October 23, 2024 • 21 mins
In this episode of Practical Access, hosts Lisa Dieker and Rebecca Hines welcome Dr. Karen Karp, a professor emerita in mathematics education at the University of Louisville and recently a professor at Johns Hopkins University. Her scholarship lies at the intersection of mathematics education and special education. She is the author or co-author of numerous book chapters, articles, and books, including the U.S. Department of Education Institute of Science’s What Works Clearinghouse Practice Guide on Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades, and other titles such as Strengths-based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K-6, The Math Pact: Achieving Instructional Coherence within and Across Grades, and Elementary and Middle School Mathematics: Teaching Developmentally which has been translated into seven languages. She also was on the authoring team of the NCTM- CEC Joint Position Statement.
Dr. Karp is a former member of the board of directors of the National Council of Teachers of Mathematics (NCTM) and a former president of the Association of Mathematics Teacher Educators. In 2020, she was selected for the NCTM Lifetime Achievement Award for Distinguished Service to Mathematics Education. She also is a member of the U.S. National Commission on Mathematics Instruction. This summer she represented the United States as the Chair of the Topic Study Group on Teaching Mathematics to Students with Special Needs at the International Congress on Mathematical Education in Australia. She holds teaching/administrative certifications in elementary education, secondary mathematics, K-12 special education, and K-12 educational administration.
Karp's scholarship stands out for its direct and visible impact on practicing mathematics teachers. Her work goes beyond theory, with her ideas being actively implemented in classrooms, shaping how mathematics is taught. In this podcast, Dr. Karp offers invaluable advice for general education teachers working with students with disabilities in math. She emphasizes the importance of early collaboration between general-ed and special-ed teachers, advocating for a proactive, rather than reactive, approach to math interventions.
Throughout the conversation, Karp discusses strategies like using multiple representations in math instruction, focusing on the strengths of students rather than their perceived weaknesses, and ensuring that Individualized Education Programs (IEPs) are written with concepts and skills. She shares practical methods to engage and empower students to succeed in math, using examples such as the "Whole School Agreement" and success stories from students she's worked with.
We love to hear from our listeners! If you have any questions, feel free to reach out. We look forward to receiving your questions on our Twitter (@Accesspractical) or Instagram (@Practical_Access).
Karp’s bio and publications: https://www.mathbykarp.com/publications
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Transcript
Episode Transcript
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Unknown (00:00):
Music.
Lisa Dieker (00:07):
Welcome to Practical Access. I'm Lisa
Dieker.
Rebecca Hines (00:10):
And I'm Rebecca Hines and Lisa, keeping with our
theme this season, I know youhave someone that you're excited
Lisa Dieker (00:18):
Yeah, so I'm actually giddy. That's a great
to present.
word for today. I'm so happy wewere able to get Karen Karp with
us, who's a professor in matheducation, who really does in
our work, have the intersectionof special education and
mathematics. So Becky, we don'thave enough friends in that
area, so we're super happy tohave Karen on the call with us
(00:38):
today. So thanks for joining us,Karen.
Karen Karp (00:40):
Thank you so much for inviting me. I'm really
looking forward to ourconversation.
Lisa Dieker (00:44):
Well, I'm gonna start with the first question,
and I would just love for you,imagine I am a brand new
teacher, and I have a student infront of me that has a
disability in mathematics, andI'm a little intimidated. I'm a
general-ed teacher, I don't knowwhere to start. What would be
your beginning advice for me tothink about or to do? Or, you
(01:08):
know, you, you are the experthere. What? What? What should I
be thinking about as that newnovice, first-year teacher
working with kids withdisabilities?
Karen Karp (01:17):
Well, you said general-education teacher, and
that's, you know, an importantstart, because they are the ones
who are delivering the mathcontent on one level. But I'd
ask that new teacher to partnerpretty quickly with a
special-education teacher intheir building, and start to
develop a partnership with them,because I really believe that
that is the best approach. I'mafraid in some cases, that a
(01:42):
student with disabilities is inkind of a limbo space. If we're
not careful, that the gen-edteacher might say, well, I don't
know that much about special ed,so I'm not sure that this child
is fully mine. And then thespecial-ed teacher will say,
Well, I'm not sure about themath part, so I'm not sure. I
(02:03):
think it's the other person's todo and and no one does. And so
what we need to do is start apartnership right away, because
it's everybody all in,everyone's in. And so that, I
think, you know, is critical.
But the main thing is, is tokeep trying different things and
be very proactive. The one thingI'm working on right now is math
(02:26):
interventions is proactive. Itwas the original intent of
response to intervention, and itwas preventative and after the
medical model. But in fact,that's not how it's played out.
It's very reactive, and we waitfor a child who's struggling in
math as the one you describe,before we act and do anything.
(02:46):
Well, we're saying to havelittle collaborations between
the special-ed teacher and thegen-ed teacher, where they work
two weeks in advance of newcontent together and they prep
each other as they're primingfor what interventions will take
place. And the interventions arenot pre-teaching the lesson you
(03:08):
have no goal or no interest inthat. They are building in
everything that goes into thelesson to come. So for example,
for something like perimeter,you know, what we want to do is
have those kids measure just alot of length and just practice
with a ruler and constantly bemeasuring. And we want them also
(03:28):
to see that if we add anotherline to the line they have, they
can measure this length and thatlength. We're not going to do
the parameter thing. We're justprepping them. And then the gen
ed teacher, and that's our newteacher on board. The special-ed
teacher will say, these are thethings that I've done with the
(03:49):
children in the interventions.
Start your first lesson withthese. And so we're going to use
those as a way to have thesekids shine, that these kids are
going to do things they just dida few days ago in their
intervention class that I'vealready reviewed, and now the
new teacher gets to call onthose children first. And so
(04:12):
we're trying to make it that thechildren really, really are
feeling that the lesson istheirs and not flying over their
head at fast speed. And so thatnew teacher has to learn this
new model, proactiveintervention. So that's one of
the things that I suggest.
Rebecca Hines (04:29):
Yeah, I love, I love to hear the word
collaboration. Lisa, I harp oncollaboration all the time. So
your your basic tip is, let'smake sure that we're
collaborating to ensure success.
And for this young teacher, whenthey go to a special educator
and say, I'm having trouble withX, Y or Z, I generally would
(04:53):
advise them go with. You know,go with the sample of work, and
don't say I'm having a problemwith this kid. I'm having a
problem with the way with thissolution. So do you have ideas?
But what do you think is a good,a good entry into that
conversation? Karen, how do theyhow do they go and elicit this
(05:15):
help, what they might not evenknow the special educators in
the school?
Karen Karp (05:20):
I love your idea of bringing a piece of students'
work, because one of the thingsI always say to all teachers is
we're not about fixing children,we're about fixing structures,
and so that's why I'm focusingon the structure of the
collaboration, because we're notabout at all thinking that the
child is it some way. You know,the change, it's not that it's
(05:47):
changing everything around thechild and and I think that
that's, that's quite theimportant piece, and I may be
missing what you're asking.
Rebecca Hines (05:56):
Yeah, let me. Let me. Let me. I'll ask that a
little more specifically, as afaculty member in special ed, we
talk to special-ed teachersabout collaboration. I don't
know that all of the gen-edfaculty when they're preparing
teachers, I don't know if theysimilarly present our special
(06:20):
educators as also experts.
They're just experts insomething different. So as a
faculty member who might workwith, you know, math education
majors, what would you tell themwhen it comes like, literally
like, if you were preparingteachers, how would you tell
them to approach a specialeducator, you know, with, with
(06:42):
the problem?
Karen Karp (06:44):
Total partner I mean, I really think it's got to
be that way. We each have, youknow, a collection of
information, and we just have tofind ways to share it well. And
I think that the preparation ofboth kinds of teachers, the
gen-ed teacher and the teacherwho's gone through special
education is quite different.
And so they are definitelydifferently prepared. And yeah,
(07:08):
we can say what's a good thingto do there, or what's not, but
the reality is, is thattogether, they have to make this
work. And you know, with manychildren, it's not only students
with disabilities. It takes twopeople to think about the
situation.
Rebecca Hines (07:27):
Right.
Karen Karp (07:28):
And it could be two gen-ed teachers. It could be, I
need two more special-edteachers if they're available in
the building, and even sometimesparaprofessionals and teaching
assistants who are workingclosely with that particular
child, they need to be in on theconversation too.
Rebecca Hines (07:45):
Oh, good. I think, I think we have a good, a
good article to write there.
Karen Karp (07:48):
We have something called, we have something called
the Whole School Agreement wherewe work to get everybody on
board across the entire schoolso that math is taught well, and
that, you know,special-education teachers,
paraprofessionals, teacher,long-term subs all go to the
same math PD as the gen-edteachers.
Rebecca Hines (08:10):
Love it. I love that.
Karen Karp (08:10):
Totally aware of what's going on. They're not
used as subs during a PD eventat a school. They are in,
they're in it.
Lisa Dieker (08:20):
I there's so many things you've said. I like, I
like the Whole School Agreement.
I like everybody's in I evenlike your really strong,
proactive focus on the strengthsof the kid, not the failure of
the kid in math. And I, I thinkthat's so much what the field
needs to hear. So I know weagree on this, but I would love
to hear your thoughts and helpfor any teacher, teacher, coach,
(08:43):
about that kid who we know needsto be in with their peers having
discourse, but really strugglesin being in with their peers and
having discourse. What are somethings that you found helpful?
Especially in the area of math,where, you know, some kids have
math anxiety, which we know thatliterature is high there.What
(09:04):
are some things you've seenteachers do, or you would
suggest to teachers for that kidwho we want them to be sitting
next to their peers and havingthat rich mathematical
discourse, but they mightstruggle with that?
Karen Karp (09:18):
Again, you know, again, I, you know, I think some
of this proactive work willsupport, you know, all children,
but there are complexsituations, and we have to think
about those as well. The mainthing is, is to use multiple
representations for all groups.
And I didn't mention thisbefore, but this is a great
resource for brand new teachersas well as veteran teachers, but
(09:38):
I was involved with a wonderfulbunch of other co-authors on the
IES practice guide forassistance, assisting students
struggling in math that justcame out about three years ago.
And in it, we make six importantrecommendations that it's mainly
for the elementary school, butit really travels all the way
(09:59):
up, and we made six importantrecommendations that teachers
should consider that's based onevidence-based research, and one
of the ones that I think is mostimportant, and if I go to a
school I talk about, and when Italk about any child in general,
multiple representations. Nowspecial ed uses well may still
(10:19):
call this CRA math educatorscall it CSA, because the R that
is used for representations,they're all representations.
Concrete is a representation,abstract is a representation. So
that R doesn't really stand forwhat it really is, which is
semi-concrete, like a drawing ora sketch or sometimes even a
(10:42):
chart, depends. And I and we inmath education like to overlap
those so that you're seeingconcrete. And if I need to, for
this particular student, writethe equation that goes with it,
first time I will do that, thenI might have a collection of
(11:02):
cards that have differentequations on it, and say, which
one do you pick that goes withthis model that we just made?
Then I get them to write it. So,you know, there's lots of
progressions that we can tosupport that child in, in moving
towards more, more of anindependent ability to handle
some of those questions, butthere are very, very important
(11:23):
models that help children thinkand do math and take action and
make it less anxiety producing,where we're not demanding
memory, where we're notdemanding time, where we're
giving the time to think, andwe're giving the supports that
are needed with even acting outproblems, taking the time to
(11:46):
just stop and act it out. A lotof kids need that role-playing.
Others just sometimes will say,imagine this situation in your
head like a story, and thatthat's helpful too. So there's
lots of things we can do to tryto bring them into the action
part of this. So it's not justrote memorization, and to be
(12:07):
frank, things that 10 years fromnow will be completely done by
AI or my watch.
Rebecca Hines (12:17):
And do you? Do you? Do you think, Karen, that
that on those occasions when wewhen we have students who are
who individually, are strugglingand but we suspect that you know
intellectually, they're capableof understanding the the
concept, the broad concepts, butthey're just lacking some of the
skills, and there may not evenbe time for them to get all they
(12:41):
had caught up in all of thoseskills. So how do we, how do we
as instructional coaches, youknow, what? What can we do? Or
what ideas do you have, whetherit's me or I'm bringing a para
in to to provide support or evena volunteer to help with the
coaching piece to get themcaught up on the sideline, just
(13:04):
a little bit?
Karen Karp (13:06):
Well, one of the things that I think, and this is
tangential to your actualquestion, but I think would be
useful in that, is that the IEPshave to be written to be more
conceptual. A lot of the timesI'm seeing IEPs written, and the
IEP is strictly about skills,and it talks about an assessment
where we're getting more digitscorrect than we did yesterday or
(13:27):
whenever it was done. And Ireally asked teachers all over
the country, what do you do withthat information about the
digits? How does it inform yourinstruction? And none of them
can really answer me. It's notthat. It's not doing the trick.
So I say write them moreconceptually, talk about talk
(13:48):
about place value, knowledge andthings like that, that we can
really bring the students in onwith these materials that we're
talking about. And those providethe total foundation for the
other components, but it isn'tputting kids in a tight kind of
situation of constantly be doingalgorithms and procedures and to
(14:11):
be frank, those are very elegantways of doing math, but they can
they. They are not some of themost joyous things in math.
Sometimes, that I'd like them toexperience some of the joy and
beauty of the subject, too. Andthey sometimes don't even have
an IEP on geometry, which can befor some children, the place
(14:35):
where they can really, reallyshine. And I'd like to see more
of that. And I also learned, youknow, of course, that you can't
write the same IEP every year.
Yet we see this multiplicationfacts thing travel along, and
the Supreme Court came outagainst that same IEP can't be
written two years in a row oreven again. So we need to delve
(14:55):
into some. Of the other thingsthat may, in fact, be a doorway
for children who do havetremendous strengths. I never go
in thinking that they can't doit. I always go in thinking they
can, and I just have to find away.
Lisa Dieker (15:15):
And so, so my last question, but I went a little
bit of commentary with it, soit's funny. I wish my son
growing up could have had you asa math teacher, but my husband,
I were literally just talkinglast night about our son works
for Trek and has sold lots ofbikes. I'm not allowed to say,
but he's one of the top 40salesmen, and yet I laugh that
(15:36):
he couldn't do hismultiplication facts. Still
can't, but he conceptuallystruggled, right, and he had a
calculator. But I do remember infifth grade, and I think you'll
find this funny, we got aletter, and I was like, Josh, I
think this is a wrong backpack.
And he said, I'm putting yourson in gifted math. And it like,
yeah, but again, he had thisamazing teacher in fifth grade.
And she said, look, Lisa, heprocedurally is not strong, but
(16:01):
conceptually, he gets it. Hebeyond gets it and and so I
think it's a good example forour listeners to realize,
realize, you know what Karen'ssaying, is life changing for
kids, because I do think thatwas a tipping point that allowed
him to go to college and dowell. And so with that, I just
and our listeners to hearbecause I got the privilege of
(16:22):
chatting with you on the phonebefore the podcast. I really
want them to hear your profoundwisdom in the IS report from
your perspective, and I wouldlove to put that link out on our
podcast when we're done. Butcould you share with me if my
son were born today and I wassitting there in third grade and
he still trying to do as facts,and I wish I hadn't done
flashcards all the way to thegym, because it didn't matter.
(16:43):
What would you tell me are sixthings I should be thinking
about for my son today?
Karen Karp (16:49):
Okay, and so, well, some of the recommendations I'll
give in general, one issystematic instruction. And by
that, I don't mean explicitinstruction. I mean giving kids
the chance to think and dofirst, and then I'm here to
support them but to assume thatthey have strengths that can
(17:11):
play into the information that'sabout to come their with. And so
that, you know, is a veryimportant shift that was very
different from the last goaround on the IES practice guide
that came out in 2009 themultiple representations is all
over the place in the practiceguide. So I've talked a little
(17:34):
bit about that already with CSA.
And another thing is thelanguage, the precision of
language is particularlyimportant. And this goes to that
conversation I had about theWhole School Agreement, where
we're all using the samelanguage or not like we're not
using borrowing and carryingbecause they're not conceptually
sound. We're using regrouping ortrading to replace value
(17:54):
purposes. Then kids here it overand over and over and again,
which is precisely what youknow, students with disabilities
need, and multilingual learnersand everyone else too. We don't
want we want reducing fractionsto be said one year and
simplifying the next. We want itto be a small stream where
(18:14):
everyone knows what's going onand kids aren't saying such
things as math is differentevery year. You know, it's not
it's a continuum, and we wantthem to be on it. Then we
separated in theserecommendations, one
representation out from theothers, because the research is
so compelling about it, and wewant to have all teachers
(18:36):
realize K-12, they'reresponsible for using it
officially, and it's the numberline. And so we started in
kindergarten with number paths,and obviously it moves up to
very complicated lines andgraphs and other components as
they move to middle and high.
But that one was pulled out. Andthen there was another one about
(18:58):
solving word problems that thatis an important piece of what
kids do, and we suggest evenusing gestures to help them
start to see patterns. You know,if I'm dividing and I'm doling
out like I'm dealing out cards,that sharing motion is a
something that can generalize toother problems, and you feel
(19:20):
like you have to share equally,you might be dividing and so and
then another one was aboutfluency activities. It's titled
timed activities in thedocument, but I'm going to be
straight with you. I think itshould have been called fluency
activities, because that's whatit's about timed activities are
(19:41):
one component of that, butthere's lots of other things
that help build students'fluency, and so those, those are
very important. And, um, youknow, you you told the story of
your son, which just reminded meof something that I would like
to share. I just returned fromthe National Council of Teachers
of Mathematics annualconference, and was fortunate to
(20:03):
see one of the teachers I'vebeen working with in Tennessee,
there with her, nine of herstudents with disabilities,
presenting with her, and theydid an unbelievable job. They
have just surprised over andover again, everyone with their
strength and interest in math,they call themselves the math
(20:25):
scholars, or the FBI, theFantastically Brilliant
Investigators. Depends on whatgrade they're in, what name
they've created for themselves,but the children love math. See
themselves as mathematicians,and were a knockout for everyone
who was at that conference. Soit's wonderful. Lots of
(20:46):
strengths, lots of strengths.
Lisa Dieker (20:48):
Well, thank you for sharing, and I think that was
our last question. We appreciatenot only your wisdom, but I love
the FBI. I'm sharing that witheverybody in America. So if
anyone has questions, you cansend us a post on our Facebook
page at Practical Access, orsend us a Tweet at
AccessPractical thank you again,Karen, for joining us.
Rebecca Hines (21:09):
Thank you Karen.
Karen Karp (21:10):
My Pleasure
Music.
Lisa Dieker (00:07):
Welcome to Practical Access. I'm Lisa
Dieker.
Rebecca Hines (00:10):
And I'm Rebecca Hines and Lisa, keeping with our
theme this season, I know youhave someone that you're excited
Lisa Dieker (00:18):
Yeah, so I'm actually giddy. That's a great
to present.
word for today. I'm so happy wewere able to get Karen Karp with
us, who's a professor in matheducation, who really does in
our work, have the intersectionof special education and
mathematics. So Becky, we don'thave enough friends in that
area, so we're super happy tohave Karen on the call with us
(00:38):
today. So thanks for joining us,Karen.
Karen Karp (00:40):
Thank you so much for inviting me. I'm really
looking forward to ourconversation.
Lisa Dieker (00:44):
Well, I'm gonna start with the first question,
and I would just love for you,imagine I am a brand new
teacher, and I have a student infront of me that has a
disability in mathematics, andI'm a little intimidated. I'm a
general-ed teacher, I don't knowwhere to start. What would be
your beginning advice for me tothink about or to do? Or, you
(01:08):
know, you, you are the experthere. What? What? What should I
be thinking about as that newnovice, first-year teacher
working with kids withdisabilities?
Karen Karp (01:17):
Well, you said general-education teacher, and
that's, you know, an importantstart, because they are the ones
who are delivering the mathcontent on one level. But I'd
ask that new teacher to partnerpretty quickly with a
special-education teacher intheir building, and start to
develop a partnership with them,because I really believe that
that is the best approach. I'mafraid in some cases, that a
(01:42):
student with disabilities is inkind of a limbo space. If we're
not careful, that the gen-edteacher might say, well, I don't
know that much about special ed,so I'm not sure that this child
is fully mine. And then thespecial-ed teacher will say,
Well, I'm not sure about themath part, so I'm not sure. I
(02:03):
think it's the other person's todo and and no one does. And so
what we need to do is start apartnership right away, because
it's everybody all in,everyone's in. And so that, I
think, you know, is critical.
But the main thing is, is tokeep trying different things and
be very proactive. The one thingI'm working on right now is math
(02:26):
interventions is proactive. Itwas the original intent of
response to intervention, and itwas preventative and after the
medical model. But in fact,that's not how it's played out.
It's very reactive, and we waitfor a child who's struggling in
math as the one you describe,before we act and do anything.
(02:46):
Well, we're saying to havelittle collaborations between
the special-ed teacher and thegen-ed teacher, where they work
two weeks in advance of newcontent together and they prep
each other as they're primingfor what interventions will take
place. And the interventions arenot pre-teaching the lesson you
(03:08):
have no goal or no interest inthat. They are building in
everything that goes into thelesson to come. So for example,
for something like perimeter,you know, what we want to do is
have those kids measure just alot of length and just practice
with a ruler and constantly bemeasuring. And we want them also
(03:28):
to see that if we add anotherline to the line they have, they
can measure this length and thatlength. We're not going to do
the parameter thing. We're justprepping them. And then the gen
ed teacher, and that's our newteacher on board. The special-ed
teacher will say, these are thethings that I've done with the
(03:49):
children in the interventions.
Start your first lesson withthese. And so we're going to use
those as a way to have thesekids shine, that these kids are
going to do things they just dida few days ago in their
intervention class that I'vealready reviewed, and now the
new teacher gets to call onthose children first. And so
(04:12):
we're trying to make it that thechildren really, really are
feeling that the lesson istheirs and not flying over their
head at fast speed. And so thatnew teacher has to learn this
new model, proactiveintervention. So that's one of
the things that I suggest.
Rebecca Hines (04:29):
Yeah, I love, I love to hear the word
collaboration. Lisa, I harp oncollaboration all the time. So
your your basic tip is, let'smake sure that we're
collaborating to ensure success.
And for this young teacher, whenthey go to a special educator
and say, I'm having trouble withX, Y or Z, I generally would
(04:53):
advise them go with. You know,go with the sample of work, and
don't say I'm having a problemwith this kid. I'm having a
problem with the way with thissolution. So do you have ideas?
But what do you think is a good,a good entry into that
conversation? Karen, how do theyhow do they go and elicit this
(05:15):
help, what they might not evenknow the special educators in
the school?
Karen Karp (05:20):
I love your idea of bringing a piece of students'
work, because one of the thingsI always say to all teachers is
we're not about fixing children,we're about fixing structures,
and so that's why I'm focusingon the structure of the
collaboration, because we're notabout at all thinking that the
child is it some way. You know,the change, it's not that it's
(05:47):
changing everything around thechild and and I think that
that's, that's quite theimportant piece, and I may be
missing what you're asking.
Rebecca Hines (05:56):
Yeah, let me. Let me. Let me. I'll ask that a
little more specifically, as afaculty member in special ed, we
talk to special-ed teachersabout collaboration. I don't
know that all of the gen-edfaculty when they're preparing
teachers, I don't know if theysimilarly present our special
(06:20):
educators as also experts.
They're just experts insomething different. So as a
faculty member who might workwith, you know, math education
majors, what would you tell themwhen it comes like, literally
like, if you were preparingteachers, how would you tell
them to approach a specialeducator, you know, with, with
(06:42):
the problem?
Karen Karp (06:44):
Total partner I mean, I really think it's got to
be that way. We each have, youknow, a collection of
information, and we just have tofind ways to share it well. And
I think that the preparation ofboth kinds of teachers, the
gen-ed teacher and the teacherwho's gone through special
education is quite different.
And so they are definitelydifferently prepared. And yeah,
(07:08):
we can say what's a good thingto do there, or what's not, but
the reality is, is thattogether, they have to make this
work. And you know, with manychildren, it's not only students
with disabilities. It takes twopeople to think about the
situation.
Rebecca Hines (07:27):
Right.
Karen Karp (07:28):
And it could be two gen-ed teachers. It could be, I
need two more special-edteachers if they're available in
the building, and even sometimesparaprofessionals and teaching
assistants who are workingclosely with that particular
child, they need to be in on theconversation too.
Rebecca Hines (07:45):
Oh, good. I think, I think we have a good, a
good article to write there.
Karen Karp (07:48):
We have something called, we have something called
the Whole School Agreement wherewe work to get everybody on
board across the entire schoolso that math is taught well, and
that, you know,special-education teachers,
paraprofessionals, teacher,long-term subs all go to the
same math PD as the gen-edteachers.
Rebecca Hines (08:10):
Love it. I love that.
Karen Karp (08:10):
Totally aware of what's going on. They're not
used as subs during a PD eventat a school. They are in,
they're in it.
Lisa Dieker (08:20):
I there's so many things you've said. I like, I
like the Whole School Agreement.
I like everybody's in I evenlike your really strong,
proactive focus on the strengthsof the kid, not the failure of
the kid in math. And I, I thinkthat's so much what the field
needs to hear. So I know weagree on this, but I would love
to hear your thoughts and helpfor any teacher, teacher, coach,
(08:43):
about that kid who we know needsto be in with their peers having
discourse, but really strugglesin being in with their peers and
having discourse. What are somethings that you found helpful?
Especially in the area of math,where, you know, some kids have
math anxiety, which we know thatliterature is high there.What
(09:04):
are some things you've seenteachers do, or you would
suggest to teachers for that kidwho we want them to be sitting
next to their peers and havingthat rich mathematical
discourse, but they mightstruggle with that?
Karen Karp (09:18):
Again, you know, again, I, you know, I think some
of this proactive work willsupport, you know, all children,
but there are complexsituations, and we have to think
about those as well. The mainthing is, is to use multiple
representations for all groups.
And I didn't mention thisbefore, but this is a great
resource for brand new teachersas well as veteran teachers, but
(09:38):
I was involved with a wonderfulbunch of other co-authors on the
IES practice guide forassistance, assisting students
struggling in math that justcame out about three years ago.
And in it, we make six importantrecommendations that it's mainly
for the elementary school, butit really travels all the way
(09:59):
up, and we made six importantrecommendations that teachers
should consider that's based onevidence-based research, and one
of the ones that I think is mostimportant, and if I go to a
school I talk about, and when Italk about any child in general,
multiple representations. Nowspecial ed uses well may still
(10:19):
call this CRA math educatorscall it CSA, because the R that
is used for representations,they're all representations.
Concrete is a representation,abstract is a representation. So
that R doesn't really stand forwhat it really is, which is
semi-concrete, like a drawing ora sketch or sometimes even a
(10:42):
chart, depends. And I and we inmath education like to overlap
those so that you're seeingconcrete. And if I need to, for
this particular student, writethe equation that goes with it,
first time I will do that, thenI might have a collection of
(11:02):
cards that have differentequations on it, and say, which
one do you pick that goes withthis model that we just made?
Then I get them to write it. So,you know, there's lots of
progressions that we can tosupport that child in, in moving
towards more, more of anindependent ability to handle
some of those questions, butthere are very, very important
(11:23):
models that help children thinkand do math and take action and
make it less anxiety producing,where we're not demanding
memory, where we're notdemanding time, where we're
giving the time to think, andwe're giving the supports that
are needed with even acting outproblems, taking the time to
(11:46):
just stop and act it out. A lotof kids need that role-playing.
Others just sometimes will say,imagine this situation in your
head like a story, and thatthat's helpful too. So there's
lots of things we can do to tryto bring them into the action
part of this. So it's not justrote memorization, and to be
(12:07):
frank, things that 10 years fromnow will be completely done by
AI or my watch.
Rebecca Hines (12:17):
And do you? Do you? Do you think, Karen, that
that on those occasions when wewhen we have students who are
who individually, are strugglingand but we suspect that you know
intellectually, they're capableof understanding the the
concept, the broad concepts, butthey're just lacking some of the
skills, and there may not evenbe time for them to get all they
(12:41):
had caught up in all of thoseskills. So how do we, how do we
as instructional coaches, youknow, what? What can we do? Or
what ideas do you have, whetherit's me or I'm bringing a para
in to to provide support or evena volunteer to help with the
coaching piece to get themcaught up on the sideline, just
(13:04):
a little bit?
Karen Karp (13:06):
Well, one of the things that I think, and this is
tangential to your actualquestion, but I think would be
useful in that, is that the IEPshave to be written to be more
conceptual. A lot of the timesI'm seeing IEPs written, and the
IEP is strictly about skills,and it talks about an assessment
where we're getting more digitscorrect than we did yesterday or
(13:27):
whenever it was done. And Ireally asked teachers all over
the country, what do you do withthat information about the
digits? How does it inform yourinstruction? And none of them
can really answer me. It's notthat. It's not doing the trick.
So I say write them moreconceptually, talk about talk
(13:48):
about place value, knowledge andthings like that, that we can
really bring the students in onwith these materials that we're
talking about. And those providethe total foundation for the
other components, but it isn'tputting kids in a tight kind of
situation of constantly be doingalgorithms and procedures and to
(14:11):
be frank, those are very elegantways of doing math, but they can
they. They are not some of themost joyous things in math.
Sometimes, that I'd like them toexperience some of the joy and
beauty of the subject, too. Andthey sometimes don't even have
an IEP on geometry, which can befor some children, the place
(14:35):
where they can really, reallyshine. And I'd like to see more
of that. And I also learned, youknow, of course, that you can't
write the same IEP every year.
Yet we see this multiplicationfacts thing travel along, and
the Supreme Court came outagainst that same IEP can't be
written two years in a row oreven again. So we need to delve
(14:55):
into some. Of the other thingsthat may, in fact, be a doorway
for children who do havetremendous strengths. I never go
in thinking that they can't doit. I always go in thinking they
can, and I just have to find away.
Lisa Dieker (15:15):
And so, so my last question, but I went a little
bit of commentary with it, soit's funny. I wish my son
growing up could have had you asa math teacher, but my husband,
I were literally just talkinglast night about our son works
for Trek and has sold lots ofbikes. I'm not allowed to say,
but he's one of the top 40salesmen, and yet I laugh that
(15:36):
he couldn't do hismultiplication facts. Still
can't, but he conceptuallystruggled, right, and he had a
calculator. But I do remember infifth grade, and I think you'll
find this funny, we got aletter, and I was like, Josh, I
think this is a wrong backpack.
And he said, I'm putting yourson in gifted math. And it like,
yeah, but again, he had thisamazing teacher in fifth grade.
And she said, look, Lisa, heprocedurally is not strong, but
(16:01):
conceptually, he gets it. Hebeyond gets it and and so I
think it's a good example forour listeners to realize,
realize, you know what Karen'ssaying, is life changing for
kids, because I do think thatwas a tipping point that allowed
him to go to college and dowell. And so with that, I just
and our listeners to hearbecause I got the privilege of
(16:22):
chatting with you on the phonebefore the podcast. I really
want them to hear your profoundwisdom in the IS report from
your perspective, and I wouldlove to put that link out on our
podcast when we're done. Butcould you share with me if my
son were born today and I wassitting there in third grade and
he still trying to do as facts,and I wish I hadn't done
flashcards all the way to thegym, because it didn't matter.
(16:43):
What would you tell me are sixthings I should be thinking
about for my son today?
Karen Karp (16:49):
Okay, and so, well, some of the recommendations I'll
give in general, one issystematic instruction. And by
that, I don't mean explicitinstruction. I mean giving kids
the chance to think and dofirst, and then I'm here to
support them but to assume thatthey have strengths that can
(17:11):
play into the information that'sabout to come their with. And so
that, you know, is a veryimportant shift that was very
different from the last goaround on the IES practice guide
that came out in 2009 themultiple representations is all
over the place in the practiceguide. So I've talked a little
(17:34):
bit about that already with CSA.
And another thing is thelanguage, the precision of
language is particularlyimportant. And this goes to that
conversation I had about theWhole School Agreement, where
we're all using the samelanguage or not like we're not
using borrowing and carryingbecause they're not conceptually
sound. We're using regrouping ortrading to replace value
(17:54):
purposes. Then kids here it overand over and over and again,
which is precisely what youknow, students with disabilities
need, and multilingual learnersand everyone else too. We don't
want we want reducing fractionsto be said one year and
simplifying the next. We want itto be a small stream where
(18:14):
everyone knows what's going onand kids aren't saying such
things as math is differentevery year. You know, it's not
it's a continuum, and we wantthem to be on it. Then we
separated in theserecommendations, one
representation out from theothers, because the research is
so compelling about it, and wewant to have all teachers
(18:36):
realize K-12, they'reresponsible for using it
officially, and it's the numberline. And so we started in
kindergarten with number paths,and obviously it moves up to
very complicated lines andgraphs and other components as
they move to middle and high.
But that one was pulled out. Andthen there was another one about
(18:58):
solving word problems that thatis an important piece of what
kids do, and we suggest evenusing gestures to help them
start to see patterns. You know,if I'm dividing and I'm doling
out like I'm dealing out cards,that sharing motion is a
something that can generalize toother problems, and you feel
(19:20):
like you have to share equally,you might be dividing and so and
then another one was aboutfluency activities. It's titled
timed activities in thedocument, but I'm going to be
straight with you. I think itshould have been called fluency
activities, because that's whatit's about timed activities are
(19:41):
one component of that, butthere's lots of other things
that help build students'fluency, and so those, those are
very important. And, um, youknow, you you told the story of
your son, which just reminded meof something that I would like
to share. I just returned fromthe National Council of Teachers
of Mathematics annualconference, and was fortunate to
(20:03):
see one of the teachers I'vebeen working with in Tennessee,
there with her, nine of herstudents with disabilities,
presenting with her, and theydid an unbelievable job. They
have just surprised over andover again, everyone with their
strength and interest in math,they call themselves the math
(20:25):
scholars, or the FBI, theFantastically Brilliant
Investigators. Depends on whatgrade they're in, what name
they've created for themselves,but the children love math. See
themselves as mathematicians,and were a knockout for everyone
who was at that conference. Soit's wonderful. Lots of
(20:46):
strengths, lots of strengths.
Lisa Dieker (20:48):
Well, thank you for sharing, and I think that was
our last question. We appreciatenot only your wisdom, but I love
the FBI. I'm sharing that witheverybody in America. So if
anyone has questions, you cansend us a post on our Facebook
page at Practical Access, orsend us a Tweet at
AccessPractical thank you again,Karen, for joining us.
Rebecca Hines (21:09):
Thank you Karen.
Karen Karp (21:10):
My Pleasure
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