PAUL RICCOMINI: Good afternoon. How are we doing? Is the sun still out outside or thunderstorm, kind of, a lack of a?
AUDIENCE MEMBER: [inaudible]
AUDIENCE MEMBER: [inaudible]
AUDIENCE MEMBER: It always been is.
PAUL RICCOMINI: It's raining and the weather is horrible out there. So you might as well just be happy to be in here.
AUDIENCE MEMBER: [inaudible]
AUDIENCE: Yes.
PAUL RICCOMINI: But very excited to be here, some familiar faces which is always nice to see, a repeater from my first session, so she is the repeater.
AUDIENCE MEMBER: Yes.
PAUL RICCOMINI: But we're going to really talk about RTII and where I focus most of my effort is on the Is, the instruction, and I really think that the instructional piece whether it's your core or
your intervention is often the last thing addressed in math. There are some unique challenges in RTII application to math that are not in reading, and it leads to a circumvention so to speak, of
really how the teacher is teaching. And I really think RTI will either be made or not be very effective based on the instructional piece. You can spend all the time in the world talking about
assessments, all the time in the world talking about how that data is going to be presented and looked at, and grouping, and interventions, and structure, if you -- and adding more time, if you don't
address what is being done in that time, then we're really going to -- your RTI model will be, sort of, spinning its wheels in terms of effect. I'm sure we'll help some kids but it's not going to be
as effective as we need it for the majority of kids. So, I'm going to -- you know, in my 75 minutes they said, "We'd like you to present RTI in 75 minutes." And I said, "For 10 days?" You know. So, I
had to be very selective in terms of what I pick. So I'm going to briefly talk about RTII, the pieces of RTII and you all know the pieces. If you've done RTII in reading, then you know the pieces in
math. The issues are, how -- what does that look like, and there are some differences in terms of mathematics. And I'll share what I'm seeing across the country in terms of what I see, either called
RTII or RTI or MTSS, Multi-Tiered System of Support, some states have mandated it, others have left it as an option, Pennsylvania is a little bit more specific in terms of what they require, so we'll
talk about that. But then I want to talk to about really two stress -- two pieces that have to be in your RTII model, they absolutely have to be in Tier 2, but they really need to be in Tier 1, and
depending on your core math program, it will either be there or it will not be there. And that's kind of the idea, and one of which is this fluency component. Fluency/Automaticity, it's in every
grade level standard K-7 in the common core. The word fluent, fluently, fluency or by memory is in all the grade level standards. And it's probably the single most left out thing, the single most
debatable piece in math over the last 20 to 25 years and were basically realize that, "Jeez, when you're not fluent in math that will create problems later on." So now, it's actually written in the
standards, so there's no debating it. However, most commercial programs have not caught up with the common core. So, that's sort of what we're going to talk about. And then the second piece I decided
to pick was working with problem solving, word problems. In terms of trying to get teachers -- at the elementary level we have to begin to teach the underlying structure of the word problems versus
getting the answer. And that -- and I'll talk briefly about that today. But the main piece is this fluency thing that we're going to talk about today. So we're going to briefly go over the eight core
principles -- actually three, the belief system, instruction and research interventions. And, sort of, one of the issues that we see is this trend and I just want you to look at the right column
there by fourth grade for students with learning disabilities. Almost already by fourth grade, 40% are below basic. Now that is almost half of our students. So, that is going to lead to a trend that
when they get to high school, they're going to be slammed, and now that the common core is really adjusting what we are teaching when with the focus on algebra. Now, right or wrong that can be
debated. That's the focus. And really when is -- when is -- when is the common core really focusing most kids taking algebra now? Eight grade, if not all kids. Where -- when I was teaching, who took
algebra in eight grade? These people did take it in eight grade, who were they? The gifted or honors kids. Everybody else really cycled in around ninth grade, so now we're trying to make everybody
focus. So there are challenges. The only way that that will happen is if the K-5 mathematics programs significantly take a look at what they're doing, and in terms of how long they're teaching math,
and how they're doing it. And I'm working in elementary schools across United States; they have their elementary math at 120 minutes from kindergarten through fifth grade. And so I see ranges from 90
to 120, I know you have a look of stunned on your face.
PAUL RICCOMINI: This is -- no it's not with intervention, that's their math. Now, some are saying 120 minutes, 90 is for their math, 30 is for intervention. So -- but the time is significantly
AUDIENCE MEMBER: [inaudible] intervention.
increasing. And now, you got to keep in mind it's -- that's not just time, it's what you do in that time. And I'm not -- I'm not -- for kindergarten it's not a hundred and twenty sustained minutes,
but it's devoted to math. And, you know, I go to a lot of schools and they say, "Jeez, our reading scores okay, but our math scores are horrible." So it's very interesting because they have kids that
are -- meeting and exceeding expectations in reading. The same kids are below basic in math. And that's a very interesting sort of dynamic and that they're getting to read. So I start asking them,
"Tell me what you're for reading." Well we have 90 minutes uninterrupted, they get 30 minutes of intervention, and we have this intervention and that intervention, and we have these interventionists.
"Okay. What are you doing in math?" "Well, we have about 60 minutes. We try to fit it in." And then that's why you have the disconnect in terms of the performance. So one of the things to really
think about is, we're trying to prevent this. Now, here are three critical resources for all of you trying to do RTI. Do you have this slide in your materials? Okay. And they're all free. The first
one is the National Mathematics Advisor Panel, that's not really RTII. That's general math instruction. How many of you have read it? Okay. Now that's a problem. You really need to get this. It's
really shaping what has to take place in terms of our math instruction. This next one is the RTI document that the IES produced. The co -- my co-author that I do a lot of work with Brad Witzel was
the author on this. It's basically a recommendation guide to what should be taking place in RTII. So if you have it -- don't have that they highly recommend that you get that. The third one is
screening for mathematics, and I'm not really going to get into the assessment piece, there's other sessions that are covering the assessment. I do think they're -- we're going to have to pay
attention to our assessments because of the new standards and how that has arranged things. Most of the current assessments have been based on other standards from a long period of time. And then I
also think we're going to have to really look how they predict these new part or smarter balanced assessments, we don't know. So these are things we're going to have to pay attention to, but these
are some very helpful resources in terms of, as you begin the RTI model in math or you begin to refine what you're doing. This is the -- this is the information that is to me, just amazing. This is
what we have gotten from our math education system over the last 15 to 20 years. Seventy-eight percent of adults cannot explain how interest is calculated. That's why our new credit card statement
that now says, "If you pay the minimum, it'll cost you this much and it'll take you this long to pay off." And when we have a society that cannot make financial -- you know, does not understand
financial decisions, then they're apt to make bad decisions. The second one, in calculating the miles per gallon, of course on my truck I just push a button and it tells me, trust me I never push the
button, all right, because I don't want to see it. But the last one, this one is shocking to me. You know, I was a former waiter in college. So this is shocking, but half -- over half can't calculate
a 10% tip. Now, let's think about that for a second from a math perspective. That's not algebra 2, that's not geometry, that's certainly not calculus. That's like fifth grade arithmetic and, you
know, we can't do it. Of course, people say, "Well I have the -- an app." Right. Okay, if your phone flips, you can just keep it in your pocket, there's no app for it, right. But you have -- there's
people with apps I -- whenever I talk with my students at Penn State, I teach the math methods class for special ed students majoring in special ed. What -- they're so -- they have no idea what
they're getting into, they're so na?ve. But I'll show them this, and we'll be talking about it and then -- and usually somebody raises their hands and, "Well that's really -- that doesn't matter for
where -- at the restaurant that I work at." I'm like, "What do you mean?" "Because on our bill at the bottom. We say, a 15% tip, a 20 -- 18 and 20." So we give them multiple-choice. So if you think
about all the arithmetic that we've taken out, mental math out of our daily lives, there's no wonder that we have kids that have problems with arithmetic. I remember when I was a little kid bowling
and learning how to score bowling. And it was, you know, it wasn't just the calculating your score, you would always like, "Okay. What will I need to get this?" Now who's bowled lately? Anybody been
to a bowling alley? Do you even have to keep score or you just throw it? And it scores. So you think about all the arithmetic we've taken out of our daily lives, it's no wonder we are, as a society
are doing so poor in math. Why algebra? Everything is boiling to algebra, because essentially that's the gatekeeper to get into any post-secondary school whether it is a four year college or a trade
school, is algebra. And the positive benefits of getting through algebra are pretty profound and long-term in terms of everything. And there was a just -- an article written in Forbes Magazine just a
couple of weeks ago. Did anybody see it about the extra math class versus the personal finance class? So you remember 10 years ago where in high school you could get the college track, algebra,
geometry, trig, cal, you know, or then there was, sort of, consumer math, finance math kind of things. Well this group, they looked at which kids took extra math, the college track versus the
personal finance and they looked at them at a dolts and they looked at foreclosure rates, credits score and bankruptcy. And guess who -- if they took the extra math class, you were less likely to
have your house foreclose, you are less likely to go into file for bankruptcy and you'd have higher credit score. So the kids that took the personal finance had more of those three things. So they
were arguing math is important, but if you think about back when that was pretty common, who was getting pushed into those? Personal finance classes, the non -- you know, the kids that struggled in
math. But you see all these long-term benefits of kids who do very well in math. And that's why there's been such a focus in math. As a matter of fact, there has have been two new -- within the last
year a longitudinal studies published, where they followed individuals for close to 25 years from birth on. And there were different researchers and they had all these assessments in school and so
forth. So they looked at what was the most important predictor variable for success. So they looked at reading, they looked at math, they looked at social, they looked attention, and there was one
other one they looked at. And when they controlled for socioeconomic status, gender, birth weight, all the nine yards; guess, what was the most important thing for success? Math not reading, it was
math. But our whole elementary system, including preschool, is focused on pretty much what? Reading. Now, I'm not saying throw that out the door, but what I'm saying is, we need to equally -- we need
to focus as much on mathematics. Now what within math was most important? What do you think it was? Sub skills. What?
AUDIENCE MEMBER: Fluency.
PAUL RICCOMINI: Fluency? No. The specific math content knowledge, specific skill within math was most important. There are two of them. Nope. Fractions and guess what the second one was?
AUDIENCE MEMBER: [inaudible]
PAUL RICCOMINI: No. Division. Fractions, division. So it's interesting. You know, my sister is a preschool teacher at a Early Childhood Development Center and she works with that kids that are having
problems. And I said, "So what do you do in your day?" "Well 90% of my day is spent on literacy." "What's your other 10% spent on?" "Behavior." "Well, when do you do math?" "Oh, whenever I can fit it
in." So we tend to ignore math. Well, I had a daughter almost two years ago. Thursday, she'll be two. When they were giving us our papers to leave the hospital, you know how they give you this giant
packet of stuff. So as the husband, I didn't have much to do, right? So I'm sitting there leafing through, and I come to this whole pamphlet on literacy skills with your baby. And it was like a step
by step, this is what you need to be doing with your baby from the day you get them, for literacy. So -- oh, excellent. So I figured if I turn the next pamphlets, will be math.
AUDIENCE MEMBER: Well, that's what you need to do then.
PAUL RICCOMINI: Oh, maybe I should do that. Math, but it was not there. We tend to really avoid math as much as possible. When RTII came into play, what was the very first focus? Reading. Now, we're
slowly moving to math. This is the one challenge at the elementary level in RTII with math that is not the case in reading, and that is elementary teachers really are uncomfortable with mathematics.
And because of that, we have a big teacher variable in mathematics, that isn't necessarily the case in reading and if there is an issue with the teacher in the reading part of RTII, there are enough
well-designed and research-based interventions that teachers can use as guidance. In math, there isn't and that's one of the big issues. All right. So the other thing I'm going to try to do today, it
may make you uncomfortable and I'm going to violate a major rule on RTI presentations and that is, I am not going to show a triangle for this whole 75 minutes, there will be -- I know some of you
will be like, "Well then it's not RTII. There's no triangle, it's not RTII." That's like a major rule, you have to -- how many of you have been in RTII session today? Did you see a triangle?
AUDIENCE MEMBER: Yes.
PAUL RICCOMINI: Okay. See if you don't see any triangle except here. I'm going to try it. I'm a little uncomfortable. I made it in the first session but there will be no triangles. All right. We got
to get away from the triangle, I had to get my triangle RTI tattoo removed and I had to go this one on here, but these -- this is what you're -- this is what you're trying to address in this RTI
model is, are these three circles. And I see school spending a lot of time here, not enough time here. And at the elementary level, the biggest issue with the teacher is, the content knowledge, and
the instructional strategies that they have. Now the great thing about elementary teachers is they'll try any strategies you ask them, they are awesome. Very positive, they'll get on the floor,
they'll sit on -- they'll try anything. The challenge is, they're really not comfortable with the math, the content. Now it's not everybody, but in my general working, that's the impression that I
get. As a matter of fact, teachers will willingly sit, tell to -- say to me, "I became an elementary teacher so I wouldn't have to teach math." We'll now, third, fourth and fifth grade elementary
teachers are going to have to be teaching a whole lot of math, rational numbers with this common core, so there's some issues there that we have to take a look at. But this is where we're looking at,
the math panel looked at some data and interestingly enough, at the elementary level, the teacher is the most important variable in a kid's math performance. They can -- they can account for close to
14 to 16 percent of the variance of a student's test score. So if you get a child who gets two or -- in two years, gets an ineffective math teacher, now ineffective does not mean good or bad all the
teachers are good, but if they're not teaching math effectively that can be very problematic for that student's test score when they start taking them in third grade, so the teacher is the most
important piece. So we have the math panel report and I just want to pull out a couple of things directly related to fluency. The report is free, I highly recommend you get it in, if you downloaded
the materials for this session in the back, you will see a two-page summary of the math panel report. For those of you that read a lot of books in high school by the author cliff notes, I put that
too -- a summary in there for you. But -- it, sort of, highlights it but I'm just sort of pulling out one slide that we -- that is really the key piece with elementary. And in your RTI plan, this is
-- there's -- these are -- these two bullets are two questions you have to ask. The math panel report said, "Look, in order to get kids ready for algebra, we need elementary programs, K-8 programs,
developing these four things. We need to develop the conceptual piece, we need the foster computational fluency, we need factual knowledge, vocabulary, procedures, algorithms, and problem solving
skills." So your first question in your RTI meanings is what is your core program promoted as? The publishers will promote it as. This is a conceptual program, this is a problem solving program or
this is a balance, but these needs to be addressed. If your program is not addressing each of these, then it has to be supplemented. Most programs at the elementary level are not adequately
addressing computational fluency. Some flat out leave it out; omit it because they don't believe in it. So that's why you have to make a decision, are you going to get it? Now, here's what happens,
if you're in a core program that leaves out fluency, here's where the teacher enters into play, if the teacher believes fluency is important, that teacher will what? Do it. If they don't, they won't.
Now, the other thing that we're going to get into is, a lot of teachers are trying to do fluency activities but they're not fluency activities. My -- one of my son's teachers she said, "They've got
to memorize their multiplication facts." And I said, "Great." So I asked my son, "How are you -- how are you supposed to memorize these facts?" And he said, "Well, I have to write them down." And I
said, "What do you mean, why do you have to write them?" "I have to write them down." "Well, what do you have to write down?" "Well, today we're on the fours." "So how are you writing them down?" So
how do you think my son wrote them down? Four, four, four, four, times, times, times, times, one, two, three, zero, four, eight, twelve. That's not fluency, that's a relationship activity. So there's
a big, sort of, misunderstanding about what is fluency versus something else, so we have to pay attention to that. But that's the big issue there. Now, the second piece here is also a cognitive piece
that is directly related to fluency. What their finding is kids that tend to struggle in math more than typical kids. So you've got your students with learning disabilities, as well as your chronic
low achievers. What their finding is, they have greater limits in their working memory. So that means they're not able to process as much at once as other students. So what -- this is getting a lot
of tension in some of the research, what's happening is, even though the teacher is giving really good instruction, they're engaging, the kids are involved, manipulative, whatever, they're
overloading the student's working memory, and once working memory is overloaded, learning stops. No matter how many Jolly Roger -- Ranchers you give the kids, it's done. So we have to take the
working memory piece into account in terms of how much information we're presenting. Now, the panel said there are ways that you can address this. One of the ways was automatic recall. So the math
panel use automatic recall, the common core uses fluency, fluent, fluently and by memory. Now, what does that mean? Now, there are some people used -- there's this discussion fluency, automaticity.
In reading, you don't hear automaticity, you hear what? Fluency. And fluency in reading is defined as, reading quickly, accurately, and effortlessly. And when kids do not read fluently, they are
reading very what? Choppy, because they're at the word level. So what happens is, when they're reading at the word level, even if they -- so they sound out every word and they sound out every word
accurately. So they read 100% accurately, but they were slow and choppy. When they get done reading and you say, "Tell me what you read." They go, "I have no idea." Why? From a cognitive perspective,
they are using all of their working memory to decode the words. They have nothing left for what? When we have kids in third grade and fourth grade doing this or whatever or they were taught, they're
using up all of their working memory on that basic fact. That's okay in first, second and third grade, the problem is when they hit fourth in really fifth grade fractions, which by the way is now
going to be fourth grade, they get smoked. So we've got to help with this automatic recall. Now, here's how I sort of -- so fluency automaticity, they're getting used interchangeably, some people say
there's a difference. The purpose is we want the students to be able to answer the fact without thought, in other words, quickly. So here's an example, blank out your minds, blank them out, I know
you're like [makes noise] then blank. But blank out your minds and do not answer the question I'm about to ask you. Do not answer it, okay? Everybody ready, are you focused? Here we go. Five times
four, you answered it, and you answered it, and everybody in here answered it. And why is -- from a math perspective, that's not really that important, but from a learning perspective, you used no
what? Working memory, so your working memory is free to understand, apply, problem solve. So that's why there's this emphasis on fluency. Most individual's working memory will be overloaded with five
to seven pieces of information. So anytime the teacher is explaining something that has over five to seven pieces of information, we have to take into account working memory or we'll overload it. And
the way this happens is, teachers are teaching, the kids seemed to be following along, and then when it's time for the kids to try a problem on their own, what happens? They can start it and then?
AUDIENCE MEMBER: They need help.
PAUL RICCOMINI: ?they need help, you go over and help them, and then they're able to what? Finish it. They're literally -- in the instructional phase, they're literally only hearing the first thing
you're saying and the last. So we have to pay attention to this. Now, this is key in the core, but it is of the utmost importance in intervention because the majority of those kids that need
intervention at elementary do not know -- are not fluent and with this information, have already limits in their working memory. So these are two things that we have to address. So, fluency should be
a part of your core classroom at some level. It absolutely has to be apart of any intervention that you do. Now, fluency is at all levels, like at the high school level. Any high school, former high
school teachers in here for math? If you are -- think about simplifying radicals, you know that -- remember that fun thing? What would be helpful for you to be fluent with, in simplifying of
radicals? Perfect squares. So there's levels of fluency at every step in math. Now, the other thing that you have to address in your RTII plan is the type of instruction. This is the 900-pound
gorilla in the room. How is the instruction occurring? Well, the math panel tried to address this and essentially what they said is, exclusive use of either a student-centered, which is often
associated with discovery, inquiry or exploration or exclusive use of teacher-directed is not supported in the research, there needs to a balance. So just like in the content, we need conceptual
understanding, computational fluency, factual knowledge, and problem solving. We need a balance, with that we also need a balance in the instructional piece for your core. So what is the core? Now,
this is one thing that I want you to pay a special attention to, then I'm starting to get -- I'm hearing and that's making me a little uncomfortable, and that is the common core standards in no way
shape or form recommends, advocates or dictates and instructional approach, it is about the content. There is no recommendation on how kids should learn. There are standards about what they should
learn and what they should be able to do. And I'm hearing publishers saying, "The common core says this. The common core says this from an instructional standpoint." And that's simply not the case,
it's the content. The instruction must be guided by best evidence. Now in math, unfortunately that best evidence is greatly reduced or smaller compared to reading, but there are things we know. So
first is, there needs to be a balance. So the first question you should ask, is your core program, is it a balanced approach or is it more student-centered or teacher-directed? Programs are marketing
themselves as these, and if it's all student-centered, then teachers are going to have to supplement and modify to make it more explicit for the struggling kids. I haven't come across a program
that's for the core, that's all teacher-directed. I haven't come across a program for the core, that's all procedural-based. It tends to be on the other side, but that's a question, what is your core
program? What's the emphasis in terms of what they're doing? Now, when you look at these three sub-groups of kids, low achievers have difficulties in math or have learning disabilities, which ones --
first of, do you -- any of you come from a school that does not have these sub-groups -- sub-groups of kids? No? There's nobody from Lake Wobegon, everybody is above average kind of thing. These
groups of kids need these instructional techniques, approaches on a regular basis. That means these things have to be part of the core instruction. If you and your RTI framework for math, if you put
all your efforts on the intervention side, your RTI programmer -- framework will be weak, you've got to look at the core. Now, the idea of this cognitive learning theory and this fluency working
memory piece, is simply this we have spent a lot of effort in the United Sates Education System trying to figure out how kids are different in their learning, and once you can find out how they
learn, then you can differentiate, right? That's how we spend a lot of our time. What we really need to look at is how kids learn in similar fashions, and all individuals learn through the same
process, which is the cognitive piece. We all have a working memory, short-term memory that takes in information visually, auditory, touch, smell -- I don't know, does math smell? Some people would
-- some kids would say math smells. I read, there was a survey, they asked ninth grade kids, "Would you rather go to algebra class or the dentist?" And more -- the majority of the kids said, "I'd
rather go to the dentist." Now think about that for a second, that's pretty bad. I hope there's no dentist in here, I apologize for that. Short-term memory, if you're short-term memory is overloaded,
learning stops. You get the blue screen of death look in the kids. Have you ever been teaching and the kids are like, "Oh," And have no idea what you said. So the idea, is how can we, through
instruction address the issues in the working memory? If we can alleviate the load on the working memory, that will help transfer of information to long-term memory, that's the learning piece. That's
how we all learn. We take new information, we process it, we anchor it in previous information, and we move it to long-term memory. Now, we have to make sure to do things to keep in long-term memory
or you'll forget it, but that is essentially the entire process. So, what does not change is this, now our students that struggle that need tiered intervention, their working memory is smaller. So we
have to, through instructional strategies and interventions, address that piece. Now, I'm going to talk about fluency and problem solving, but it's also about how you rearrange information in terms
of the amount you're giving and you have to pay attention to that. You really have to pay attention to that, because if you overloaded it, sort of, stops. This is one of the reasons why that honey do
list you give your husbands, never gets finish because you're putting too much on it and you're overloading our working memory. You're not buying it?
AUDIENCE MEMBER: No.
PAUL RICCOMINI: Cognitively, the theory is there. You got to keep there, like, one or two. No, you're buying it?
AUDIENCE MEMBER: That's why they put it on the list.
PAUL RICCOMINI: Oh, they put on the list?
AUDIENCE MEMBER: Have an idea?
PAUL RICCOMINI: I tried. Working memory is the key piece. All right. Now, the guiding principles to RTI and the three that I'm going to, sort of, highlight here and then I'm going to get to the
instruction and the intervention for fluency and problem solving. The first one is the believe system, this is where I really think that we have a unique challenge at the elementary level for
reading. First, elementary teachers do not take a lot of math content classes in their prep programs, so that's the first mistake -- first issue. Second issue, they don't feel comfortable with math.
Now, if you don't feel comfortable in any content area, how is that going to come out in your instruction? It's going to be -- you're going to do just what you think you need to do and that's it.
Now, I was the same way in -- when I taught geometry, I loved two-column proofs, do you remember? I really loved two-column proofs. You're looking at me like, "You are crazy." But I -- so, I loved
two-column proofs. So when I taught it, how do you think that came out in my teaching? I was enthusiastic, we spent time on it and I communicate, it was important. And if student struggled, the
expectation was, I helped them until they what?
PAUL RICCOMINI: Got it. Now, I hated teaching translations and transformations. Part of it was, back then we had to actually draw it in the rotation. So, I would teach it just to what?
AUDIENCE: They got it.
AUDIENCE: [inaudible]
PAUL RICCOMINI: Get it done with. And that's something that is problematic at the elementary level, if that's happening for the whole math program. Second, is we have a belief system in the United
States that math is evil, and if you're really good at math, you must be evil. So we have a stereotype issue of a cultural issue. How many of were -- who are teachers in here? So, what happens when
you get a parent -- you finally get the parent in, and you start talking to the parent about the math? What is often one of the first things that come out of the parents' mouth about math?
AUDIENCE MEMBER: That he wasn't good in math.
AUDIENCE MEMBER: "I wasn't good in Math. I don't like it." Now, that is bad in and of itself, but when the child is sitting there and hearing that, they are give -- their closest role model, good or
bad, their closest association has basically given them a free pass to when math gets hard to what? Stop. Worse is, when the teacher responds to the parent by saying, "Yeah, I didn't like math
either." And elementary teachers will say that, and that's a problem, all right. No elementary teacher has come up to me and said, "I almost failed third grade reading. I can barely read." Nobody
would admit that if they -- if that were the case, but for math, it's willingly admitted. Just the other day I was flying to Atlanta and I -- my first flight got cancelled, I had all these issues. I
got an upgraded to first class. So I'm sitting in first class, "So, what are you doing?" I'm like, "I'm going down to Atlanta. I'm working with their math teachers." And he goes, "Oh, math, whew.
Algebra man almost killed me. I hate Algebra." And I go, "What do you do?" "Oh, I'm a banker." "What, you're a banker?" But in this contrary, math has very negative connotations and that's comes out
with our kids, so one that causes them not -- to want to give up quickly, not pressure. Third, if parents have a negative attitude about it, they're more than likely not going to help the kids as
much as they need to at home. So that is something that is a unique challenge in the reading. But the four core beliefs, this is sort of what you need to judge at in your school, all students can be
mathematically proficient. Now, in this country that is not I believe that we have. As a matter of fact, most people think you either have the gene or you don't. Now, I think we should be able to get
all kids to be successful through algebra. Now, calculus, geometry, trig, that's another discussion, but we should be able to get kids successful through algebra. Algebra is really an extension of
arithmetic on a coordinate system. We need high quality math program for all students. Then this is the key piece right here. We need conceptual, computational, factual, and problem solving. So in
your RTII framework, what's the core, what are their strengths, what are their weaknesses? There are few programs that are truly balanced, more are emerging that are trying to balance this. So,
that's what we want to ask our self, where -- in my opinion, we're in bizarre world in curriculum right now, because we have the common core that has come into play. Most of the main popular programs
when the common core first came out said, "No, we're not aligned. We disagree with this." Then 46 governors or 44 governors said, "We're going to adapt the common core." The publishers immediately
said what? "Oh, yeah, we're aligned." And the biggest issue with that is the common core is a very coherent progression within grades, and across grades, where the majority of commercial programs
have approached it from a spiraling prospective, where they spiral. The common core is not spiraling. You very clearly see the conceptual to the process, to the procedural, to the fluency within and
across grade levels. So, if you take your spiraling programs and then just try to each the Common Core, we're going to be end up getting the same disastrous results that we have been getting. And
then instruction is the key, there has to be a focus on the instruction. The instruction is what the teacher is doing on a daily basis at the student level with the kids, that's -- the key is the
instruction. Now here's the other problem, Tom and Jerry, that's the problem for math. How many of you seen this cartoon? My kids were watching this one day, I have sixth grader and a third grader.
They were watching it I think when he was in fourth grade and second grade, but what caught my attention was how math was presented in these cartoons. So I want you to listen, and then of course the
more I watch Tom and Jerry as an adult, the more I realize it's not really kids cartoon, they're violent, steal, lie, take each others friends.
[VIDEO STARTS]
GIRL: Yeah, it's that darn cat again. Yeah, I can go if I get a passing grade in algebra. Oh, I hate algebra, gosh, whoever thought that stuff up.
[VIDEO ENDS]
[VIDEO ENDS]
math is what? Crazy. So here we have a propaganda movement in the United States against Mathematics. We do.
AUDIENCE MEMBER: So, you go.
PAUL RICCOMINI: What?
AUDIENCE MEMBER: Only you.
PAUL RICCOMINI: Only me? A very popular movie Hangover, all right. Now, I'm saying this is what you show kids, but who saw the movie Hangover? There was a math scene in Hangover that was showing the
importance and how math can be applied. Does it -- who knows what I'm talking about? What scene I am talking about?
AUDIENCE MEMBER: Counting cards.
PAUL RICCOMINI: Counting cards. Remember they lost all that money and they had to go gamble and win it back. Of all of the characters, who was the one good at math?
AUDIENCE MEMBER: The idiot.
PAUL RICCOMINI: The idiot. The crazy one, the nutso, but that's what we have. So, here's how we're all playing into that. If I go to your school and I decided to do a frequency data collection
activity. And I have clipboard and in the left side, I have reading, and on the right side I have math. And I walk around every nook and cranny in your school and any time I see something promoting
reading, I put a check. And anything I see something promoting math, I put a check. What am I -- what's my clipboard going to look like? Is it all reading? Anybody think they'd be equal?
AUDIENCE: No.
PAUL RICCOMINI: So, we're indirectly doing what that cartoon did very directly, we promote reading over math. And what the data is clearly showing is we're getting kids to a functional level in
reading. We're not getting kids to a functional level in math. So, that's one of the things to think about in terms of what you're doing. So, low expectations will lead to low expectations. So, if
teachers have low expectations of their mathematic skills, that's going to come out in their teaching. All right. So in your tier, what you want to look at in the tier is the -- what content is being
addressed, what's the instructional approach, balance in both of those is necessary in Tier 1. Tier 2 and Tier 3, this is when the instructional intensity must increase. Now, the intensity can occur
in a couple of different areas. Tier 2, a big mistake some schools make with RTI is they try to re-teach everything in Tier 2. Tier 2 needs to be focused and targeted and there are certain skills and
concepts at grade levels that are more important for long term success. So Tier 2 needs to be intensive in terms of focused on certain content pieces. Second, the intensity needs to be how much time
they're getting, 30 minutes, 40 minutes. Now, if you say, "I've got a 30-minute intervention time for kids," how long actually is that time probably for those kids? Probably 20 minutes because you
got to get the kids there, they got to get back. So you got to think in terms of really how much is the time, so the intensity level. I'm seeing intervention at elementary ranging from 30 to 60
minutes depending on the school. The next level of intensity is how long that -- in other words, the duration, a week, two weeks, three weeks, three days a week, five days a week. I see all different
scenarios. Here's where also things are a little bit different in math. In reading, Tier 2 is often looked as temporary, like we get them in that, we get them caught up and once they get caught up in
reading, they tend to stay what? Caught up. Math is not the same because each year, math become [inaudible] more involved. There are going to be some kids that their Tier 2 is permanent. Now, that
requires -- that is a lot of challenges as far as [inaudible] but because the nature of math continually gets more involved, a lot of times that Tier 2 -- kids will be successful while in Tier 2 in
their math class, but as soon as they exit it, they end up having what? More problems. So that's something to take into account, is how much time you're doing with that. Then Tier 3, and I know some
-- is Pennsylvania a four tiers? Are they -- it's three tiers. So really, Tier 1 kind of has two levels. There's the core that everybody gets and then there is the teacher doing extra instruction for
the kids that struggle there. And then there's Tier 2 which is literally going somewhere else. Now, Tier 3 could be just for students with disabilities. I'm seeing some districts pick a completely
different program for Tier 3. That's called like a dual core program. Sort of the way I look at Tier 3, you know, when you're -- when you're getting kids into fourth grade and they are simply not
even close to where they need to be, what we really have to ask ourselves is that means kindergarten, first, second and third grade in their program did not work. They literally probably need
something as explicit and directed as you can find, because essentially that's four years that had no effect. And that's something that we're starting to -- districts are getting a little bit more
open to having dual tracks and I think the reason they are becoming more open to it is even though they're dual tracks, everybody is still learning the what? The state standard. So I think that's
kind of taking some of that out, but that's something that I'm starting to see. And usually the Tier 3 program, for the most low students or most struggling kids, it's very much a concrete
model-based approach. CRA is really what those programs tend to be. And then what's nice now is they're starting to emerge these replacement programs that are actually taking kids off through middle
school math on a -- on a very much a concrete approach. Wherein the past, it was concrete at the young levels and really not expanding. Now in your document, you have this assessment and I call it an
Instruction and Intervention Needs Assessment. This is a sheet that I developed in working with some states. New Jersey is one of them. It was more developed for middle school, but I also work with
some other schools -- districts that were sort of developing or moving towards trying to focus on math. And what this is is -- and I think you have the full page in the back, is that correct? This is
a good activity to have your teachers fill out as you start to look at RTI in math. Now there's sort of a district level, a school level and then it gets down to the instructional level. And the
point with the instructional level is you're trying to get at what are the strategies that the teachers think they're using or are using and are those strategies aligned with what we know best
evidence says. And in most cases, the majority of teachers have not looked at the Math Panel report. The majority of teachers have not looked at those IES guides and they really are not using
instructional strategies. What they're doing is they're giving kids fewer problems, more time or individual help. So we're trying to get beyond that. We're trying to raise the instructional
sophistication. And again, I'm not blaming teachers. They really were not prepared to deliver these certain strategies, but that -- this is a good, sort of, discussion point whether you have --
whether you have not started RTI in math or whether you're into it for a year or two and this will help sort of address where you need to go in terms of strengthening or professional development or
whatever it might be, but that's in your document for you to look over and possibly use. All right. So standards based classroom, that's where we're moving to, core Instructions, standards based
classrooms. Standards are dictating the classroom. So in the standards based classroom, we need to have a balance of explicit and inquiry-based instruction. Students with disabilities, they need
opportunities to explore. However, it has to be guided, it has to be directed, but it can -- you can't always just lecture or do direct instruction. They need opportunities to explore, but the
majority of their instruction cannot revolve around that. We need to have purposeful learning experience. So in a standards based classroom, the ownership and the responsibility is shared with the
teacher and the students. In other words, it's not just the teacher using the standards or the language, the kids must also use the standards, use the language that are in those standards. When you
ask a student, "What are you doing today?" It can't be, "Chapter 5.1." It needs to be, "Well, we're learning about volume," or, "We're learning about area or perimeter." So there's a shared
responsibility in terms of what you're doing. Now explicit instruction, I have about three or four slides in here that are getting into what explicit instruction is. There's a misconception of what
it is. Most people who don't have a good understanding of explicit instruction, they think that it's simply lecturing to the students, and explicit instruction is far more than that. It's a
structure. It's increasing levels of engagement with a lot of student-teacher interaction, but there's three or four slides that are in here that are talking about what explicit instruction is. The
key pieces I just want to point out is it's rich with example and demonstration. Now, this is something we have to really pay attention to in terms of our core programs. A lot of times, the core
program will recommend or will give the teacher two or three examples for her -- for her to use to demonstrate. Sometimes the books are set up, here's the teacher examples and you have guided
practice and then you have independent, A, B, C, right? The way books have tried to scaffold this is the problems that they're giving the teacher to use as examples are generally the simplest
occurrence of what they're trying to teach. The next point, the problems get what? A little bit more involved, but what are the most involved problems? Independent homework. So if you think about it
from an instruction and a learning standpoint, we're giving the most instruction on the simplest problems and we hope they're able to transfer. And for students with learning disabilities, one subtle
difference in the problem and they have -- they're lost. So we really have to take a look at the progression in terms of how we are aligning things up and that sometimes guided practice should extend
into, what would have been the homework for kids. Now in intervention, most interventions pay a lot more attention to the sequence of examples where they try to make it much more clearer in terms of
the connection, but that's what you want to pay attention to. All right. So the other big thing is there's active practice. Now, this is where we're going to get to the fluency piece. Most teachers,
the way they're doing fluency is really testing, not practice. If you do Mad Minutes -- have you ever heard of Mad Minutes? It's like five minutes, you have a sheet of, what, sixty problems. First
mistake with that is five minutes is way too long. You're not building fluency. You're building accuracy. Second, of the 60 or 90 problems that are on there, each fact is really only on their what?
Ones. How do you get fluent on something, anything? You practice it over and over. So that's more testing than practice, but we're going to talk about the fluency piece here right now. So the six
critical features of core line up with -- these are terms. Here are what interventions should look like. This is what I want to get to. This is what -- these are the components of a standard based
classroom. There should be fluency practice. There should be reviewing of the standards and vocabulary. On Thursday, I'm doing a longer session on teaching math vocabulary and it's something that's
very problematic at the elementary level and I'll just illustrate it for you right now. I want everybody to write down the definition of numerator. Go ahead. Write it down. Write it down. This is a
test. You don't get to leave. If you don't get it right, you're staying for intervention, Tier 2. Oh, you're going straight to Tier 3? Okay [inaudible] here, but if you were just going to write top
and bottom, that has absolutely nothing to do with numerator and denominator. It has absolutely nothing to do with the meaning or understanding of numerator and denominator. So do decimals have
numerators and denominators? What's the numerator of .47? .47, what's the numerator? Forty-seven. What's the denominator? There's no top or bottom. What about 57%? What's the numerator? What's the
denominator? There's no top or bottom. So when we allow kids to just say top or bottom, we're not teaching understanding. And then there should be no surprise when kids don't see that decimals and
fractions are the same. Ready to really blow your mind away? What's the denominator of the number five? One, but there's no top or bottom. So this vocabulary is key. We need to teach understanding
and meaning versus, what I call, level one which is identification. It's in the top. It's in the bottom. So vocabulary is a key piece here. Then you need to have whole group lessons and small group
lessons. This was a model that I developed working with a school district in Georgia. This is what set their elementary classroom. Now if you start adding up these times, twenty, thirty, sixty,
ninety, a hundred minutes. So they had -- some of their elementary schools, mostly the ones that were Title I, the greatest risk, were getting up to 90 minutes. And then they would also do this, so
this was 90 minutes, and then they would do additional instruction for all students grouped on a -- an assessment. So your strongest students would get extra instruction on them, whatever they need,
average, whatever they need and so forth. They also became a Title I, Blue Ribbon School. They had the 99th percentile of improvement from their scores and it was because they maximized the
instructional time, they were very focused in what they did and they provided all students extra practice and instruction on what they needed. And this was a Title I school that had about 85% free
and reduced lunches. So it was -- there were -- there were needy kids in that particular school. All right. So Tier 3, two tracks that you could do Tier -- I'm sorry, Tier 2. You can do
teacher-directed. So you have 30 minutes. She's my Tier 2 teacher. She decides what to teach or you can get an intervention program. Eight years ago, I would have said option one is the way to go.
You got a teacher. You give her data. She can figure out what to teach. After working with a lot of schools at the elementary level, that is no longer my mindset because that is far more difficult
for elementary teachers to do than anybody ever thought. And I think it has to do with the fact that they're -- they don't have the math background. So I'm much more apt to say you should try to find
an intervention for that tier 2 teacher to deliver. Now, it's going to depend on the personnel that you have, but I really -- working with these tier 2 teachers, they had all this data. First, thing
is they got paralysis by analysis. They had too much data. They didn't know what to do with it. Second, they did not -- it's not easy to make the transition to identify what are the key areas these
kids need and then develop instruction. So what we started -- what I started to see in that approach to tier 2 was worksheets and it just became a worksheet after worksheet. Now, I don't have a
problem with worksheets, but if that's all it is, that tier 2 is not going to be very helpful. So I'm much more thinking there should be some level of guidance, either a full blown intervention or
more of a structured, "This what we're going to do." Now we found this -- we were really reluctant to give that to elementary teachers because we were afraid -- you know sometimes how teachers -- if
you say, "Here's the structure," then they do five minutes and ten minutes and twenty. But what we found was they really gave us a lot of positive feedback that this really helped them in their math
instructions because it gave them something to follow. Now again, we spend a lot of time telling them that this isn't set in stone. You have flexibility. Let's say you're teaching something at the
third grade level that you know is very important and kids really struggle with it, then you have the option to not do fluency practice or go over homework that day so you have more time to spend on
the what? The instruction. We also encourage them that for some days there was no whole class instruction. It was all small group. So there was flexibility, but our reluctance turned in to be very
positive that this gave teachers sort of a map in terms of how to manage their math time at the elementary level which they were very appreciative of. Okay. So the two things I want to talk about now
are fluency and then problem solving with word problems. So fluency, in -- when you teach fluency or when you -- when you -- when you begin to develop the operations, there's really three stages --
three and a half stages that occur. The first one is the understanding stage. This is when you are taking the manipulatives and you're modeling to the kids, putting together for addition, pulling
apart the difference in sets. Multiplication -- the conceptual development of multiplication starts with connecting it to repeated addition and then moving that to the arrays. Division is taking
numbers and putting them into groups -- equal groups. So that's the conceptual piece. Most programs do a good job with that. The second piece is the relationship. So after the concept has been
developed, you move into the relationship phase and this is where you teach like fact families, the [inaudible] the doubles, the plus ones, the times zeroes. You're developing the relationships
within the operations and across the operations. Now at the end of that stage, you get into this mastery stage. Now some people say there's two parts to it. The first part is the initial phases of
fluency where the kids have learned a strategy. So counting up, counting back, tally marks, they -- and they begin to get fluent with the strategy. The problem with that is those strategies,
counting, tallies, fingers, will actually become a barrier to the automaticity phase. If you allow kids to continue to count on their fingers, they will continue to what? Count on their fingers, all
right. Now some people say the -- if they're using a strategy like this, that's not fluency, but that's the -- in between from understanding -- or I'm sorry. I have those flipped. Understanding
should be first and then relationships and then the mastery. That counting and strategies is that bridge. That's where programs essentially stop. They don't take it to the next level of fluency. So
why did the common core put fluency in there? Well I get a lot of responses to that, but essentially, this the progression as to why fluency became embedded, not just insinuated, but directly stated.
What we've began to realize is calculators. Guess which kids use calculators effectively? The ones that know their facts. Estimation which is a primary strategy of thinking in elementary school
really requires arithmetic facts. Then kids who are slow on their facts, because they're having to do this, or tap or under the desk, what we see is it takes them longer to work through problems. So
they fatigue cognitively very fast which leads to persistence issues. But what really happens is they take forever to do the simpler problems, they never get to the complex problems. And then
student's multiplication facts is really the key to manipulation of fractions in the primary piece is the equivalents. You know, what allows all of you to know that four tenths is equivalent to eight
twentieths? It's a multiplication piece. And then multiplication is the key -- I'm sorry, to fractions which is the key to algebra. If you do not have fractions, you have a problem in algebra. And
that's why the common core is essentially whole numbers is K-3, rational numbers is three, six level. Now, road blocks to learning the facts, most of the time teachers are trying to teach too many at
one time. Most people will overload their working memory with five pieces of information. So when my son came home and he was focused on the fours, from zero to twelve, how many facts was he trying
to memorize, zero to twelve? Thirteen. So that's too many. The second thing is, what teachers think is automaticity or fluency practice is really testing or a relationship building activity. And then
the last one is, I see a lot of teachers having fluency focused games and the problem with that is if they are not purposeful, planned or targeted. Mostly they're not targeted. A lot of times the
games involve rolling dice or spinning a dial. And as soon as that is entered into it, you have lost all instructional control. You have no idea which facts they are going to what? Practice. So
that's kind of what I'm seeing. Now the other things that I'm seeing -- or here are the standards. Here--these are copied directly out of the common core. So, there's a fluency standard in
kindergarten. They want kindergarten to be fluent with addition and subtraction to fives. There's the second grade. Now fluently add and subtract by end of grade two, know from memory single -- two
one digit numbers. So, that -- there is no if, ands or buts about it. The common core wants memorization by the end of second grade with addition. Now notice it's only two one digit numbers, so we're
talking zero to nines. Most other country is go to sixteens or twentys, but we're just trying to get zero's to nines. Now, the other thing that I notice what else is -- they want fluency with
addition and subtraction, but they only want by memory with what? Addition. I haven't got a clear explanation as to why not subtraction as well, but it's by memory with addition. Here they are for
third grade. By end of third grade, know from memory all products of two one digit numbers, so that third grade multiplication. Now this is where I think a lot programs previously, they didn't really
develop multiplication until starting about the middle of third grade. So there's going to -- you don't want kids memorizing until they have the understanding and the relationship. All right. But
these are -- these are the standards. However, fluency continues beyond the arithmetic facts. Here's another one. Fluently add and subtract within a hundred using strategies and algorithms based on
place value. Now you -- if you've looked at the common core, you see place value based strategies ramped in elementary school. Fifth grade, perform operations with multi-digit whole numbers. Fluently
multiply multi-digit whole numbers using the standard algorithm. That should be a red flag or a big question in your RTII Framework. The common core is calling for a standard algorithm. Does your
core program teach the standard algorithm? There are some that do not, but this is in -- these are in the standards. And think about how -- how long -- how far we've come with these statements. Five
years ago, the standard algorithm by most was considered what? Bad. And now it's embedded in the standards. Fluently divide multi-digit numbers using the standard algorithm, so there's long division,
you know. Here's another vocabulary, you know, put the number in the house, right? That's not -- it's the division bracket.
AUDIENCE MEMBER: Is there a difference between know from memory and fluently?
PAUL RICCOMINI: Well that's -- the common core doesn't say that.
AUDIENCE MEMBER: Okay.
PAUL RICCOMINI: Know -- so here's my take on it. Know from memory is without thought. You're not going to be automatic on long division, but you can do it quickly. Does that make sense? So by memory,
four times six -- by memory four times six is twenty-four. Fluently, it could be four times six, four, eight, twelve, sixteen. You could do that fluently. Memory is like this.
AUDIENCE MEMBER: Okay.
PAUL RICCOMINI: Fluently, with long division, is going to be you're able to execute it quickly.
PAUL RICCOMINI: Does that make sense?
AUDIENCE MEMBER: Okay.
AUDIENCE MEMBER: Yes.
PAUL RICCOMINI: The common core doesn't give any definitions of these things, but I'm showing what they're -- what they're writing here. So fluently means you can do it quick -- like reading. You can
read quickly and effortlessly.
AUDIENCE MEMBER: Correctly.
PAUL RICCOMINI: And correctly, yes. Memory is, boom, you know it, like sight words. I think sight word is kind of automaticity where reading connected texts is more fluently. So fluently in reading
means you've internalized your strategies when you come to a word you don't know quickly. So I think fluently in math in long division is you know the process, you can say the process and you can do
it quickly. You will never be able to do fluently long division if you don't know your arithmetic facts. Here's one in seventh grade. Now this one caught -- you know, I'm learning the standards like
everybody, but this one was very interesting to me. This -- first off, this is the last time the word fluently is used in the common core is seventh grade, but look at what they are saying. So this
is -- use variables to represent quantities, so we're talking about making an algebraic expression. That makes sense, but they sneak the word fluently in. So after they make the expression, the kids
are expected to what? Solve it fluently. The common core very clearly emphasizes fluency with everything, by memory with their addition facts. And I think it's something that core -- common core
programs are not addressing. Teachers are going to have to be aware of it. Schools that have larger numbers of at-risk students are going to have larger number of kids that need fluency practice. All
right. So by the way, here's an app. Do you -- do you know there's a common core app? If you have your [inaudible] -- your smart phone, you can go to your app store and type in Common Core State
Standards and it's free -- there's multiple ones in there, but it's free. So download it. If you're a special ed teacher, it's a must have because you probably are supporting kids across grade
levels. You have all of the standards for reading in math at your fingertips. So I highly recommend that you get this app. I know it's one iPhones and iPad's and droids. I don't know about
BlackBerrys if it's on -- if you can get it on the BlackBerry. But anyway, I highly recommend it because you can really engage in conversation. It's much easier than trying to leaf through papers and
so forth, plus it's free. All right. So fluency, you've got about ten minutes to go through these things. So fluency here, these are what I'm seeing take place. The problem with these is they're not
purposeful, planned and targeted. They're all over the place. So here are the six steps that you want to engage in fluency. Now the RTI document from IES recommends ten minutes of tier 2 be devoted
to fluency. Fluency should also be in the general ed -- the core classroom as well, but now I'm talking about tier kids. So these kids have not learned their facts. So how do we set up a program to
do it? Well, the first thing you want to do is ask yourself, "Is it that they don't know all the facts?" So let's do multiplication. Is it that they don't know all of the multiplication facts
automatically? All of them. Which ones do they do automatically usually? Fives?
AUDIENCE MEMBER: Zeroes.
PAUL RICCOMINI: Twos, ones, tens. Okay. You've just reduced the number of facts to focus on by 50%. If they know those, then they should not be included in practice because they're automatic with
them. So what you do, is once you reduced the facts, pick three or four they do not know. Now the reason I'm saying three and -- three to four and not eight or nine is their working memory can really
only handle less than five. So you pick three or four they do not know. So there's the chunk. So now we're targeting. Now we're going to do this in a purposeful fashion. Each of those facts is
written down on four flashcards each. So if you pick four facts, each one of them is written on four flashcards. How many flashcards do we have? Sixteen. So now they're going to get intensive
practice on the targeted facts. There's the purposeful. So we've got targeted and purposeful. And then we're going to do planned and that you'll have a continuous cycle. So to start off with your six
four facts on four cards, pick four that they know and mix it in. So now you have 20 facts. Four they don't know on -- four times each that they'll get to do those and then you mix in four they know
and that cycle will continue. So you practice those four for ten minutes every day for a week and you'll be shocked that even your students with learning disabilities all of a sudden will learn the
four facts. Because remember, these kids that don't know their facts are also the kids that can tell you every level of Mario Brothers and where every hidden coin is or whatever soldier game they're
playing. So is it really a memory issue or is it how we're doing it? Now you practice that for a week. Once you think they are now fluent and automatic on those four, this is where the gradual
release begins to take place. Those four are each on four flashcards. So once you think they are fluent with it, take two of the flashcards away for each fact. So we're going from sixteen to eight.
So instead of having four opportunities to practice each fact, they'll have what? Two opportunities. The four that we added in, they -- that we said they know that we added in, get rid of them. Then
pick four new ones, put them on four flashcards, so we'll have sixteen of the new flashcards, eight of the previously practiced. That's the continuous or systematic practice on previously introduced
facts. So you slowly keep the cycle going. As they learn them, you reduce the number of times they practice them to make sure they still have them. And if they still have them, you eventually get rid
of them so you don't have 500 flashcards in two months and then that cycle continues.
AUDIENCE MEMBER: So take away four and then take away the eight?
AUDIENCE MEMBER: ?and then add in?
PAUL RICCOMINI: So?
PAUL RICCOMINI: So you -- so you have the four that we targeted that they practiced that they now know. Those were each on four flashcards each. So now you take two of them away, so two of each
flashcards. So now instead of practicing them four times each, they're only practicing them two times each. The four that we mixed in, we just get rid of and then you pick four new ones and they go
on four flashcards. So that's step one. So the cycle is just continuing there.
AUDIENCE MEMBER: Four cards each?
PAUL RICCOMINI: Four cards each.
AUDIENCE MEMBER: Sixteen plus?
PAUL RICCOMINI: The eight is twenty-four.
AUDIENCE MEMBER: All right.
PAUL RICCOMINI: So we went from 20 to 24. So you're not ever going to get over 30 because you're going to keep dropping them out as the cycle continues. Now most people are not practicing this way
unless you have a program and I know in State College, my daughter was in the Mastering Math Facts Program which basically -- this is how it's set up. Now she was having problems. She got stuck on
some of the sets. So what I did is I made flashcards of the set she was on and we had extra practice at home. So that's sometimes a supplement with that. Now, steps four & five in tier 2, the
recommendation is five to ten minutes of fluency practice. There are at least four middle school interventions in the second stage of research for fractions. Each of those interventions, they all
have a fluency component in it. So all the interventions now are -- whatever it is, is building enough fluency component. And what we're realizing is, yes, we can get the kids to understand it and be
able to do it, but if they cannot do it fluently, that will cause problems later on. So five to ten minutes. If you're in a core classroom -- so the general ed classroom, you should get this fluency
practice down to three to four minutes with arithmetic facts. It's not the only thing. It's a piece. And then record keeping, good teaching, record keeping and motivation. Keep track of the facts,
chart the kid's progress and so forth. Now there are programs that are starting to emerge that are doing these things. You don't need it. I just showed you how to do it. The key piece is it's a
purposeful targeted and it's planned. Mass practice of all the facts or get with your partner or do it on the computer, we need a purposeful plan and targeted for these kids. I have a high school
that I'm working with in Kansas. They're lowest from the 35th percentile down in 9th grade are doing multiplication flashcards every day for five minutes because the algebra teacher said, "Look, we
can explain the conceptual piece, but they cannot execute any of this algebra because they don't know their arithmetic facts." So that's at the high school level that they're doing that with their
kids and no complaints by the kids. They explained to the kids what they were doing, why they were doing it and the kids recognized that's one of their problems they have. So in the elementary level,
this is probably left out of your core program. Now, I'm not saying it's absolute, but it is probably left out. Two, if you have teachers trying to do this, they're probably doing it not in such a
targeted way or planned or purposeful. And three, if you have a tier 2 intervention, you should consider five to ten minutes being devoted to fluency, in particular, addition and multiplication. So
kind of in your RTI question, so peer-mediated is a -- is a good way to do this, but that's also beyond fractions. So when you get into fourth and fifth grades -- so my son was in fifth grade last
year, his teacher made them memorize, like, eight fraction to decimal conversions. So he had to automatically know 1/2, 1/3, 3/4, 1/5. He had to know automatically the conversion in decimals. So they
taught the concept, but his teacher says, "Look, there are certain anchor fractions that I don't want you have to figure this stuff out. You should automatically know the decimal conversion." So the
way that I helped him do that was this way. We picked the three or four he was having problems with. We wrote them down on flashcards. We did the structure practice. But what's happening now is mass
practice. It's inefficient and it's ineffective. And then teachers don't want to do it because they're doing it over and over again and the kid's still what? Didn't get it. So they say, "Here's a
calculator," and then that becomes -- that accentuates the problem because then the kids don't learn it. They just want to do it on the what? The calculator.
AUDIENCE MEMBER: Have you ever [inaudible] because I had a student that wouldn't like to write anything and he has them [inaudible]
PAUL RICCOMINI: Well, there's different -- you know, I think there is something called -- there's some computer-based programs with fluency, but I think when you're doing it with computer, you enter
in a couple of things. Like they have to type the answer, how is it controlled. I -- so I'm not saying it wouldn't work, what you want to make sure is, are these -- are these steps being addressed.
And then the other big thing with this fact is they really need to say the number sentence out loud. They literally need to verbalize four times five is twenty, so oral practice.
AUDIENCE MEMBER: And not just say the answers.
PAUL RICCOMINI: Yeah. Yes. They're saying the sentence. Now probably the worst instructionally-designed fact practice game ever is a game -- I did it as a student, I did it as a teacher and we
probably all did it as well is around the world. It's the worst instructionally-designed game ever. Is everybody familiar with that?
AUDIENCE MEMBER: My kids do.
PAUL RICCOMINI: But who loves it?
AUDIENCE MEMBER: The winners.
PAUL RICCOMINI: And who are the winners?
PAUL RICCOMINI: The kids that already know the facts. All the other kids get it one time and then they're out.
AUDIENCE MEMBER: The ones that don't need it.
AUDIENCE MEMBER: [inaudible]
PAUL RICCOMINI: Yeah. So the thing is you want to maximize every -- I mean give every -- if you're going to do that game, give everybody a dry race for it so everybody has to answer. If you just do it
the way the game that I played it, that's the worst designed game ever for fluency practice. All right. So here are other questions you want to ask yourself. How many students are not proficient? If
it's over 30% to 40%, you need to address it in the core. If it's 10% or less, address it in the tier. And I realized it's already overtime. I'm keeping you over. So the last thing that I wanted to
talk about a little bit was purposeful planned targeted for fluency was word problems and scaffolding. And what I want to get to is, in elementary school, there's literally three types of problems,
change, group and comparison. That's basically it. And if you can get your teachers spending a little bit of time teaching the kids to look at a problem and I'd say, "Oh, this is a change problem
because it has these attributes." That is a huge benefit to the kids. And in your tier 2, if you have that time, one of the things you want to address is problem solving but not from getting the
answer correct problem solving, but looking for the underlying features. So a Change problem -- here's an example of Change problem. What the features are is there's a beginning amount, a changing
amount and the ending amount. And every Change problem has that in it. So if we can get kids to recognize, "Oh, this is a Change problem," that will cue the solution. Right now, we have kids looking
at problems and go, "Oh, this is about balloons." "This is about this." Versus, "Hey, this is about this type of problem. This is how we address it." So I sort of gave you some examples of Change
problems, the different levels of problems that you have in there. This is one of the primary recommendations in that IES Practice Guide, that we need to teach the underlying structure of word
problems. We need to do it in the core, but we -- in the tier intervention, it's an absolute must. So when you look at these things -- I don't want to hold you too long. I just want to come to this.
Fluency and automaticity needs to be address in your RTI Framework whether it's a core or definitely in tier 2. The profile of kids in tier 2 is they don't know their arithmetic facts among other
things. The second issue is in -- your core is -- or I'm sorry. The second issue is the profile of kids in tier 2 is they don't know how to problem-solve. They're inefficient. They don't know where
to start. What happens is they pull the numbers out and they do whatever the operation is. So in your tier 2, you should be addressing problem solving from a structural standpoint versus getting the
right answer. So literally, you have -- teachers who have discussions with kids reading a word problem and not answering it, but looking at what are the key features and what type of problem that is.
Because if you can do that, that will help cue the solution path. Remember, it's always easier to work smarter, not harder, doing fluency in a more purposeful, planned and targeted fashion is going
to be better and more efficient. Going beyond the answer in word problems is something that we need to do. So with that being said, does anybody have any questions? I know it's -- I know I've already
kept you six minutes longer. Yes, sir.
AUDIENCE MEMBER: Are there any research-based intervention [inaudible]
PAUL RICCOMINI: Yes, but I hate having to answer that question. I'll talk to you afterwards, but there are some emerging programs. However, the research is still trying to catch up with them. Yes.
AUDIENCE MEMBER: Can you talk all of us about that?
PAUL RICCOMINI: After we shut the camera off. Any other questions? All right. Great. Thank you.
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