December 3, 2024 • 46 mins
Math mistakes can open up new learning opportunities.
Today we are joined by middle and high school math teacher Russell Hanes, who has been teaching for two decades in public and private schools in the U.S. and abroad. In this episode, Russell discusses how to help students step out of their math comfort zone and see themselves as “math people.” Plus, Russell shares teaching strategies to use in the math classroom, like helping students embrace and learn from their math mistakes.
Teachers in America profiles K–12 teachers across the country. Hear firsthand from the people who are shaping young lives in the classroom every day. If you or someone you know would be a good candidate for Teachers in America, please email us at shaped@hmhco.com.
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Episode Transcript
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Speaker 1 (00:01):
Let students see that there are actually multiple
pathways that get them to thecorrect answer.
And to honor different sorts ofsolutions, honor different ways
of thinking about it, reallyhonor that.
Students have done a lot of thethinking.
It just might not look exactlyperfectly crystallized math
right, but it's stillmathematical thinking.
Speaker 2 (00:25):
From paper and pencil to Wi-Fi and AI.
Education is ever evolving.
On this new season of Teachersin America, we'll keep you on
the forefront of what's new.
We connect with teachers and edleaders to talk trending topics
and real issues, bringing youinspiring ideas that will
influence the future of yourteaching.
Today, host Kaylee Rhodesconnects with her former
(00:46):
colleague, math teacher RussellHaynes.
Russell has been teaching fortwo decades in public and
private schools in the US andabroad.
Throughout his career, he hastaught public speaking, debate,
civics and every math subject,from fractions in sixth grade to
AP statistics in high school.
Today, russell and Kayleediscuss how to help students
(01:07):
step out of their math comfortzone and see themselves as math
people.
Plus, russell shares teachingstrategies to use in the math
classroom, like helping studentsembrace and learn from their
math mistakes.
Now here's Russell and Kaylee.
Speaker 3 (01:22):
Russell, welcome.
I'm so glad that you're here.
How are you?
Speaker 1 (01:27):
Very good, very good.
Thank you so much for having me, kaylee.
This is really awesome.
Yeah, I love that you're doingthe podcasting thing now.
This is such an awesome stuff.
Speaker 3 (01:40):
It's a perfect fit, right, I like to talk and you're
like I have to go teach.
Speaker 1 (01:45):
Yes, Well, I love that.
I got a random text that waslike, do you want to be on the
math podcast?
And I was like I can only beone person.
Speaker 3 (02:00):
Yeah, but then you, in true Russell form, had to don
on talking about how to getstudents from their you know,
very, very understandable mathtrauma into their math comfort
zone, helping even teachers stepmore into that math comfort
zone.
And there's no better person totalk to than you, because you
have been so formative in myjourney as seeing myself as a
math person, because I didn'tstart as a math teacher.
(02:22):
You, I started in the Englishclassroom and you were my first
mentor as start as a mathteacher.
You, I started in the Englishclassroom and you were my first
mentor as I became a mathteacher.
Actually, one of the firstconversations you and I had was
about quote, not a math person.
That was one of the firstthings we were in your office.
So how do you?
How do you respond?
Let's just start with a student, because everyone says it right
(02:44):
.
Speaker 2 (02:44):
But how do you?
Speaker 3 (02:44):
respond when a student says I'm not a math
person.
Speaker 1 (02:49):
I mean, I think there's like sort of two flavors
that you can get, right, likeone is the student is saying
it's just not really my interest, like it's not like something
I'm super passionate about.
And then you get the studentswho are saying that because
they've been super traumatizedby math.
Right, this is a like just as atrue story.
(03:10):
I one time was getting myhaircut and the lady said what
do you do for a job?
And I said math teacher.
She hissed and jumped backRight, this is how traumatized
some people people are aboutmath, right.
So I think the first thing thatyou have to do is figure out,
like why the student is sayingthat.
(03:31):
Are they telling you like theyare afraid of math, or are they
telling you that it's just nottheir thing, right?
yeah which, if they're tellingyou that it's not their thing,
like you know you want toconnect them to all of the
amazing things that you can dowith math, all of the
interesting properties that theycan learn about, like connected
(03:53):
to their interests, like thesubject that they're.
You know they're interested inscience Great.
They're interested in art Great.
Like let's find the connectionsto math that they would find
really interesting.
Right, that's maybe just afunction of they haven't had a
teacher, like really look forprojects and applications that
they find interesting.
(04:14):
But, as you well know, rightfrom teaching sixth graders who
many of them came into it likeinto your classroom, like really
traumatized and upset, uh, likeyou have to figure out, like if
that's what is going on andsort of help them start to
unpack it, and that that's awhole different ball of black.
Speaker 3 (04:37):
Right, yeah, I, um, for context, I have our, our
group of sixth grade students,um, who need the most math
support, and I think that whatshocked me because I mean I'm
going to say it like I'm not amath person and I'm not supposed
to say that, like I'm notsupposed to say that but I'm not
(04:57):
a math person and like what Imean, what I mean when I say
that is like math does not comeby osmosis for me, like I can't
just watch a teacher do it andlike see it and just go
replicate it or even be likewhat about this?
And like get up there andba-doop-boop-boop like jazz riff
on whatever I just saw.
(05:18):
I have to be like I need a lotmore questions answered before
I'm ready to really understandthis, but I think that that's
normal.
But what I saw in school wasjust prodigies.
It felt like prodigies andplebeians, Like and I was
definitely a plebe and so I wasjust that.
That equaled if you're not agenius, ergo you are not a math
(05:40):
person Like that's what it feltlike.
Now I have to tell my studentsthat I said that too.
You and I have to reclaim ourspeed, because speed's a big
trigger in math.
We have to reclaim our speedand we have to reclaim that
maybe I.
This is something that Iactually really love about the
(06:03):
Common Core is it mandates thatwe have different ways of
instruction, instructing thesame concept, and I feel like
that really like honors what Ineeded.
Speaker 1 (06:13):
And so what has also surprised me is that a lot of
kids come into my class with uh,with the lowest math, uh,
current like application ability, and they say they love math
yeah, that's mean I think it's atestament to like your skills
connecting with students, right,um, and I think what you're
also saying is really importanttoo about the curriculum, right,
(06:34):
the way that we have taughtmath, right, where you're trying
to go at the fastest possiblespeed, right, uh, does not work
for a lot of kids.
It doesn't particularly workfor me either, like I don't find
it really pleasurable to sitdown and take a timed math test,
(06:56):
right, no, um, and and there'salso ways of like the ways that
we have set up instruction,where we're like trying to get
students to like replicate, likedown a very specific narrow
pathway, is not going to workreally well for lots of students
.
And if you have a broader, openpathway, more open pathway,
(07:21):
that's good for a lot of kids,that's good for more kids.
That's good for a lot of kids.
That's good for more kids.
So I think a lot of the problemis that the way that we've
taught creates a reallystressful environment for kids.
If we use timed tests, I don'tparticularly enjoy that.
It's stressful.
I recently have had to take aclass where there were timed
(07:42):
tests I, you know I didn't enjoyit like it's trying to recall
stuff as quickly as possible,which doesn't work for every
moment, for every learner right,and the way that we've done
instruction too in the past hassort of limited the number of
pathways that students can godown.
(08:03):
Like we show them one pathway,we're like here's how to get to
the answer, and we sort ofexpect students to be able to
follow along that pathway andreplicate it, whereas a better,
I think, way of instruction isto let students see that there
are actually multiple pathwaysthat get them to the correct
answer and to honor differentsorts of solutions, honor
(08:25):
different ways of thinking aboutit, really honor like that
students have done a lot of thethinking.
It just might not look exactlyperfectly crystallized math,
right, but it's stillmathematical thinking, right.
We kind of like fetishize, likea outcome, like students are
(08:47):
supposed to write proofs orsomething when they're still
learning material, right.
Speaker 3 (08:52):
Which is why in your class you do a ton of like group
work, where maybe themathematical thinking is
crowdsourced and then maybeyou've got the student that can
kind of push it through to thatdistillation.
Speaker 1 (09:07):
Right.
Right, and I think part of itis just not trying to rush the
students to that point, right,part of it is that we want to
have the students get to likethis distilled, crystallized
result in three weeks or fourweeks or whenever we're wrapping
up the unit, and we all knowthat that's like setting a
(09:29):
timetable that like might not berealistic for certain kids,
right, and it would be better tojust sort of acknowledge, like
okay, your understanding of thisis still a work in progress,
you're not like the mostcrystallized form, but you, you
still understand the coreconcept, like recognizing that
(09:49):
kids can still be in process,like at the end of the unit yeah
, which makes uh grading reallycomplicated oh, it's a mess,
right?
Speaker 3 (10:00):
well, because if we're really if we're really
like alive this idea of growth,it's not about achievement, it's
about growth and if we'rereally therefore, nuanced about
you have to understand eachkid's kind of brain, not just
what's on the paper, but whatyou know is going on back there,
and that does make giving ascore or a letter to that really
(10:22):
, really tricky.
And I'm actually going to I knowthat you and I could talk about
grading all day, so I'm goingto make sure that what I want to
do is press pause and be likeokay.
So that moment that a studentsays I'm not a math person, you
said just kind of suss out, whatare they telling you?
Are they telling you that theywould rather be in art, or are
they telling you that they havetrauma or both?
(10:42):
And then making sure that I'veheard a lot of like speed.
We've both been talking just alot about speed and we've also
both been talking a lot aboutlike externalizing, um, this
very conversation that we'rehaving right now, kind of almost
doing it in front of the kids.
Speaker 1 (11:00):
Yeah, I think recognizing, like talking to
kids and saying, you know, ifyou have been traumatized in a
previous class, like I'm reallysorry that that happened, like I
don't think that that was right, like let's sit down and
actually figure out what youreally know.
You know, let's figure out whatyou really can do, yeah, what
(11:22):
you really can do without all ofthe stress, without all of the
like you know, I mean, I've I'veseen people, uh, you know,
working with students who reallyjust add to their stress, and
I've seen people who like, taketheir stress away, right, and I
think the whole thing that Iwould argue is that we need to,
(11:44):
you know, as teachers, find waysto help take the stress off,
because then you're going to geta more accurate read of, like,
what the student really knows,what they actually really feel
Like.
Math doesn't have to beeverybody's favorite subject,
yeah, and that's okay, you know,but they can all do it, you
know, we should figure out whatthey are actually capable of
(12:06):
doing.
Speaker 3 (12:07):
Right, and we have a math pledge of allegiance in my
class and the last line of it isjust, I will go at my own pace
and I will endeavor to see thebeauty of math around me, me
because if, even if you are nottrying to go further with your
(12:27):
math studies, which we're goingto talk about in a second you
can at least appreciate thatmath is probably, as you said
earlier, they're interested inscience.
Math's everywhere in science,you know, um, but if you're, if
they're interested in anime,math is all over anime.
So just like it's everywhere,so just like let's, let's
embrace it.
So when we picture this mathclassroom that you and I are
trying to like, kind of, maybemove away from a lot of people,
(12:51):
the image that pops into theirminds and they might even still
be educators, but the image thatpops into their minds is like a
lot of bent heads over paperand pencil, doing these kind of
repetitive tasks to get thealgorithm down.
Doing these kind of repetitivetasks to get the algorithm down,
but teaching math?
I was surprised, coming from,like the speech and rhetoric
(13:11):
world, which you also occupy asa debate teacher, but coming
from an English teacher.
We talk so much in math.
Math is so much discussion andargument, so how has your
experience as a debate teachershaped the way that you are able
to hold space and facilitatethat math discourse?
Speaker 1 (13:28):
Well, I think a big part of like what we need to do
as math educators is actuallythinking about entertaining
hypotheticals.
Right, Timmy might not have thecorrect answer, but has made an
interesting mistake and we needto walk through that mistake
and see where they slipped upand if other students made that
(13:54):
mistake, and to understand whyit's wrong and to understand how
to correct it.
Right, that isn't to say thatlike, like there is absolutely a
place in math for likecorrecting students and saying
what's right and what's wrong.
Like there's absolutely anecessity for doing that, unless
you are intentionally likeleaving them with a cliffhanger,
(14:15):
right.
But I think that we should beable to entertain hypotheticals
and like ask students to explaintheir reasoning.
Like what's your argument forwhy this is true?
Walk us through the logic.
That's the key part that holdsthat math uh, has to like hang
together by like logic, right?
Speaker 3 (14:37):
if the students can't explain the thinking that got
there, it doesn't matter whetherthe answer is right or wrong
it's kind of like when you'reassigned a side in debate that
you don't necessarily personallyagree with and you still have
to mine it for what's there, andthere's definitely something
there.
(14:57):
I my favorite thing to do is, um, if a student has made an
interesting mistake, like, say,on the board, number four,
everybody take a look at numberfour.
You know, and I've privatelychecked in with number four
beforehand and been like, hey,I'm going to you have a really
cool mistake, don't erase it,it's about to become the
backbone of our lesson.
Um, but one of my favoritethings to do is, like, mute that
kid.
It they can't defend, like, andthey're not being defensive,
(15:22):
they literally are defendingtheir math.
But muting them and making therest of the class try to explain
what they thought happened notonly enlivens the rest of the
class but makes that one kid goinsane.
And you're like.
I never thought I would see youwrithe from wanting to talk
about math.
You're welcome, you're a mathperson.
Speaker 1 (15:45):
Exactly.
Yeah, no, I think you'reabsolutely right.
Like the issue is like yousometimes have to step into
other people's shoes right andwalk through the logic that they
did, even when you can see thatthere's like a mistake.
Like you have to be able tolike articulate.
I do think the problems thatlike being included more in
(16:07):
curricula, where it's likehere's what two students thought
explain what their reasoning is, explain where they went wrong
I think that's a really goodexercise for students to see
mistakes and see mistakes asnormal right.
That's a big part of we have tolike see mistakes and see
mistakes is like normal right.
Yes, that's a big part of likewe have to normalize mistakes,
(16:29):
we have to normalizedisagreement.
That's a that's a big part toothat, like, the students look up
to the teacher and think thatthe teacher never makes mistakes
, and that's that's just not agood rhetorical stance to have
as a teacher right.
Speaker 3 (16:44):
Right?
No, it also makes you, as ateacher, feel so.
I, as a math teacher, felt thesame amount of pressure that I
felt as an English teacher toanswer everyone's grammatical
question and I'm supposed to beable to spell every word that
ever worded.
So now, of course, I'mresponsible for calculating
everyone's taxes because I'm ateacher.
Speaker 1 (17:08):
That's terrible.
No, I think it's like mathteachers, like we should feel
comfortable with ambiguity, likewe should model that for our
students, like I think it'sperfectly OK to say that's a
really interesting question.
Speaker 3 (17:26):
You've said that to me.
I don't know if you rememberthis, but a couple years ago I
couldn't figure something outand you were next to me teaching
and I came over and interruptedyou and I was like I have a
problem, I don't know.
Will you help me?
I've done it to Chris too,another colleague of ours.
(17:48):
I was just like I want them towatch two adults who are curious
about a math problem and maybethey can't solve it.
Like that is math in progress.
A lot of the math that we'reteaching is discovered math kind
of like science.
A lot of the science we'reteaching is established science.
But when you watchmathematicians math or when you
watch scientists science it'sbecause there's a question mark.
Speaker 1 (18:14):
Absolutely, and it doesn't have to be something
that's like at the forefront ofthe limits of our research with
math in order to be a validquestion.
Right, right, it's literallyhow much more parking do I need
to?
Speaker 3 (18:28):
put in my meter if this is what they charge and,
like Russell, can your phonereach my parking?
Here's my phone.
Go pay my parking Right.
But that's silly.
Speaker 1 (18:47):
I'm excited to discover that there's so many
parallels between what and thatmaybe you know, no one has the
answer uh per se, or, like youknow, we're we're going to
(19:21):
figure out the answer togetheras a result of doing this
process.
Um, you know, I always tell,tell my students in debate that
I have had students actuallychange my mind on a on an issue,
and that it's not reallyimportant.
You know what my position is.
In a debate class, like, whatis important is that you can
(19:44):
actually justify and back upyour own answer.
Right, that you can.
You can use research andexplain your own reasoning.
That's the important bit, and Ithink that's the same, exact
same thing in math, right, youshould be comfortable with
ambiguity, like.
The teacher doesn't have to bethe final authority on every
question.
Speaker 2 (20:06):
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(20:26):
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Speaker 3 (20:40):
Okay, speaking of debate, there seem to be two
schools of thought when it comesto math facts.
A lot of people are still inthis camp of we need to memorize
them.
And I'm saying a lot of peopleare still in this camp because I
, on every other day I'm in thiscamp of we need to memorize
math facts.
(21:00):
And then others say to focus onthe problem solving and the
math facts will come, Like if astudent just knows seven times
eight, it doesn't necessarilytell us if they understand why.
But what's your perspective onhow students should build
fluency with those math facts?
Speaker 1 (21:17):
So I think in this case both of the extremes are
sort of caricatures that I thinkare not best practices for like
helping kids.
I'm sorry, what, what word didyou?
Speaker 3 (21:35):
just say.
Speaker 1 (21:37):
Curricatures, curricatures.
Speaker 3 (21:38):
Oh my gosh, where are you from From?
Where are you from From?
Speaker 1 (21:43):
Did I say it wrong.
Speaker 3 (21:50):
No.
I don't just I say I say itwrong, I say caricatures.
Speaker 1 (21:54):
Can we write a song called caricatures, caricatures.
I think they wrote one.
You say potato, I say potato.
Speaker 3 (21:59):
Okay, that's just like the unknown verse.
That's like the deep cut it'sthe deep cut, okay, sorry.
So yeah, both extremes Not good.
Like don't make students justlike wrap them on the knuckles
until they know all their theirmultiplication tables, but also
like we need some kind ofcommitment to memory.
Speaker 1 (22:17):
Yeah, I mean, we know that like being like being
unable to like draw from factsis going to hinder kids who are
not able to like see a pathwaythrough a problem, who are not
able to like see a pathwaythrough a problem right?
So just to give an example, Ihad a student in a pre-algebra
class who was still counting ontheir fingers, perfectly
(22:38):
understood all the linearequations that we were doing,
but every time this kid had tosit down and like simplify
fractions, they were likecounting on their fingers right
In eighth grade and you couldsay, well, you could pull out a
calculator.
But the kid who's like able tolook at a fraction and say, oh,
(23:00):
six, sixteenths, I know that sixis twice a three.
I know 16 is twice an eight.
It's going to be able to likesimplify it much faster.
They're going to be able tolike simplify it much faster.
They're going to be able tomake insights and just not have
the cognitive load Like this kidtook like an hour to answer a
question on a test because theywere doing everything.
Speaker 3 (23:20):
Even though they're ready, they're ready, they get
it, oh yeah.
Speaker 1 (23:26):
The abstract reasoning that we were doing
with linear equations.
This kid understood right.
But their cognitive load wassuper high because and the way
that I understand cognitive load.
Speaker 3 (23:40):
you taught me that term because I was coming to you
and being like their gears aretoo frictious in their head and
they get fatigued and you'relike, yes, there's a word for
that that's.
Speaker 1 (23:52):
That's exactly what it is, right.
It's just you can only juggleso many balls and working memory
and you need to be able tochunk things and working memory
so that you can get to thebigger stuff, right?
Yeah, if you're constantlymanaging small chunks of
information because you haven'tmemorized something, then it's
(24:14):
certainly going to slow you downand impair you when all these
chunks are, like you know, needto be kept in mind at once.
Speaker 3 (24:23):
Yeah.
Speaker 1 (24:25):
I think that's the best argument.
Speaker 3 (24:27):
I think that's the best argument.
It's just like it's not aboutturning our kids into into like
a militant memorization thing.
It's about smoothing the gearsfor later, when they are like
ready to fly, and the smallstuff isn't like gumming up
their wings, exactly, exactly.
Speaker 1 (24:47):
It's ice on the wings , right, exactly, exactly.
It's ice on the wings, right,right.
But by the same token, there'sgood memorization and bad
memorization.
Like they can just sit thereand memorize their times tables
just completely rotely.
You know, 7 times 9 is 63,right.
Or they could actually memorizewhere they're looking for
(25:19):
patterns, right.
Oh, seven times nine.
Well, I also know, seven times10 is 70.
Seven times nine must be lessthan 70, right.
How much less.
Well, it's one seven less.
Then the chances that you cango and recall something when you
need it just becomesexponentially higher, right?
If you just memorize somethingas like a disconnected, isolated
(25:43):
fact, your recall of it isgoing to also be kind of poor,
right of it is going to also bekind of poor, right.
You're going to have to likeland the one pathway to recall
that memory.
Speaker 3 (25:56):
But if you're like building an interconnected set
of memories, yeah, if you'recultivating flexible agile, a
playground of math in your head,rather than like one slide, one
slide, one slide.
Speaker 1 (26:09):
Exactly.
It's not just about crammingthe stuff in and somehow recall
happens magically, right?
You want recall to be almost so.
You want to have created somany pathways that it's almost
hard not to recall it that theyalmost would have to like
intentionally not wander acrossa pathway and recall it.
Speaker 3 (26:34):
Oh well, and you're, uh, there's a one of my tricks,
one of my classroom tricks isthat I buy like a ball and I
write math, uh, multiplicationproblems all over it, and where
we throw it around and whereveryour right thumb lands, you have
to answer that math, thatproblem.
But there's no um, you don'thave to play, you can sit down,
(26:54):
um, you can say pass, likethere's a lot of, there's a lot
of uh safety nets, because Iknow that that that could sound.
Not only have I entered some,that's some people's hell.
Right, I have to catch and thendo math, um, but but uh, I have
a couple of things in place formy like high flyers too.
When they catch a ball and theysay a math fact, really fast,
(27:14):
you know, like seven times nine,sixty three, and they like rear
back to throw the ball tosomeone else, and I'm like wait,
can you tell me another, canyou tell me why?
Like can you just walk methrough?
And they'll do your 71, becauseI'm all seven times ten minus
seven, and I'll be like, can youdo it any other way, a
different way?
And then they start gettinglike playful with 21.
(27:34):
And so I asking people to like,asking students to like
lubricate their gears externallyand in front of other kids.
Kids, like throwing a newpathway to even the high flyer,
(27:56):
is essential to showing kids whyit's not good enough to just
know a 63.
That's not, that's not the endgoal.
That kid, that would haveintimidated Kaylee middle school
.
Kaylee Rhodes actually wasn't asas a maybe fluent as I thought.
Speaker 1 (28:07):
No, I, I totally agree.
I mean, I think that that's anexcellent activity and it's a
really clear indication thatlike the stuffing memories in is
(28:29):
not to like have all of thesefacts.
It's to have like useful factsand connections and see the
connections so that we can thinkflexibly Right, it's building.
It's building muscles, like youplay scales so that you can
then play things that are notscales Right, but you need to
know where your fingers need togo on the keyboard so that you
(28:51):
can do the scale correctly, sothen you can start jumping.
Speaker 3 (28:55):
Yeah, and the more like in your body the scale is,
the the less friction you'regoing to have as you fly higher,
as you, as you start composingWell, and so like this, this
kind of like roteness versusrhythm, I guess is something
that we see a lot in curriculumold curriculum, new curriculum
(29:15):
because a lot of teachers swearby practice sets where students
work on the same skill over andover again, just like get it in
your body, get it in your body,which I understand.
But there's also another schoolof thought where we're looking
at these open-ended, rich, longmath tasks that take whole class
periods or longer.
How do we strike a balancethere, and what does a good math
(29:38):
task look like in your opinion?
Speaker 1 (29:41):
So I think with like open-ended tasks, the same thing
is true, that there can be goodopen-ended tasks and bad
open-ended tasks.
Right, if you threw a problemat students and basically said
here you learn, you knowderivatives on your own, like
you need them to be able toanswer this question, but I'm
(30:02):
not going to teach you.
I mean, that's just too much.
Right, it's not scaffolded forthe students it's a bad escape
room yes, exactly, exactly.
What you really need is anopen-ended task where, like,
they're bringing a motivation ontheir own, they're interested
in the subject matter.
Maybe it's the kid who's, like,passionate about art, getting
(30:25):
to connect, uh, but where?
Where you've scaffolded themath task for them, right?
I think the question of, like,what defines a good activity
versus a bad activity, likeacross the board, is, you know,
number one is it somethingthat's like in the appropriate
(30:46):
zone for the kids, right?
Is it something that they'reactually able to understand and
to do productively?
Is it something where they willbe able to think rich, make
rich connections and thinkdeeply about the problem?
And have you set them up in away where the clear onus of
(31:11):
thinking is on them?
And there's a whole gamut ofactivities, from, like, fun
games, memorizing, to doingopen-ended projects, to doing
group work.
All of those can meet thosecriteria.
If you just are being reallythoughtful about what my purpose
(31:31):
is as a teacher, like, what ismy pedagogical purpose?
What do I want the students toaccomplish here?
So I think all of those can beset up as good tests.
Speaker 3 (31:43):
Do you have a favorite?
Creating something?
I know about me being a mathteacher is inventing math
problems is hard.
Inventing whole class, richtask, perfect zone of proximal
development, perfectlydifferentiated.
I've created the.
That is really tricky and so Ihave.
(32:07):
I look to resources, right.
What are some favorite?
Like hey, if you are ready toengage your kids in some rich
whole class tasks and yourcurriculum isn't maybe meeting
that need, where would youdirect one of your teachers?
Aka, me.
Speaker 1 (32:25):
I would actually say I think a lot of the things that
we need to do are pulling fromthose resources, just like you
mentioned, from textbooks, fromother resources that you have,
from like websites.
But I think the key thing isyou, as a teacher, having the
(32:50):
confidence to improvise and toadapt right.
You know the.
The saying is no battle plansurvives contact first, contact
with the enemy.
Uh, and I think no lesson plansurvives the first five minutes
of class, like as soon as thestudents see the problem, you
might as well just throw yourlesson plan away right, because
it's not going to go to plan.
No, and I think the differencebetween an experienced teacher
(33:13):
who's really focused on like thegoals is that they know how to
like, adapt and respond.
They recognize where thestudents are struggling, where
there's room for growth.
So I don't, I don't think youhave to come up with like here's
the perfect lesson plan.
I have defined this, I havepulled it out of the heavens and
(33:36):
I've put it into paper form andit's going to, you know, amaze
the students and wow myadministrators.
Speaker 3 (33:43):
It's going to tap dance across the desk.
Speaker 1 (33:46):
Exactly right.
That's not the goal.
Like the goal is to say what dowe need to do today?
We need to talk about linearequations.
Let me pull some lesson plansthat I can find online and other
textbooks.
Where are my students going tostruggle doing that?
Pre-thinking makes a hugedifference.
(34:09):
And then, as soon as you get inthe classroom, taking the
opportunities and like likelooking for the students who've
made interesting mistakes, likelooking for the uh, looking for
the one-offs that just happenedthat one day and they don't
happen again, right.
Speaker 3 (34:26):
So deviating from your script, making sure that
you walk in with a rich thingthat you've thought about.
But if your goal is to watchthem ignite with thinking and
interacting with the problem,then they have about 100
different ways they can do thatand you just need to follow them
where they go.
Speaker 1 (34:45):
You're kind of a.
Yeah, I was just going to say.
If your goal is to get thestudents to think, how would you
do that?
By yourself shutting down inthe classroom?
Speaker 3 (34:58):
Yeah, if your goal, what's your goal?
To get them to think it's soand like what does that look?
We haven't gotten to numberthree, which is when I show you
this graph and you, like I, likewe know we never got to number
three because at number onethere was enough for them to be
(35:21):
thinking and that was my goal.
But it is like letting go.
So much of teaching is lettinggo.
It's so, it's like a soap is in.
Speaker 1 (35:29):
You've heard the, the expression in editing, that you
have to murder your darling yesthat's the, that's the
fundamental rule of teaching.
I think too, it's like.
Speaker 3 (35:41):
But number three is so exciting to me I photocopied
it front and back in the colorprinter.
It was all across campus.
Who am I making fun of Me?
Okay?
No, you'll recycle it, okay.
So what you're recalling for mefrom the top of our
conversation is this idea that,being honest about what thinking
(36:09):
looks like and so it can't.
Even if you have a kid thatknows all the math facts, is
there thinking?
Even if you have a kid that'sstill counting on the fingers,
is there thinking?
And so, just um, coming back tothis whole idea of not a math
person, one of the things that Iget, uh in my classroom are,
you know, brand new little sixthgraders who are not used to uh,
(36:31):
not walking out of theclassroom with an answer and or
or knowing they did it wrong orwell, this was your mistake.
Okay, bye, see you tomorrow.
And that they get veryfrustrated by that.
They, they, a lot of people'sfrustration with math actually
can lie in that open-ended stuff, because they are like just
tell me the answer, just tell mehow to do it, and I think that,
(36:51):
like norming from day one, thatpart of undoing your math
trauma is getting morecomfortable with that ambiguity.
I mean, all this is clickingfor me.
You already said this.
You're nodding, you're like yes, I've been saying this the
whole time and this is very truefor us, this tracks, but just
like it's all like coalescingfor me, where I'm like oh,
that's what you meant byambiguity, and that is probably
the most uncomfortable part, notonly for us, but definitely for
(37:14):
them.
Speaker 1 (37:16):
Yeah, no, I mean no other subject I think in middle
school or high school puts kidson the spot as much.
Right, at least in your scienceclass there's a body of facts
that you can sort of memorizeand like same thing in your
(37:38):
history class.
Like, even if your thinking hasnot really developed in that
subject, you can still getsomething down and get right for
something.
And it feels like in math, likeeverybody is expecting that
there's just the right answerthere.
(37:59):
It doesn't matter what thethinking is, and I think we just
have to get students a lot morecomfortable with sometimes
you're wrong, right.
Sometimes the problem isoutside of your ability to solve
it, and that's okay.
The problem is outside of yourability to solve it, and that's
okay, right.
And maybe we don't get ananswer that day, but maybe we
come back to it later in thesemester.
And we didn't.
Speaker 3 (38:18):
And that that's not the answer.
The presence of or absence ofan answer is not the presence or
absence of success.
That's not the those are.
We have to break that and Ithink that's a myth that a lot
of kids walk in with, and that'swhy they feel like a failure is
because they're like that and Ithink that's a myth that a lot
of kids walk in with, and that'swhy they feel like a failure is
because they're like I didn'tget the right answer, I'm a
failure.
But if we transform, if wealchemize that into, you came in
(38:39):
here today.
You were on your feet, you wereengaged, you were thinking, you
were making mistakes left andright because you were trying.
You tried so much.
Therefore, you failed some, andthat is success in math class.
Speaker 1 (38:50):
You failed some, and that is success in math class.
Speaker 3 (38:54):
Well, I want to end on one last little question.
Why are you so obsessed withstatistics, Mr?
I'm writing a textbook onstatistics and you have to keep
it short, I know, I know this islike its own podcast episode
one of multi-seasonRussellsell's obsession with pot
, with statistics I think thatthere are two main reasons.
Speaker 1 (39:18):
The first is what other class has a greater claim
to actually being useful in youradult life as, like a citizen
right?
Kids coming out of high schoolshould understand how polling
(39:39):
and surveys work.
They should understand how youknow research studies are done.
They should understand howexperiments are done.
Do we think that you know, ifpeople were more statistically
literate that the pandemic wouldhave unfolded the same way that
it did?
I don't.
(39:59):
I think if people were actuallystatistically literate, I think
they would have understood moreand behaved differently.
Speaker 3 (40:09):
You know, and also questioned demanded good data,
noticed flaws in the way thatthings are conducted sometimes,
or sample sizes or things likethat.
Look at me trying to act like Iknow any of this vocabulary?
I don't.
I'm so sorry, russell.
Speaker 1 (40:25):
No, the sample size is the most important thing.
Oh my God.
Speaker 3 (40:31):
I know, see, I know.
Speaker 1 (40:33):
There you go, there you go, you're right.
Speaker 3 (40:35):
Chapter one of your textbook.
I'll write the foreword.
You don't even have to ask.
Speaker 1 (40:40):
Thank you, I appreciate that.
Yeah, I mean, I can't think ofanything that's more important
for students to understandgraduating high school right.
Speaker 3 (40:50):
And you know you're making me think like what,
speaking of real world fodderfor your whole class?
I mean you just must open thenewspaper every day and be like
this is today's lesson.
Speaker 1 (41:06):
I mean, we do this like with some regularity where
I'm like all right, like today'slesson, I've brought in like
this, you know, sample thissurvey that's just been done and
we're going to talk about whatwent right, what went wrong,
like why they got the results.
And then I think the secondreason that's super important
for studying statistics is thereare so many jobs where people
(41:31):
encounter data and it is so, soeasy to open up Excel and like
to put numbers in a spreadsheetand have the spreadsheet do
stuff, and everything that youdo not see about how the data
was collected is actually super,super important.
(41:53):
And if you don't know something, you are so likely to be misled
by data that looks like itsupports your conclusion and
actually doesn't.
I was at a school and the headof school like made this
announcement and like shared thedislike data with with the
(42:15):
whole, uh, with all of the thethree statistics teachers.
We all just sort of heard thisand we all go.
Speaker 3 (42:26):
Oh no, not the head tilt.
Speaker 1 (42:28):
Oh no, because we all immediately knew what the flaw
was.
Speaker 3 (42:33):
Do you remember?
Speaker 1 (42:34):
what it was.
It was basically, like I said,like, the data that you don't
see is often what gets you right.
So when you're saying like, oh,we've seen the sample increase,
we've seen this populationincrease like it's average over
(42:54):
time, the question is like whyis it increasing over time?
Is it because the population ischanging?
And that was exactly what washappening.
It didn't actually indicateanything good was happening, it
just indicated that thepopulation was changing.
Speaker 3 (43:09):
Man, data is.
You're right, it's everything Imean coming from the NWEA
perspective of like needingthose map growth scores to just
you have to have data to knowwhere you've come from and where
you're going, and you have tohave data.
That's, we say, trustworthydata, and this is what this is.
It's data that we're trustingis not being cherry picked to
(43:30):
tell a certain narrative or leftout a very big consideration or
a big skew.
Again, the incredibleresearchers are probably like
stop, stop trying to usevocabulary, but you're right.
And this idea of if we trulywant to educate critical
consumer kids, critical kidswhere is statistics?
(43:51):
You're right.
Well, when am when is your?
When am I going to be able totake your textbook and read it
before I go to bed every night?
Speaker 1 (44:00):
It's definitely bedtime reading it will.
It will put you to sleep?
No, I hope not.
No, I'm like a couple monthsaway from finishing it, but
things keep happening.
Life is life is busy.
Speaker 3 (44:13):
So it'll probably be another 10 years, but hopefully
soon that is so exciting,russell, that you are like just
I feel so lucky to know someoneas mathy as you, because you,
you do a, you do a great job ofyour.
Math.
Prowess never makes me feelinadequate and you, therefore,
(44:34):
you, you do the opposite.
You amplify my mathiness, youmake me feel proud of my own
like math speed and math journey.
Um, and so you being my mathdepartment head when I came on
and now being my math colleague,I just really really feel
grateful.
Um, so thank you so much forcoming on and talking about all
of this cool stuff today.
Speaker 1 (44:54):
Absolutely, absolutely.
I really love the journey thatyou've been on.
It's amazing to see someonestart out and say I'm not a math
person and then do the amazingwork that you've been doing.
So it's wonderful to see.
Speaker 3 (45:14):
Thank you.
You know that if you ever wantto like make me feel amazing,
just tell me how the Englishteacher can become a math
teacher and like, really I havea hard time picturing myself
going going back to teaching notmath.
(45:38):
There's just something reallybeautiful about struggling with
it as a student myself andstepping into not only reclaim
that, but reclaim it with mykids.
It's really big and, russell,thank you so much for joining us
today.
Speaker 2 (45:50):
If you or someone you know would like to be a guest
on the Teachers in Americapodcast, please email us at
shaped.
At hmhcocom.
That's S-H-A-P-E-D.
At H-M-H-C-Ocom.
Be the first to hear newepisodes of Teachers in America
by subscribing on Apple Podcasts, spotify or wherever you get
your podcasts.
If you enjoyed today's show,please rate, review and share it
(46:18):
with your network.
You can find the transcript ofthis episode on our Shaped blog
by visiting hmhcocom.
Forward slash shaped.
That's hmhcocom.
Forward slash S-H-A-P-E-D.
The link is in the show notes.
The Teachers in America podcastis a production of HMH.
Thank you to the productionteam of Christine Condon, tim
Lee, jennifer Corujo, neo Fry,thomas Velasquez and Matt Howell
.
Thanks again for listening.
Let students see that there are actually multiple
pathways that get them to thecorrect answer.
And to honor different sorts ofsolutions, honor different ways
of thinking about it, reallyhonor that.
Students have done a lot of thethinking.
It just might not look exactlyperfectly crystallized math
right, but it's stillmathematical thinking.
Speaker 2 (00:25):
From paper and pencil to Wi-Fi and AI.
Education is ever evolving.
On this new season of Teachersin America, we'll keep you on
the forefront of what's new.
We connect with teachers and edleaders to talk trending topics
and real issues, bringing youinspiring ideas that will
influence the future of yourteaching.
Today, host Kaylee Rhodesconnects with her former
(00:46):
colleague, math teacher RussellHaynes.
Russell has been teaching fortwo decades in public and
private schools in the US andabroad.
Throughout his career, he hastaught public speaking, debate,
civics and every math subject,from fractions in sixth grade to
AP statistics in high school.
Today, russell and Kayleediscuss how to help students
(01:07):
step out of their math comfortzone and see themselves as math
people.
Plus, russell shares teachingstrategies to use in the math
classroom, like helping studentsembrace and learn from their
math mistakes.
Now here's Russell and Kaylee.
Speaker 3 (01:22):
Russell, welcome.
I'm so glad that you're here.
How are you?
Speaker 1 (01:27):
Very good, very good.
Thank you so much for having me, kaylee.
This is really awesome.
Yeah, I love that you're doingthe podcasting thing now.
This is such an awesome stuff.
Speaker 3 (01:40):
It's a perfect fit, right, I like to talk and you're
like I have to go teach.
Speaker 1 (01:45):
Yes, Well, I love that.
I got a random text that waslike, do you want to be on the
math podcast?
And I was like I can only beone person.
Speaker 3 (02:00):
Yeah, but then you, in true Russell form, had to don
on talking about how to getstudents from their you know,
very, very understandable mathtrauma into their math comfort
zone, helping even teachers stepmore into that math comfort
zone.
And there's no better person totalk to than you, because you
have been so formative in myjourney as seeing myself as a
math person, because I didn'tstart as a math teacher.
(02:22):
You, I started in the Englishclassroom and you were my first
mentor as start as a mathteacher.
You, I started in the Englishclassroom and you were my first
mentor as I became a mathteacher.
Actually, one of the firstconversations you and I had was
about quote, not a math person.
That was one of the firstthings we were in your office.
So how do you?
How do you respond?
Let's just start with a student, because everyone says it right
(02:44):
.
Speaker 2 (02:44):
But how do you?
Speaker 3 (02:44):
respond when a student says I'm not a math
person.
Speaker 1 (02:49):
I mean, I think there's like sort of two flavors
that you can get, right, likeone is the student is saying
it's just not really my interest, like it's not like something
I'm super passionate about.
And then you get the studentswho are saying that because
they've been super traumatizedby math.
Right, this is a like just as atrue story.
(03:10):
I one time was getting myhaircut and the lady said what
do you do for a job?
And I said math teacher.
She hissed and jumped backRight, this is how traumatized
some people people are aboutmath, right.
So I think the first thing thatyou have to do is figure out,
like why the student is sayingthat.
(03:31):
Are they telling you like theyare afraid of math, or are they
telling you that it's just nottheir thing, right?
yeah which, if they're tellingyou that it's not their thing,
like you know you want toconnect them to all of the
amazing things that you can dowith math, all of the
interesting properties that theycan learn about, like connected
(03:53):
to their interests, like thesubject that they're.
You know they're interested inscience Great.
They're interested in art Great.
Like let's find the connectionsto math that they would find
really interesting.
Right, that's maybe just afunction of they haven't had a
teacher, like really look forprojects and applications that
they find interesting.
(04:14):
But, as you well know, rightfrom teaching sixth graders who
many of them came into it likeinto your classroom, like really
traumatized and upset, uh, likeyou have to figure out, like if
that's what is going on andsort of help them start to
unpack it, and that that's awhole different ball of black.
Speaker 3 (04:37):
Right, yeah, I, um, for context, I have our, our
group of sixth grade students,um, who need the most math
support, and I think that whatshocked me because I mean I'm
going to say it like I'm not amath person and I'm not supposed
to say that, like I'm notsupposed to say that but I'm not
(04:57):
a math person and like what Imean, what I mean when I say
that is like math does not comeby osmosis for me, like I can't
just watch a teacher do it andlike see it and just go
replicate it or even be likewhat about this?
And like get up there andba-doop-boop-boop like jazz riff
on whatever I just saw.
(05:18):
I have to be like I need a lotmore questions answered before
I'm ready to really understandthis, but I think that that's
normal.
But what I saw in school wasjust prodigies.
It felt like prodigies andplebeians, Like and I was
definitely a plebe and so I wasjust that.
That equaled if you're not agenius, ergo you are not a math
(05:40):
person Like that's what it feltlike.
Now I have to tell my studentsthat I said that too.
You and I have to reclaim ourspeed, because speed's a big
trigger in math.
We have to reclaim our speedand we have to reclaim that
maybe I.
This is something that Iactually really love about the
(06:03):
Common Core is it mandates thatwe have different ways of
instruction, instructing thesame concept, and I feel like
that really like honors what Ineeded.
Speaker 1 (06:13):
And so what has also surprised me is that a lot of
kids come into my class with uh,with the lowest math, uh,
current like application ability, and they say they love math
yeah, that's mean I think it's atestament to like your skills
connecting with students, right,um, and I think what you're
also saying is really importanttoo about the curriculum, right,
(06:34):
the way that we have taughtmath, right, where you're trying
to go at the fastest possiblespeed, right, uh, does not work
for a lot of kids.
It doesn't particularly workfor me either, like I don't find
it really pleasurable to sitdown and take a timed math test,
(06:56):
right, no, um, and and there'salso ways of like the ways that
we have set up instruction,where we're like trying to get
students to like replicate, likedown a very specific narrow
pathway, is not going to workreally well for lots of students
.
And if you have a broader, openpathway, more open pathway,
(07:21):
that's good for a lot of kids,that's good for more kids.
That's good for a lot of kids.
That's good for more kids.
So I think a lot of the problemis that the way that we've
taught creates a reallystressful environment for kids.
If we use timed tests, I don'tparticularly enjoy that.
It's stressful.
I recently have had to take aclass where there were timed
(07:42):
tests I, you know I didn't enjoyit like it's trying to recall
stuff as quickly as possible,which doesn't work for every
moment, for every learner right,and the way that we've done
instruction too in the past hassort of limited the number of
pathways that students can godown.
(08:03):
Like we show them one pathway,we're like here's how to get to
the answer, and we sort ofexpect students to be able to
follow along that pathway andreplicate it, whereas a better,
I think, way of instruction isto let students see that there
are actually multiple pathwaysthat get them to the correct
answer and to honor differentsorts of solutions, honor
(08:25):
different ways of thinking aboutit, really honor like that
students have done a lot of thethinking.
It just might not look exactlyperfectly crystallized math,
right, but it's stillmathematical thinking, right.
We kind of like fetishize, likea outcome, like students are
(08:47):
supposed to write proofs orsomething when they're still
learning material, right.
Speaker 3 (08:52):
Which is why in your class you do a ton of like group
work, where maybe themathematical thinking is
crowdsourced and then maybeyou've got the student that can
kind of push it through to thatdistillation.
Speaker 1 (09:07):
Right.
Right, and I think part of itis just not trying to rush the
students to that point, right,part of it is that we want to
have the students get to likethis distilled, crystallized
result in three weeks or fourweeks or whenever we're wrapping
up the unit, and we all knowthat that's like setting a
(09:29):
timetable that like might not berealistic for certain kids,
right, and it would be better tojust sort of acknowledge, like
okay, your understanding of thisis still a work in progress,
you're not like the mostcrystallized form, but you, you
still understand the coreconcept, like recognizing that
(09:49):
kids can still be in process,like at the end of the unit yeah
, which makes uh grading reallycomplicated oh, it's a mess,
right?
Speaker 3 (10:00):
well, because if we're really if we're really
like alive this idea of growth,it's not about achievement, it's
about growth and if we'rereally therefore, nuanced about
you have to understand eachkid's kind of brain, not just
what's on the paper, but whatyou know is going on back there,
and that does make giving ascore or a letter to that really
(10:22):
, really tricky.
And I'm actually going to I knowthat you and I could talk about
grading all day, so I'm goingto make sure that what I want to
do is press pause and be likeokay.
So that moment that a studentsays I'm not a math person, you
said just kind of suss out, whatare they telling you?
Are they telling you that theywould rather be in art, or are
they telling you that they havetrauma or both?
(10:42):
And then making sure that I'veheard a lot of like speed.
We've both been talking just alot about speed and we've also
both been talking a lot aboutlike externalizing, um, this
very conversation that we'rehaving right now, kind of almost
doing it in front of the kids.
Speaker 1 (11:00):
Yeah, I think recognizing, like talking to
kids and saying, you know, ifyou have been traumatized in a
previous class, like I'm reallysorry that that happened, like I
don't think that that was right, like let's sit down and
actually figure out what youreally know.
You know, let's figure out whatyou really can do, yeah, what
(11:22):
you really can do without all ofthe stress, without all of the
like you know, I mean, I've I'veseen people, uh, you know,
working with students who reallyjust add to their stress, and
I've seen people who like, taketheir stress away, right, and I
think the whole thing that Iwould argue is that we need to,
(11:44):
you know, as teachers, find waysto help take the stress off,
because then you're going to geta more accurate read of, like,
what the student really knows,what they actually really feel
Like.
Math doesn't have to beeverybody's favorite subject,
yeah, and that's okay, you know,but they can all do it, you
know, we should figure out whatthey are actually capable of
(12:06):
doing.
Speaker 3 (12:07):
Right, and we have a math pledge of allegiance in my
class and the last line of it isjust, I will go at my own pace
and I will endeavor to see thebeauty of math around me, me
because if, even if you are nottrying to go further with your
(12:27):
math studies, which we're goingto talk about in a second you
can at least appreciate thatmath is probably, as you said
earlier, they're interested inscience.
Math's everywhere in science,you know, um, but if you're, if
they're interested in anime,math is all over anime.
So just like it's everywhere,so just like let's, let's
embrace it.
So when we picture this mathclassroom that you and I are
trying to like, kind of, maybemove away from a lot of people,
(12:51):
the image that pops into theirminds and they might even still
be educators, but the image thatpops into their minds is like a
lot of bent heads over paperand pencil, doing these kind of
repetitive tasks to get thealgorithm down.
Doing these kind of repetitivetasks to get the algorithm down,
but teaching math?
I was surprised, coming from,like the speech and rhetoric
(13:11):
world, which you also occupy asa debate teacher, but coming
from an English teacher.
We talk so much in math.
Math is so much discussion andargument, so how has your
experience as a debate teachershaped the way that you are able
to hold space and facilitatethat math discourse?
Speaker 1 (13:28):
Well, I think a big part of like what we need to do
as math educators is actuallythinking about entertaining
hypotheticals.
Right, Timmy might not have thecorrect answer, but has made an
interesting mistake and we needto walk through that mistake
and see where they slipped upand if other students made that
(13:54):
mistake, and to understand whyit's wrong and to understand how
to correct it.
Right, that isn't to say thatlike, like there is absolutely a
place in math for likecorrecting students and saying
what's right and what's wrong.
Like there's absolutely anecessity for doing that, unless
you are intentionally likeleaving them with a cliffhanger,
(14:15):
right.
But I think that we should beable to entertain hypotheticals
and like ask students to explaintheir reasoning.
Like what's your argument forwhy this is true?
Walk us through the logic.
That's the key part that holdsthat math uh, has to like hang
together by like logic, right?
Speaker 3 (14:37):
if the students can't explain the thinking that got
there, it doesn't matter whetherthe answer is right or wrong
it's kind of like when you'reassigned a side in debate that
you don't necessarily personallyagree with and you still have
to mine it for what's there, andthere's definitely something
there.
(14:57):
I my favorite thing to do is, um, if a student has made an
interesting mistake, like, say,on the board, number four,
everybody take a look at numberfour.
You know, and I've privatelychecked in with number four
beforehand and been like, hey,I'm going to you have a really
cool mistake, don't erase it,it's about to become the
backbone of our lesson.
Um, but one of my favoritethings to do is, like, mute that
kid.
It they can't defend, like, andthey're not being defensive,
(15:22):
they literally are defendingtheir math.
But muting them and making therest of the class try to explain
what they thought happened notonly enlivens the rest of the
class but makes that one kid goinsane.
And you're like.
I never thought I would see youwrithe from wanting to talk
about math.
You're welcome, you're a mathperson.
Speaker 1 (15:45):
Exactly.
Yeah, no, I think you'reabsolutely right.
Like the issue is like yousometimes have to step into
other people's shoes right andwalk through the logic that they
did, even when you can see thatthere's like a mistake.
Like you have to be able tolike articulate.
I do think the problems thatlike being included more in
(16:07):
curricula, where it's likehere's what two students thought
explain what their reasoning is, explain where they went wrong
I think that's a really goodexercise for students to see
mistakes and see mistakes asnormal right.
That's a big part of we have tolike see mistakes and see
mistakes is like normal right.
Yes, that's a big part of likewe have to normalize mistakes,
(16:29):
we have to normalizedisagreement.
That's a that's a big part toothat, like, the students look up
to the teacher and think thatthe teacher never makes mistakes
, and that's that's just not agood rhetorical stance to have
as a teacher right.
Speaker 3 (16:44):
Right?
No, it also makes you, as ateacher, feel so.
I, as a math teacher, felt thesame amount of pressure that I
felt as an English teacher toanswer everyone's grammatical
question and I'm supposed to beable to spell every word that
ever worded.
So now, of course, I'mresponsible for calculating
everyone's taxes because I'm ateacher.
Speaker 1 (17:08):
That's terrible.
No, I think it's like mathteachers, like we should feel
comfortable with ambiguity, likewe should model that for our
students, like I think it'sperfectly OK to say that's a
really interesting question.
Speaker 3 (17:26):
You've said that to me.
I don't know if you rememberthis, but a couple years ago I
couldn't figure something outand you were next to me teaching
and I came over and interruptedyou and I was like I have a
problem, I don't know.
Will you help me?
I've done it to Chris too,another colleague of ours.
(17:48):
I was just like I want them towatch two adults who are curious
about a math problem and maybethey can't solve it.
Like that is math in progress.
A lot of the math that we'reteaching is discovered math kind
of like science.
A lot of the science we'reteaching is established science.
But when you watchmathematicians math or when you
watch scientists science it'sbecause there's a question mark.
Speaker 1 (18:14):
Absolutely, and it doesn't have to be something
that's like at the forefront ofthe limits of our research with
math in order to be a validquestion.
Right, right, it's literallyhow much more parking do I need
to?
Speaker 3 (18:28):
put in my meter if this is what they charge and,
like Russell, can your phonereach my parking?
Here's my phone.
Go pay my parking Right.
But that's silly.
Speaker 1 (18:47):
I'm excited to discover that there's so many
parallels between what and thatmaybe you know, no one has the
answer uh per se, or, like youknow, we're we're going to
(19:21):
figure out the answer togetheras a result of doing this
process.
Um, you know, I always tell,tell my students in debate that
I have had students actuallychange my mind on a on an issue,
and that it's not reallyimportant.
You know what my position is.
In a debate class, like, whatis important is that you can
(19:44):
actually justify and back upyour own answer.
Right, that you can.
You can use research andexplain your own reasoning.
That's the important bit, and Ithink that's the same, exact
same thing in math, right, youshould be comfortable with
ambiguity, like.
The teacher doesn't have to bethe final authority on every
question.
Speaker 2 (20:06):
Hey teacher friends.
If you're an HMH user, did youknow you have access to
Teacher's Corner on Ed Includedwith every HMH program?
Teacher's Corner is a communityof teachers, learning experts
and instructional coachesgathered in one place to support
you with a new kind ofprofessional learning bite-sized
, teacher-selected andteacher-driven, with on-demand
(20:26):
sessions, lesson demonstrations,program support and practical
resources.
Teachers' Corner lets youchoose how you interact with our
content.
I like to think about it asinspiration on demand.
Speaker 3 (20:40):
Okay, speaking of debate, there seem to be two
schools of thought when it comesto math facts.
A lot of people are still inthis camp of we need to memorize
them.
And I'm saying a lot of peopleare still in this camp because I
, on every other day I'm in thiscamp of we need to memorize
math facts.
(21:00):
And then others say to focus onthe problem solving and the
math facts will come, Like if astudent just knows seven times
eight, it doesn't necessarilytell us if they understand why.
But what's your perspective onhow students should build
fluency with those math facts?
Speaker 1 (21:17):
So I think in this case both of the extremes are
sort of caricatures that I thinkare not best practices for like
helping kids.
I'm sorry, what, what word didyou?
Speaker 3 (21:35):
just say.
Speaker 1 (21:37):
Curricatures, curricatures.
Speaker 3 (21:38):
Oh my gosh, where are you from From?
Where are you from From?
Speaker 1 (21:43):
Did I say it wrong.
Speaker 3 (21:50):
No.
I don't just I say I say itwrong, I say caricatures.
Speaker 1 (21:54):
Can we write a song called caricatures, caricatures.
I think they wrote one.
You say potato, I say potato.
Speaker 3 (21:59):
Okay, that's just like the unknown verse.
That's like the deep cut it'sthe deep cut, okay, sorry.
So yeah, both extremes Not good.
Like don't make students justlike wrap them on the knuckles
until they know all their theirmultiplication tables, but also
like we need some kind ofcommitment to memory.
Speaker 1 (22:17):
Yeah, I mean, we know that like being like being
unable to like draw from factsis going to hinder kids who are
not able to like see a pathwaythrough a problem, who are not
able to like see a pathwaythrough a problem right?
So just to give an example, Ihad a student in a pre-algebra
class who was still counting ontheir fingers, perfectly
(22:38):
understood all the linearequations that we were doing,
but every time this kid had tosit down and like simplify
fractions, they were likecounting on their fingers right
In eighth grade and you couldsay, well, you could pull out a
calculator.
But the kid who's like able tolook at a fraction and say, oh,
(23:00):
six, sixteenths, I know that sixis twice a three.
I know 16 is twice an eight.
It's going to be able to likesimplify it much faster.
They're going to be able tolike simplify it much faster.
They're going to be able tomake insights and just not have
the cognitive load Like this kidtook like an hour to answer a
question on a test because theywere doing everything.
Speaker 3 (23:20):
Even though they're ready, they're ready, they get
it, oh yeah.
Speaker 1 (23:26):
The abstract reasoning that we were doing
with linear equations.
This kid understood right.
But their cognitive load wassuper high because and the way
that I understand cognitive load.
Speaker 3 (23:40):
you taught me that term because I was coming to you
and being like their gears aretoo frictious in their head and
they get fatigued and you'relike, yes, there's a word for
that that's.
Speaker 1 (23:52):
That's exactly what it is, right.
It's just you can only juggleso many balls and working memory
and you need to be able tochunk things and working memory
so that you can get to thebigger stuff, right?
Yeah, if you're constantlymanaging small chunks of
information because you haven'tmemorized something, then it's
(24:14):
certainly going to slow you downand impair you when all these
chunks are, like you know, needto be kept in mind at once.
Speaker 3 (24:23):
Yeah.
Speaker 1 (24:25):
I think that's the best argument.
Speaker 3 (24:27):
I think that's the best argument.
It's just like it's not aboutturning our kids into into like
a militant memorization thing.
It's about smoothing the gearsfor later, when they are like
ready to fly, and the smallstuff isn't like gumming up
their wings, exactly, exactly.
Speaker 1 (24:47):
It's ice on the wings , right, exactly, exactly.
It's ice on the wings, right,right.
But by the same token, there'sgood memorization and bad
memorization.
Like they can just sit thereand memorize their times tables
just completely rotely.
You know, 7 times 9 is 63,right.
Or they could actually memorizewhere they're looking for
(25:19):
patterns, right.
Oh, seven times nine.
Well, I also know, seven times10 is 70.
Seven times nine must be lessthan 70, right.
How much less.
Well, it's one seven less.
Then the chances that you cango and recall something when you
need it just becomesexponentially higher, right?
If you just memorize somethingas like a disconnected, isolated
(25:43):
fact, your recall of it isgoing to also be kind of poor,
right of it is going to also bekind of poor, right.
You're going to have to likeland the one pathway to recall
that memory.
Speaker 3 (25:56):
But if you're like building an interconnected set
of memories, yeah, if you'recultivating flexible agile, a
playground of math in your head,rather than like one slide, one
slide, one slide.
Speaker 1 (26:09):
Exactly.
It's not just about crammingthe stuff in and somehow recall
happens magically, right?
You want recall to be almost so.
You want to have created somany pathways that it's almost
hard not to recall it that theyalmost would have to like
intentionally not wander acrossa pathway and recall it.
Speaker 3 (26:34):
Oh well, and you're, uh, there's a one of my tricks,
one of my classroom tricks isthat I buy like a ball and I
write math, uh, multiplicationproblems all over it, and where
we throw it around and whereveryour right thumb lands, you have
to answer that math, thatproblem.
But there's no um, you don'thave to play, you can sit down,
(26:54):
um, you can say pass, likethere's a lot of, there's a lot
of uh safety nets, because Iknow that that that could sound.
Not only have I entered some,that's some people's hell.
Right, I have to catch and thendo math, um, but but uh, I have
a couple of things in place formy like high flyers too.
When they catch a ball and theysay a math fact, really fast,
(27:14):
you know, like seven times nine,sixty three, and they like rear
back to throw the ball tosomeone else, and I'm like wait,
can you tell me another, canyou tell me why?
Like can you just walk methrough?
And they'll do your 71, becauseI'm all seven times ten minus
seven, and I'll be like, can youdo it any other way, a
different way?
And then they start gettinglike playful with 21.
(27:34):
And so I asking people to like,asking students to like
lubricate their gears externallyand in front of other kids.
Kids, like throwing a newpathway to even the high flyer,
(27:56):
is essential to showing kids whyit's not good enough to just
know a 63.
That's not, that's not the endgoal.
That kid, that would haveintimidated Kaylee middle school
.
Kaylee Rhodes actually wasn't asas a maybe fluent as I thought.
Speaker 1 (28:07):
No, I, I totally agree.
I mean, I think that that's anexcellent activity and it's a
really clear indication thatlike the stuffing memories in is
(28:29):
not to like have all of thesefacts.
It's to have like useful factsand connections and see the
connections so that we can thinkflexibly Right, it's building.
It's building muscles, like youplay scales so that you can
then play things that are notscales Right, but you need to
know where your fingers need togo on the keyboard so that you
(28:51):
can do the scale correctly, sothen you can start jumping.
Speaker 3 (28:55):
Yeah, and the more like in your body the scale is,
the the less friction you'regoing to have as you fly higher,
as you, as you start composingWell, and so like this, this
kind of like roteness versusrhythm, I guess is something
that we see a lot in curriculumold curriculum, new curriculum
(29:15):
because a lot of teachers swearby practice sets where students
work on the same skill over andover again, just like get it in
your body, get it in your body,which I understand.
But there's also another schoolof thought where we're looking
at these open-ended, rich, longmath tasks that take whole class
periods or longer.
How do we strike a balancethere, and what does a good math
(29:38):
task look like in your opinion?
Speaker 1 (29:41):
So I think with like open-ended tasks, the same thing
is true, that there can be goodopen-ended tasks and bad
open-ended tasks.
Right, if you threw a problemat students and basically said
here you learn, you knowderivatives on your own, like
you need them to be able toanswer this question, but I'm
(30:02):
not going to teach you.
I mean, that's just too much.
Right, it's not scaffolded forthe students it's a bad escape
room yes, exactly, exactly.
What you really need is anopen-ended task where, like,
they're bringing a motivation ontheir own, they're interested
in the subject matter.
Maybe it's the kid who's, like,passionate about art, getting
(30:25):
to connect, uh, but where?
Where you've scaffolded themath task for them, right?
I think the question of, like,what defines a good activity
versus a bad activity, likeacross the board, is, you know,
number one is it somethingthat's like in the appropriate
(30:46):
zone for the kids, right?
Is it something that they'reactually able to understand and
to do productively?
Is it something where they willbe able to think rich, make
rich connections and thinkdeeply about the problem?
And have you set them up in away where the clear onus of
(31:11):
thinking is on them?
And there's a whole gamut ofactivities, from, like, fun
games, memorizing, to doingopen-ended projects, to doing
group work.
All of those can meet thosecriteria.
If you just are being reallythoughtful about what my purpose
(31:31):
is as a teacher, like, what ismy pedagogical purpose?
What do I want the students toaccomplish here?
So I think all of those can beset up as good tests.
Speaker 3 (31:43):
Do you have a favorite?
Creating something?
I know about me being a mathteacher is inventing math
problems is hard.
Inventing whole class, richtask, perfect zone of proximal
development, perfectlydifferentiated.
I've created the.
That is really tricky and so Ihave.
(32:07):
I look to resources, right.
What are some favorite?
Like hey, if you are ready toengage your kids in some rich
whole class tasks and yourcurriculum isn't maybe meeting
that need, where would youdirect one of your teachers?
Aka, me.
Speaker 1 (32:25):
I would actually say I think a lot of the things that
we need to do are pulling fromthose resources, just like you
mentioned, from textbooks, fromother resources that you have,
from like websites.
But I think the key thing isyou, as a teacher, having the
(32:50):
confidence to improvise and toadapt right.
You know the.
The saying is no battle plansurvives contact first, contact
with the enemy.
Uh, and I think no lesson plansurvives the first five minutes
of class, like as soon as thestudents see the problem, you
might as well just throw yourlesson plan away right, because
it's not going to go to plan.
No, and I think the differencebetween an experienced teacher
(33:13):
who's really focused on like thegoals is that they know how to
like, adapt and respond.
They recognize where thestudents are struggling, where
there's room for growth.
So I don't, I don't think youhave to come up with like here's
the perfect lesson plan.
I have defined this, I havepulled it out of the heavens and
(33:36):
I've put it into paper form andit's going to, you know, amaze
the students and wow myadministrators.
Speaker 3 (33:43):
It's going to tap dance across the desk.
Speaker 1 (33:46):
Exactly right.
That's not the goal.
Like the goal is to say what dowe need to do today?
We need to talk about linearequations.
Let me pull some lesson plansthat I can find online and other
textbooks.
Where are my students going tostruggle doing that?
Pre-thinking makes a hugedifference.
(34:09):
And then, as soon as you get inthe classroom, taking the
opportunities and like likelooking for the students who've
made interesting mistakes, likelooking for the uh, looking for
the one-offs that just happenedthat one day and they don't
happen again, right.
Speaker 3 (34:26):
So deviating from your script, making sure that
you walk in with a rich thingthat you've thought about.
But if your goal is to watchthem ignite with thinking and
interacting with the problem,then they have about 100
different ways they can do thatand you just need to follow them
where they go.
Speaker 1 (34:45):
You're kind of a.
Yeah, I was just going to say.
If your goal is to get thestudents to think, how would you
do that?
By yourself shutting down inthe classroom?
Speaker 3 (34:58):
Yeah, if your goal, what's your goal?
To get them to think it's soand like what does that look?
We haven't gotten to numberthree, which is when I show you
this graph and you, like I, likewe know we never got to number
three because at number onethere was enough for them to be
(35:21):
thinking and that was my goal.
But it is like letting go.
So much of teaching is lettinggo.
It's so, it's like a soap is in.
Speaker 1 (35:29):
You've heard the, the expression in editing, that you
have to murder your darling yesthat's the, that's the
fundamental rule of teaching.
I think too, it's like.
Speaker 3 (35:41):
But number three is so exciting to me I photocopied
it front and back in the colorprinter.
It was all across campus.
Who am I making fun of Me?
Okay?
No, you'll recycle it, okay.
So what you're recalling for mefrom the top of our
conversation is this idea that,being honest about what thinking
(36:09):
looks like and so it can't.
Even if you have a kid thatknows all the math facts, is
there thinking?
Even if you have a kid that'sstill counting on the fingers,
is there thinking?
And so, just um, coming back tothis whole idea of not a math
person, one of the things that Iget, uh in my classroom are,
you know, brand new little sixthgraders who are not used to uh,
(36:31):
not walking out of theclassroom with an answer and or
or knowing they did it wrong orwell, this was your mistake.
Okay, bye, see you tomorrow.
And that they get veryfrustrated by that.
They, they, a lot of people'sfrustration with math actually
can lie in that open-ended stuff, because they are like just
tell me the answer, just tell mehow to do it, and I think that,
(36:51):
like norming from day one, thatpart of undoing your math
trauma is getting morecomfortable with that ambiguity.
I mean, all this is clickingfor me.
You already said this.
You're nodding, you're like yes, I've been saying this the
whole time and this is very truefor us, this tracks, but just
like it's all like coalescingfor me, where I'm like oh,
that's what you meant byambiguity, and that is probably
the most uncomfortable part, notonly for us, but definitely for
(37:14):
them.
Speaker 1 (37:16):
Yeah, no, I mean no other subject I think in middle
school or high school puts kidson the spot as much.
Right, at least in your scienceclass there's a body of facts
that you can sort of memorizeand like same thing in your
(37:38):
history class.
Like, even if your thinking hasnot really developed in that
subject, you can still getsomething down and get right for
something.
And it feels like in math, likeeverybody is expecting that
there's just the right answerthere.
(37:59):
It doesn't matter what thethinking is, and I think we just
have to get students a lot morecomfortable with sometimes
you're wrong, right.
Sometimes the problem isoutside of your ability to solve
it, and that's okay.
The problem is outside of yourability to solve it, and that's
okay, right.
And maybe we don't get ananswer that day, but maybe we
come back to it later in thesemester.
And we didn't.
Speaker 3 (38:18):
And that that's not the answer.
The presence of or absence ofan answer is not the presence or
absence of success.
That's not the those are.
We have to break that and Ithink that's a myth that a lot
of kids walk in with, and that'swhy they feel like a failure is
because they're like that and Ithink that's a myth that a lot
of kids walk in with, and that'swhy they feel like a failure is
because they're like I didn'tget the right answer, I'm a
failure.
But if we transform, if wealchemize that into, you came in
(38:39):
here today.
You were on your feet, you wereengaged, you were thinking, you
were making mistakes left andright because you were trying.
You tried so much.
Therefore, you failed some, andthat is success in math class.
Speaker 1 (38:50):
You failed some, and that is success in math class.
Speaker 3 (38:54):
Well, I want to end on one last little question.
Why are you so obsessed withstatistics, Mr?
I'm writing a textbook onstatistics and you have to keep
it short, I know, I know this islike its own podcast episode
one of multi-seasonRussellsell's obsession with pot
, with statistics I think thatthere are two main reasons.
Speaker 1 (39:18):
The first is what other class has a greater claim
to actually being useful in youradult life as, like a citizen
right?
Kids coming out of high schoolshould understand how polling
(39:39):
and surveys work.
They should understand how youknow research studies are done.
They should understand howexperiments are done.
Do we think that you know, ifpeople were more statistically
literate that the pandemic wouldhave unfolded the same way that
it did?
I don't.
(39:59):
I think if people were actuallystatistically literate, I think
they would have understood moreand behaved differently.
Speaker 3 (40:09):
You know, and also questioned demanded good data,
noticed flaws in the way thatthings are conducted sometimes,
or sample sizes or things likethat.
Look at me trying to act like Iknow any of this vocabulary?
I don't.
I'm so sorry, russell.
Speaker 1 (40:25):
No, the sample size is the most important thing.
Oh my God.
Speaker 3 (40:31):
I know, see, I know.
Speaker 1 (40:33):
There you go, there you go, you're right.
Speaker 3 (40:35):
Chapter one of your textbook.
I'll write the foreword.
You don't even have to ask.
Speaker 1 (40:40):
Thank you, I appreciate that.
Yeah, I mean, I can't think ofanything that's more important
for students to understandgraduating high school right.
Speaker 3 (40:50):
And you know you're making me think like what,
speaking of real world fodderfor your whole class?
I mean you just must open thenewspaper every day and be like
this is today's lesson.
Speaker 1 (41:06):
I mean, we do this like with some regularity where
I'm like all right, like today'slesson, I've brought in like
this, you know, sample thissurvey that's just been done and
we're going to talk about whatwent right, what went wrong,
like why they got the results.
And then I think the secondreason that's super important
for studying statistics is thereare so many jobs where people
(41:31):
encounter data and it is so, soeasy to open up Excel and like
to put numbers in a spreadsheetand have the spreadsheet do
stuff, and everything that youdo not see about how the data
was collected is actually super,super important.
(41:53):
And if you don't know something, you are so likely to be misled
by data that looks like itsupports your conclusion and
actually doesn't.
I was at a school and the headof school like made this
announcement and like shared thedislike data with with the
(42:15):
whole, uh, with all of the thethree statistics teachers.
We all just sort of heard thisand we all go.
Speaker 3 (42:26):
Oh no, not the head tilt.
Speaker 1 (42:28):
Oh no, because we all immediately knew what the flaw
was.
Speaker 3 (42:33):
Do you remember?
Speaker 1 (42:34):
what it was.
It was basically, like I said,like, the data that you don't
see is often what gets you right.
So when you're saying like, oh,we've seen the sample increase,
we've seen this populationincrease like it's average over
(42:54):
time, the question is like whyis it increasing over time?
Is it because the population ischanging?
And that was exactly what washappening.
It didn't actually indicateanything good was happening, it
just indicated that thepopulation was changing.
Speaker 3 (43:09):
Man, data is.
You're right, it's everything Imean coming from the NWEA
perspective of like needingthose map growth scores to just
you have to have data to knowwhere you've come from and where
you're going, and you have tohave data.
That's, we say, trustworthydata, and this is what this is.
It's data that we're trustingis not being cherry picked to
(43:30):
tell a certain narrative or leftout a very big consideration or
a big skew.
Again, the incredibleresearchers are probably like
stop, stop trying to usevocabulary, but you're right.
And this idea of if we trulywant to educate critical
consumer kids, critical kidswhere is statistics?
(43:51):
You're right.
Well, when am when is your?
When am I going to be able totake your textbook and read it
before I go to bed every night?
Speaker 1 (44:00):
It's definitely bedtime reading it will.
It will put you to sleep?
No, I hope not.
No, I'm like a couple monthsaway from finishing it, but
things keep happening.
Life is life is busy.
Speaker 3 (44:13):
So it'll probably be another 10 years, but hopefully
soon that is so exciting,russell, that you are like just
I feel so lucky to know someoneas mathy as you, because you,
you do a, you do a great job ofyour.
Math.
Prowess never makes me feelinadequate and you, therefore,
(44:34):
you, you do the opposite.
You amplify my mathiness, youmake me feel proud of my own
like math speed and math journey.
Um, and so you being my mathdepartment head when I came on
and now being my math colleague,I just really really feel
grateful.
Um, so thank you so much forcoming on and talking about all
of this cool stuff today.
Speaker 1 (44:54):
Absolutely, absolutely.
I really love the journey thatyou've been on.
It's amazing to see someonestart out and say I'm not a math
person and then do the amazingwork that you've been doing.
So it's wonderful to see.
Speaker 3 (45:14):
Thank you.
You know that if you ever wantto like make me feel amazing,
just tell me how the Englishteacher can become a math
teacher and like, really I havea hard time picturing myself
going going back to teaching notmath.
(45:38):
There's just something reallybeautiful about struggling with
it as a student myself andstepping into not only reclaim
that, but reclaim it with mykids.
It's really big and, russell,thank you so much for joining us
today.
Speaker 2 (45:50):
If you or someone you know would like to be a guest
on the Teachers in Americapodcast, please email us at
shaped.
At hmhcocom.
That's S-H-A-P-E-D.
At H-M-H-C-Ocom.
Be the first to hear newepisodes of Teachers in America
by subscribing on Apple Podcasts, spotify or wherever you get
your podcasts.
If you enjoyed today's show,please rate, review and share it
(46:18):
with your network.
You can find the transcript ofthis episode on our Shaped blog
by visiting hmhcocom.
Forward slash shaped.
That's hmhcocom.
Forward slash S-H-A-P-E-D.
The link is in the show notes.
The Teachers in America podcastis a production of HMH.
Thank you to the productionteam of Christine Condon, tim
Lee, jennifer Corujo, neo Fry,thomas Velasquez and Matt Howell
.
Thanks again for listening.
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