PAUL RICCOMINI: Good afternoon. How are we doing? Good. So we're going to talk about Math in an RTI framework at the high school level. It's something that has a -- it's beginning to get more
attention but it's also -- it also presents a lot of unique challenges. One in particular is by the time kids get to high school, in mathematics, they have significant deficits and it really is a
challenge from a content perspective to allow these kids to have any chance of being successful. And on top of that, the motivation is also a big issue with kids at the high school level. So we're
going to talk a little bit about the components but one of the pieces that I focus on in RTII is really the Is; the instruction and the intervention. There's a lot of sessions about decision-making
and assessments and things of that nature but the most important piece in RTII is the instruction and the intervention. And it is also -- not only is it the most important piece, in my opinion, I
think it's one of the most challenging aspects to address because we're really talking about teacher's day-to-day behavior in terms of how they have -- you know, their whole approach to instruction
which is based on their experiences, based on their training and most importantly, it's based on how the teachers feel they learn math. So there's a lot of challenges at the high school level much
more than I think at the elementary level. Now, I was a high school math teacher, both a general ed and a special ed teacher. So I was the general ed teacher for a couple of years with students with
disabilities coming into my classroom and trying to support them in a class of 30 students in algebra and so forth. Not really -- I didn't have any in Algebra 2 or Geometry, although that's where
everything is heading but I was also then the learning support teacher at the high school level for a couple of years where I was trying to take kids and put them into the general ed math classrooms.
So I've kind of seen both perspectives and there's no way -- easy way or no way to sugar coat this. It is a huge challenge at the high school level to support students with disabilities in terms of
their math. And there's a lot of variables that are impacting this; you have the common core standards in math, you have new assessments coming down the pipe. Has anyone had a chance to look at the
park in the smarter balanced assessment items? If you haven't, I would encourage you to download them and just start taking a look at them. They -- there are definitely some challenges in those
assessments for our students in terms of reading and then I also think in terms of persistence which is, you know, one of -- one very common characteristic that I vividly remember with my students at
the high school level was the first problem that they encountered in the context of solving something or as they got stuck, what did they often do? Stopped, and that was it. And that creates a lot of
challenges. Part of -- part of what I'm going to talk about today, I'm going -- I'm going to try to focus on two strategies for you in terms of what we need to be seeing in our either instruction or
intervention piece. One of which will be a problem-solving progression. How many of you are high school math teachers from -- in special ed? Special ed -- special ed math teachers at the high school
level? A couple. How many of you are math teachers at the high school level? Any? Okay. Good. So who else is in here? School Psychologists? Middle school -- some middle school?
AUDIENCE MEMBER: Curriculum coordinator. Curriculum?
PAUL RICCOMINI: Curriculum Coordinator.
AUDIENCE MEMBER: I'm a combination. I taught math and also a school psychologist and counselor [inaudible]
PAUL RICCOMINI: Excellent.
PAUL RICCOMINI: Okay. Excellent. Anybody else? Have I missed anybody?
AUDIENCE MEMBER: Principal in?
AUDIENCE MEMBER: Assistant principal, middle.
PAUL RICCOMINI: Assistant principal, middle. Okay. Good. Good. This is a nice mix of a group. This -- the other thing that has -- we also have to recognize is that RTI is founded on special ed and
general ed working together, and working together is not defined by they're in the same room. Working together means there's a dialogue, there's a discussion, there's a mutual type of
responsibilities being shared. So we're going to -- I'm going to talk about the eight core principles. Now, I'm really going to -- of the eight, given seventy-five minutes that I have, I'm really
going to just focus on this belief system now. That is the one part of RTII in math that's different than in reading is our belief about students. And then I'm going to really focus on instruction
and intervention and I want to give you -- or for principals and administrators, curriculum folks, what you should be seeing in the core classroom and then if you're a teacher, you'll leave here with
two strategies that you could actually start doing. They're not too difficult and they really -- one of them is one of my favorite strategies, and if I had that strategy when I was a teacher, I would
be doing a lot of things very differently. So that's sort of the idea here. Now, this is a great small group so please ask lots of questions. Part of the other -- part of the challenge at the high
school level with RTII is there's not a whole lot of research done at our level, most of it is at the elementary level. But we're -- these are sort of what we're going to talk about, and the two
strategies will be Content Scaffolding and Interleave Worked Solution Strategy, the IWSS strategy. But I'd first start off with this. One of the things that high school kids -- middle school and high
school kids do is they adapt. When they cannot do something, they adapt. And I saw this little video from a long time ago but I really think it shows how kind of -- for good or bad, they adapt. So
we'll watch this real quick.
[VIDEO STARTS]
TEACHER: One minute. One minute, please. Time. Thank you. Could you all please put down your pens and bring your papers to the front of the room? Well done. Thank you. Thank you. Oh, I'm sorry. You're
too late. [inaudible] time. You failed. Sorry.
STUDENT: Excuse me. Do you know who I am?
TEACHER: I have absolutely no idea.
[VIDEO ENDS]
STUDENT: Good.
PAUL RICCOMINI: Now I think -- I think that is -- that's illustrative of what -- one, with a lot of -- a lot of kids that are really struggling at the high school level kind of think they feel they're
lost. No one knows who they are. No one cares about them, but -- and then they develop strategies to avoid all things math; they forget their books, they don't do their homework, they pretend they're
doing something, they develop all kinds of defense mechanisms to get them out of their math. The forgetting of the pencil, you know, at the high school level, it's like they think if they forget
their pencil, they're automatically excused from all work that day. And it's really -- it creates a lot of challenges and, you know, I think back to when I was teaching and, you know, some of the
kids that I had -- first off, of the students with learning disabilities that I had in my classrooms, 90% of them would be in the general ed classroom today. I had kids that quite literally, if they
came to school, stayed for the whole day and had a pencil, that was a success for them. It might have even been an IEP goal back in the days but now, these kids are having to take and are expected to
learn these upper level math content classes and it creates a lot of new challenge. So they would develop strategies, good or bad, they develop strategies and a lot of times, the strategies are
avoidance versus trying to actually learn the content and one of the things to keep in mind is, part of their avoidance strategies have developed because they have been failing math in tenth grade.
How long that they have been failing math? Ten years. And it's an inversion. And to be honest, I'm surprised they still come given that they have their failing day after day after day... or
reaffirming, confirming that failure. So a very classic example of a structure in the middle school and high school math classroom is something that's called a warm up or a bell ringer. Now do you
have any -- does anybody have a secret code name because -- so everybody has got some names. What do you call it?
AUDIENCE MEMBER: At the bell or bell?
PAUL RICCOMINI: At the bell.
AUDIENCE MEMBER: Do now.
PAUL RICCOMINI: Do now. Anybody else? There's all secret things out there. Now the issue with that is, how is -- what's the purpose of that? Go ahead.
AUDIENCE MEMBER: It's a job there I think.
PAUL RICCOMINI: It's a cumulative review so there's usually three to five problems that have been selected that the students should have learned. They're different, right? And then the teacher gives
the kids, the kids have been really brainwashed, I know that's not a good word, but they've been taught that as soon as they walk in a classroom, what are they supposed to do?
PAUL RICCOMINI: Sit down. Do those five problems. And the teacher is checking attendance or at the hallway or whatever it is. After about five minutes, then what happens? The teacher goes over and
AUDIENCE MEMBER: Sit down.
that takes five minutes, right?
AUDIENCE MEMBER: Or something, something.
PAUL RICCOMINI: Or 20 or 30 because nobody could do it. So what -- here's what you have to ask yourself, and this is what I'm really trying to start think -- get teachers thinking. If you're a teacher
or you're a principal and you've observed one of these, were there a group of kids that could do those problems in a classroom? Yes. Were there a group of kids that is kind of like 50-50? The demo
switch kids. Sometimes they can do them, sometimes they can't. Then is there a group of kids, they're not getting any of those problems right 90% of the time? That's right. So you've differentiated
into three groups, right? What do we make all the kids do?
AUDIENCE MEMBER: The same problem.
PAUL RICCOMINI: The same problems, the same thing. At the lowest level of differentiation, we've got to think about doing that differently because those kids that aren't getting them right 90% of the
time, they're usually the kids that don't like math. They're usually the kids that have motivation issues and every single day, they start off a math class on a what?
AUDIENCE MEMBER: Failure.
PAUL RICCOMINI: On a failure. So these are the things that you got to think about. The -- everybody has a structure and we got to start thinking about changes. Now the structure in an RTII framework,
you have your instructional core and then you have intervention or extra time or small group or however you want to set it up. Many states that I work in, they are doing something that is called like
-- it's called various names but one of it is called an IEP, an Extended Instructional Period. And essentially, it's an additional 45 minutes to 60 minutes of math at middle school and high school
level. Now I know some of the principal are thinking, "Oh, my goodness. How do you schedule that?" It happens. I'm not usually involved at that level but there's various ways. And in that additional
math period, about 40% is spent on going back and re-teaching gap deficit areas. Sixty percent of that time is extending what the core teacher is teaching. Does everybody follow that? That's one of
my big points for today's session is you got to start asking yourself how much time are my struggling students getting in math? Then once you look at that, the next question is, how much time is the
non-struggling student getting? And if they're the same, that's an inherit problem in an RTII framework because [inaudible] of multiple [inaudible] time and they're expected to get not just the same
growth as the non-struggling kids but [inaudible] you wonder what. So they're expected to get more growth but yet they have the same amount of time. Now, so those -- that's a big message is that
you've got to take a look at the timing. Now, don't over simplify and say, "Well, if I just got time that'll fix." The issue is, what do you do in that time? Trust me. I've been in enough classrooms
for 90 minutes and I was about ready to pull my hair out, and I love math. So that's one of the things that we have to keep in mind. So, you know, why is there such a focus on algebra and math? Well,
they're sort of a convergence of information from some longitudinal data sets, from previous research that essentially, if you can get kids through algebra, they're four times more likely to
graduate. Their success after like -- after school is much better, so that's the focus. Now, where I come in to play is this instructional piece. We have -- we have to start trying to facilitate
learning. Now, here's the other issue at the high school level that we have to talk about a little bit which is why did high school math teachers become math teachers at the high school level? You're
a high school math teacher, right?
PAUL RICCOMINI: So why are you a high school math teacher?
AUDIENCE MEMBER: Yes.
AUDIENCE MEMBER: Well, when I was in high school, it was very easy for me so when I went to college, I said, "This was so easy in high school why don't I try it in college?" And then -- and?
PAUL RICCOMINI: Bingo. Bingo. And you like people, that's the other thing. He's good in math. He likes it. He's good in math. And the kids we're working with are the exact opposite and we have to
recognize that and, you know, a lot of times high school teachers will go, "Well, this is how I learned it, this is how they have to learn it." And the problem with that is they're not us, they need
totally different -- and that's a challenge for high school teachers. We're very content driven. In middle school, we're very content driven and sometimes the instructional piece is a little bit of a
challenge to adjust for. So that's kind of where we sort of -- these are the -- like as you're looking at your RTI model and beginning to plan, these are kind of questions you want to ask and start
talking about. But here's what this -- and me -- and I'm going to show this in the elementary, but this here just absolutely is amazing to me. This is what our math instructional programs have gotten
us over the last 25 to 30 years, which is 78% of adults cannot explain interest -- how interest is computed. Now just -- let's think about that for a second. That's not algebra. That's middle school
or actually that's probably fifth grade. Now, that might help explain some of the economic issues we've had when you don't understand finances, you're susceptible to making what? Bad decisions.
Seventy-one percent cannot calculate miles per gallon, all right? Now maybe that's because gas cost so much no one wants to. But the last one is a former waiter. It's just painful to me. Fifty-eight
percent cannot calculate a 10% tip. Strip away the context, round, move the decimal, and we can't do that. You know, when I work with my students at Penn State in my mathematics class whenever we're
discussing that at the beginning of the semester, one of the -- one of my students usually raises her hand and say, "You know what, that's okay because at the restaurant I work at, at the bottom of
the check, we give them multiple choice so they can decide 15, 20, whatever the tip they want." So if you think about how much arithmetic or mental math has been taken out of our daily lives, we
start to understand why we're where we're at in terms of math. Now, we have --we have a lot of people not doing this. Now when you're looking at these percentages of students, these are not students
with disabilities in the general population. We're talking our average kids that have been doing okay cannot functional -- function in terms of applying mathematics, but here's the model that you
want to look at. Now obviously, in a 75-minute session, I can't get into each one but these are the three things. Now, I should have said this earlier on. I'm going to try -- I'm going to violate a
major RTII presentation rule, which is I am going to do this section without showing or displaying a single triangle. Okay. Now I know that for some of you, you're thinking, "Well, then you're not
talking about RTII." But I'm doing this without any triangles. I'm tired of the triangle. It's what's in this triangle that's important. Now that's not a triangle. It's close but it's not. But these
are the three areas that we have to look at. In other words, your curriculum, is it align with the standards? Standards is what we're supposed to teach in every -- for the majority of states are
adopting the Common Core State Standards in Math. I know there's some discussion in Pennsylvania about that but that's sort of the -- what we're supposed to teach. Then you have your materials and
interventions, then you have assessments. The key piece with assessments is that data-based decisions are made. Now in my opinion, the data-based decisions that are critical are connected to
instruction, teacher instruction. And then the bottom circle there is the teacher content in instructional knowledge. That's where I really tend to put most of my efforts and I think that a lot of
districts I work with, they're spending a lot of their time, on the top two circles, trying to figure out what assessments, what materials, what interventions. They give these wonderful charts,
there's usually somebody called a DQ, a data queen. Is there a data queen? They're in charge of the data. There's a wall room that has all these things posted on the wall. But really, the only way
that we will focus in a way that can improve mathematical out -- learning outcomes with students is by the instruction, that's the key. Now here's something that I'm just going to mention to you
also. You're all middle school or high school. In your RTII plan, there must be vertical planning with the elementary schools and middle and high school together. Now depending on districts,
sometimes there's a curriculum coordinator at the elementary, there's a curriculum at the middle school, curriculum at high school. You're the lucky one. You're in K-12, right? So there needs to be
vertical communication. Now just -- the high school teachers will really understand this. As soon as you start having a planning time with elementary teachers, the elementary teachers are immediately
uncomfortable dealing with math and high school teachers, all right? Some of that has brought on by ourselves. We have what I call content arrogance, all right? Oh, it was easy for -- do you -- do
you know calculus? Do you? Do you? No. You need to go over there. Physics? Okay, you're with me. We have content arrogance. We have a finite set of skills that not a lot of people have, so there
needs to be vertical communication in a very positive fashion. And high school teachers can take a very active role in helping with elementary teachers' content understanding in terms of what they're
teaching. Now here's the special education concern for special ed teachers at the high school level. You maybe asked to co-teach a high school classroom where you yourself are not comfortable with
the what?
PAUL RICCOMINI: The math. And it's really not, I mean, it's not your fault. You were not trained on the content. So there's a lot -- like I said, there's a lot of issues that has to be addressed but
AUDIENCE MEMBER: The math.
one question is, is there any type of vertical planning within your district for math at all levels? Second, how knowledgeable are your special ed teachers? Or I shouldn't say knowledgeable. How
comfortable are your special ed teachers with the content they're going to be co-teaching? And, you know, if you're a teacher, you've had a statistics class. So it's not like you can't do it, it's
your -- most of the time you're what? Uncomfortable with it. But this is -- really frames everything and everything has to go back down to the -- at the teacher level. If you spend all your time
trying to figure out an intervention, figuring out a program, the bottom line is who's delivering all of that stuff for the most part? Teachers. Now, you are seeing some computer programs come in to
play but in general, the teacher. And my opinion is you -- teachers have the -- you cannot replace a teacher with a computer program. I think they can supplement and add to that, but the teacher is
the key piece. So when you're looking at the guiding principles for RTI, there's eight and, you know, depending on who you talk with, there could be more or less, depending what they put together.
And I'm just going to briefly talk about three of these in my 75 minutes which is the belief system. This is one that is very different than RTI reading, and what I mean by that is pretty much,
there's no question at the elementary level that all kids or almost all kids should be able to read at some level of functioning. Would people argue about that? No. In math, it is exactly the
opposite. As a matter of fact, there's articles written in national newspapers arguing against more math, arguing against the rigger of the new Common Core. And that is one of the biggest challenges
with RTI is the belief system. And then I'm going to talk about the instructional tiers and research-based intervention in terms of what that should look like. Now with that being said, I hate to
sort of be the bad news bearer but there is no simple solution to what we have at the high school level. It's a challenge. It is a major challenge that we have. And to be quite honest with you, we
have to address the elementary mathematics in an RTII framework. Now I think if the Common Core State Standards are implemented correctly, the middle school teachers have the most to benefit. The
problem is it's going to take several years for these kids to cycle through and the big, you know, question is implemented correctly. If we continue to do the new Common Core Standards like we've
done the previous standards, we will end up getting the same results which is already by middle school, which is a really -- you see it in about fifth or sixth grade, the gap becomes enormous. And
quite frankly, what this gap is is rational numbers. The arithmetic to algebra gap essentially is going down to rational numbers; fractions. How many of us--now how many of you, as soon as I said
fractions got a little uncomfortable, just with fractions? Fraction is the problem, when kids do not get fractions. They really have problems with algebra, would you agree with me?
AUDIENCE MEMBER: Yes.
PAUL RICCOMINI: I mean if you're looking at -- think back to some of your algebra classes and you start actually looking at their math. A lot of times they conceptually kind of understand what's
happening but they're unable to what? Execute it. And fractions is a big issue. So, you know, one of the things you're going to have to do at high school, at the high school level is there should be
some re-teaching in small groups on the manipulation and execution of fractions. And I know someone said, "But I got to teach algebra. I got to teach geometry." Well, bottom line is if we don't try
to fill in some of those gaps, the problem is we're going to have the same problems. Now middle school, one in the -- anybody else in middle school in here? One of the big things in middle school
that if I had it my way -- and again, the system is not set up with this. RTII at the middle school would be a two-year intervention for math sixth and seventh grade with the sole purpose of prepping
them to be successful in algebra. The problem is we're testing after sixth grade. We're testing after seventh grade, so the principles and the district want the results after each grade level. And
what we really should look at -- you know who is at risk and who's entering sixth grade. You already know. We -- those -- by the time kids are in fifth grade, the wealth of data that they have on
their math you know already who is way behind. We should look at them as a two-year intervention. The problem is the system's not set up to do that. Now RTI, you may be able to finagle it a little
bit that you do do something like that. But what happens is we're too focused on getting those results in sixth grade, seventh grade and we're not getting -- we're not filling in the circle enough.
AUDIENCE MEMBER: As a person that goes in as a consultant and just observe the teacher because I'm working as student [inaudible] you know, you develop an IEP for the students. I observed. Even though
Yes?
I haven't taught math for years, that math was taught in such a different -- in such a different way in third and fourth grade that I would have to go back to college to teach it in third and fourth
grade. And I thought you might know all of this stuff to multiply. It was so much easier the way we taught it in the way I learned and the way you learned or you probably taught it too. And the way
you're teaching with all these [inaudible] I mean, and by the time that it gets to sixth or seventh grade, I don't see how they can do anything, except -- and to try.
PAUL RICCOMINI: And she's sort of getting in to the -- there's been a big argument about standard algorithms versus, uh, alterative algorithms, like the Lattice Approach, partial -- you know, there's
various different ones. All the place in my opinion, they can get a place value and do some things. The problem that we sort of -- that we had, there was actually an article in the Washington Post
just about this -- a couple of days ago that we sort of left the standard algorithm emphasis. And as a high school teacher, you know that is problematic when you get there. But you're right, you
know, there's been -- we are all familiar with Reading Wars, right? I mean that's a term that has been public knowledge. But there's been Math Wars probably for almost three decades, arguing over
what to teach, how to teach and really, we got a mess. I mean when you start looking at your kids that we have it's -- I mean we have a big challenge in terms of what we have. So what happened is, we
have kids that they don't really have a good conceptual understanding so they're trying to memorize procedures, and then they mix them up. We have kids that have conceptual understanding but don't
really -- aren't able to execute it. Well, they have elaborate ways of thinking about things which then causes them problems when they have to do it in the broader -- context of a broader problem. So
yeah, I agree with you. There's a lot of issues there. Now, the core beliefs. This is where RTII is so much different in middle school and high school than it is in elementary school. All students
can be mathematic -- as a country, we sort of have the idea that math is either you have the math gene or you don't, right? And it is literally -- it is perfectly acceptable not to be good in math in
the United States. As a matter of fact, if you're really good in math, what's the stereotype?
AUDIENCE MEMBER: [inaudible]
PAUL RICCOMINI: That's right. It's negative. When you start looking at international countries, that's probably one of the bigger differences. In the U.S., it's acceptable not to be good in math. Kids
are bombarded by if you're good in math you are a nerd, it's not good, where in other countries it's the exact opposite. If you're not good in math, it's generally looked at as, "What's wrong with
you?" On top of that, how many of you had finally get some parents in to have a parent conference with them, with your kids? And as soon as you start talking about math, what does -- what's the first
word out of the parent's mouth often?
AUDIENCE MEMBER: I was never good at it.
PAUL RICCOMINI: Oh. And so one, that tell -- that tells you, number one, that they're not really going to be able to help. Number two, that child right now has the closest role model to them, good or
bad, that is essentially saying math's bad. So you see the challenges that we have compounding? And, you know, unfortunately, that parent that's saying that to you is also saying that to the
elementary teacher in first grade in front of that child. So now, the child from first grade on is seeing math's bad, math's hard and my mom and dad weren't good at it so why should I be good at it.
So we got, I mean, the challenges are very daunting but we've got to focus on instruction.
AUDIENCE MEMBER: Well, take that one step further. I have never met an elementary teacher who went into elementary teaching because they're [inaudible]
PAUL RICCOMINI: Yes. I mean elementary has their own challenges. High school teachers, we know content and I love that. However, high school is sometimes resistant on instruction. Elementary teachers,
they're fantastic in trying strategies but they shun math. So yeah, they -- I mean there's challenge -- there are specific challenges at every level for sure.
AUDIENCE MEMBER: And the time spent in math is difficult too.
PAUL RICCOMINI: Well, that's the other thing that I'm seeing changing in a lot of states is -- there's elementary schools I'm working in that are up to a hundred and twenty minutes of math every day
for all kids, 120 all day.
AUDIENCE MEMBER: A few years ago, we had an elementary teacher. She has since retired and says she taught fifth grade. I sure had her started teaching fractions because I -- she knew how to do it to
PAUL RICCOMINI: Yeah. Yeah. And that's, I mean, that's the problem. And right with the Common Core Standards, fractions really start in the middle of the third grade, fourth and fifth. So I mean,
fifth grade.
there's -- that's -- that is the unique problem at the elementary level with RTI is that all teachers in elementary school, they can all read. If I go to a high school, Shakespeare class, take out
the Shakespeare book, they all can read it and they can understand it. They might not like it but they all -- every one of them can read it and comprehend it. If I go next door to your Algebra 2 Trig
class and you bring that content down to elementary, you've lost 80% of them. Algebra 1, still a lot and that's the --that's the problem at the elementary level. They're teaching the foundations of
math but don't really see where they're going. But the amount of time is your next, I mean, we've already talked about that, is how much -- and I'm seeing elementary schools moving to 120 minutes of
math. You know, if math's the priority focus then you should be spending more time teaching math to those kids. Now at the high school level, you run into this -- the challenges with the Carnegie
Units, right? They have [inaudible] and the scheduling and the [inaudible] of those different challenges but that's what you sort of have to think about. Yes?
AUDIENCE MEMBER: [inaudible] be able to have a math approach that really knew math, a new concept that could actually be able and help delivery, like help to teach the teachers to teach because as an
administrator, I don't even always know exactly what it is they're supposed to teaching, so I often rely on people like that to be able to help me to say, "Here's what I'm saying. I'm not sure if
it's what I should be saying," and then I have an explanation that I -- to me, to kind of interpret it actually.
PAUL RICCOMINI: I'm seeing a lot of math coaches at all levels. It's a good [inaudible] they seem good. A lot of times at the elementary, this is what the math coach?
AUDIENCE MEMBER: [inaudible] math coach.
PAUL RICCOMINI: This is what they say to me, "You got to help me out. I know how to do reading but I'm not so good in math," and they're the math coach. So it's a -- you got to get the right people in
the right spot. So that's -- but at the high school level -- what I'm finding is at the high school level, a math coach is just as important for helping the teachers adjust their instruction a little
bit. All students need a high quality program. This is right -- this one right here in the three and four is really where I want to focus, and that is we need programs that are developing conceptual
understanding computational fluency, factual knowledge, vocabulary, procedures and then problem solving. This is where we have to really evaluate our curriculum. Now, this is where high school can
have an input and middle school. What are your elementary programs? Are they focused on these things and I got to tell you, it's not always the case. There are a lot -- some of the most popular
elementary programs are basically marketed as conceptual and problem solving. That is going to cause problems later. It's almost like we have a delayed effect. Kids can get by in elementary but they
got slammed in middle school. That's really where it starts. And then finally, instruction matters. And this is where I want high school teachers to really think about both special ed and general ed.
A lot of times you are working with kids that are really struggling, all right? They have bad, poor motivation. Now you -- I'm sure some of you have kids that they come in, the disengage kid. They
come in, they put their head on their desk, they put their hood over their head and they're completely disengaged. Those kids need way more than instruction, not [inaudible] intervention for those
kids. But a lot of times middle school and high school teachers, they immediately think of that child when someone's trying to teach -- take them through a strategy and we use those kids as sort of
the reason not to try certain things. But what we want to focus on is there are a lot of kids that are coming to school everyday that are just not getting it with how we're going it. They tried their
homework. They asked questions. They just are not getting it with the way we're doing it. That's what we have to really focus on. But instruction matters. As soon as you say, what -- "There's nothing
I can do with these kids. What'd they expect? The parent can't do math, look at him. What can I do?" You're essentially saying instruction does not matter. And if you're saying instruction does not
matter, who's delivering the instruction? The teacher. And we're indirectly saying we don't matter. Now, to every complex problem there's a simple solution that doesn't work. Mark Twain, a literary
giant. He actually had profound statements for math and I think this really sums it up. We've got a complex problem here. We've got significant motivation issues. We've got significant gaps. We've
got all of a sudden a ramping up of standards at high levels. We've got the new test coming down the pipe, so we've got a lot of issues. Some of these issues, we the teacher, we have no control of.
The only thing we really have control of is what? When that door is closed, how we teach, how we prep, how we teach, how we set up the lesson, the language that we use, the feedback that we give
kids, how we do guided practice and independent practice and, you know, talking louder and slower is not a Tier 2 intervention, all right? So we've got to, you know, think about those things. So in
the tiers, what you're trying to build is multi-levels of support. As the kids that struggle, they need more intensive support, and intensive can be defined in several fashions. One is smaller
groups, two is additional time, three is more explicit intervention or more explicit instruction. Those are essentially the three ways. Now, you also have duration and time, how long and how much. Do
not expect a turnaround in two to three weeks even if it is every single day for 45 minutes. Our students not only need the intensity but they need time for processing practice. Now one of the
strategies I'm going to show you today would be -- was a little bit different way to -- that you can help with practice as well. Assigning kids 20 problems for practice homework, that may work for me
and you. But for our kids, forget it. That's not going to work. And I know that math teachers sometimes have issues with that but I don't know. I should probably go back and find the kids I had in my
first year of teaching and literary write them letters of apology for some of the things I did with them. Just because that's the way it was. That's how I did it. And I -- they probably, you know,
man -- think about some of the things I did just because that's the way we did it. That's how I did it so that's how they were going to do it and we got to start thinking about doing things a little
bit different way but just so you know, I'm seeing all different arrangements for middle school and high school classrooms. I'm seeing -- I'm seeing the traditional 45 minutes periods, as much as 90
minutes. I'm also seeing 45 for everybody, 45 extra for kids that struggle. Some districts are having kids -- instead of doing two electives in a nine weeks, they do one elective and one extra math
class. Now the issue you got to really pay attention at the high school level is -- so what's your name?
AUDIENCE MEMBER: Laura.
PAUL RICCOMINI: So Laura has been identified by her assessment. She's a struggling ninth grade student. So we're just going to set up a schedule for Laura that she gets 60 minutes from me and then
she's going to get for her regular instruction, then she's going to get 45 minutes additional of instruction. Laura in ninth grade probably does not really care for what? Math. And now we're telling
Laura what? You're taking double. So that extra math has to be much more supportive, much more successful-driven or Laura will learn to hate math even worse. Yes?
AUDIENCE MEMBER: The only thing we did this year and I wasn't really -- a real big fan with this first one. It turned out it was -- it was kind of a hit or miss process but we were glad we had
administrative [inaudible] that was hired and she came up with the idea of a reach program first thing in the morning. Like for 30 minutes right of the get-go. And so it started out that we had books
that we were reading, the kids would write in the books and we would read to them and they would write the math problems in the book, you know, it was kind -- it was different, all right? But the
only -- and I -- we went -- I, myself had like six or seven different reach groups as the year progressed. The one that was the most effective and it really surprised me is I taught -- one of the
classes that I teach is algebra 2. And so I had a whole group and there was maybe like 15 kids that I tried [inaudible] that were all in that group. And so I said to them, "Let's do our homework."
And those kids really look forward to that but they said, you know, because I can walk around, I could talk to them and I love this. And I had liked kids when they come in to my reach class because
they all pass those grades. Their grades were not, you know, quite a bit and that -- well, I had it only for a month though and then they change recently to get on me, but it was brilliant to see how
those kids took from it. They got no points for it, there was no reward for them [inaudible] and they understanding them, and the fact is they love it.
PAUL RICCOMINI: So what they've done is the way they've looked at their Tier 2 kind of is they got additional 30 minutes, and the way you did your Tier 2 was you gave them more guided practice.
Probably the first time most of those kids could actually do the homework and then what he saw was, jeez, with this additional guided practice in my regular math class, what did I start to see?
Moving now, let's take this another level, so that same structure. So let's say you have the same structure next year. We got 30 minutes. Here's what I would recommend that you do. Do your homework
like you were doing, guided practice but take 10 minutes out of that reach, maybe every other day and pre-teach the algebra 2 skill or concept that you're then going to teach in that class and you'll
see those kids come to your class and when you ask a question they're going to raise their hand because they were pre-taught what you were going to do and then you'll build their motivation. You see
how some of this extra thing can happen? Now the key is you've -- it's -- you've got to be careful. The extra time can't just be seatwork and practice. It's got to be some level of guidance but what
I would strongly recommend is that 30 minutes you have with these kids is you start to begin to pre-teach some of the things you're going to teach in your regular class and then the other thing to
consider is looking at those kids and identify where they have a gap. And my guess it'll be something with fractions. And spend 10 minutes doing mini lessons and giving them extra instruction on
certain pieces of fractions.
AUDIENCE MEMBER: It's so interesting though to see these kids and their enthusiasm before they will sit in a class like this, you know, they would exactly do that. But whenever they understood it, you
know, off that little bit of reach thing, they're there and likely to say, you know I didn't get -- and I only handled them for less than a month but they were asking questions, you know, and let me
ask you this, but let me put it on the board you know but it was surprising to?
PAUL RICCOMINI: So if you could get those kids for the whole year. That's really the Tier 2. That's that duration thing. You -- success can happen. Sometimes they surprise the heck out of you, right?
Because you probably had no -- and I'll say, "Holy cow." So, couple things that are beneficial for what he says. So let me pull out the part one. The extra time he -- that he was doing it. So he had
those kids. That's not always the case. Does anybody have sort of extra time where somebody else is doing it or special ed teachers doing it? If that's the case, there needs to be some communication,
the flow has to happen. The -- in his scenario was he had them in his regular math class and then he had them in the extra time. Now, it was Algebra 2, Trig? Was that just Algebra 2?
AUDIENCE MEMBER: Well, we teach Trig separately.
PAUL RICCOMINI: Oh, it's a separate? Okay.
PAUL RICCOMINI: So just Algebra 2?
AUDIENCE MEMBER: [inaudible]
AUDIENCE MEMBER: Just Algebra 2.
PAUL RICCOMINI: And, you know, the benefits of this is, like you said, kids start to feel successful. They're more willing to engage. They're more willing to try. That can have profound effects. How I
would tweak it is spending some time in that 30 minutes on an instructional remediation of something important/reteaching -- or I'm sorry, pre-teaching.
AUDIENCE MEMBER: The only thing that might be happening is you might be teaching it in a slightly different way than their actual teacher is teaching it and it's just another?
AUDIENCE MEMBER: I'm the actual teacher.
PAUL RICCOMINI: It was him.
AUDIENCE MEMBER: Well, it's me.
AUDIENCE MEMBER: Oh, you're the actual teacher? Okay.
PAUL RICCOMINI: ?how many kids were in your -- how many kids are in your general class?
AUDIENCE MEMBER: I thought there were?
PAUL RICCOMINI: Yeah. But?
AUDIENCE MEMBER: The general class is like 20-25.
PAUL RICCOMINI: How many is in Reach?
AUDIENCE MEMBER: Well, between 10 and 15.
PAUL RICCOMINI: So there's that small group.
AUDIENCE MEMBER: Between 1 and 120, yeah.
AUDIENCE MEMBER: There isn't -- there isn't so much [inaudible] but even how I present it, it was more in general.
PAUL RICCOMINI: So?
AUDIENCE MEMBER: It wasn't, "Let me put it on the board. Let me put on the screen." It was -- it was more, "Let's get the homework done."
PAUL RICCOMINI: In a couple -- a couple of byproducts. That smaller group, they read, so they're all struggling kids so they're closer in skill conceptual level. They're going to be more willing to
ask questions or going to be more comfortable saying, "Hey, I don't know. Help me." So these are things that can be very beneficial, so I see that setup exactly the way you've explained it. I see
also an after-school. I'm not a big fan of after-school, to be honest with you, because oftentimes the kids are tired; the teachers are tired, kind of, like the first thing in the morning. So, making
it a little more instructional focus, I think you'd even get better results in for a longer period of time.
AUDIENCE MEMBER: Now, when we did this -- I wish I could tell you the name because I'm sure you've written it right away, is it scripted lessons?
PAUL RICCOMINI: Yes.
AUDIENCE MEMBER: That was a great effect to the kid where you read something, then you tap the table and then the kids will give you response.
PAUL RICCOMINI: So that's called -- that's explicit instruction, that's a signaling. Most of those -- most -- I would just tell you, most if not all interventions are now scripted. Now, the scripts
are really not designed for the teachers to stand there and read it, they're designed to sort of prep and guide the teachers but almost all interventions. And, you know, was that the first time you
AUDIENCE MEMBER: Yeah.
used it?
PAUL RICCOMINI: So if you use it a second time, you're going to be less reading and more instruction but it's sort of set to guide.
AUDIENCE MEMBER: And I like it [inaudible] and you can see the enthusiasm of the kids whenever they came into the class.
PAUL RICCOMINI: Yeah. Middle -- getting middle school and high school, the signaling can kind of have some negative effects, but my guess is you weren't real comfortable with it and -- because it was
the first time and then the kids -- that's going to play off in the kids but almost all interventions that I'm seeing for math are all scripted.
AUDIENCE MEMBER: Do you [inaudible] the school that they are grouping by ability?
PAUL RICCOMINI: Well, that, I'm starting to see that at the elementary level and?
AUDIENCE MEMBER: I mean, in the upper level.
PAUL RICCOMINI: Well, in the upper levels, they all -- they're inherently already done. They're more homogenous because you start having like Algebra classes, gifted?
AUDIENCE MEMBER: Let's say, like a lower Algebra and higher Algebra?
PAUL RICCOMINI: Yeah. I'm not seeing that. I think there's a lot of discussion. I'm going back to that. The -- in the pack -- in the past, that was very negative because that was associated with
tracking and the reason that's negative is the low kids, they got something totally different. I don't think that's as big an issue anymore because everybody has to learn the common core standards.
The issues that I have problems with with that is teachers often will teach to the average kid. So when you group, if you have a high Algebra, their average is here and the low Algebra, their average
is here, it's going to -- so sometimes the teacher will teach to that. So I have mixed?
AUDIENCE MEMBER: I was just thinking if you took that group out, they could teach to that level.
PAUL RICCOMINI: But then, they never get them forward, that's?
AUDIENCE MEMBER: And that's what I mean, separating them out.
PAUL RICCOMINI: That's what I'm talking about. When you have a mixed group, the average is here. If you take all the low kids out and put them in this group, their average is here. Teachers tend to
teach to the average, so now they're teaching way down here. I have mixed on it. Some districts, there's some reports saying they're getting good results but it's almost all at the elementary level,
some in the middle school. If you do that, I would insist that groups can be changed, kids can be moved, and that's where things get hairy. So, like, I'm still -- I don't know yet on that one. Yes,
sir?
AUDIENCE MEMBER: [inaudible] a good point. The students really do respond to that guided practice. They're almost individually working with individual students, individual [inaudible] the issue is we
got to do the instructions and I think when we [inaudible] flipped classroom where the homework is viewing that model, so it uses a bit more time, most of your time in the classroom actually moving
from student to student and doing what you're doing within 20 minutes instead of what's on the board [inaudible] so the students really do a deductive response?
AUDIENCE MEMBER: [inaudible] one-on-one attentive class.
PAUL RICCOMINI: Yeah. That's the?
PAUL RICCOMINI: That's the trend with the flip model cluster that you hear a lot of -- just -- I mean, I think the verdict is still out on that whether it works and who it works for and I think that's
AUDIENCE MEMBER: Do you guys -- do you guys do flips? Do you use flips?
the key.
PAUL RICCOMINI: No, what -- I don't -- I'm not -- I don't -- I think there's a lot of challenges with the flipped classroom. Our kids are going to watch the instruction. Our kids are going to have
access to it, things of that nature. What I like about it is the instruction is usually videoed, so kids are able to watch a video over and over and over again. And if they get lost, they can do a
pause where a real teacher delivering that, if someone's lost, they raise their -- "One more time, listen up because you get kind of frustrated." So I think that has advantages, I'm not sold on the
flipped classroom yet. I think it's certainly something to be considered and looked at; and if it's working, let's go for it. There's no clear evidence yet that has been compared and contrasted. So I
think it's all a big, you know, a question mark but what I think is advantageous about that is making our instructional modeling available for kids to access beyond the classroom. You know, think --
a lot of times math classrooms is you -- the teacher is modeling two or three problems to the kids and then the kids have a guided practice section and then they have like 10 or 15 for homework. So
they're getting more independent than instruction. The way textbooks have done the scaffolding of this is the problems the teacher are modeling are almost always the simplest occurrence of what
they're trying to teach. They get a little bit difficult, more challenging in guided practice. Were the most difficult problems independent? And we hope that the kids are able to what? Transfer. So I
think there's a lot -- like I said, at the high school level, the research is so lacking that I think there's a lot of sort of -- well, let's see what's happening, let's try it, let's evaluate it,
who's it working for, who's it not working for; and adjust as needed. That's my take on it.
AUDIENCE MEMBER: I think the best part, of course -- and that's -- it is a good point that they can watch it over and over again, but instead of time spent in class [inaudible]
AUDIENCE MEMBER: ?a student would look at that on Friday, now you go back to the teacher almost [inaudible] point and say, "I just got to stop on this."
PAUL RICCOMINI: Guided?
PAUL RICCOMINI: Guided feedback is key. Guided feedback is key in math and I agree 100% with you. We -- they don't get enough of that. If you think about your own kids, how many of you have your own
kids that you've had to help with their math homework? They're getting -- that's guided instruction that if you don't -- if we're not here doing it, they may or may not have it, and a lot of times if
you have an at-risk population, they're going to not have that additional guidance. So I think, you know, however it happens, that's what we want to look at and that's the question, get -- so when
you're talking about adding 30 minutes and you're talking about the flipped classroom really in reality, you're at the teacher level instruction and that's the key. Here's what you're trying to do --
again, no triangles, hopefully you're not uncomfortable with that. This is what you're trying to build. So you know -- we know who needs the support, what's the plan, so in -- just to you use your
example, your plan right here was the kids got your core instruction, for how long is your period?
AUDIENCE MEMBER: Forty-five.
PAUL RICCOMINI: So they got 45 minutes of math and then they had an additional 30 minutes for a month, right? So the question you want to ask yourself is, "Well, how did it work? Did you evaluate it?
Did the kids improve during that month and then it tapered away or did that help them accelerate?" Those are the questions you want to ask. You probably didn't get to that level yet, but that's kind
of the evaluation because if it doesn't work, in other words, if a hundred kids go into that extra time and at the end of the year, they still are way behind, then it didn't really what, work and you
have to adjust. But that's you always wanted but this is the model we're trying to build here; how do you support it? Systematic and an explicit instructional support is the key, more teacher
instruction. So, in a standards-based classroom, remember, there's the core class, there should be explicit instruction and there should be some inquiry-based instruction, opportunities for both.
Purposeful learning experiences, knowledgeable about the learning objectives. The kids need to be using the language and the standards, speaking that type of vocabulary ownership. It's not about,
"What do you do and say?" "Well, the teacher says we're doing section 3.2." What's the standard? What are you doing? Why are you doing that scenario? Now, in your RTII framework, here are the three
things that you want to address. Core instruction, can we adjust how we're doing core instruction? And in other words, is there a small group instruction in the core? Can we adjust how we present
information? Which is I'm going to get to here in just a second. Strategic instructions, so -- I'm sorry, what's your name?
AUDIENCE MEMBER: Randy.
PAUL RICCOMINI: Randy, sorry to pick on, Randy, but, Randy, that 30 minutes -- and what did you call it?
AUDIENCE MEMBER: Reach.
PAUL RICCOMINI: The 30-minute Reach was really what -- in a RTI Framework is called strategic instructional support, and essentially what they were getting was extra practice with guidance. Now, my
guess is that with those kids as you began to see their success in Reach, I'll bet you dealt with them a little differently in your core classroom. You might have asked them questions, given them a
little bit more time to think about it, checked on them?
AUDIENCE MEMBER: Well, they were [inaudible] ask me. I mean, it was unbelievable.
PAUL RICCOMINI: And I'll bet you were too.
PAUL RICCOMINI: I mean, this is -- these are things that are probably happening that you didn't really like, do on purpose. Subconsciously, you got to know the kids a little bit better, you got to
AUDIENCE MEMBER: Well, I did.
know their strengths and weaknesses, and I bet you adjusted your instruction a little bit in that -- in that general.
AUDIENCE MEMBER: What was interesting too is what -- this week's program we did a lot of things like, some Reach classes, all they did was read a book and one person would read, the next person would
read. As soon as I left my Reach class, they will write back into where they were before. I mean, as far as your enthusiasms towards the class, their grades would just write back to where they were
before, and everything just [inaudible] at once.
PAUL RICCOMINI: That's -- well, that's the strategic support at our high school level. At the elementary, the strategic support is often viewed as a temporary piece to get them caught up and then you
leave. At the high school level, there are kids that are going to need this the entire year everyday and that's a challenge. So as you go back to your school, can you -- you know, that's important
information that you want to share with the team. "These are good one. They are getting this extra time. Is there a way we can get this extra time longer more the whole year?" That's the challenge we
run into because odds are those kids that are struggling in your Algebra class and getting Reach, probably also struggled in reading, in writing, in every other subject. So, then you have -- now,
here is what I think should be occurring in a core classroom. There should be some fluency practice. At the middle school and high school, fractions, integers, perfect squares, there should be some
fluency practice. Then, there should be reviewing of the vocabulary and the standards. This is what we're going to do. On Thursday, I'm doing a session on how to teach vocabulary and mathematics.
It's a very important piece that we have left out in our content area. And we have low levels of vocabulary teaching. But then you get a whole class, small group. That flex grouping, there needs to
be small group instruction in your general classroom some of the time because those kids need extra instruction at some level. Of all of these, the one that is left out almost all the time is number
five, closure. And oftentimes, teachers loose track of time and they end up running out of time and the lesson closes like this, "Do problems five and ten for homework," and that's how the lesson is
closed; and the problem with that, the teacher is not getting any feedback on whether they were learning what they're supposed to do. And the students with disabilities, they have forgotten what and
why, what they -- in terms of what they were doing in that particular day. So it's important to close that lesson. Now, there's a variety of ways you can close it, what I really recommend and I've
seen improvements in the closure is the teachers put a timer on and it goes off with five minutes left in the period and no matter where they're at, they close the lesson and that's something that
can be done pretty simple. And, you know, what happens is you get in there and you're teaching a way and kids are asking questions and you're going with the flow or you're realizing they're stuck and
you're going back and then the time got away from you. So that's the one that I really recommend is that closure. Now, there's all different ways you can do it. You can summarize, the kids can
summarize, take it out the door, all different ways. The key is that you're closing the lesson. That's -- this is the ticket right here, if you can get some of this happening in the general ed
classrooms. So back to his example. So in this algebra classroom on Thursdays for that period, the class that you have the most struggling kids in, the way you structured your 45 minutes is you don't
do a warm-up, a warm-up's out that day. You don't want to waste 10 minutes on the warm-up. So there's no warm-up. Go on with their homework. You take these eight or nine kids and you take them to the
back of the room or they huddle around your desk or wherever, and you give them additional guided practice of whatever you're teaching for that day. And then what you've just done is you've done
small group intervention in your core 45 minutes. That's a very -- that's not something high school or middle school teachers generally do in their core classroom. It's usually whole group most of
the time, but that's how you can begin to increase time without having to add because you've increased instructional time.
AUDIENCE MEMBER: Where would a special ed person or a support person where?
PAUL RICCOMINI: So co-taught?
AUDIENCE MEMBER: Where will they -- where will they come in later? How?
PAUL RICCOMINI: What I would -- what I would recommend is, during that if you're going to do small group. I'm the special teacher -- is it Dave?
PAUL RICCOMINI: Randy. I'm the special ed teacher. Randy is the general ed teacher. On Thursdays, we decided we're going to do small group. Sometimes I take the small group. Sometimes Dave takes the
AUDIENCE MEMBER: I'm Randy.
small group. Dave?
AUDIENCE MEMBER: Randy.
AUDIENCE MEMBER: You're such a?
PAUL RICCOMINI: Randy.
PAUL RICCOMINI: Randy takes the small group.
PAUL RICCOMINI: It shouldn't always be the special ed teachers because quite honestly in Algebra 2, it might need to be Randy until I've got caught up on the math. And the special ed teacher then can
AUDIENCE MEMBER: Okay.
monitor the other kids. Now, if in a -- in unique settings, what would happen is I take a group of kids, the general ed teachers takes a group of kids; and there's another group of kids doing
independent. Now, that's kind of getting -- I don't see that often.
AUDIENCE MEMBER: Is it on the elementary level?
PAUL RICCOMINI: I don't see it much at high school. There's a lot of reasons like, one, you got big kids in small rooms and the spaces aren't really set up for that.
AUDIENCE MEMBER: What happened is when we're regressing. We can't find?
PAUL RICCOMINI: But that's how I think. I always looked at this. What did I do instructionally different? And if I can get them 10 minutes of instructions once a week for eight weeks, that's 80
minutes actually they got within the general class. Now, there's a document that you have -- well, you actually don't have it if you download the material. Somehow it did not get into my handout for
this. However, it's in my elementary session packet online. So if you download the elementary session, you will get this handout. And essentially what it is is a sort of an instructional evaluation
of where you're at. This might be a good thing to fill out in an RTI team meeting in terms of where were at in our -- in our model in our system in terms of what we're trying to do but it's really
instructionally focused. It makes the teachers answer the questions. What are you doing instructionally different? Are you differentiating your warm-ups? No, everybody does the same. Okay. There's an
area to target. Does everybody get the same homework? Well, there's an area to target. How are you teaching problem solving? How are you doing practice? And it really starts getting teachers talking
about the teaching piece. Now, so it's in -- I added this slide once I realized it didn't make it into my materials. It's in the elementary RTI session, so the materials that -- you can get to
download all the -- all the handouts from everything. It's in that packet. And I do apologize for that. Now, what I want to get to is, you know, there's information in here about what needs to take
place. I want to model it to you in terms of instructional scaffolding and interleave. And we -- we'll have just enough time to get -- to get through this. Not as much as I would like to spend on
this but content scaffolding is where I want to focus on right now but before I do that, is there any general questions or comments up into this point? We were kind of talking broadly, seeing some
examples. The one thing that I encourage schools at the high school level is get a plan in place. I don't care what it is. Get a plan in place so that you have somewhere to start. A lot of time that
the high school level, we kind of get paralyzed with we don't know what to do and our kids are so low that it's hard to then refine but get a plan in place. So they -- you have to plan this year.
Hopefully, you won't totally abandon it. When you come back and you sort of revisit, you can -- you have a lot of important information to say about that Reach. Especially, what I really queued in is
like, "Men, when they had them -- when I had them for that 30 minutes, their grades were better." That's important information, but the idea is you got to get a plan in place first before you can
begin to evaluate and see how things are working. Now, scaffolding by definition is a -- is a process in which a teacher does something with quotes to enhance learning. Scaffolding can be this at
this level. "Do this. Do this." She can write something down and look at me and I go yes. I'm scaffolding her. Special ed teachers -- where are my special ed teachers? We scaffold too much, way too
much because we're -- we're looking at these kids going, I've got to help this kid what? Survive. So what happens is they can do it whether in our power circle. Then, what happens when they leave?
Because what's happening is we're scaffolding him too much and we're not fading in away. General ed teachers, we don't scaffold enough. Mostly because we got 30 kids in the classroom and we got to
move through that or if we do do a scaffold, we one -- we do one scaffold that everybody gets. So the key is targeting a scaffold and fading to independence. If you never fade, the kids will never be
able to do it independently. And if you fade too quickly, they crash and burn, and at all level they do not like to reengage. So that's kind of -- now, how do -- how does that look in terms of
instructions? So now, I'm going to do something that's called a Scaffolded Progression. Now, I pick a basic Algebra 1 problem that's very common and I'm going to show sort of the features. One of the
things that we have to do with our students is getting them to look at the underlying features of word problems. When I look at a word problem, I don't look at, "Oh, this is about a tree. This is
about money. This is about a car." I'm looking at it and saying, "Oh, this is about growth. This is about units. This is about whatever." Now, when you're looking at it that way, then you are --
you're having a general approach to problem solving. When kids says, "Oh, this is about a tree," then they're missing the whole general piece. And our instruction is often focused on kids not really
teaching them problem solving, it's really teaching them how to solve a problem that happens to be in front of them for that day. So how can we sort of scaffold this in this progression? Which --
that I'm going to look at. So there's this thing called Content Scaffolding. Now, there's three types of scaffolding. There's content, task, and material. I'm just going to do content. I think this
is the area that we as a field have not applied at all. I see task and I see a material. Tasks are like steps, charts, task lists. Material, graphic organizers, tables, things of that nature. But
with content scaffolding, the idea is you're trying to move -- to take everything out of something that's going to distract the kids from a cognitive piece. So in word problems, what is it that
distracts kids cognitively? The words. If they can't read the words, that's going to be problematic. But -- so let me phrase this, what is the first thing kids try to do when they see a word problem?
When you put a word problem up, what tends to happen?
AUDIENCE MEMBER: Figure out what we need to do.
AUDIENCE: [inaudible]
AUDIENCE: [inaudible]
label half the time. So what's actually the issue is the answer. They -- if you ask kids what's problem solving, they're going to say, "Get the numbers, determine the operation, and do it," when
really problem solving is much more involved. So the question is often what is difficult for kids. So here is a word problem. It's a basic growth rate problem. Robert planted an oak seedling. It grew
10 inches the first year. Every year after, it grew an inch and a quarter, how tall is the oak tree after nine years? Immediately, half of your kids are going to see this thing right here. What are
they're going to say? "I don't do that. I'm sorry. I'm not doing that. It's a mixed fraction, thus I'm not doing that." And they're done. It's over. The other half are making fun of the Robert that's
in the class, "Oh, you plant trees." And then what? They're done, right? And then the other -- then this is the other thing that happens. You know that you've lost the kids cognitively when you put
that problem up. You give them a minute or two to think about it, "It's okay. Let's talk about this." And from the back of the room, Johnny goes, "It's 25." And you go, "Twenty-five?" And he goes,
"Sixteen?" "Did you add?" "Yes." "You did?" "No." All his doing is what? Guessing. Now, I've had that conversation with students in my class and at that point, they're tossed. They are cognitively
disengaged because they literally have learned by high school that math is about getting an answer. Not about the correct answer because they've learned that if they just put something down on their
paper, pretend to work, stay quiet, do not make eye contact, you will eventually do what? Getting the correct answer. So can we adjust that in the scaffolding progression? So this is what I'm going
to recommend. The first thing you do is rewrite the problem. And again, this -- you don't have this. It didn't get in but you're fine. All it is was a sheet that had these problems. So what I did
here is I rewrote this problem. We're going to set up a three-to-five problem progression. This is where I want to get to students at the end. Here's the first problem I'm going to show them. Notice,
what did I do?
AUDIENCE MEMBER: Got the fraction.
PAUL RICCOMINI: I took out the fraction.
AUDIENCE MEMBER: Took out Robert.
PAUL RICCOMINI: Took out Robert but those are common. You hear that all the time but most -- what else did I do? And this is the key with this progression. I took out the question and I put in the
answer. Now, I have something. Kids are going to be more willing to engage in because it's no longer about the what? The answer. Second, for your students with learning disabilities that are horrible
computationally speaking. There's no calculating. This will allow kids to focus on the process of problem solving which is identifying the key features and translating those into a number sentence.
And we -- in the progression, we will slowly work our way back to where they have to solve a problem. Everybody followed me on this? How many of you do this? I bet you none because we're all about
what? The answer. This is de-emphasis of the answer to focus on the process. Now, if I -- if I had your setting, I would teach this in that 30 minutes. The day I was going to do it in the -- in the
core. And you would have those kids come in. They'd be sitting up with their chests all pumped up because they knew how to do it, and these other kids that are getting the answer right before them
all the time don't. And you will see a huge improvement in their self-confidence. So here is the word problem. This is the problem I'm going to start with. All right. But now, I want to show you how
-- when you take the answer out, you can scaffold it down to elementary. We're going to scaffold -- you don't -- all you know is addition. That's it. You know no other operation and you'll be able to
solve this Algebra problem because the answer's taken out. So when we look at this, we're going to write our number sentence and in this first problem it's all teacher guided. So you would read the
problem, you would model the think-aloud, identify the important pieces of information; but I'm going to have in something else, something that's called a guided think-aloud. Okay. So I'm going to
model this question and for the sake of time I just thought aloud this question. I'm going to do this very quickly for time. An oak seedling grew 10 inches in the first year. Okay. So we got 10
inches in the first year. Every year after, it grew one inch. So it grew a lot in the first year and then it levels off. After nine years -- so this tree grew for nine years. The first year grew 10
inches. So that means we have eight years that it grew one inch each year. And in the end it was 18 inches tall, how tall did it -- how much did it grow in the first year, class? Ten inches. How much
did it grow each year after the first year? One inch. How many total years did it grow? Nine inches. How tall was it in the end? Eighteen inches. So let's write our number sentence. So I want you to
pick up your pencils. You're going to write our number sentence, but before we do that we got figure out what operation we're working with here. So what's happening to this tree? It's doing what?
It's growing. All right. So it's getting bigger, taller. What operation generally gives us more? Now, remember all you know is addition.
PAUL RICCOMINI: Add. Very good. So we have to add here. So let's right a horizontal number sentence. Now, I would be writing this with the students. How much did our tree grow on the first year?
AUDIENCE: Add.
AUDIENCE: Ten.
PAUL RICCOMINI: So everybody write ten. Now, we have to add how much it grew after the first year. So we know that after the first year, it grew one inch year. The three grew for nine years. However,
how many years did it grow ten inches? The first year so how many years do we have left?
PAUL RICCOMINI: Eight. So we have to add one eight times. So add your one eight times. Then, the notice the language there is really pushing what? Multiplication. But add your one eight times. Make
AUDIENCE: Eight.
sure you have eight ones there. And then how tall was it in the end? Eighteen inches. So that equals eighteen. I need everybody to draw one little line under the first year's growth. Go ahead. Did
everybody underline the ten?
AUDIENCE: Yes.
PAUL RICCOMINI: Now, draw a squiggly line under all of the subsequent growth. Did everybody underline all their ones? Okay. Put a box around the total growth. Did everybody box their 18? Okay. Now,
that's the think-aloud. You're all doing that at some level. Here's the guided think-aloud. You would have the students find partners and have them rethink aloud or explain to their partner that
number sentence we just did. Does everybody see how that's a guided think-aloud. Most of the time after we get done explaining a problem, what do we do? In most math books they get another problem
that's different and we hope that they're able to what? Transfer. That's right. So now, let's go ahead. Now, let's look at our number sentence. Here's our number sentence. Here would be a student
with multiplication. The bottom one's the Algebra. Okay. That's the Algebra. That's where we want to get kids too. But listen, if we keep starting off with our original problem, what are we going to
keep getting from our kids? Shutting down. So, what's the underlying features? Now, I talked about these but there are three underlying features in all growth problems that we really talked about.
The first one is the initial growth. Now, it could be zero but as your initial amount, now, growth could be money, height, weight, anything; but in a growth rate problem there will always be, what?
Initial growth. From that the next part is the subsequent growth. Well, after the initial growth, how much did it grow? And then total growth, when a proficient person in math looks at that problem,
we are basically filtering out tree. We immediately see, "Uh-hah, we've got this tree and it's growing," and that's it. As soon as we hear a growth, that cues us to say, "Okay, there's probably an
initial, a subsequent, and a total." And that's how we start solving word problems. Now, that was heavily guided by me. I know I did it in a condensed timeframe but here would be the next problem in
my progression. What is the same or different? It's the exact same problem with different numbers, so I modeled it heavily. Now, I'm going to begin to what? Fade. Now, at this point, the teacher has
to do some professional judgment. Is my class ready to try this on their own? Is the class want -- do I need to do it in a group? Or do I need to remodel it again? We -- our textbooks, our first --
the problem is about a growth, the next one is go into the movie; the next one is getting on an airplane. It's all over the place. And we would -- how you decide to model or prompt this is up to you
but basically here's our number sentences. So that's the second step in this progression. Here's the third step, what do you think is going to be introduced now in the third step, third part of this
progression in the word problem?
AUDIENCE MEMBER: [inaudible]
PAUL RICCOMINI: Now, depending on what -- you can do whatever you want. I think putting a fraction is too early. I think the names are irrelevant, so what I'm going to first put in now is a question.
This will be the first time that they have to do a calculation, so that's why I kept the fraction out, but you could put the fraction in. At this point, there's no right way to do it. It's all based
on your kids. So now, this will be the first time that they try to what? Answer. You've done two models; one heavily modeled, the second one guided. Now, they're releasing yourself, gradual release.
Did everybody follow me on this? Is this -- this is not how we do word problem in math. I didn't do it this way. It's not how books are set up. It's about a problem, then the kids try it; you help
them out. It's always about getting the what? Answer. So now, I'm fading that in slowly. And now, they get the answer, 16 meters tall. Now, I usually do instructional progressions in three-to-five
problem sequences. So the first two, no calculation, the answer was in. The third one was the first time they had the question. The fourth problem I've determined that the class is ready to go back
to the original problem. Now, is it going to guarantee they can get this problem right? No, however, they have really focused on the process. If we keep starting out with this problem which is what's
in the book, we are going to keep getting kids what? Can't do it, don't want to try. That's the key. This is a progression now. There's a disadvantage in this -- a progression. You're spending 20 or
30 minutes of a math class on one problem type. So this is not an everyday progression but there should be a regular progression. You know there are certain problem types at each grade level that
tend to get focused on, and that's where I would target this. But this is teaching in depth, highly scaffolded in releasing of your support; and on top of that, you take out calculation initially.
Now, in my warm -- so let's go to that -- what do you call them, do-now's? So let's say I'm going to do this. In my do-now for this day, the warm-up, the fluency, what am I going to have the kids do
for two minutes as fluency practice when they're going to do this progression in my class? I'm going to have them adding fractions but not just any fractions. I'm going to do what? The quarter. So
they freak out in the warm-up and they're primed for the problem solving. The warm-ups and do-nows were really designs to prime the kids for the lesson of that day. What they've all morphed into is a
cumulative review. Okay. Now, I've got about three minutes left. You -- I know you're probably going to get to the next section but I really want to finish this because this strategy, I think, it's
very simple. It will take me two minutes to explain it but it is perfect for Algebra and anything in middle school as well. So interleave means to alternate. Okay. So like when you shuffle a deck of
cards, so what these researchers developed in this interleave work solution strategy was quite literally they alternated homework problems; solution provided no solution, solution provided no
solution; and the kids were told to study the solution, it will help you solve the next problem. So in the progression that I just did, where was all the guidance coming from? Me. In this strategy,
where's the guidance coming from? The materials. So what -- and homework for math hasn't really changed. When I was in school, I prayed that the teacher assigned the odd problems, right? Because if I
couldn't figure it out, I could at least look at the answer and try to what? Work backwards. This is going one step level in giving the solution. So what these researchers did was half their group
got traditional homework problems; solve, get the answer, problem solving or straight arithmetic. The other half, this is what their homework looked like. The first problem was solved for the kids,
the whole solution, and they were told, "Study this solution. It will help you solve the next problem." Now both groups got 10 problems. They -- you had 10 problems that you had to what? Solve each
of them. This group, how many problems did you actually have to solve? Five alternated, ten problems five solutions. So this group practiced what? Half as many. Guess which group produced better
learning outcomes when assessed. This group. My big message for all of you in here is giving kids answers and solutions to study is in and of itself an effective strategy. Now, this hit home for me
because I was never a genius in math. Okay. I had to study. So when it came time for me to study in college, how do you think I studied? Do you think I just practiced problems? No. I went into my
notebook and I found problems that were what? Already solved. And what did I do? I studied. I verbally rehearsed them to make sure I understood what was happening. Once I thought I understood, what
did I do? I covered it up and tried to what? Solve it. And if I got stuck, I could look guidance and then redo it. This is a huge strategy with application in multiple areas in your classroom.
Homework is one of them. Another application is in your openers or your warm-ups. Instead of having them do five problems, give them a problem already what? Solved. This could also be in your group
work. Do you ever have time where you have kids in a group and you say, "Here's the problem, work together and try to what? Solve it." So give the group an already solved problem and have them work
together to explain how it was solved. Maybe they have to write down how it was solved. That's going to help with the writing part of these new assessments but this -- now, in some of the research
they just gave the steps. Others wrote some annotation out. My guess -- this was not specifically done with students with learning disabilities, so my guess is the students with learning disabilities
may need some of that. In the schools that I work in that have tried this strategy the biggest mistake that we make is we don't spend enough time in our classroom teaching the students how to study
the solution. If you just say, "Hey, study the solution." Your LD students who are not strategic in the learning, they're going to what? They're just going to skip it. Think aloud, model that. This
Interleave essentially is providing students full solutions, having them study verbally rehearsed, discuss that solution can be very powerful in improving their learning outcomes. So all of these
information that I just talked about, this came out of an IES Practice Guide which has a lot of information and strategies. Here's an example -- you don't have this in your handout or do you?
PAUL RICCOMINI: Oh, it is. Okay. This is some schools I worked with. A middle school teacher actually developed this interleave. So, you can see here they're providing the full example and then
AUDIENCE MEMBER: [inaudible]
they've got the scaffold built in where the first problem is fully solved. The kids have to solve the next one and the next one and then here's a scaffold partially solved. And they have to solve,
solve, and then this is partially solved, and then they have to solve. So it was not exactly interleave but the idea is they're giving the students solutions. Now, here's another one that was
developed which is far more scaffolded where fully solved, partially solved, fully solved, partially solved, less partially solved, partially solved, and then they have to do their own. Essentially
this is giving kids additional guidance built into the what? The materials. Anyone seen the strategy before, heard of the strategy? Guess what, it was initially developed, 1989. And it was developed
all through the 90's by cognitive folks that focused on short-term working memory kind of things, and it just didn't get into the mainstream. But I think this is also why the flip classroom can be
beneficial is they have a lot of this in that modeling that they're going to see in style. So scaffolding, content scaffolding is what we did without word problem, big emphasis there, put answers in
these word problems. It will help kinds engage in the process and slowly work your way to where they have to answer a question. And then interleave has a lot of modeling and guided practice
inherently built in to that piece. So future planning, this is what you might want to talk about or how are you teaching the underlying structures of word problems, are you doing it? How are we doing
it? How might we implement some of these recommendations in terms of the content scaffolding piece? Questions? That was quick. I'm five minutes over. I apologize. Any questions? You have the -- my
e-mail. Feel free to e-mail me any follow-up questions if you like but, you know, sort of big idea summary here, RTII has a lot of working pieces. One major piece of importance is how the teacher is
teaching, and I gave you two strategies that are little different than what we're used to; one of which puts the answer in; the second one, takes advantage of solutions in terms of helping them learn
the process. Questions? Thank you. I hope you enjoy the rest of the conference. Thank you very much.
AUDIENCE MEMBER: Thank you so much for sharing your knowledge in strategy.
PAUL RICCOMINI: Sure thing.
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