STEPHANY BROWN: –works

for tiered interventions in elementary and middle school. I welcome you to

today’s online seminar. I’ll begin with an overview

of the webinar goals and objectives, today’s agenda,

and a little information about the Regional Educational

Laboratories serving in the central region, who is

sponsoring today’s webinar. And then we’ll introduce

the presenters. When you entered

the seminar today, your audio was muted due to

the number of participants. However, as Joe mentioned,

you do have access to the chat box, which you

can use to ask questions anytime during the webinar. The facilitator and panelists

will see the questions, and will have several

minutes at the end of the webinar for responses. The online seminar

or will be recorded, and will be posted

within the next few days to the Institute of Education

Sciences’ YouTube site. A link to the site

will be provided at the end of this webinar. So our goals and objectives

for today’s session are to increase understanding

of research-based strategies, to improve mathematics

instruction for struggling students, and to acquire

a greater understanding of available resources and

actionable knowledge that can be effectively implemented

to meet the needs of students who struggle in mathematics. Our agenda today features

Dr. Russell Gersten providing an introduction

to the IES practice guide, Assisting Students

Struggling With Mathematics, our participant

activity, discussion of fractions intervention

by Robin Schumacher, and Introduction to Data-Based

Instruction and the National Center on Intensive

Intervention. And again, several minutes

at the end for questions. If you post your questions

during the webinar, we will capture

some of those and be able to answer them at the end. And then we’ll also

provide the information on participant contacts if you

have any additional questions. The Regional Educational

Laboratories, or REL, work in partnership with

educators and policymakers to develop and use

research that improves academic outcomes for students. The 10 Regional

Educational Laboratories work in partnership to conduct

applied research and training with a mission of supporting a

more evidence-based education system. REL Central at Marzano Research

service the applied education research needs of Colorado,

Kansas, Missouri, Nebraska, North Dakota, South

Dakota, and Wyoming. We welcome our colleagues

from the REL Central states, along with everyone

from other REL regions and states to today’s webinar. Our presenters today

our Dr. Russell Gersten and Dr. Robin Schumacher. Dr. Gersten is the executive

director of the Instructional Research Group in Los

Alamitos, California, professor emeritus in

the College of Education at the University of

Oregon, and a subcontractor for the Regional

Educational Lab Southeast. He served as the chair

of the panel that developed the What Works

Clearinghouse practice guide that is being discussed

in this webinar. Dr. Gersten has

authored the book Understanding RTI

in Mathematics, as well as multiple chapters in

books on mathematics screening efforts and conducting

rigorous group studies. Dr. Robin Schumacher

is a research associate with the Instructional

Research Group, and currently manages an

NSF grant investigating a fractions intervention

for struggling mathematics students. She has coordinated several

other large scale research studies funded by

IES and NIH, all focused on increasing

outcomes in mathematics. Dr. Schumacher has

written on topics related to fractions intervention,

intensifying instruction for low performers, and

analyzing error patterns in mathematics, and has

authored multiple articles in peer-reviewed journals. Welcome, Dr. Gersten

and Dr. Schumacher. And Dr. Gersten, the

panel is yours now. And Dr. Gersten, if your

phone is on muted, please– RUSSELL GERSTEN: Oh, I’m sorry. I’m very sorry about that. Yeah, OK. Good afternoon. STEPHANY BROWN: We can hear. RUSSELL GERSTEN: Yeah. Can you hear me now? Correct? I’m Russell Gersten,

and I’m going to quickly begin by introducing

the practice guide and who helped create it. It was done a decade ago,

when RTI in math was new and rarely implemented. I’m going to, at the end,

give a quick update on some of the research since then. But in my view–

and I think a belief of some of the leadership at

IES is– an update of a guide like this would

be a nice project to begin in the near future. In any case, I chair it. We have, intentionally,

a research mathematician, Sybilla Beckmann, whose

text is used heavily in pre-service training courses. on the group. We had

two folks with more of a school of psychology

background, Ben Clarke and Anne Foegen, who knew a lot about

screening progress monitoring; Laurel Marsh, who was then

a math specialist, beginning some implementation of

interventions for kids struggling in math, and is

now an assistant principal or principal; Jon Star is more

of a cognitive psychologist; and Brad Witzel, who had done

some pioneering work, really, in algebra instruction for

kids with learning problems. Okay. What we tried to do here– and given the fact that 10 years

ago, when the panel met and we did the research

searches, there was not a lot out there on RTI in math,

there was not a lot going on, we had to borrow pretty

extensively from the special ed research at that point. Because that was pretty

much all that there was. So our goal was to

take all of this and figure out

what can we create that’s practical and coherent. And these guides are

downloadable for free. And Stephany can talk a

little about that at the end, and how they may be used. But basically, the idea

was to try to make, in clear, comprehensible

language, ways to improve practice in this

kind of neglected area, helping kids who struggle

in math, before teachers or parents consider an

actual special education possible placement. So we wanted things

that were not crazy, but that took some risks, that

didn’t have the typical thing that we read and hear about– I just came from a

conference where– on the other hand, we can

overgeneralize from this one study in whatever. We were encouraged

to take some risks. And most importantly, to develop

something that was coherent. Because I think all of us have

read literature reviews, where there were all these

things in there, but you don’t really

know how to fit, and how to get a

hold of what they’re trying to say about improving

teaching, or improving those folks who supervise

or train interventionists to improve intervention

instruction. This document has been

pretty consistently, over the past decade, the most

frequently downloaded document from IES, which is the research

branch of the Department of Ed. And that’s how to download it. And you can– what I usually

do is just Google RTI practice guide and math, and you get it. What each of these guys have–

and I imagine quite a few of you are familiar with

them in some area or other– is specific recommendations,

and then some how-to steps, or just action steps,

and levels of evidence. And this took a

lot of work of us. And this was one of

the early half dozen to figure out how

to give relatively clear, sensible information

on the level of evidence. And we also talked

about roadblocks, because anything you do in

any field, any walk of life, you run into roadblocks– some ways how to overcome them. The levels of evidence

at that point– and they really have not

dramatically changed– were strong, meaning there were

at least three high quality, rigorous studies that met really

rigorous standards that IES initiated 15 years ago

when Congress decided it’d need to radically

change the nature of educational

research so that it had the rigor of

many other fields like engineering, public

health, economics, workforce studies, etc. Moderate means there’s one

or two studies suggesting that this is a good way to go,

but we’re not totally sure. Minimal means the panel

thought it was a good idea, they’d maybe seen anecdotal

evidence of it being effective, but there is no hardcore,

rigorous evidence. Now, in some cases, people

believe more strongly in the minimals than

they did in the strong. But we wanted this

to infuse principles of the scientific

method and rigor. And this is a quick overview

of the eight recommendations we made. And these are quite

truncated, but you can download the practice guide. Some of you, in

advance, have maybe taken a look at it and all. And what I used to do is walk

through all eight of these. And then I realized

I was starting to get bored by the time I

got to about number four, and thought, if

I’m getting bored, what about the folks out there. So we’ve arranged for more

either interactive– well, some level interactive

way to do this. And what we’ve done

is split them in two. And what I’m asking you to do

is to look at each set of four– and many of you may be watching

this together with colleagues, you can have a

little bit of time to chat with your

colleagues about them– and then we’ll poll you and see

which is the most surprising. So I’m going to

turn things over now to Joe, who’s going to

oversee this polling process. But essentially, the idea is

to look at the first four, see which surprises

you the most. OK, Joe? JOE: Indeed. Here is the question. Which levels of evidence

are most surprising? Please choose one

from each group. And I believe you’ll

now see the poll. And just go ahead and click

on which one you think is the most surprising when

you’ve come to a conclusion. RUSSELL GERSTEN: And remember,

the one minimal one here– I don’t know, Joe,

if we can go– well, we probably shouldn’t go back. But the one with

minimal evidence is that the core

should be instruction in number, basically–

whole numbers more or less. You can see that here, that

that had minimal evidence. And screening was moderate,

the other two strong. Yeah. That’s perfect. JOE: All right. People are still polling. All right. It looks like everybody

has chosen one. I’m going to go ahead

and end the poll. And here are the results. RUSSELL GERSTEN: So

I’ll talk these through and get a little context. Then if questions come

up, please enter them in the chat area. And at the end, Stephany

will go through those and ask me and my

colleague those that can fit into this

eight or so minutes. It seemed like you were

surprised about the importance, as we could imagine,

of using word problems. And one issue that we

felt very strongly about, we didn’t have a lot of hard

evidence on, is integrating word problems with computation

work– be it with fractions, decimals, whole numbers,

geometry, et cetera– doing more what Singapore,

Korea, and hopefully, increasingly, as

some American texts are doing to integrate them. And the idea that instruction

needs to be systematic, and kids need adequate practice

and feedback surprised you. Focusing heavily on number, that

was an idea that was pushed– it was pushed very hard by

the National Math Panel, which I also served

on and chaired– the Instructional

Practices Committee– it was pushed very hard in

that period about 10 years ago, the idea being that in

these earlier grades, if kids don’t– and Sybilla,

the research mathematician, said if kids don’t

understand number, especially rational number,

the whole idea of geometry, which relies so heavily on

proportionality and visualizing relationships among

and between numbers– it’s just not going to sink in. It’s not going to be meaningful. It’s not going to be understood. So that’s why we focused

so heavily on math. And there is an

evidence update, which I’ll share with you

in a few minutes. But at that point, it

was simply a belief. Universal screening–

I’d be curious why people were surprised. But I think when we looked at

the realities of the evidence on the screeners and how well

they did, it was pretty good. It wasn’t great– could

be better, we think. Maybe there’ll be

newer ones out– I haven’t necessarily seen

them– that may do better. They tend to very often be time

measures, looking at just one dimension of the numbers. So it seemed an important

thing to do, but something that the evidence– it would be nice if

there were measures that were better at predicting

who might need help, and especially– what the tendency is

for young students, especially– is to say these

kids require intervention, when studies have shown many of

them would do fine without it. So that’s a little feel

for the evidence for these. And let’s do the same

with the second set, Joe. JOE: Great. So here is your second set. Did you want to

talk these through? RUSSELL GERSTEN: This

is the first set again. JOE: Whoops, I’m sorry. Sorry about that. RUSSELL GERSTEN: Yeah. So quickly, this is

cryptic, but it’s really stressed that kids use

both concrete objects but semi-concrete, or

visual representations, like tape diagrams,

strip diagrams, and various other visuals

to reinforce things. I think the others are

pretty self-explanatory. So again, in the poll, which

is the biggest surprise? JOE: All right. The polling is up. All right. I’ll give it a couple

more seconds here. I saw a couple

stragglers coming in. All right. Closing the poll, and

here are the results. RUSSELL GERSTEN: These usually

are big winners, the two that came in the highest. Progress monitoring–

beginning when MTSS or RTI was implemented,

progress monitoring was stressed extremely heavily. This is the reason why

the level of evidence was minimal at that time, and

still probably is minimal. It may get into that moderate

category, but not really. Almost every study we read,

and reviewed, and re-read, and looked into every detail,

and sometimes inquired by the researchers what really

happened when it was unclear– they did not do the progress

monitoring that many of you are familiar with from AIMSweb,

STAR, DIBELS Math, easyCBM. That’s not what they did. Those measures, which

tend to have better psychometric properties, tend

to look at the big picture, be based on the

year’s objectives, or sometimes the

semester’s objectives. Or, sometimes, even

a test like STAR, or some of the math

measures, include material from lower grades

and upper grades, but they tend to be

big picture measures. And they tend to do a

better job at correlating with various state assessments

or other standardized tests. What they did in these studies

was either very often daily, but if not, weekly– is the kind of probes or quizzes

that people have been doing in math since time immemorial–

and in special education type interventions,

and often in Title I interventions for

about 50 years– that they did daily, that

kids mastered this material, or do I need to

spend more time on it during our next lesson

tomorrow or the day after. So with no

evidence that this was– people who did not give an

AIMSweb or DIBELS or anything, they had the kids

for four months– no evidence that there was

any change, you know, due to this. So the kids did

fine when they had the visual representations,

and the explicitness, and the systems. So that’s the reason

for that. Motivation. It kind of was upsetting many. We looked at the

National Math Panel, and they said motivation

is very important. And they cited the work of

Carol Dweck and others, but none of it was in math– not, zero rigorous

studies in math. So it’s something

to think about. It does seem to be key, as

well as ways of moderating– basically, helping

kids focus, ways to help kids increase the amount

of time they persist and attend with tasks. But it has not really

been studied in math. Now, I don’t know if

this guide were updated. There may be some new studies. I hope there would be. So that is the reason there. I do want to say this. One thing that we

have experienced– and Robin might be able to talk

better about this firsthand from our research– is you

don’t necessarily want to overdo this constant praise, which

goes back historically, of praising everything positive. Because more contemporary

techniques that really try to build a sense

of self-regulation, or now called

executive function– that kids develop inner

motivation seems important. So it definitely seems

important, but minimal evidence, unfortunately. And I just have one more slide

before I turn things over, which is more or less on time. So, Joe, maybe it

might be as easy for you to just click

onto the next slide. The only real update

of the evidence is– and this is really

quick– it needs to be done more exhaustively. This is just me, informally– that the evidence of the

importance of teaching number– now, notice I didn’t

say not to also spend time on data

science, statistics, which is increasingly

stressed, especially in an upper elementary

and middle schools– but a lot of time on

number and making sure kids understand numbers. It’s not so

important that kids– and you’ll notice in most

contemporary state standards, if not all, that

some of the problems we did when we were younger

about converting 9/51 into 17ths, and a lot of

these more obscure fractions, are probably unnecessary. But understanding fractions,

that we’re doing things with fractions, even if an

instruction involves primarily– and Robin

will give some examples– halves, quarters, thirds,

fifths, 10ths, and lead into then decimals as a

tool for computation– but understanding

number, and especially using the number line. And you will get that

a lot more in-depth. But there have now been

about a half dozen studies. Robin’s been involved

in almost all of them, so it seems perfect time to

turn things over to Robin. ROBIN SCHUMACHER: So

just to revisit the eight recommendations that we

polled on and discussed– and that Russell gave

such a nice overview for– today, because of the

reasons he stated earlier, really want to highlight

two, three, and five. And I bring up two again mainly

because that recommendation of the way that whole numbers

and rational numbers were divided with K-5 and 6-8– now with the more

contemporary state standards, rational numbers is

really also becoming more included in

grades 4 and 5 as well. And so some of the material that

I’m going to talk about today are two separate fractions

intervention programs that focus on grades 4 and 5. And we’re also going to look

at some systematic construction in terms of the design

of building skills within fractions

within an intervention, and then the use of visual

representations within that. So those are really the

three recommendations that I’m going to focus

on for a few minutes. So I’m unable to

advance my side. There we go. OK. So the two fractions

interventions that I’m going to speak

about, the first one is called Fraction Face-Off! And it was researched over five

iterative years in a study– a fraction center funded by IES. And that was focused

primarily on fourth grade. And then TransMath

is a curriculum that includes many

content areas, but the approach to teaching

fractions is really wonderful. And it spans fourth, fifth,

sixth, through middle school, but the fraction material that

I’m going to talk about today is levelled for fifth grade. So some of the big ideas

within Fraction Face-Off! is to build understanding

of a fraction as one number, so really helping

students internalize that a fraction is its own

number with one magnitude rather than two

separate whole numbers. And the approach that

was taken in this program is the use of linear

representations as a primary focus, which

builds on the measurement interpretation of

fractions, and that they are all a distance from zero

on a number line or a ruler. Fraction tiles were used as a

concrete visual representation, as a way to transition

from something that can be manipulated

with hands and seen in 3D to number lines that are

represented, 2D, on papers. And really, linking those helped

to build students’ magnitude understanding, and to help

form some abilities to reason about the size of fractions with

a focus on benchmark numbers. A more secondary

focus was looking at part-whole understanding,

which is really the more traditional way

of introducing fractions to young students, often talked

about in the form of how many slices of pizza. And that’s really

been the hallmark of fraction instruction

across the US for many years, whereas Asian countries

and Asian curricula really stress the measurement

interpretation and number lines. So in terms of thinking about

the systematic construction and visual representations, the

Fraction Face-Off! intervention started off with having

number line representations, building on unit fractions, and

adding unit fractions together to end up with fractions

that have numerators larger than one, and connecting the

different representations together, marking fractions

on the number line. So you can see how

the visuals here link the understandings together

to various computations. So showing the 1/8 plus

1/8 plus 1/8 equals 5/8 can be shown using the number

line and moving across. Or, those different fractions

are each added, and then tying it into the part-whole

understanding– so really, linking part-whole

and measurement. And so this was

how fractions began to be introduced in the program. And then moving toward

understanding magnitude through comparing two

fractions using inequality symbols or the

equal sign, and also ordering fractions from

smallest to largest or least to greatest. And in terms of

thinking about this the systematic instruction,

this was sequenced intentionally to start off with two

fractions of comparison, then moving to three fractions

that would be compared, and integrating similar

thinking strategies for solving these problems. So students learned

about when fractions have the same

denominators, and how you might think about

those fractions first to evaluate magnitude,

and then fractions with the same

denominators, and then how to use 1/2 as

a benchmark number. And so you can see on those

cards on the right side, it goes through the steps more

clearly and more step by step. But that’s essentially

the process, is moving towards

benchmark numbers, and then other methods

for evaluating magnitude without doing cross multiplying,

which is the way that I was taught in elementary

school, and I know is still sometimes included. But that then precludes students

from having to understand the magnitude of a fraction. So then, to extend

on that, number lines are continued to be used, not

just as a representational tool but as a way to compare two

or more fractions’ magnitude, and really build on the

magnitude understanding. So number lines are taught next,

first with zero to one number lines, then with zero

to two, and again, building on the

idea of magnitude very intentionally

and sequentially while including these visuals. Then, after all three

skills are taught, there’s time devoted

intentionally about building

management understanding and how all three

of these activities are essentially

doing the same thing. The students are thinking

about how big or small their magnitude is to try

to order them, place them on the number line, or

compare two fractions. And so this tying

in together is also very intentional in pulling

all of those understandings together. So this study was

researched over five years. This is results

from three years. All the results that

are grouped together, I didn’t have all in one place. So these are effect sizes

for comparing fractions. 1.82 is quite large. An effect size of 0.8

is considered large, so a 1.8 was a very

impressive effect size between students who

received intervention and those that did not. 1.14 was for students’

ability to estimate fractions on a number line. The 0.94 was on an assessment

of released NAEP items. And then the 2.51 was on a

procedural calculations measure that looked at addition

and subtraction. Again, this was

for fourth grade. So then, I’m now going to

transition to TransMath. It also introduces things

very systematically and with intention,

and relies on visuals. That number line is

also very, very much highlighted and centralized

in this curriculum, and so are Cuisenaire

rods, which are different than fraction tiles. You can see them on the right

side of your screen there. They are wooden bars of

different and increasing sizes so that different fractions

can be represented with various colors representing

the unit or the whole, and so different comparisons

can be made in that way. And so here you can

see on the number line, as a tie in to the

Fraction Face-Off! program, they used thinking

about relative size as an approach for comparing

fraction magnitude, or assessing fraction

magnitude rather. So a fraction of 2/3

would be closer to 1, because the 2 is relatively

large compared to 3, whereas 1/5 is closer

to 0, because the 1 in the numerator– 1 part is relatively

small compared to the denominator at 5. And then building

on number lines, TransMath uses them to

teach all four operations. And because I’m

focusing on fifth grade, We also– I included a whole

number times a fraction, and a whole number divided by

a fraction– how the number line can be used there. So you can see

addition, starting with the first fraction,

moving to the right. And then with subtraction,

similar procedures starting with the first

number in the equation, and then moving toward the left. And these can also be

used when fractions have different denominators. There’s just the extra step

within showing on the number line what an equivalent

fraction with that denominator would look like. And then you can see with the

multiplication and division, when you’re multiplying

3 times 2/5, students learn that it’s

similar, three groups of 2/5, and so moving on the

number line that way. And then similar with

division, if you start with 3 and you divide into 1/2,

you have 6 as your answer. So that was just

a quick overview of different curriculum that

really systematically presents information and builds

sequentially in a smart way so that students

can connect ideas, and then also uses visuals in

a nice, smart, mathematically correct way. And so what we’re going to do

next is view a video that– it’s a short clip. And what I want you to

think about and look for during the video is

about foundational skills, and whether or not

those were included, and if there was

anything else regarding the design or

explicit instruction that you noticed or

want to comment on. One thing that I forgot to

highlight as I was talking is part of the

systematic instruction in both of those programs is

that foundational skills were included throughout as needed

to build new understandings, and to remind students about why

multiplication and basic facts might be important for

finding equivalent fractions. And so earlier

skills are embedded to help students have

access to later skills. So with that, move to the

video, and I’ll release control. [VIDEO PLAYBACK] – 2/3 minus 1 times– – Does everybody see mine? [INTERPOSING VOICES] Everyone should write

on their boards. – Are we doing the boxing thing? – So we’re subtracting. So would we draw

boxes in subtracting? – Oh, no. – No. Instead we followed other

steps with making sure that what are the same? – The denominator. – Good. Denominators have to be the

same when you add or subtract. Does that matter

with multiplication? – No. – No. – OK. So let’s look here. We have 2/3 minus 1/2. Are these denominators the same? – No. – No. – No. OK. So when you see that the

denominators are not the same, what should you do? – You should find

out each factors. – OK. So factors is what we use

when we’re simplifying. So instead, we need– – Multiples. – Multiples. – Multiples. – I was going to say that. – OK. So 2 and 3. So the first thing

that we would always do is look at the smaller

denominator– which is? – 2. – 2. – 2. And is 3 a multiple of 2? – Yes. – No – No. – No. – No, it’s not. Because you can’t mult– – [INAUDIBLE] – OK. Just a second. You can’t multiply 2 by

any number and get 3– by any whole number, I

should say, to get 3. So instead we have to change

both of these fractions, right? – Yes. – OK. So we need to figure out what

the least common multiple is for 2 and for 3. And Dawson had his hand up. What do you think it is? – I think it’s 1. – You think it’s 1? Could we change 1/2 to be an

equivalent fraction with 1 in the denominator? – Well, wait. 1/2, that would be [INAUDIBLE]. – Then they wouldn’t be

equivalent, would they? – No. – No. OK. So we need the least

common multiple. Remember the multiples for 2– 2, 4, 6, 8, 10. Let’s list multiples for 3. – 3. – 3. – 6. – 6. – JJ, stop. – [INAUDIBLE] – 9. – 9. – 12. – So which is the

least common multiple? – 6. – 6. – Very good. So what we need to do is

rewrite each of these fractions with 6 in the denominator. – I already knew this. – [INAUDIBLE] – You’re making it harder

than it needs to be, huh? OK. So what number

times 3 gives us 6? – 2. – So 2 is the factor we’re

going to use for 2/3. So what is our new

numerator for 2/3? – 1. – Who said that? – I did. – Can you say it again? – 1. – Dawson, please talk normally. It’s 4. – 4. – It is 4. Because 2 times 3, we

move down to the 6. 2 times 2 is 4. OK? What fraction is equivalent to

1/2 with 6 in the denominator? What factor do we

need here, Willow? – Oh, 3. – So what is our new numerator? – 3. – I know it, 3. – 3, because 1 times 3 is 3. So what is the new

problem that we have here? Marley? – 1/6. – That’s the answer. What’s the problem? [INTERPOSING VOICES] – 4/6 minus 3/6 equals 1/6. – Good. So you were right, Marley. 1/6 is the answer. But the new problem

is 4/6 minus 3/6. OK? So I want to– [END PLAYBACK] OK. So we’ve seen the case study. If you have any

questions specifically about the case study, you can

pose them in the chat box. And the questions that

I had posed before were thinking about which

foundational skills might have needed to be

reviewed or included, or was there anything

else about the instruction that you noticed. So we can wait and hold some

of these video questions for the end as

well, because I want to be sure to get through

the rest of the slides before we have

time for questions. So one thing I

want to mention is that both of the programs,

Fraction Face-Off! and TransMath, include

ongoing cumulative review. It’s not sporadic and

short-lived but included throughout lessons– sometimes just

briefly, but usually included– as you

saw in the video, with reviewing least common

multiples for the students when it was relevant. Also a key element of

including cumulative review in a smart way is

having problems embedded that caused students to

discriminate between problem types and procedures. So to keep from doing

multiplication of fractions over and over and over, and

then have students forget about procedures

for subtraction, is one reason to keep all the

different types of problems that have been taught

included, so that students learn that discrimination. Also, all of them include

very systematic learning progressions, as I went over,

and have foundational skills to support grade level content

like the multiplication facts for common multiples. So also, both programs

offer the opportunity to give immediate

feedback, which is more attainable in a

small group intervention setting than it is in a large

group intervention setting. But it’s also

extremely important, because teachers are

then able to eliminate false assumptions or

other overgeneralizations before students become

ingrained in thinking of them that way, which could

potentially lead to longer inaccurate understandings. Also, both programs are linked

to the grade level standards. So Fraction Face-Off! was teaching fourth

grade material. The material that I showed you

from TransMath was fifth grade. However, they also

include other time devoted to difficult

essential concepts more often than is typical. So other features

of both, going back to the eight recommendations,

both programs do also include word

problem instruction. Fraction Face-Off! also includes

embedded motivational systems. So Russell mentioned that

that goes beyond praise. The motivation system that’s

included in Fraction Face-Off! includes trying to

solve problems correctly and thinking about

how many they solved to get better and improve each

time they solve problems– so a self-regulation

type of activity. And students are also

motivated with a activity by staying on task

and being focused. What the programs are

missing, as far as the eight recommendations go, is a

progress monitoring tool and built in individualized

components, which leads me to give a quick

overview of the National Center on Intensive intervention– NCII. Many and most of

their materials, in fact, maybe all

of their materials, are publicly available. They focus on databased

individualization. And a lot of their

resources talk about how that can really

be a key for some students to progress to the

next level of learning. They have a lot of resources. This is their primary website. They have a large focus on

intensifying instruction and using progress monitoring. Their databased

individualization framework looks like this, in that

students start with a validated intervention program at Tier

2, are progress-monitored, and then might– if they’re not

responsive– then might look at more diagnostic

or academic assessments or a functional assessment,

adapting intervention, continuing to monitor

progress, and going through to try and get

learning to accelerate. So these are also some extra

links for mathematics resources that are free to you and

anybody, available from NCII. So some cover counting

basic facts, place value, and computation. Others look at college and

career readiness standards with math instructional guides. There’s also specific resources

for progress monitoring, diagnostic assessment for

planning intervention, and then also

intervention design, and then also math

interventions, and assessment tools

for progress monitoring and for screening. So I think I got us for

10 minutes of questions. I’m going to hand

it back to Stephany to pose some questions for

Russell and I to answer. STEPHANY BROWN: Great. Thank you so much,

Russell and Robin, for a great presentation. We have a couple of questions. First is, going back

to the practice guide, one participant asked, we were

surprised by the whole number and rational because it

had minimal evidence. We thought it would be strong. Can you give an

explanation for this? RUSSELL GERSTEN: I can do

that, because I was hoping to. I think there are two problems. One is that– maybe

a major one is– not many studies or researchers

think about comparing, let’s say, a fifth grade

curriculum or an intervention that focuses primarily

on rational number and whole number like most

state standards to do, versus one that covered a

wide array of things including geometry, and

measurement, and some data and probability, which would

then be less intense on real– the kind of in-depth understanding

of rational number that Robin’s two curricula had. So as I say that,

I think it would be a quite important study

to do for that reason, that it’s a critical issue. It’s a common belief. And so it’s good to have

evidence to support belief. And there are a lot of

intervention programs that are linked to– I know big programs are GO Math! in the elementary grades,

and Everyday Math is big. And to compare those

intervention programs, which tend to cover whatever

is done that week, provide support in

the week’s topic for the fourth or fifth

graders, versus something that really hones in on rational

and whole number concepts, and use of the number line–

it would be a good study to do. Who knows? It’s for another

generation of researchers. So it’s just lack

of hard evidence. So I was surprised, too. But I will say this, that

the big belief, going back to something like the ’90s,

was that math curricula should show that number quantity,

geometric concepts, are all around life. They’re in our

everyday experiences, and what you learn in

your science courses related to astronomy,

physics, biology. So that idea is quite

different than what we see in other curricula,

where there really is– no one says that isn’t true,

and that it’s a great way to augment your curriculum. But the key thing,

especially in intervention, is making sure kids really

understand what equivalence is, that it’s not something that

you focus on for two or three weeks, and then

you drop, and then you come back to it when

you do adding factions, but then other times

you ignore it when you’re doing multiplication. That’s really what you need to

understand in grades 3, 4, 5. So I think it will be

a good study to do. They haven’t really been done. STEPHANY BROWN: Great. Another question was, in regard

to the motivational strategies, what about Jo Boaler’s work– if

I’m pronouncing that correctly. It seems that she’s done a

great deal of work on mindsets. RUSSELL GERSTEN: I

think what we did– and it’s not just our

particular panel, Institute of Education Sciences does– is try to differentiate between

rigorous experimental research, where we control for

confounding factors, and other kinds of

observational work, case study work, for actual hard

evidence to rely on the latter, on the rigorous studies. I believe a lot of

Dr. Boaler’s work has been more in the

qualitative case study mode. I know she had done one

quantitative evaluation. I’m not familiar

with all the details. But that certainly would have

been eligible for review. And if it didn’t pass the

standards, I’m not sure. So people are definitely

working, exploring. There’s a lot of scholarship

on mindset and motivation. But we really– we’re looking

for controlled studies that showed, if you had a kind of

motivational system in place and compared it to just more

traditional teaching, where every so often you may praise

a child, or challenge a child, is it effective. We did not find such studies. STEPHANY BROWN: And there

was a little confusion about the strategies that were

shown to have minimal evidence. Do you still suggest

these strategies as ones that should be used? RUSSELL GERSTEN: I

think the answer is yes. And that comes up every time. And I’ve presented on

practice guides and RTI in reading and English learners,

and a little on algebra as well. Yeah, the panel did believe

these were important. It’s just there was no evidence

as of, in this case, 2008. And as time goes by, they do

need to be updated, especially in an area where there is– so much research has been

conducted in the past decade. So the answer is yes. We do believe them. But you do have to be

aware that people– expert opinion has been

wrong on everything from the rotation of the Earth

to a thousand other things to Newton’s laws, which are

not scientifically valid. So we need to keep that in mind. But we do recommend

those as practices still. STEPHANY BROWN: And

one last question. Marjorie Petit has some

valuable insights for all of us around whole number reasoning

applied inappropriately. Can you speak about the impact

of this issue for struggling learners when fractions,

2/3 for example, are portrayed as

two sticks or marks on top of a horizontal bar over

three or marks under the bar? Do these programs ease this

way of portraying fractions? ROBIN SCHUMACHER: Do you want

me to take that one, Russell? RUSSELL GERSTEN: Yes. Yes, Robin, that’s you. ROBIN SCHUMACHER: OK. The programs do not portray

them with two sticks over three sticks with 2/3. And there is, in both

programs, a large focus on a fraction being

one number and not two separate whole numbers. So I’ve read several articles

about whole number bias. I think it’s another– is a term I’ve seen often used

for whole number reasoning applied inappropriately. And so speaking to

that a little bit, part of why many mathematicians

believe that the number line is a superior way to

represent fractions is that it helps students

consolidate and integrate the whole number principles

and understandings with rational number

principles and understandings. Because it’s really

the best representation where you can include both

of those kinds of numbers, and really start to

integrate and consolidate rational numbers being part– especially between zero

and one, and then moving to fractions that

have quantities larger than one involved– part of why the measurement

understanding is becoming more emphasized in many

curriculum now. So to answer your big

question, no, the sticks are not used in these

program at all– and in fact, really try to build

the understanding of them being one number, and the relationship

between the numerator and denominator as

determining magnitude. STEPHANY BROWN: Great. We had a couple more comments

come in on Dr. Boaler’s work, but we will forward

those to the panelists, since we need to

close out our webinar. But thank you all

for those questions. We really appreciate it. These are just some additional

references on today’s topic. Somebody asked if a copy of the

PowerPoint will be available. And yes, it will be. I will show that

in just a minute, but wanted to thank

you all for your time today, and really thank Russell

and Robin for a great session, and you all as

participants for joining us for this webinar focused

on Assisting Students Struggling with

Mathematics: What Works for Tiered Interventions

in Elementary and Middle Schools. This is the contact

information for our presenters, in case you would like

to get in touch with them with any additional questions

or for more information on the work that they’ve done. And this gives some information

on the PowerPoint presentation materials, where

they’ll be available. There will be an archive. The recording of

this will be posted on the Institute of Education

Sciences’ YouTube channel. And you can also

follow our website, or follow REL

Central on Twitter, for more information

about our events, and to access many of

our free resources. So thank you again,

everyone, for participating. And we hope you

have a great day. ROBIN SCHUMACHER: Thank you.