see themselves as capable mathematicians.
We also delve into innovative teaching methods that engage students in mathematical thinking. Kevin discusses the importance of moving away from traditional procedural teaching and towards presenting students with rich, contextual problems that ignite curiosity and facilitate productive struggle. By embracing diverse problem-solving methods and recognizing the value of students' unique approaches, both teachers and learners can cultivate a dynamic, inclusive math experience. We wrap up with insights into the intersection of math and coding, and how these disciplines promote essential critical thinking skills in our technology-driven world.
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Chris Colley (00:12):
Welcome back.
Another episode of Shift Edpodcast coming to you from
Montreal, canada, and I'mreaching down to Michigan, I
believe.
Kevin Nikoma is coming in toshare some math mindset stuff
with us.
And it's Michigan, right, kevin?
It is Absolutely Southwestcorner of Michigan.
(00:33):
Amazing.
And are you still the presidentof the NCTM?
Kevin Dykema (00:38):
Yeah, so my term actually it was a two-year term
ended like the 1st of October,so now I'm technically the past
president for a year, so I getthe honor of supporting the
current president and helpingher succeed Amazing.
Chris Colley (00:54):
Amazing, Great stuff, too, coming out of.
I mean, there's so manyresources out there for math
teachers and expertise as wellout there for math teachers and
expertise as well.
It seems to be one of oursubjects that gets a lot of
attention, a lot ofmisinterpretations,
misunderstandings and struggleas well, and that's kind of what
(01:17):
we'll focus on here today isthat productive struggle.
But before we start, Kevin,were you always into math?
Kevin Dykema (01:29):
Was that your jive at a young age?
As you grew up it was.
I always felt successful inmath and I mean, looking back
now I can argue I didn'tunderstand a lot of what I did,
but I always did very, very wellin mathematics and memorized
things.
I was a good rule memorizer.
I could follow the procedures.
It wasn't until I startedteaching that I actually had to
(01:49):
get to the understanding stageand I think I learned more my
first few years of teachingmiddle school math than I did
actually as a K-12 or a collegemajor in mathematics, when you
actually have to start to seethe why behind things and to
start to see connections betweendifferent things.
And to this day I mean I thinkevery time I work with a group
of teachers, work with a groupof students, I learn new things
(02:11):
or I see things differentlybecause when we allow our, when
we allow our learners to sharetheir thinking, good things
start happening and they oftenmy students often see things
differently than I see thedifferent content areas.
Chris Colley (02:25):
Amazing, amazing, and like, we tend to teach the
way we were taught, right, yes,and math is.
You know, I remember my mathclasses in particular, obviously
, and how kind of removed thestudent was from the whole
learning process.
The student was from the wholelearning process and the
(02:48):
teachers I see pre-serviceteachers and first-year teachers
coming into the system thatthat tend to, you know, go to
what they know, which is howthey were taught.
Um, is there a disconnect youfind between, like, um, how
we're, we're getting teachersready to teach math?
Um, because in elementaryschool, for example, I mean,
it's a lot of non-math experts,right, you're a general in
(03:09):
elementary school here in Quebecanyway, and then, as you go
into high school, you'reexpected to be, you know, more
of an expert.
But, like, is there adisconnect between how we
prepare our math teachers to thereality of it?
Kevin Dykema (03:25):
Yeah, I'm not sure if there's necessarily a
disconnect.
I think a lot of our collegesof education are doing a great
job of saying this is what itcould look like, but then they
get into a school system whereit doesn't look like what
they're doing.
That you know, in educationworld we're slow to change,
especially in the math world.
And you know, when I thinkabout the secondary folks, for
(03:46):
many of us we were great rulememorizers and school worked for
us.
Having the teacher just sayhere is the steps, here's step
one, here's step two, here'sstep three, memorize it and
you'll be good.
That worked for us and webecame math teachers.
And because it worked for us,we think it should work for
everybody, and I'movergeneralizing here.
But for Autism, we think itshould work for everybody and
(04:08):
the reality is it does not workfor everybody.
Having math be taught very, veryprocedurally has not worked for
decades and decades and decadesfor all.
It works for some and if we'retruly interested in meeting the
needs of all of our learners, weneed to look at doing things
differently and change is hard.
So I think they're in manycolleges of education.
They're being taught what theyshould be doing, but then they
(04:31):
get into the school setting andthe school setting looks the
same as it did 30 years ago, 40years ago, 50 years ago,
oftentimes in math.
That doesn't mean we haven'tmade some improvements in math,
but there's a lot of room togrow and I love how you noted.
I mean I don't love how younoted, but I appreciate how you
noted.
You know, in math it hasn'tbeen very student-centered in
(04:51):
the past.
It's been very muchteacher-driven.
And when we think aboutproductive struggle.
Chris Colley (05:03):
we need to get our students engaged in that
learning.
That's required in order tomake sense of the mathematics.
Absolutely, and Kevin, what ismathematics Like?
I saw one of your presentationswhere you led with that
question Like what is it Like?
Kevin Dykema (05:19):
could you expand on, like what that term is?
Yeah, and I think that's a.
I think it's a fundamentalquestion and I think the way
that you answer that question ofwhat is mathematics affects how
you think that math should betaught, how math should be
learned, or even why we have tolearn math.
I think for so many of ourstudents.
I'll go from the studentperspective first.
I think many of our studentssee math as I just need to learn
this formula, I need to learnthis equation, I need to follow
this procedure and poof, I'llget a correct answer.
(05:42):
Getting correct answers is very,very important, but I think
when you talk with a lot ofmathematicians, when you talk a
lot of mathematics educators,words that come to their mind
instantly.
When we talk about what ismathematics, it's problem
solving, critical thinking,reasoning and sense making,
explaining the real world aroundthem.
So there's this disconnectbetween what we think
(06:02):
mathematics should be and whatmany of our students see
mathematics as, and that's on usas a mathematics education
community to change that and toreally help our students begin
to see that math isunderstandable.
It's not all these random setsof procedures and we know
they're not random sets ofprocedures, but for many
students, they're viewing themas just random sets of
(06:24):
procedures that they have tofollow.
We need to teach math in such away that it makes it coherent
for our students and so that itbuilds from grade to grade to
grade and they see, oh, what I'mlearning in grade seven is
really taking some of that workthat I did in grade three and
just generalizing a little bitmore.
And then, oh, when I go tograde 10, I'm going to take that
(06:51):
same learning and just extendit a little bit more.
Chris Colley (06:52):
And we don't have as much of that as we could if
we're truly interested inmeeting the needs of all of our
kids.
Totally, totally, yeah, superinteresting.
And I mean your book ProductiveMath Struggle.
You mentioned worthy ofstruggle, right, that students
have to go through this and asteachers, I mean we're very
compassionate and empathetictowards our students.
Sometimes it makes usuncomfortable when we see them
(07:14):
struggling, right.
How do we change that mindsetthat we need to let them
struggle and that they're worthyof the struggle?
I love that term.
Kevin Dykema (07:25):
Yeah, and I think we know it's got to make sure
that we're defining strugglecarefully, right, whereas I'm
certainly not advocating, foryou know, when I walk into class
and all the kids are in tearsor all the kids that put their
heads down, I'm not like, oh,this class is rocking it, it's
that productive struggle, it'sgot to lead somewhere.
And is rocking it.
It's that productive struggle,it's got to lead somewhere.
And I think about you knowlearning in general, if I go out
of the math classroom for alittle bit, when you think about
(07:49):
you know learning a newinstrument, there's a lot of
struggle involved with that.
But yet we value that struggleand we recognize it's okay that
you don't have it perfect rightoff the bat.
It's okay that you're exploring, that, you're messing around,
trying to figure things out,sort of grappling with how to
hold the instrument, how to blowwith a horn, whatever the case
may be.
But then in math it comes sortof to a grinding halt and too
often we just teach math as this, procedure to procedure after
(08:11):
procedure, and our studentsdon't see math then as something
that they need to be studyingbecause realistically they say I
have a calculator, I'm at alltimes with my cell phone.
So I think when I think aboutyou know, mathematics seems to
be worthy of a struggle and it'sthat all students should be
doing that we need to help ourstudents recognize that math is
understandable.
There's a reason for that.
(08:32):
It makes sense, and let's teachmath as sense-making.
Let's get our students activelyengaged wrestling, struggling,
grappling whatever word you wantto use at that point in time to
have them begin to make some ofthat sense.
I often think, you know, in atypical traditional classroom
(08:54):
and it's for decades and decadesand decades the teacher is the
one that's doing all of theintellectual work maybe not all
doing the vast majority of theintellectual work in a math
classroom and the kids are sortof along for a free ride.
We need to get our kids doingthat deep thinking that's
required to be able to makesense and the teachers are
providing that support along theway and helping to ensure that
(09:15):
every student is beingsuccessful.
Chris Colley (09:18):
Right, I love your examples too, that it is a
skill that you, you develop.
You know, I mean similar tocreativity, example, right, like
some teachers, you know, orsome people, I should say, oh,
I'm not creative, right, butagain, it's this muscle that you
work on, right, and grow anddevelop.
Um, oftentimes, though, I'venoticed that, the relevancy,
(09:40):
right.
So you mentioned, like learningan instrument, I see the value
because I'm motivated in it'srelevant to me, right, I'm
interested in how do you turnthat in a math class to make it
relevant?
Um, and I I remember you hadmentioned that math is all
around us and, again, thatdisconnect between students
(10:01):
seeing it relevant in theirworld.
You know, when they walkoutside of the school, that they
start to notice these patternsor things that are similar.
Or can you expand on that alittle bit?
Kevin Dykema (10:13):
Absolutely, and I think some of it's.
You know it comes back to thehow are we thinking about math
and what are we?
What are we looking at withmath?
And, if we're being honest,much of the math that we do in
the K-12 setting is not the maththat they see in the world
around them.
You know I pick on high schoolsometimes that you know you
factor trinomials in high schoolbut you're not factoring
(10:35):
trinomials outside of the wallsof your school for most adults.
I mean there may be some thatare doing that for their career.
So we have to quit trying tofind every single topic that we
may teach in math and say, oh,it definitely applies to the
real world in this way.
But we need to help ourstudents recognize that math was
developed for a reason,somebody at some point in time,
(10:55):
and math is still beingdeveloped.
I want students to walk awaythinking, oh, it's just all this
past stuff that we're justredoing.
But then somebody had a reallife problem that they needed to
solve, and because they neededto be able to have some way to
describe a curve, differentmathematics was generated.
Because they needed a differentway to describe the way a leaf
(11:18):
may grow on a tree and we getnew math that is created at that
point in time.
So we need to help our studentssee we need to do a better job
of helping our students see theconnections between developing
math and that math has been usedto solve real-world problems.
We can look at some real-worldsituations and use some
mathematics, use some data, usesome statistics to help analyze
(11:40):
some of those differentsituations that are going on in
the world around them andhelping them just begin to see
there's a lot of math in there.
People are using some of thatlogical thinking, that critical
thinking.
They're using data to makedecisions and when we look at
you know, especially the last 10years, the amount of data
that's being collected and theamount of data that's being used
(12:01):
to make decisions has rapidlyincreased and we owe it to our
students to have them develop agood understanding of that world
around them and how we canmaybe describe it mathematically
.
Chris Colley (12:14):
Right, right, totally cool.
And I mean I love these ideastoo, that that when we are
teaching math and that studentsare going through that process
of figuring it out, that theybring certain luggage with them
the kids and you talk about itin your book this, this kind of
(12:34):
math trauma of sorts, where theydon't feel like they belong yes
, In math you know like theybelong, in math you know like
they.
Just there's this wall and it'sreally hard to break down.
But I love in your book youtalk about the belongingness in
that struggle.
Can you expand on that a bit?
Because I find it sofascinating that this sense that
if I don't feel like I'm, Ihave a purpose within this class
(12:58):
that's talking math, that I,you know, I'm excluded from it,
which again perpetuates thismath trauma that our young kids
go through.
Kevin Dykema (13:09):
Very much so and you know, sometimes I like to
frame it around this idea of amathematical identity United
States and Canada and I can'tspeak for all of Canada and all
of the United States, but as Iwork with educators, primarily
in the United States and some inCanada, you know I hear that
frequently, that you know, insociety it's generally it's very
cool to say I'm not good atmath, right yeah.
(13:32):
But you don't hear that sameadult say I'm not good at
reading.
They may say they don't enjoyreading.
So as a society we've sort ofmade it cool to say I'm not good
at math, so it's okay to feellike you don't belong in there
because nobody does good at mathunless you know.
We think of who is a math personFor many of us.
We grew up in a time you knowwhere it was.
Those that were pocketprotectors were those that did
(13:54):
math or those that hadsuspenders or it was sort of the
geeky type of stuff.
So we have to break down someof those walls and we need to
help our students recognize thatwe're all capable of learning
math and we need to sharestories of people who are doing
math.
When you ask a typical K-12student describe a mathematician
(14:16):
.
A mathematician it's an oldperson, often somebody who's
dead, somebody who's Caucasianmost of the time male, frizzy
hair.
As a math education community,we need to be sharing stories of
other mathematicians.
We need to be findingmathematicians who are still
developing math.
We need to find thosemathematicians who are young, so
(14:39):
that students see themselves ascapable of learning math.
They're recognizing oh, it'snot just Pythagoras, it's not
just Euclid, it's not justArchimedes, it's not just Gauss,
it's not just those that wethink of from centuries and
centuries ago as mathematicians.
People are still doingmathematics and it's not just
(15:00):
dead white males that didmathematics that they see
themselves.
And when they see themselvesreflected in people who are
doing math currently, they'regoing to begin to get a sense of
belonging.
And I also think that when wefocus on really getting to math
by understanding, rather thanjust math by memorizing,
students start to feel like theybelong in there.
(15:21):
Then because they recognize oh,I am capable of understanding
this.
Math is an understandablesubject and there's so much work
that we can do to help increasemathematical opportunities for
all of our students.
Chris Colley (15:37):
Absolutely Well said, well said.
Could you elaborate a bit?
Students, absolutely Well said,well said.
Could you elaborate a bit?
In the book it talks about thesix-point action plan for
fostering this kind ofperseverance and I'd even extend
that in developing thatcommunity, that math community
within your class where everyonefeels that they can contribute
to the thinking that's going on.
Can you talk a bit about thosesix points and how that leads to
(16:02):
?
Kevin Dykema (16:03):
Yeah, yeah.
So you know, when John Susieand I wrote the book, we said
you know we need to come up withsort of an action plan for
teachers, because it's not justgoing to happen instantly that
all of a sudden the kids aregoing to be like oh.
I'm so excited to have to thinkdeeply about math and to do that
.
It's not like a light switchthat you can go and flick on.
So what are some of thoseintentional steps that we can do
(16:23):
?
So the first thing we said youknow we need to work on valuing
this notion of really wrestling,grappling, making sense of the
math max, both from the educatorperspective as well as helping
our students see there's valuein not just being told what to
do and just memorizing.
There's value in having to workhard at developing a good sense
of understanding.
So that first action step isvalue.
(16:45):
That second action step is tofoster positive mathematical
identity.
We talked about that with thebelonging.
If they don't feel like theybelong in the world of
mathematics, they're not goingto feel capable of doing that.
So we need to foster thatpositive mathematical identity
and help all students recognizethey are capable of learning
mathematics.
The third action, then we needto build a classroom community
(17:06):
that's supportive of reallywrestling.
And what does it look like?
What are the norms?
What does it look like whenyou're, when you sort of get
stuck?
How might we get unstuck, forlack of a better word?
What are some things that wecan do at that point in time.
That fourth action, then, is toplan our lessons for it.
What can we do?
Where can we really provokethat deep thinking?
(17:27):
What are some strategic changesand some questions that we may
have asked in the past?
How can we change, then, aproblem that we may have done to
make it a little bit deeperthinking at that point in time?
And then, as part of thatplanning, then it's also
anticipating what are thestudents going to do?
How are they going to do itcorrectly?
What are some of those correctstrategies they may do, as well
as what are some of thosemisconceptions or partial
(17:48):
conceptions that they may bring?
And then how am I going torespond to that?
What am I going to ask?
So it's not just me rescuingtheir thinking or rescuing their
answers.
I'm rescuing their thinking andreally helping them go from
there.
That fifth step, then, is tosupport the productive struggle.
What am I going to do when thekid hits that point where they
say they're stuck, and I thinkso much of that's because of the
(18:09):
planning?
If I've planned well, I'm goingto be able to support better at
that point in time, and when wesupport, we have a rich history
in mathematics of when ateacher helps a kid, we grab
their writing utensil and we doall the writing for them.
That's not what we're talkingabout here with supporting the
struggle.
It's really getting to thatstudent's thinking, helping them
(18:29):
explain what are they currentlythinking and then providing
some prompts to help them makesense.
And then that final action, thatfinal step, is to reflect back
on that productive struggle.
We need our students to see hey, three days ago I might have
thought this was the mostimpossible thing in the world,
(18:50):
but because I didn't give up,because I kept trying to make
sense of it, now I've made senseof it.
I'm like, oh, it's not so bad,and when we do a little bit of
that, reflecting back on it,then we can celebrate it with
the students, which then justhelps to build that positive
mathematical identity.
So we look at those six actionsthe valuing, the fostering, the
building, the planning, thesupporting and the reflecting as
a way to really engage all ofour students in this notion of
(19:15):
making math understandable anddoing math by understanding
rather than math by memorizing.
Chris Colley (19:21):
Yeah, totally.
Kevin Dykema (19:23):
And like walk us through a period Like how would
you see a successful thinkingmathematically classroom, like
how would it start and then whatwould the teacher get the
students doing, and could youkind of walk us through what
that would look and feel likeyeah, and you know, and
depending on the content, theconcept you're learning, it's
(19:44):
going to look a little bitdifferent and you know what it
looks like in the first gradeclass is going to look different
than in the grade 11 class or agrade 8 class.
But overall, you know, the kidsare going to be working on, on
a good rich task, a good richproblem, something that's going
to going to spark some thinkingat that point in in time.
I'd often like to, you know,start out with that problem that
(20:06):
so often, you know, for many ofus, we did all the.
Some people call them the nakednumber problems, where there's
no context.
And then question number 38 wasa real life application and
sometimes, let's be honest, thereal life application and
sometimes, let's be honest, thereal life applications that we
use aren't real, real life.
But starting out with acontextual problem, helping them
(20:28):
understand why we even careabout this, get the students
actually engaged, get themsharing their thinking in small
groups, and then, as we'retrying to wrap it up, that's
maybe when we get a little bitmore of that procedural fluency,
when we get some more of thatprocedural stuff, I think,
historically, one of the flipsthat I like to think about.
Historically in math, we've toldour kids here's the procedure
(20:50):
to follow, here's the steps youneed to do.
Now you think, when I'm thinkingabout productive struggle and
I'm thinking about what a goodmath classroom should look like,
could look like, let's get ourkids thinking right off the bat.
We can provide more of thatstep-by-step at the end as a way
to wrap up, as a way toformalize their thinking, as a
way to make sure that, yes, weare good to go on from there.
(21:15):
But a good classroom, the kidsare doing the work, the kids are
thinking, the kids are not justsitting there listening to the
teacher do all of the thinking,all of the talking all class
long.
And it's hard.
It's hard to shift that becauseyou know, we talked about it
earlier For so many of us aseducators.
We grew up in a time where theteacher did all the work in the
(21:37):
math classroom and we just hadto sort of follow along and hope
that we could mimic theteacher's steps.
We need to be changing that.
We need to be getting ourstudents to do that rich, deep
thinking.
Help the students see theconnections between different
things, help the students makesense of the mathematics and
then we can provide some of thatstructure towards the end of a
(21:59):
typical math class.
Chris Colley (22:00):
Then yeah, for sure, I love that idea too.
It's a small tweak, but justthrowing the question at the
start or the problem at thestart and allowing the students
to kind of like struggle with ita bit and then if there's any
misunderstandings, you can cleanthose up at the end, yes, um
yeah, and we have to recognizenot not all kids are gonna do
the problem the same way andthat's okay.
Kevin Dykema (22:23):
And if I'm being honest, sometimes my students
see problems a whole lot neaterthan I do, that my brain,
because I'm driven just sofocused on math, math, math,
math, math.
I jump straight all the time tolet's write an equation for it.
Most students do not jumpstraight to let's write an
equation for it.
Most students wrestle throughand actually think with that.
With that One of the things Ioften like to do when I'm
(22:47):
leading some professionaldevelopment either, with sharing
a math night for parents,working with teachers, working
with administrators, workingwith students, I may say how
would you do 245 plus 98?
And for most people they say,oh, if I'm going to do 245 plus
98, I'm going to think of it as245 plus 100 and subtract 2.
Or some other strategy thatthey may have.
There's lots of differentstrategies Like all right, this
(23:09):
is what we need to be making ourmath classes like.
We need our kids to be doingthat thinking.
We shouldn't just say, oh, backin 19-whatever, here is the one
and only one way that we coulddo the 245 plus 98.
Let's get our kids thinking,sharing their reasoning, and
that means we need to have thatcomfort of recognizing it's okay
if they don't do it the exactsame way that I may have done
(23:32):
and it's okay if they have a waythat I'm like, oh, I'm not
positive that it works for us tosay, all right, hey, let's try
it with a different set ofnumbers and to see if it works.
And it's a shift for the kidsand it's a shift for the
teachers.
But it's so powerful for ourstudents and it helps our
students to see that math iscapable of being understood and
(23:52):
math is useful.
It's not just the subject thatpeople did decades, centuries
ago and that we're just redoing,relearning everything that they
did, however, many years ago,and there's really no value in
it.
We had to have our students seethe uses of that, see when they
would use the mathematics in avariety of different settings
(24:14):
For sure, you know.
Chris Colley (24:15):
It's interesting that you're saying that too,
because I'm thinking about whenI'm working with kids in coding.
You know, either doing ascratch project or like
programming in Arduino orsomething like that thought
process is very similar to whatyou were mentioning there, and I
wanted to ask you thatcrossroads, because coding
definitely seems to be somethingthat is becoming more and more
(24:37):
relevant.
It's going to affect way morepeople's lives.
Where does coding and math meet?
Kevin Dykema (24:46):
Yeah, that's a great question.
That's one of those things thatI think about and I talk with
other people and you know Idon't think as a collective
education community we've cometo any resolution yet about how
to intersect those.
Everybody's saying, yeah,there's a lot of overlap in
there, but to figure out, how dowe fully integrate that into
(25:06):
there?
And you know we have a finiteset of minutes that we have our
students in there.
But to figure out how do wefully integrate that into there?
And you know we have a finiteset of minutes that we have our
students in school.
So anytime we try to addsomething in, theoretically,
something needs to go out and weneed to figure out what is it
that needs to go out.
I often like to, instead ofthinking you know, what are we
eliminating?
What are we de-emphasizing?
What are we going to emphasize?
(25:27):
What are we going to tode-emphasize a little bit, and
and sometimes when we startthinking about, oh, I can
de-emphasize this after a periodof time, we're like all right,
why am I even doing this anymore?
But sometimes it feels harshjust to say, oh, I've loved
doing x for however many years,I can no longer do it.
Let's just sort of gradually doa little bit of phasing out,
(25:49):
and you know some of it's.
We've got to recognize what arethe skill sets that our
students are going to need tohave in order to be productive
citizens in the world.
And you know, coding isdefinitely one of those that
they need to be able to have abetter understanding of what it
is and the more and moretechnology driven that we become
, we need students who have anappreciation and have some skill
(26:13):
set in that world of coding.
Chris Colley (26:16):
Right, right.
Well, this has been a reallyfascinating conversation, kevin.
I really appreciate you carvinga bit of time to share your
thoughts with us and I'm reallyexcited that you're going to be
supporting, um, our mathconsultants and teachers and, um
, I think that these kinds ofconversations are super rich and
(26:36):
just kind of reflecting on ourpractice a bit, um and, and
realizing that it's not a youknow, like we have to change
everything.
We can make small adjustmentsthat allow more thinking into
the classroom and giving it abit more back to the student,
which I really appreciate.
Those thoughts and your book isjust, really just a great
(26:59):
plethora of ideas and starters.
I wanted to talk a little bitabout rich tasks, but I mean,
your book touches on those a lot.
But maybe my final question toyou as we close here is what
makes a good rich task in youropinion?
Kevin Dykema (27:15):
Yeah, I think a good, rich task is something
that has an interesting contextand I acknowledge an interesting
context for student one is notan interesting context for a
student two, so you're not goingto have a task that every
single kid is going to be likeoh, I love the context of this.
But it has to be in some sort ofa relative interesting context.
It has to have a variety ofdifferent strategies that
(27:37):
students may use for it.
Some may make a table of values, some may jump to an equation,
some may make a graph, some mayreason through it.
There has to be some way forall the students to be able to
at least get started on theproblem.
They may not all have theability initially to find a
solution in a relatively quickamount of time, but whether they
(28:00):
all can get started at thatpoint in time it has to be
aligned to the content.
We can't just pull out thesethings and say, oh, this is kind
of a fun thing to do.
It has to actually promote thatgood, solid thinking that's
necessary in order for them tolearn that content.
But it's really you know themultiple strategies something
that's contextual, based, sothat they see that math is
(28:20):
useful, math is relevant to mylife as a whatever grade student
I am at that point in time.
Chris Colley (28:28):
Amazing.
Well, these have been some mathnuggets for sure Again.
Well, I mean just that richtask.
I mean I'm just it's startingin the reflective process, which
is amazing, so amazing kind ofthoughts that you've thrown out.
And again, thanks so much and Iwish you all the best, have a
great holiday season with yourloved ones and again looking
(28:51):
forward to seeing your influencein our system throughout this
year.
Kevin Dykema (28:57):
Well, thanks for having me on to talk math
education Awesome.
Chris Colley (29:01):
Thanks, so much, thank you.
Welcome back.
Another episode of Shift Edpodcast coming to you from
Montreal, canada, and I'mreaching down to Michigan, I
believe.
Kevin Nikoma is coming in toshare some math mindset stuff
with us.
And it's Michigan, right, kevin?
It is Absolutely Southwestcorner of Michigan.
(00:33):
Amazing.
And are you still the presidentof the NCTM?
Kevin Dykema (00:38):
Yeah, so my term actually it was a two-year term
ended like the 1st of October,so now I'm technically the past
president for a year, so I getthe honor of supporting the
current president and helpingher succeed Amazing.
Chris Colley (00:54):
Amazing, Great stuff, too, coming out of.
I mean, there's so manyresources out there for math
teachers and expertise as wellout there for math teachers and
expertise as well.
It seems to be one of oursubjects that gets a lot of
attention, a lot ofmisinterpretations,
misunderstandings and struggleas well, and that's kind of what
(01:17):
we'll focus on here today isthat productive struggle.
But before we start, Kevin,were you always into math?
Kevin Dykema (01:29):
Was that your jive at a young age?
As you grew up it was.
I always felt successful inmath and I mean, looking back
now I can argue I didn'tunderstand a lot of what I did,
but I always did very, very wellin mathematics and memorized
things.
I was a good rule memorizer.
I could follow the procedures.
It wasn't until I startedteaching that I actually had to
(01:49):
get to the understanding stageand I think I learned more my
first few years of teachingmiddle school math than I did
actually as a K-12 or a collegemajor in mathematics, when you
actually have to start to seethe why behind things and to
start to see connections betweendifferent things.
And to this day I mean I thinkevery time I work with a group
of teachers, work with a groupof students, I learn new things
(02:11):
or I see things differentlybecause when we allow our, when
we allow our learners to sharetheir thinking, good things
start happening and they oftenmy students often see things
differently than I see thedifferent content areas.
Chris Colley (02:25):
Amazing, amazing, and like, we tend to teach the
way we were taught, right, yes,and math is.
You know, I remember my mathclasses in particular, obviously
, and how kind of removed thestudent was from the whole
learning process.
The student was from the wholelearning process and the
(02:48):
teachers I see pre-serviceteachers and first-year teachers
coming into the system thatthat tend to, you know, go to
what they know, which is howthey were taught.
Um, is there a disconnect youfind between, like, um, how
we're, we're getting teachersready to teach math?
Um, because in elementaryschool, for example, I mean,
it's a lot of non-math experts,right, you're a general in
(03:09):
elementary school here in Quebecanyway, and then, as you go
into high school, you'reexpected to be, you know, more
of an expert.
But, like, is there adisconnect between how we
prepare our math teachers to thereality of it?
Kevin Dykema (03:25):
Yeah, I'm not sure if there's necessarily a
disconnect.
I think a lot of our collegesof education are doing a great
job of saying this is what itcould look like, but then they
get into a school system whereit doesn't look like what
they're doing.
That you know, in educationworld we're slow to change,
especially in the math world.
And you know, when I thinkabout the secondary folks, for
(03:46):
many of us we were great rulememorizers and school worked for
us.
Having the teacher just sayhere is the steps, here's step
one, here's step two, here'sstep three, memorize it and
you'll be good.
That worked for us and webecame math teachers.
And because it worked for us,we think it should work for
everybody, and I'movergeneralizing here.
But for Autism, we think itshould work for everybody and
(04:08):
the reality is it does not workfor everybody.
Having math be taught very, veryprocedurally has not worked for
decades and decades and decadesfor all.
It works for some and if we'retruly interested in meeting the
needs of all of our learners, weneed to look at doing things
differently and change is hard.
So I think they're in manycolleges of education.
They're being taught what theyshould be doing, but then they
(04:31):
get into the school setting andthe school setting looks the
same as it did 30 years ago, 40years ago, 50 years ago,
oftentimes in math.
That doesn't mean we haven'tmade some improvements in math,
but there's a lot of room togrow and I love how you noted.
I mean I don't love how younoted, but I appreciate how you
noted.
You know, in math it hasn'tbeen very student-centered in
(04:51):
the past.
It's been very muchteacher-driven.
And when we think aboutproductive struggle.
Chris Colley (05:03):
we need to get our students engaged in that
learning.
That's required in order tomake sense of the mathematics.
Absolutely, and Kevin, what ismathematics Like?
I saw one of your presentationswhere you led with that
question Like what is it Like?
Kevin Dykema (05:19):
could you expand on, like what that term is?
Yeah, and I think that's a.
I think it's a fundamentalquestion and I think the way
that you answer that question ofwhat is mathematics affects how
you think that math should betaught, how math should be
learned, or even why we have tolearn math.
I think for so many of ourstudents.
I'll go from the studentperspective first.
I think many of our studentssee math as I just need to learn
this formula, I need to learnthis equation, I need to follow
this procedure and poof, I'llget a correct answer.
(05:42):
Getting correct answers is very,very important, but I think
when you talk with a lot ofmathematicians, when you talk a
lot of mathematics educators,words that come to their mind
instantly.
When we talk about what ismathematics, it's problem
solving, critical thinking,reasoning and sense making,
explaining the real world aroundthem.
So there's this disconnectbetween what we think
(06:02):
mathematics should be and whatmany of our students see
mathematics as, and that's on usas a mathematics education
community to change that and toreally help our students begin
to see that math isunderstandable.
It's not all these random setsof procedures and we know
they're not random sets ofprocedures, but for many
students, they're viewing themas just random sets of
(06:24):
procedures that they have tofollow.
We need to teach math in such away that it makes it coherent
for our students and so that itbuilds from grade to grade to
grade and they see, oh, what I'mlearning in grade seven is
really taking some of that workthat I did in grade three and
just generalizing a little bitmore.
And then, oh, when I go tograde 10, I'm going to take that
(06:51):
same learning and just extendit a little bit more.
Chris Colley (06:52):
And we don't have as much of that as we could if
we're truly interested inmeeting the needs of all of our
kids.
Totally, totally, yeah, superinteresting.
And I mean your book ProductiveMath Struggle.
You mentioned worthy ofstruggle, right, that students
have to go through this and asteachers, I mean we're very
compassionate and empathetictowards our students.
Sometimes it makes usuncomfortable when we see them
(07:14):
struggling, right.
How do we change that mindsetthat we need to let them
struggle and that they're worthyof the struggle?
I love that term.
Kevin Dykema (07:25):
Yeah, and I think we know it's got to make sure
that we're defining strugglecarefully, right, whereas I'm
certainly not advocating, foryou know, when I walk into class
and all the kids are in tearsor all the kids that put their
heads down, I'm not like, oh,this class is rocking it, it's
that productive struggle, it'sgot to lead somewhere.
And is rocking it.
It's that productive struggle,it's got to lead somewhere.
And I think about you knowlearning in general, if I go out
of the math classroom for alittle bit, when you think about
(07:49):
you know learning a newinstrument, there's a lot of
struggle involved with that.
But yet we value that struggleand we recognize it's okay that
you don't have it perfect rightoff the bat.
It's okay that you're exploring, that, you're messing around,
trying to figure things out,sort of grappling with how to
hold the instrument, how to blowwith a horn, whatever the case
may be.
But then in math it comes sortof to a grinding halt and too
often we just teach math as this, procedure to procedure after
(08:11):
procedure, and our studentsdon't see math then as something
that they need to be studyingbecause realistically they say I
have a calculator, I'm at alltimes with my cell phone.
So I think when I think aboutyou know, mathematics seems to
be worthy of a struggle and it'sthat all students should be
doing that we need to help ourstudents recognize that math is
understandable.
There's a reason for that.
(08:32):
It makes sense, and let's teachmath as sense-making.
Let's get our students activelyengaged wrestling, struggling,
grappling whatever word you wantto use at that point in time to
have them begin to make some ofthat sense.
I often think, you know, in atypical traditional classroom
(08:54):
and it's for decades and decadesand decades the teacher is the
one that's doing all of theintellectual work maybe not all
doing the vast majority of theintellectual work in a math
classroom and the kids are sortof along for a free ride.
We need to get our kids doingthat deep thinking that's
required to be able to makesense and the teachers are
providing that support along theway and helping to ensure that
(09:15):
every student is beingsuccessful.
Chris Colley (09:18):
Right, I love your examples too, that it is a
skill that you, you develop.
You know, I mean similar tocreativity, example, right, like
some teachers, you know, orsome people, I should say, oh,
I'm not creative, right, butagain, it's this muscle that you
work on, right, and grow anddevelop.
Um, oftentimes, though, I'venoticed that, the relevancy,
(09:40):
right.
So you mentioned, like learningan instrument, I see the value
because I'm motivated in it'srelevant to me, right, I'm
interested in how do you turnthat in a math class to make it
relevant?
Um, and I I remember you hadmentioned that math is all
around us and, again, thatdisconnect between students
(10:01):
seeing it relevant in theirworld.
You know, when they walkoutside of the school, that they
start to notice these patternsor things that are similar.
Or can you expand on that alittle bit?
Kevin Dykema (10:13):
Absolutely, and I think some of it's.
You know it comes back to thehow are we thinking about math
and what are we?
What are we looking at withmath?
And, if we're being honest,much of the math that we do in
the K-12 setting is not the maththat they see in the world
around them.
You know I pick on high schoolsometimes that you know you
factor trinomials in high schoolbut you're not factoring
(10:35):
trinomials outside of the wallsof your school for most adults.
I mean there may be some thatare doing that for their career.
So we have to quit trying tofind every single topic that we
may teach in math and say, oh,it definitely applies to the
real world in this way.
But we need to help ourstudents recognize that math was
developed for a reason,somebody at some point in time,
(10:55):
and math is still beingdeveloped.
I want students to walk awaythinking, oh, it's just all this
past stuff that we're justredoing.
But then somebody had a reallife problem that they needed to
solve, and because they neededto be able to have some way to
describe a curve, differentmathematics was generated.
Because they needed a differentway to describe the way a leaf
(11:18):
may grow on a tree and we getnew math that is created at that
point in time.
So we need to help our studentssee we need to do a better job
of helping our students see theconnections between developing
math and that math has been usedto solve real-world problems.
We can look at some real-worldsituations and use some
mathematics, use some data, usesome statistics to help analyze
(11:40):
some of those differentsituations that are going on in
the world around them andhelping them just begin to see
there's a lot of math in there.
People are using some of thatlogical thinking, that critical
thinking.
They're using data to makedecisions and when we look at
you know, especially the last 10years, the amount of data
that's being collected and theamount of data that's being used
(12:01):
to make decisions has rapidlyincreased and we owe it to our
students to have them develop agood understanding of that world
around them and how we canmaybe describe it mathematically
.
Chris Colley (12:14):
Right, right, totally cool.
And I mean I love these ideastoo, that that when we are
teaching math and that studentsare going through that process
of figuring it out, that theybring certain luggage with them
the kids and you talk about itin your book this, this kind of
(12:34):
math trauma of sorts, where theydon't feel like they belong yes
, In math you know like theybelong, in math you know like
they.
Just there's this wall and it'sreally hard to break down.
But I love in your book youtalk about the belongingness in
that struggle.
Can you expand on that a bit?
Because I find it sofascinating that this sense that
if I don't feel like I'm, Ihave a purpose within this class
(12:58):
that's talking math, that I,you know, I'm excluded from it,
which again perpetuates thismath trauma that our young kids
go through.
Kevin Dykema (13:09):
Very much so and you know, sometimes I like to
frame it around this idea of amathematical identity United
States and Canada and I can'tspeak for all of Canada and all
of the United States, but as Iwork with educators, primarily
in the United States and some inCanada, you know I hear that
frequently, that you know, insociety it's generally it's very
cool to say I'm not good atmath, right yeah.
(13:32):
But you don't hear that sameadult say I'm not good at
reading.
They may say they don't enjoyreading.
So as a society we've sort ofmade it cool to say I'm not good
at math, so it's okay to feellike you don't belong in there
because nobody does good at mathunless you know.
We think of who is a math personFor many of us.
We grew up in a time you knowwhere it was.
Those that were pocketprotectors were those that did
(13:54):
math or those that hadsuspenders or it was sort of the
geeky type of stuff.
So we have to break down someof those walls and we need to
help our students recognize thatwe're all capable of learning
math and we need to sharestories of people who are doing
math.
When you ask a typical K-12student describe a mathematician
(14:16):
.
A mathematician it's an oldperson, often somebody who's
dead, somebody who's Caucasianmost of the time male, frizzy
hair.
As a math education community,we need to be sharing stories of
other mathematicians.
We need to be findingmathematicians who are still
developing math.
We need to find thosemathematicians who are young, so
(14:39):
that students see themselves ascapable of learning math.
They're recognizing oh, it'snot just Pythagoras, it's not
just Euclid, it's not justArchimedes, it's not just Gauss,
it's not just those that wethink of from centuries and
centuries ago as mathematicians.
People are still doingmathematics and it's not just
(15:00):
dead white males that didmathematics that they see
themselves.
And when they see themselvesreflected in people who are
doing math currently, they'regoing to begin to get a sense of
belonging.
And I also think that when wefocus on really getting to math
by understanding, rather thanjust math by memorizing,
students start to feel like theybelong in there.
(15:21):
Then because they recognize oh,I am capable of understanding
this.
Math is an understandablesubject and there's so much work
that we can do to help increasemathematical opportunities for
all of our students.
Chris Colley (15:37):
Absolutely Well said, well said.
Could you elaborate a bit?
Students, absolutely Well said,well said.
Could you elaborate a bit?
In the book it talks about thesix-point action plan for
fostering this kind ofperseverance and I'd even extend
that in developing thatcommunity, that math community
within your class where everyonefeels that they can contribute
to the thinking that's going on.
Can you talk a bit about thosesix points and how that leads to
(16:02):
?
Kevin Dykema (16:03):
Yeah, yeah.
So you know, when John Susieand I wrote the book, we said
you know we need to come up withsort of an action plan for
teachers, because it's not justgoing to happen instantly that
all of a sudden the kids aregoing to be like oh.
I'm so excited to have to thinkdeeply about math and to do that
.
It's not like a light switchthat you can go and flick on.
So what are some of thoseintentional steps that we can do
(16:23):
?
So the first thing we said youknow we need to work on valuing
this notion of really wrestling,grappling, making sense of the
math max, both from the educatorperspective as well as helping
our students see there's valuein not just being told what to
do and just memorizing.
There's value in having to workhard at developing a good sense
of understanding.
So that first action step isvalue.
(16:45):
That second action step is tofoster positive mathematical
identity.
We talked about that with thebelonging.
If they don't feel like theybelong in the world of
mathematics, they're not goingto feel capable of doing that.
So we need to foster thatpositive mathematical identity
and help all students recognizethey are capable of learning
mathematics.
The third action, then we needto build a classroom community
(17:06):
that's supportive of reallywrestling.
And what does it look like?
What are the norms?
What does it look like whenyou're, when you sort of get
stuck?
How might we get unstuck, forlack of a better word?
What are some things that wecan do at that point in time.
That fourth action, then, is toplan our lessons for it.
What can we do?
Where can we really provokethat deep thinking?
(17:27):
What are some strategic changesand some questions that we may
have asked in the past?
How can we change, then, aproblem that we may have done to
make it a little bit deeperthinking at that point in time?
And then, as part of thatplanning, then it's also
anticipating what are thestudents going to do?
How are they going to do itcorrectly?
What are some of those correctstrategies they may do, as well
as what are some of thosemisconceptions or partial
(17:48):
conceptions that they may bring?
And then how am I going torespond to that?
What am I going to ask?
So it's not just me rescuingtheir thinking or rescuing their
answers.
I'm rescuing their thinking andreally helping them go from
there.
That fifth step, then, is tosupport the productive struggle.
What am I going to do when thekid hits that point where they
say they're stuck, and I thinkso much of that's because of the
(18:09):
planning?
If I've planned well, I'm goingto be able to support better at
that point in time, and when wesupport, we have a rich history
in mathematics of when ateacher helps a kid, we grab
their writing utensil and we doall the writing for them.
That's not what we're talkingabout here with supporting the
struggle.
It's really getting to thatstudent's thinking, helping them
(18:29):
explain what are they currentlythinking and then providing
some prompts to help them makesense.
And then that final action, thatfinal step, is to reflect back
on that productive struggle.
We need our students to see hey, three days ago I might have
thought this was the mostimpossible thing in the world,
(18:50):
but because I didn't give up,because I kept trying to make
sense of it, now I've made senseof it.
I'm like, oh, it's not so bad,and when we do a little bit of
that, reflecting back on it,then we can celebrate it with
the students, which then justhelps to build that positive
mathematical identity.
So we look at those six actionsthe valuing, the fostering, the
building, the planning, thesupporting and the reflecting as
a way to really engage all ofour students in this notion of
(19:15):
making math understandable anddoing math by understanding
rather than math by memorizing.
Chris Colley (19:21):
Yeah, totally.
Kevin Dykema (19:23):
And like walk us through a period Like how would
you see a successful thinkingmathematically classroom, like
how would it start and then whatwould the teacher get the
students doing, and could youkind of walk us through what
that would look and feel likeyeah, and you know, and
depending on the content, theconcept you're learning, it's
(19:44):
going to look a little bitdifferent and you know what it
looks like in the first gradeclass is going to look different
than in the grade 11 class or agrade 8 class.
But overall, you know, the kidsare going to be working on, on
a good rich task, a good richproblem, something that's going
to going to spark some thinkingat that point in in time.
I'd often like to, you know,start out with that problem that
(20:06):
so often, you know, for many ofus, we did all the.
Some people call them the nakednumber problems, where there's
no context.
And then question number 38 wasa real life application and
sometimes, let's be honest, thereal life application and
sometimes, let's be honest, thereal life applications that we
use aren't real, real life.
But starting out with acontextual problem, helping them
(20:28):
understand why we even careabout this, get the students
actually engaged, get themsharing their thinking in small
groups, and then, as we'retrying to wrap it up, that's
maybe when we get a little bitmore of that procedural fluency,
when we get some more of thatprocedural stuff, I think,
historically, one of the flipsthat I like to think about.
Historically in math, we've toldour kids here's the procedure
(20:50):
to follow, here's the steps youneed to do.
Now you think, when I'm thinkingabout productive struggle and
I'm thinking about what a goodmath classroom should look like,
could look like, let's get ourkids thinking right off the bat.
We can provide more of thatstep-by-step at the end as a way
to wrap up, as a way toformalize their thinking, as a
way to make sure that, yes, weare good to go on from there.
(21:15):
But a good classroom, the kidsare doing the work, the kids are
thinking, the kids are not justsitting there listening to the
teacher do all of the thinking,all of the talking all class
long.
And it's hard.
It's hard to shift that becauseyou know, we talked about it
earlier For so many of us aseducators.
We grew up in a time where theteacher did all the work in the
(21:37):
math classroom and we just hadto sort of follow along and hope
that we could mimic theteacher's steps.
We need to be changing that.
We need to be getting ourstudents to do that rich, deep
thinking.
Help the students see theconnections between different
things, help the students makesense of the mathematics and
then we can provide some of thatstructure towards the end of a
(21:59):
typical math class.
Chris Colley (22:00):
Then yeah, for sure, I love that idea too.
It's a small tweak, but justthrowing the question at the
start or the problem at thestart and allowing the students
to kind of like struggle with ita bit and then if there's any
misunderstandings, you can cleanthose up at the end, yes, um
yeah, and we have to recognizenot not all kids are gonna do
the problem the same way andthat's okay.
Kevin Dykema (22:23):
And if I'm being honest, sometimes my students
see problems a whole lot neaterthan I do, that my brain,
because I'm driven just sofocused on math, math, math,
math, math.
I jump straight all the time tolet's write an equation for it.
Most students do not jumpstraight to let's write an
equation for it.
Most students wrestle throughand actually think with that.
With that One of the things Ioften like to do when I'm
(22:47):
leading some professionaldevelopment either, with sharing
a math night for parents,working with teachers, working
with administrators, workingwith students, I may say how
would you do 245 plus 98?
And for most people they say,oh, if I'm going to do 245 plus
98, I'm going to think of it as245 plus 100 and subtract 2.
Or some other strategy thatthey may have.
There's lots of differentstrategies Like all right, this
(23:09):
is what we need to be making ourmath classes like.
We need our kids to be doingthat thinking.
We shouldn't just say, oh, backin 19-whatever, here is the one
and only one way that we coulddo the 245 plus 98.
Let's get our kids thinking,sharing their reasoning, and
that means we need to have thatcomfort of recognizing it's okay
if they don't do it the exactsame way that I may have done
(23:32):
and it's okay if they have a waythat I'm like, oh, I'm not
positive that it works for us tosay, all right, hey, let's try
it with a different set ofnumbers and to see if it works.
And it's a shift for the kidsand it's a shift for the
teachers.
But it's so powerful for ourstudents and it helps our
students to see that math iscapable of being understood and
(23:52):
math is useful.
It's not just the subject thatpeople did decades, centuries
ago and that we're just redoing,relearning everything that they
did, however, many years ago,and there's really no value in
it.
We had to have our students seethe uses of that, see when they
would use the mathematics in avariety of different settings
(24:14):
For sure, you know.
Chris Colley (24:15):
It's interesting that you're saying that too,
because I'm thinking about whenI'm working with kids in coding.
You know, either doing ascratch project or like
programming in Arduino orsomething like that thought
process is very similar to whatyou were mentioning there, and I
wanted to ask you thatcrossroads, because coding
definitely seems to be somethingthat is becoming more and more
(24:37):
relevant.
It's going to affect way morepeople's lives.
Where does coding and math meet?
Kevin Dykema (24:46):
Yeah, that's a great question.
That's one of those things thatI think about and I talk with
other people and you know Idon't think as a collective
education community we've cometo any resolution yet about how
to intersect those.
Everybody's saying, yeah,there's a lot of overlap in
there, but to figure out, how dowe fully integrate that into
(25:06):
there?
And you know we have a finiteset of minutes that we have our
students in there.
But to figure out how do wefully integrate that into there?
And you know we have a finiteset of minutes that we have our
students in school.
So anytime we try to addsomething in, theoretically,
something needs to go out and weneed to figure out what is it
that needs to go out.
I often like to, instead ofthinking you know, what are we
eliminating?
What are we de-emphasizing?
What are we going to emphasize?
(25:27):
What are we going to tode-emphasize a little bit, and
and sometimes when we startthinking about, oh, I can
de-emphasize this after a periodof time, we're like all right,
why am I even doing this anymore?
But sometimes it feels harshjust to say, oh, I've loved
doing x for however many years,I can no longer do it.
Let's just sort of gradually doa little bit of phasing out,
(25:49):
and you know some of it's.
We've got to recognize what arethe skill sets that our
students are going to need tohave in order to be productive
citizens in the world.
And you know, coding isdefinitely one of those that
they need to be able to have abetter understanding of what it
is and the more and moretechnology driven that we become
, we need students who have anappreciation and have some skill
(26:13):
set in that world of coding.
Chris Colley (26:16):
Right, right.
Well, this has been a reallyfascinating conversation, kevin.
I really appreciate you carvinga bit of time to share your
thoughts with us and I'm reallyexcited that you're going to be
supporting, um, our mathconsultants and teachers and, um
, I think that these kinds ofconversations are super rich and
(26:36):
just kind of reflecting on ourpractice a bit, um and, and
realizing that it's not a youknow, like we have to change
everything.
We can make small adjustmentsthat allow more thinking into
the classroom and giving it abit more back to the student,
which I really appreciate.
Those thoughts and your book isjust, really just a great
(26:59):
plethora of ideas and starters.
I wanted to talk a little bitabout rich tasks, but I mean,
your book touches on those a lot.
But maybe my final question toyou as we close here is what
makes a good rich task in youropinion?
Kevin Dykema (27:15):
Yeah, I think a good, rich task is something
that has an interesting contextand I acknowledge an interesting
context for student one is notan interesting context for a
student two, so you're not goingto have a task that every
single kid is going to be likeoh, I love the context of this.
But it has to be in some sort ofa relative interesting context.
It has to have a variety ofdifferent strategies that
(27:37):
students may use for it.
Some may make a table of values, some may jump to an equation,
some may make a graph, some mayreason through it.
There has to be some way forall the students to be able to
at least get started on theproblem.
They may not all have theability initially to find a
solution in a relatively quickamount of time, but whether they
(28:00):
all can get started at thatpoint in time it has to be
aligned to the content.
We can't just pull out thesethings and say, oh, this is kind
of a fun thing to do.
It has to actually promote thatgood, solid thinking that's
necessary in order for them tolearn that content.
But it's really you know themultiple strategies something
that's contextual, based, sothat they see that math is
(28:20):
useful, math is relevant to mylife as a whatever grade student
I am at that point in time.
Chris Colley (28:28):
Amazing.
Well, these have been some mathnuggets for sure Again.
Well, I mean just that richtask.
I mean I'm just it's startingin the reflective process, which
is amazing, so amazing kind ofthoughts that you've thrown out.
And again, thanks so much and Iwish you all the best, have a
great holiday season with yourloved ones and again looking
(28:51):
forward to seeing your influencein our system throughout this
year.
Kevin Dykema (28:57):
Well, thanks for having me on to talk math
education Awesome.
Chris Colley (29:01):
Thanks, so much, thank you.
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