[Music] I'm sherry Pyle and I'm your host today I work with Alison Jensen on ni l DS program development team we are so pleased to have dr. Stephen Pfeifer here with us today he is a true friend ni lb I've spoken at several conferences for us and has consulted and partnered with us on the Rx for discovery math intervention program he is a true expert in the field with a passion for students who struggle I know you will gain much from his expertise today dr. Pfeiffer is an internationally renowned speaker and author in the field of learning disabilities he has authored six books on learning emotional disorders in children she has 19 years of experiences of school psychologists and was voted the Maryland school psychologist of the year in 2008 he was also awarded the 2009 national school psychologist of the year dr. Pfeiffer is the diplomat and school neuropsychology and currently works as a faculty instructor in the ABS NP School neuropsychology training program he continues to evaluate children in private practice at the menís cookie neurodevelopment Center in Frederick Maryland and consults with numerous school districts throughout the country dr. Pfeiffer has authored two tests on diagnosing learning disabilities and children's the far and the fam both published by par dr. Pfeiffer we are so grateful you are joining us today and I am pleased to turn this webinar over to you very much Shari wow what an introduction and so gracious and what a pleasure to be talking to my ni ot friends again and thank you for joining us on this webinar please know how how impressed I am with your work and what you do with children and I'm hopeful that you might find some of this information useful moving forward as we discuss the topic of our webinar the neuropsychology of mathematics and I'm very excited to talk about an introduction to the fam which is our new test on map that we will take a look at a bit towards the end of this webinar once again it's just a true delight to be here speaking with you this afternoon a lot of our information that we'll be discussing will come from our math book called the neuro psychology of mathematics I also wanted to call your attention to another book by my colleague called playing with bath the name of the game of dr. Christopher horn that word math change in there that in our full-day math workshops we do demonstrate a few loose change out of that book for those interested in either one you can read and get more information about that on our website WWF with that said let's dive into trouble bar material today we're going to talk about the world of mathematics as you know it's so important the work that n ILD has rolled out in terms of the are extra feel free math it was really a lot of fun to be a consultant with sherry and Allyson and others on that program because I don't think we give math the face time that perhaps we do with reading and writing I mean in many ways an abscess is not effective reading and writing but it is also important why is it so important to get our discussion today by looking at a bit data when you look at information from the National Assessment of Educational Progress in Washington DC into how our kids are doing in math you recognize immediately why the need for more math intervention programs why the Rx math discovery is so important let's look at just fourth-grade performance as we begin our journey down this road this is just trend in fourth-grade mathematical scores over the last 25 years or so and the National Assessment of Educational Progress actually accrues this data every two years so this is the most recent data I want to share with you and when you look at the get my cursor out here at 2015 what you're seeing is a trend line and he can probably imagine trend lines should go up not be flat and trend lines they go up suggest student progress trend lines that are flat suggests we're sort of treading water here you see in fourth grade only 40% of fourth graders four are at or above a proficient level in mathematics proficient is defined as all of your math skills are on grade level this suggests that nearly two-thirds of our fourth graders both in public and private school this reflects a compilation of both public and private 60% of fourth graders have math skills that are not on a fourth-grade level even though they are in the fourth grade now you're probably thinking yeah but you know yet developmental lags and so forth I'm sure by middle school it all catches up so when we take a look at eighth grade data currently how our kids are performing not great actually it gets worse you see just 33% of eighth graders are at or above a proficient level according to the 2015 data by the National Assessment of Educational Progress this represents two hundred and seventy-three thousand students sampled across this country in both public and private schools and I think what's discouraging and you stop this on the fourth grade trend we see it on the eighth grade trend you look back over the last 25 years or so the line is fairly flat and what's concerning folks quite a bit is you see the drop off from 2013 to 2015 there's a star by there that indicates a statistically significant drop in scores and I'm just going to back up to the fourth grade slide we looked at same thing a drop in scores from 2013 to 2015 so not only is the trend line flat over the last 25 years or so in math for both fourth and eighth grade let me jump to eighth grade but also a bit of a decline the last couple of years math is certainly a subject we need more interventions designed around we seem to be a little stagnant with respect to student performance in mathematics that's fourth grade and that's eighth grade but some of you work at the high school some of you work with older students which is always a challenge you might have a fifteen year old really struggling in mathematics but you know your performance in that by that time is the accumulation of what's occurred at the elementary and the middle school level and it's just the gap is getting wider and wider but I want to look at 15 year-olds from a different perspective I will share with you the latest of the piece of data now this is a piece of an acronym that stands for program for international this is a little bit different then the data we're going to look at for fourth and eighth graders from the National Assessment of Educational Progress the depression the piece of data is the type of math we're talking about this wasn't so much a test or a series of tests that reflect how many problems you can solve in the minutes or straight calculation field or division fluency or multiplication fluency this is a little different it's not about getting answers or getting answers quickly about quantitative thinking is about mathematical nursing it's about using math to solve real-world problems in a real-world context the term we're going to go with here is mathematics literacy and we're also going to look at student performance here compared to sixty five of their country she participated so we're going to look at a little cross-cultural research to see where our kids back up not against each other not against a particular curriculum are we at a proficient level or below that level but the power T is doing in mathematics compared to opera kids throughout the world tests of emphatically literacy and quantitative knowledge assess items such as changing relationships give student model chains and relationships with the appropriate functions and equations it covers items such as nation time understanding perspective reading math problem solving using 3d objects quantity our students able to comprehend multiple representations or numbers engage in mental method deploy estimation skills determine what will give you the answer you tell us is this a reasonable answer based on the day that's thinking differently that's about math knowledge of math literacy not so much let's see if you can get enhance a lot of kids can get answers it doesn't mean they know math so this is a little different maple mathematical literacy let's get uncertainty and data considers probability and statistics and other techniques of data representation and description to describe model and interpret uncertainty read that into high end algebra solving for the unknown uncertainty well how did we do again these 65 other countries this restored a little bit like it SAT for you know where I would be average and we didn't do so well in fact these results suggested that our score mathematics was a 481 where the International average was 494 we were below the International average out of the 65 countries who participated we were out performed by 26 and none countries has scores that were not measurably different let's look right there's 2012 kids up flute yeah well this 4 was even less than the 2009 this 2009 we had a score for 87 in 2012 we have it's 41 and it was the same thing and 2006 and the same thing in 2003 and I believe they re up the pichia was done again in 2015 they do this every three years I did check just a week or two ago and the data has not that yet been released we'll take a look at the 2015 data when it does get relief but as you can see from 2012 2009 two thousand six two thousand three when you start talking about that the quantitative knowledge that bountiful literacy solving real world problems in a real world context oh that's when we begin to drop geographically Massachusetts and Connecticut were the highest performing state and although it's one of my favorite shapes to vacation in sorry Florida did come out the lowest I know what you're you're taking but across the country I'm across the world who are the top performing countries here we go what's an international average of 494 top-performing countries Shanghai China Singapore Hong Kong China Chinese Taipei Korea batalla China Japan look at Liechtenstein cracking the top ten but in all honesty we see a bit of a trend in terms of many Asian countries are leading the world in math as we look at this data we will notice internationally something's missing ah there we are yep I got it this gives you an idea of the number of countries without perform the United States map now I would like to defend the US and for just a moment and just give a couple of reasons why the data might look the way it is and I think primarily we can talk about pedagogical styles cultural differences and values we could spend the rest of our webinar just brainstorming about this data but I'm going to talk about a couple of reasons I'll back up to why the Asian countries seem to be dominated and this comes from the work of Campbell and Shu when you look at the work of Campbell or sure they did a study where they were curious as to why the differences in countries in mathematics achievement and without jumping into the nitty-gritty of the study what they came up with were three regions that begin I don't think is you're the only reason I think there's many many more but I wanted to tell you what Campbell and shoot found that will make it sort of pause and reflect the ljubljana on the status not number one they found when you look at the actual language or counting system let's take Chinese for example the counting system in Chinese the base-10 counting system what that means is the verb is for I don't speak Chinese up there with me the verb is 437 would be 310 7-month the verbage 426 is 210 six months the verbage 412 is 110 two months in English what for the love it who came up with that we do not have a beach tent counting system it is an extra pedagogical step we have to add in because our English speaking language is not shut up head when you have a base-10 language that the accounting system itself has words that are built on base ten properties what you find is that students can do quite a proficient mental math skills as in Chinese kids in the cable industry study were able to do two-digit by two digit multiplication problems in their heads whereas generally once we get past about the 11 times table 12 times whatever most people are using paper and pencil and and it slows you down and if you more prone to error so the three pieces of table and shoot came up with the C sister starting point is that any country that has a counting system based head has a more advantageous approach to mathematics where the English language is not 10 we have to add sort of steps in the problem solving the second reason Campbell as you discussed was they saw a direct relationship between the amount of calculator usage and posture and poor math performance you see calculator usages generate not allowed in Asian countries Campbell ensure the authors of the study said hey if you want to use a calculator every time you teach a kid to push buttons you're teaching them to get an answer and if you value getting an answer great tool great technique but every time they push buttons to do so it robs students of corn percent the third reason they talked about some of these differences time on past time on top tonight Shh we go to school about 180 days a year in Japan the average school day is 243 days 243 days per year in Japan when the students on some of the school you know what they do think about school that you think in Japan on Saturdays do no student does generally goes to school in the United States we spend on average somewhere in the 47 to 52 minutes per day of instructional time in math 47 to 52 minutes a day of instructional time in math in the United States on average okay compared to Japan approximately three and a half hours of your day on mathematics so there's a lot of moving parts here a lot of explanation as to why certain countries might perform better than other countries the bottom line is we're seeing a lot of pedagogical skills in math right here in the United States because we recognize we put a little bit perhaps too much emphasis on teaching kids to get answers and to get answers quickly where maybe the emphasis should be more on mathematical literacy and quantitative knowns and that's that I think you're seeing huge changes in the curriculum according to those along those lines and I also think that is why ARX discovery you see a lot of emphasis on developing core number sense with kids developing conceptual understanding of bath as opposed to just memorizing a script or memorizing an answer one of the reasons I really like the program very very much a little terminology out of the way and you know when we talk about reading we used to term destruction and we talked about math we use the term called discount however in the literature you will see a math learning disability and discal kulia used almost interchangeably generally a math learning disability is the more general broad generic term it just refers to kids whose math performance in the classroom is substantially below each and grade-level expectations oftentimes is unexpected underachievement I mean they seem like a pretty bright kid but they're just not up to age and grade level expectations so it's unexpected underachiever discal kulia refers to a little bit more of a targeted reason why a student struggles in them so a math learning disability you just chalk it up as you know they should be doing better but they're not oh whoa I guess it's enough you know they're not doing as well as we thought but just how could get data to really see why by looking at court cognitive construction is the problem or linguistic in nature and we do use language to help us both learn store and retrieve mathematical facts I'm talking about single-digit addition single digit subtraction single digit multiplication working memory okay working memory is a very important construct involved in remembering what we call the algorithm where series of steps needed to problem-solve long division working with fractions decimals solving a proof I can't do all that in my head is finish that force that's 550 get an answer and if I have limited working memory or what I like to refer to as cognitive counter space I'm going to get step and you know what influencer is working memory quite a bit anxiety how many of us there is something about math that brings the eggs out in all of us and that's a really detrimental spiral we fall into is war to end the math testing school and we hit the panic button because we don't know an answer or we forgot a step or unsure and we start getting a little bit anxious and a little intimidated what is anxiety due to cognition anxiety interferes with cognition by wreaking havoc on working memory and then all of a sudden my goodness we can't even remember our first name let alone problem-solve on this path so working memory and anxiety goes hands as head and get anxious if constricts working memory and we forget the series of steps for algorithm when problem-solving executive functioning is part of this chunk we up executive functioning is very very important when it comes to math because it tells us what to do it wants to do win what's the hardest part about a work problem is it the math know it's knowing what to do with it's figuring out what they're asking us to do and that is really tied into understanding you know having core number sense and conceptual development so when you hear these terms discal Korea is really more of that perhaps of the neuropsychological term that you referring to yeah we understand you you're weak in math but we're looking for the cognitive explanation is there an issue with language executive function working memory and with an executive function there's a lot of little you know and working memory there's a lot of little sub components such as visual spatial thinking visual spatial working memory versus spatial reasoning quantitative knowledge and so forth we'll get to that according to muzaka no not everybody has the diagnosis of math learning disability but you know what is least a couple of kids in every single classroom have persistent difficulty with math and leadership fish I want to talk a little bit about building a math brain just talk a little bit about some of the factors needed to develop good number sense and to how we should begin this process of building a math brain in our students because if we just start memorizing symbols yep you got it like flashcards hey we're going to learn our fact I'm going to show you a flashcard and you just start memorizing symbols devoid of any kind of meaning behind the symbols I think we're slipping back into that bad habit memorizing Hampshire's a not really understanding number shift and that's the point of this talk today that's a huge factor in arch discovery for math is to build core number section kids so you can become better mathematical thinkers and not just memorize facts to regurgitate back on the test only to forget the next day so we'll talk a little bit about these four aspects of building a math brain approximate number social connectivity authenticity and quantitative knowledge let's go ahead and take these one by one now you see a URL at the bottom this particular slide something perhaps after the webinar you can play around what can go too but I'm going to start a start out with this notion of an approximate number system building a math brain and this is the work of Michelle Rocco in college the approximate number system is sort of work its inborn its pre verbal we're sort of born with this capacity of more or less and it's something you can see in babies as well it's something you use intuitively every day yeah when you go to the grocery store and you're about to check out and you immediately scan out the different checkout stands determine which line is short orbits like my house and your kids at least my kids leave about a quarter of an inch of milk left in the apartment and I get up in the morning and I'm interested perhaps in having a bowl of cereal and I have to make a snap decision is that enough milk for my cereal I'm activating this approximate number system it is a built in in the posterior parietal lobe a built in type of ability that allows us to determine more or less numbers ATO determined in her research that if she can measure disability and and by going to that URL at the bottom it's an exercise where a series of dots or flies on the screen some are blue and some are yellow you have to say what's more did you see more blue or more yellow now they're flashed on the screen for 200 milliseconds don't even try to go 1 2 3 you cannot count them it is sliced and gone so you have to activate this approximate number system to determine more or less and Amazon's were more than reading ability more than IQ it would the approximate number system that was your best predictor of math learning disabilities by second grade so fast and efficient research in that this simple task of flashing dots on a screen and again you can check it out by go to the URL by flashing those dots on the screen you can make a pretty strong prediction of who is very much at risk of having a math learning disability who is not I'm measuring this approximate number system we are all born but as you will see formal schooling helps cultivated from there so starts what the apart from the number system and the second component to building a math range called the connectivity hypothesis and what sometimes we talked about this approximate number system being in the parietal lobes of the brain I'm sure that in the back part are way up top primal ownership the spatial centers of the brain and we're going to call the ability to do magnitude representation you know more or less estimation skills things like that that is called non symbolic types of math skills to be able to determine what's more or less less non symbolic when we get into formal school in them we want to get to do more than just no more or less we want them to know object more or less by how much and we teach this symbolic aspect of math and that's how our number system and we learn to make connection between the symbol the symbolic aspect of a newer to this seven 12 14 and negative seven two-thirds 0.9 we have all kinds of symbols and they're represented in many different forms some are positive some are negative numbers some are very very large and some are so small they're represented by by a fraction or decimal without a doubt it is the symbolic form of number of this of this special information that allows us to nuance more or less so somewhere along the journey we need to make a connection between the shambhala is an option valid data no different than somewhere along drugs we need to make a connection when learning to read between what we hear phonemic awareness and what we see letters called the alphabetic code and we make a sound civil connection here we are making a facial civil and this symbol being in a number and the non-symbolic were spatial or magnitude with which it represents this process means that information is going to connect from the non symbolic with spatial centers of our brain in the right hemisphere to the symbolic centers of the brain in the left hemisphere particularly in an area referred to as the left angular gyrus of the brain that looks like this so somewhere along the journey we have the intraparietal sulcus which is this is the purple area right here this is the parietal lobe of the brain the approximate number system hangs out here in pretty much the right hemisphere but it's going to cross over to the left hemisphere once it makes the connection with dis syllable system and that is the angular gyrus that's that spatial to symbolic connection and you'll notice that the angular gyrus without down here in the temporal regions of the brain not so much we've gone from spatial and temporal because now we have sort of the code this numeric code the frontal lobes of the brain are involved in math in terms of sequencing information working memory digits and so forth you see that math is represented in multiple areas of the brain but for our purposes for right now it is highly important highly important especially for those who work with younger students to be able to measure that student's ability to make the connection from the parietal lobe of non-symbolic information to the temporal lobe which symbolic information while you're thinking I'm an ILD therapist I don't exactly have the ability to do an fMRI or brain scan on my students to determine whether that connections that a easy this is what we refer to as the distance effect this is a task that will tell us that the distance effect refers to the fact that when students are presented with two numbers you simply ask which one is the addition of the number pair what we notice are a couple of things okay when the two numbers are far apart twelve and ninety four three and forty four forty seven and one students will respond very quickly when asked to determine which is the largest of the number pair when the numbers are closer together 6 8 12 11 31 and 29 it requires me to nuance things much more precisely because this space between the numbers is so small they're going to have a slower response this second sort of moving part or element attacks this distance effect is the size of the number so they have numbers 12.94 three forty four forty seven two one those numbers are far apart and small off students will respond very quickly but if your numbers are a much larger 1211 or 1021 hey what's larger thirty eight thousand the four thirty eight thousand port or nine that takes a little more time those are big numbers to deal with so whenever both numbers are large response times tend to be slower and less accurate and the literature that's called Weber's law and that sort of a consistency we see among law students what we also see the kids the discal coil respond much more slowly than this task when making comparisons they have additionally given 60 seconds so don't worry I'm going to show you a test that does this towards the end of our talk take 60 seconds show em two numbers which one's bigger even when you control for IQ and reading ability and if the kids who struggle with this that is a huge red flag of development of the self because they have not need connection between us impossible meaning the number and its magnitude representation or amount an extra predictor not only of dystopia but of math fluency and math fact retrieval skills conductivity high polish our third element to building a math brain automaticity got to know your facts single-digit addition single digit subtraction single digit multiplication you see not only the information in the brain need to make a key shift from the right hemisphere which is the non symbolic magnitude representation hemisphere to the left hemisphere which is coding that non symbolic information with our number system or counting system but did we have to make another shift and that's from the front of the brain to the back from the front of the brain to the back and this is real easy to see who's made this shift or not from the front of the brain to the back all you have to do is a classroom observation and wants a kid work and if you have let's say the problem-solving and it's five plus four and the kid is holding up their fingers five six seven eight nine and they're counting on their fingers they're counting on their toes you're counting on your fingers as well anything out there they need to count on they're screaming to you math facts are not automatic conceptually there get it but that's a kid using the frontal lobes of the brain not the more automatic which is more posterior nose of the brain case in point when you look at some of the fMRI work that chill is done math fact retrieval is back here okay in our friend the angular drivers we're talking about single-digit addition fact so we did you to practice image of occasional digit division this means when you say what's five times six we don't have a kid playing I'm tight I want to do four five six seven eight nine ten open difference never when you say by Patrick they say thirty instantaneously reflexively immediately without hesitation no positive they bang it out when they can do that that's the back of the brain when they have to say on hang tight real quick and they're using more effortful blow strategies one two three or five and just remain together it don't get there you give up enough time and if they have enough persistence we'll get there that's the front of the brain and call your attention to the interior is in front part of the shading lyft drivers tends to be involved he's coming straight from the fMRI research of CHO on college guys no different than a bit we talked about dyslexia in reading that dyslexia is a back of the brain issue okay when you automatically know your words when you have good fluency those automatic word recognition centers of the brain in the back portion of with the angular gyrus is a big time player in are activated but if you have a kid hemming and high and trying to figure out and decode every word sweat forming on the brow and fields coming other ears they're fighting to mechanically presses the word that's the kid where the process of reading is not automatic and the frontal lobes are overly involved top-down thinking effortful control sustained attention that's all up front that's that's tough going that's tough flooding to do it that way and boy that's the kid who's going to burn out quickly they're going to fatigue quickly because nothing's automatic so just like with reading and math we need to get the facts automatic and that means a shift and then all ik activity has to open the front and back we need in addition addition and subtraction multiplication and division to be reflexive instantaneous responses to free up or Frollo and we have to free up the frontal lobe because we need the frontal lobes not to be involved in that type of problem solving but to be involved in the more higher-level math skills or what we call quantitative knowledge the development of quantitative knowledge is critical to comprehending more complex mathematics establishing cognitive flexibility with problem-solving the frontal lobes are highly dependent on executive functioning skills knowing what to do when added visual spatial reasoning skills that needs to be able to understand math we need that visual watching and I've said before one of my greatest academic accomplishments actually occurred when I was in the 11th grade and I readily admit to all webinar listeners out there that when I was in the 11th grade you know what I made a b-minus and trigonometry I'm bowing from the way thank you so much yes I made a b-minus in trigonometry but to this day I have no clue what a fine or a cosine is someone told me you straight to build bridges that's news to me I have a clue what trig if you see I couldn't visualize it and the moment we can't visualize math the moment it gets too abstract I just can't wrap my brain around this I can't visualize it anymore it gets very intimidating very frightening very abstract very cold very harsh very quickly yeah I made a b-minus because I pretty good working memory skills either memorize whatever my teacher did memorize the proofs on the board took a test I just regurgitate it right back out double-check my work why bother I had no clue what I was doing I was good at memorizing and getting answers yeah I got a b-minus and trig but I don't know trig so again you had a system for many years where if you have good memory skills you can fake your way through math just like me maybe some of you have similar stories we're trying to get at things and develop quantitative balance instead to think about math establish cognitive flexibility and that's where someone to the RX discoveries getting kids to develop that conceptual knowledge and understanding that because if you do you can you can do some cool things in that you can take a 9 x 16 and I'll gosh I'm supposed to know that off the top of my head but if you have good number sense again our language we have to teach you if you can work this to finish 10th and time 15 is 150 subtract 16 at the end that's 144 you should not need paper and pencil to solve a problem like that same thing if my wife and I go up to dinner we spend $80 at dinner supposed to live a 15% tip okay I don't have my iphone tip calculator with me you should be able to convert to base 10 10 times ladies $1 add half the value down my $12 there's my 15% tip when you understand number relationships you can take more challenging mathematical problems and put them in a more palatable form it helps and I think the key to understanding number relationships is to be able to visualize that balance is be able to think about it visually and bring up the frontal lobes of the brain if you get into more quantitative thinking and knowledge types of endeavors okay with that said I think these are some of the core issues and problems you're going to see and this is what we talk about both in our books and also we're going to get into this within our test is that in my opinion in reviewing the literature while others might call them a little different name the name doesn't matter everybody interested saying the same thing in math in terms of the subtypes or the breakdowns in math that were shaped and what's exciting to me and then we're going to talk about you know we get into a few interventions if are actually it's kind of set up around the subtype approach to minute meaning you can be good and some kinds of math but not so good enough that's what makes map a little slippery here we go subtype number one is verbal discount fully a subtype do I use that term when I do an evaluation on the kid no but it's a mouthful subtype one here the main problem being verbal is in the language system of math why is language important it is going to be the key and learning how to store and retrieve information automatically we use our language system to help do that give you an example my daughter I mean my gosh she was she was not even three years old she was two years old and we were at the dinner table and she said every time she's 42 countries might get this little brother two years old those are multiplication facts she's a genius no she hurt her big sister practicing her facts what she is is that they're verbally precocious kid so she was able to just to use her rocket power language skills and store and retrieve that information because it was done linguistically so we rely on our linguistic skills for a lot of our single digit addition subtraction multiplication facts the verbal discount fully a subtype is a big fancy word that says you have a hard time reflexively spitting out your facts you conceptually get maps that you get someone would talk Thompson they might do very well on math concepts and application but on a math literacy test very important they get it conceptually what they don't get it is reflexively they cannot automatically retrieve the information instantaneously the bottom line here is this is a kid with a language based learning disability chances are they have a reading disorder as well there's probably some writing and spelling issues and how many of these kids that learning disability spills over to that by hindering your ability to retrieve information stored in an archived fashion and it doesn't matter whether that's a letter a number or a word it's a language and retrieval issue it spills over into math in that you're just that good with automatic retrieval skills no matter what we're talking about this is a problem that impacts math whenever a child takes in that fluency test but up aspects of math are just fine conceptually they did they just need a lot of time to get the answer because they have a hard time with automatic retrieval so one of the cool things you might see in our X arch during math is some of the block two exercises are designed to work on the language system of that Mattox um in some cases to improve actual math vocabulary skills to learn how to articulate apply strategies and in verbalize the steps and problem solving and also one of the sort of creative ways to develop some automaticity is there some the rhythmic writing types of activities like metal mats or rhythmic writes or you want a candy bar that cost 80 cents is on sale for 25% off how much does the candy bar cost to you what was the amount of the discount how much space would you get back from whoops I'm sorry I interrupted how much should you get back there should be another line I think from a dollar um what the child would be doing would be making figure H on the boards that are sort of distracted and changing direction simultaneously so their working memory is you know their working memory story is is being occupied by another task surgeon simultaneously that kind of forces you into a mode of needing to rely on some more automaticity of retrieval because this rhythmic writing is occupying a lot of the working memory space that you normally would devote forward to math this is a way to get given a more reflective mode with a problem solving very creative plastic that's done another creative task you might see would be the multi game to teach automaticity specifically with fractions and decimals I cannot tell you back the national advisory panel on mathematics in 2008 put out a statement who said the absolute greatest challenge for kids entering middle school they don't understand they don't offend the relationship between a fraction a decimal into picture and what that suggests is these kids really struggle to understand that you know what between the number one and two there's more numbers yeah we're just breaking down that space and we're going to you know refer to this as at a fraction as a part of a number that's hard for gif to visualize in digest and so the multi game is a game to help kids and entities so automatically especially when it gets into fractions decimals and the relationship between them and basically it's a video game and that's what you're trying to by playing bingo developers mom insisted you try to stop the MU LTI there we go okay let's go to bar and I want to talk about our second subtype of math learning disability and this is called mana procedural subtype the procedural subtype here these guys have their facts like the proper basket number one we don't have our facts we don't have authenticity heart reflexively to spit out the answer not a problem with the procedural subtype single digit addition four digit subtraction multiplication single digit division not a problem you are not a magician what's the problem the problem tends to be when you get into a little higher level napkin single digit two-digit by three digit multiplication long division involving two digits in the Nydia four digit number working with converting fractions to decimals per say I can't do that stuff in my head this is a breakdown when I have to use paper and pencils some be three four five steps we call that a math algorithm problem here is they forget steps you see does quite awful with long division as well the automatic automatic factory will not a problem accomplished today for in two steps so we're going to tribute this to a working memory issue whereas basket number one the verbal dyscalculia was more of a language retrieval issue not so much the problem here the problem here is more working memory and you know what happens when you're in the middle of a long division problem and you forget what divide multiply subtract bring down now I can't remember the steps you know what happens yeah panic and when you panic you get anxious and when you get anxious that has nasty effects on working memory districts working memory and you fall down a deep spiral of panic and generally you don't do well you free the block you still block you can imagine these are the kids who you know they practice their homework and they do pretty well on their homework and they study for the fast and then they get into a testing situation and they bomb out you say what happened you do it at home yep but at home it was practice when you take it for real in school and you know it's for real now the anxiety comes in now try doing this when you're anxious when working memory about half the potency as it would be if you are much more relaxed then we start getting issues then we start making mistakes in my opinion the single greatest reason a student does fine on their homework and just blame that when taking a test in school anxiety they get nervous they panic and one of the things we always have to ask ourselves is where we tested are we testing knowledge are we testing test taking behavior and one of the biggest ways to help kids overcome their anxiety within a test taking situation eliminate the elements of time that's why they panic they look at the clock oh my god 15 minutes left and I've got 40 problems to do it's all over from there eliminates the element of time and the second thing we can do is for some kids they might have to take their tests in a more private location in the school because there's always that kid in class who's the first one done and once you don't know he's the first one done walks in front of everybody hands in his work to the teacher and all the other kids know oh my goodness someone finished already I'm allowing a question to what happens you panicked so I think it's the anxiety piece for a multitude of reasons that disrupts test-taking performance so with respect to are discovering that again quite a few activities you're going to see the help of procedural discount for more on the block one activities that helped with forming visual images improving a attention listening skills developing problem-solving ability internalize that facts improve language processing partners of ten reinforces that base ten idea I see which numbers to ask your partner sambar to develop more number lines military and calcium strategy I cannot emphasize the importance of number line fluency and counting strategy we have that a lot in dr. Warren's book to playing with math and name of the game excellent activity here are summary by number liability here's what we want games that are like hey Billy starting on the number twelve count forward by four starting on the number twenty six count backwards by three we want kids to be able to do that forwards and backwards number lines nor she really really helps to though sort of a procedural understanding of math what we don't want to see is for fifth always go back and count forward or when you say start at 2006 count backwards by three we don't want them to go twenty-five twenty-four twenty-three save twenty one twenty we want them to just spit it out automatically games designed for that you will also say I'll learn how to work these buttons here in a minute you'll also see other games and activities with their RF discovery next five ten what's next highest ten from seventeen that size ten from 58 again developing this kind of number line counting fluency count by seven starting with four count backwards by nineteen so forth multiple time money here's a place value kind of item in 659 what does the five tell me how many one so I have by edit - how many times would I have this was often designed to help develop better counting skills number says you will see forwards and backwards on a number line and here's what I think really highlights the discovery model of them a lot of these core skills can be built by playing games and why is it so important to be able to accomplish this by playing games simply because whether you should diet Domino's cards when you are engaged in a game you are taking the element of anxiety out of the equation I know this sounds funny but math can be fun and it is fun it's not fun if you give kids worksheet after worksheet after worksheet say get the answers there decimated by that but when we play games and all my goodness within the context of me wanting to win a game I'm developing from number knowledge to membership on providing kids with the dice dominoes unifix cubes carved those sorts of things putting less pressure on working memory that I might externalize that to something tangible out here that I can feed touch until presenting a map activities in the form of games wonderful to counterbalance any anxiety if not simply eliminating anxiety use it are extra scary math games you gotta love it let's talk about our final subtype of that and our financial type of math learn this building it's called the semantic now the semantic subtype it can come in two parts but basically you have a lot of verbage here the system I mean the semantic subtype ER for the kids you basically don't get it now I don't know when this occurred for you maybe it was algebra to which geometry was the graduate level statistics with a calculus where you walked into that first math lecture you sat down the alishan you took scrupulous notes and at the end of the lecture you got up and you said ok we're done here that's about as far as I'm getting there that I most of us mere mortals have had that experience we just don't want that to happen in the third grade semantics sub that means I don't get it and if the problem could be more on the visual spatial kind of things we cannot visualize you know and that's going to show up by our inability to estimate numbers on line numbers and their proper columns develop pattern recognition skills those sorts of non symbolic right hemisphere path but visualization can also interfere with the left hemisphere specifically something we call visual intuition such as the following word problem a laboratory used 120 fencepost and an experiment comparing two types of a 60 or than twice as many best folks but time out what what did you just say ships fewer then twice and hang on I got to think about that one for a minute that's an example of needing visual skills we call it visual inferencing for a verbal problem but part of the region we just might not get map at all can't visualize it so digital spatial issue the other reason we might struggle on the semantic side of things is just conceptual aids over my head here it's a deficit with the symbolic elements you're using this gets to be an issue was like a high level algebra 2 you get into some really complex notation now if you don't get out there - it doesn't mean yes and semantics discal Koya okay it just means that the symbols reached a level of abstract if you just don't get any more with all of us generally us mere mortals that's going to happen at some time we just felt what that's been the third grade and when the symbols are void of any meaning we live it in upper sense we can't even determine literally two times for what is that you should know it's not twenty-four that's not even in the universal possibility it if we live in another sense we cannot you know use number relationships don't take part in solving which nine times forty I think it's 38 36 I can't remember what if you have good number sense make it make it easy ten times fourth or you should talk fourth study said how do I know if I'm right because of the knives say what the answer always equals on it 9 times 4 is 36 3 plus 6 of 9 2 times 9 is 18 1 plus 8 is 9 3 times 9 is 27 2 & 7 & 9 so that's where the breakdown is conceptual semantics of type can be a problem in visual spatial visual spatial reasoning which affects more the non symbolic form of bath or conceptual region which impacts more this symbolic understanding of bath bottom line is I don't give what you're talking about it's too hard to abstract so a couple of days on discovering that a couple of activities that can address them to develop number relationships this is nice whereas if Billa successful understanding and you can play this a variety of different ways but you're trying to develop you know the perception the the equation here on the right you know what will go in the box give you the same sort of 30 and admit the equation on the left you can add V Shop math squares we can also look at some of the dot patterns and five and 10 frames that requires us to visualize and develop more of a mental math and develop a picture for what we're doing and a lot of the dot Pyron five content frame requires thinking in five intensive built in that base ten type of instructional strategy and she here is example of what some of those five and ten frame types of the cartoon activities look like a really really nice game nice activity within our X as well off the balanced activity to help in quantitative understanding and I think this is really important because this simple system we use in mathematics is an equal sign to get an absent when in reality it should be a fulcrum to teach that whatever is on the left side is the same as on the right we just alter you know what it might look like here here are seven on one five three and what on the other would balance off the seven I like this symbolic picture of a scale or a fulcrum a lot better than an equal sign it reinforces what I'm trying to accomplish in that and really build sort of a better conceptual understanding and of course some of the place value exercises as well help to understand number sense and the relationship with a 110 hundred place and I will say this for kids who really really struggle with the digital spatial elements of math the organization you don't line their columns up with problem solving I do think that can be confusing it's very helpful if kids work out math on graph paper and if you don't have graph paper my goodness I can't even make a deposit at the bank without without putting my numbers in a little box and you don't have graph paper maybe it's too expensive certainly go on your math homework on graph paper I mean it certainly helps lines things up take notebook paper turn it sideways have the new lines running vertically and simply label each column 110 and hundred and that will clean up a lot of place value issues as well as when we're doing some longer equations and lining up a lot of digits really helps us line them up in the right column as well okay just like bit of a quick overview in terms of a little bit of neuroscience and building a math brain and how we're trying to develop with the conceptual Shawn is really symbolic line and it gives you a little idea of why our expression every map was designed in the matter that it was and then it's not just hey let's get answers as quickly as you can we fear down that road we've been down that road not helpful to kids to just memorize answers ok if we want them to develop math literacy we're trying to dig in and really develop some conceptual understanding to develop numbers and that really is the essence of this program in order to measure how well we're we're doing on that on that very ambitious task it is very very exciting for me to talk a little bit about our brand new map this was that this was five years in the making and I hinted at it over the years in my work with within ILD but I I could never really talk about it I was not allowed to info the test was released and it came out last month so I want to talk a little bit about a test that is for you this is the fan test which is based on a neuro development assessment of that matter there's similar to what we just talked about we norm this on a will over a thousand students there are it goes as low as four years old all the way through 21 and what does fan do look there's a lot of math a chief and tests out there there's the Woodcock Johnson there's the Katy ea3 there's the Wyeth 300 people ask me which ones you like the best I actually they're all the same they'll tell you where a student is functioning in math this is the test that's going to tell you why and I think that why questions is important because it's going to help you I think be more effective as a therapist when you know why you know then what to do you know what to do this is a test one-stop shop one test one hour will tell you do you have procedural work or semantic some type and I think having the arts discovery and I just a very quick superficial few activities there hopefully it will say wow I know what they emphasized I know where to go with our discovery because I see where the breakdown is this is a qualification detest what does that mean that means everybody in this year to this webinar can give the Phinn it is not a test for just psychologists is a test for all educators so once again the purpose of the test we have lots of math achievement tests out there that's why this is not a math achievement test is a diagnostic educational assessment its goal is to say you fall into procedural rules semantic category and what we going to do about it again the procedural categories he struggled with working memory and you're going to struggle in your ability to count order and sequence information verbal is you struggle a they have a language based learning disability so you struggle using those wicked skills in terms of storing and retrieving mathematical facts that you should know reflexively and that automatically excuse me semantics could involve of digital spatial deficits as well as executive functioning and conceptual deficits you're going to struggle in a variety of math skills for estimation to lining numbers up in columns that can see representations reading a word problem and figure out what to do win which is the sense of a word problem choosing an algorithm to best problem solving the way that family shut up give you a quick idea is we have five subtasks there 19 and all nobody takes on my team because it's based on your grade five subtasks that make up the procedural effects we have six sub tests that make up the verbal index and we have eight sub tests that make up the semantic index under each sub testers one in red sequences linguistic math concepts number comparison that is the best representation or representative of the industry therefore we have the fam screener which is these three subsequent related past concepts numbers embarrassing you want to do the whole test do the screener it takes 12 to 14 minutes for the screener and the screen will tell you kind of where you lie on each of these industries if we're doing more of a comprehensive assessment I would do the whole thing if you wanted to use the fan for progress monitoring I did the screener okay lot of applications here as you can see most of the sub tests are very very quick you hear 19 shot F I know what you do it I see you out there in webinar world everybody's rolling their eyes 19 shut them most of them are 30 seconds for one minute show a few these are the five sub tests that make up the procedural in this the procedural image for number count backward double count America pass key sequences and object counts it give you an idea of what each of these sub tests consist of and it's a very simple test to give I mean basically once you get four wrong in a row for incorrect you move to the next section and the test is in unusual format each simply flip the page people say well I need to be trained on it right and I say well you know how to turn a page there you go you've been trained really that's all you have to do so for for number now this would be a typical question depending on whatever sample starting at four count four by four now the kit would go for eight 12 15 and then you say stop after their fourth response if they said four seven don't they stop allow them to give four responses and then simply say stop this if you cut them off the first time every time when they make a mistake they kind of know if you've cut them off they've made a mistake just let them say four responses every single time they stop you read the record it they would have to give all four digits being correct to get one point further for the option and then you do the same thing backwards starting at 50 count backwards by five 50 45 40 35 stop go to the next one always allow them for responses numeric capacity is simply a digit stand touch up in the station numbers I want to repeat them back in the same order this is what we call a symbolic memory catch up in the same numbers you have to repeat them back we're going to compare that to a non symbolic memory test later that's why this is included we have this sequences sub test the little guys free cares we just look at pictures winter spring summer fall blanket summer fall you know what goes in there where the older kids are going to infer great the above would actually use kids with 5 10 15 20 25 30 keep in mind this test goes up to age 21 there are some items that are wickedly challenging wickedly diabolical I'm just showing you some of the more straightforward ones for now it gets progressively harder sequential very fun task very important task is actually the representative of the procedural index this is a task you will see on the screen ur sequences and then only the little kids would take object counting to submit their counting machine picture which child and starting line up via typical example pretty pretty basic stuff here that's your procedural index so hopefully so far so good there are six FS that make up a verbal image and now the verbal index is comprised of e stretch and again the same feeling and basal rules meaning what you get for no wrong you you would stop with in this case just the linguistic map concept the other five sub tests are all 30-second sub tests so that feeling and basal rule only applies to linguistic math concepts but let's take a look very quickly one by one at these subtasks that comprise our verbal attacks rapid number day okay I want to do names from numbers as quickly as Ken Ready Set Joe doesn't get any more straightforward than that right say 30 seconds I was just going to go one do by three or four five you one point you know can they at least recognize the symbol and assign a name to it that's where we start then the kids will do what we call addition fluently again a 30-second sub - I want you to answer some addition problems as quickly as you can without skipping any now you don't need to read the problem out loud me just say your answer ready set go so again this is a verbal task verbal retrieval they start up here and the kid is not going to go to plus one equals through it no they're going to start and go three four five four two four or five ten six nine and so forth so they're going to do that with addition subtraction for kids in third grade above multiplication again they're not reading the equation they're just verbally giving you an answer no paper to capsule nothing to be read verbally giving you an answer and kids third grade above would also do division now there's a point to the fact this will get you in a moment that those are fluently you can imagine what we are measuring your ability to automatically and reflexively fit out the answer you should not be paper and pencil on any designer linguistic map concepts is the final shot test on the verbal side of things and linguistic math concepts one of my favorite steps on here because this is a measure of the vocabulary of math look at the third through eighth grade example this is for practice one in the problem ten minus three seven what is the seven some difference factor or ten selection this will get again very hard very quickly at no time does your student have the problem solved it is all multiple choice SuperDuper easy for the examiner it is a measure of math vocabulary linguistic math concepts and linguistic math concepts is one of the subjects that makes up the screener on the fan our last index is the semantic index and it is made up of the following eight sub - so far you can see these subsets are pretty straight for it II pretty simple gift take a quick look at these eight sub tests again very quick we'll start with spatial memory spatial memory again we've done symbolic memory where I say some numbers hit repeat them back to me make a comparison between symbolic memory and spatial memory spatial memory is you show the student to target picture you flip over the page you wait a few seconds and then you show them the it's all multiple-choice the response option and say what picture did you just see and remember this picture may be turned or rotated in some new so it's a measure of spatial memory right at the holded image and then it might be manipulated or rotated a path to be able to make that match we're going to compare a spatial memory to symbolic memory with the digits to see specifically where the breakdown is if it is a memory I have a breakdown in math equation building is one of my favorite sub tests because it's looking at executive function in your math I'm going to read you a math problem you read it to the student and the student does not solve it they simply select the equation that best represents the problem Alex did 34 push-ups for gym class today Henry did 6 more push-ups than Alex did which equation shows how many pushups and we did it all multiple choice this is your knowledge of what to do win this is executive function and mathematics knowledge of what to do web gets very hard very very quickly but that's because this test goes up to age 21 so yeah towards the end we were into calculus no question about it but it's all great level appropriate starting point really like perceptual estimation and came out very very nice on perceptual estimation everybody starts out the first five items from same two tests but more or less I'm going to show you some containers filled with different items I want you to tell me which container has more items without telling them now they only see this this for for a second you know they see the page and you just immediately turn it and you know they have to say which bookcases morbucks you and your bid so that's getting into that approximate number system you can't say a whole pipe one two three four folks you can't do that you know see a prospective more or less approximate number system but here's where what you get past final five is pretty diabolical now I'm going to show you a picture with the exact number of items written below it same you see seven fish use this picture and number as your clues to figure out how many items in a picture next to it but you're not going to have time to count the no no see this for a couple seconds you flip the page so there the answer can be within a certain range they don't get the number on the head but there is no time to say 11550 no no no you just take a quick glance at the picture magnitude symbolic amount magnitude and then they have to estimate what this ramallah tamela's so they know that actually need a number how many fish there but they won't have time to count nh4 within this acceptable range that you'll see so for this one on the protocol it might say anything between 5 and 10 fish is fine if they let something into the ballpark it's an estimation that's what we won here's your here's your number comparisons house we talked about on my conductivity hypothesis this was also a part of the screener if number comparison you're just going to look at the numbers and you're just going to draw a line through the highest number pair and starts up for you 106 7 you draw a lot you want to shake 99 1 on that drawing 1 through Monday night you work your way through this it's a 60 second task it's interesting once you get into the big numbers once you get into the fractions and oh yeah we got some negative numbers of integers as well okay 60 seconds this is going to help determine who can make that strong symbolic to non symbolic connection pretty easy to do 60 seconds then the last four sub tests on the fan are the knowledge subjects stretch out with addition I want you to stop that you have paper pad see the fluency you don't have paper to pencil here you have paper and pencil I want you to solve some addition problems now the answers in this case already there but one number is missing from the number sentence and your job is to write that for number response in the States Vermont so here they're not telling the answer you're writing this now this was a little bit different than the first you know the addition fluency from that which they just have to China to Plus you know if you can pursue they say for that is three plus one they say for whatever this requires knowledge of addition so we do this for addition subtraction multiplication division sixty seconds for each suffice but with both attention division as long as the third moon and above you can make a direct comparison between each subtest fluency short - if the kids do great influences let me back up multiplication fluency they do great but in this multiplication knowledge swap past they just completely bomb out that's telling you the challenge memorizing their math facts void of any meaning take their memorizing their way through math and they are fooling you they don't have the conceptual understanding however if they do very well on this particular task and horrible on the math the worksheet asked that is suggesting to you that these tips conceptually get multiplication but reflexively cannot fit out the answer most likely because of the language based learning disability impacting retrieval but conceptually they get what ideally we would like is for kids to do well on both shut up that was a quick overview of the fam it is a test carry five par as you heard in the introduction it is again based on a neuro cognitive theory model of how the brain develops number sense in consulting with the NI LD crew in terms of developing arch discovery I love so many activities from our Shepherd math to creative or innovative they're fun for kids and oh by the way a they tie in perfectly with this because it's building a knots of conceptual understanding but also you know on electricity and number sense it's just a wonderful match look there's other tests out there that I use in my day-to-day practice all the time you know back this morning I gave the kte a math for student because we need to know where the student is functioning in math but that's not going to help me write the IEP or write an educational plan or develop a lesson plan just knowing that Billy had an 86 in mathematics what's that I help me is a diagnostic tool and that's I think we're the new wave of testing is coming in and that's what this was trying to represent to answer not just a where question but the why question to directly inform intervention decision-making because if you have some information telling you why a student broke down in math you know what to do and you have been provided with a lg's development of a really strong math protocol with our discovery this is going to make I think a really big difference for kids whether it's the screener to help for screening or progress monitoring purposes or the entire task if you're looking perhaps to diagnose for the math learning disability or you simply need some more diagnostic information to better find to within within our discovery where to go and what to emphasize I hope it can be helpful for you hey with that said I am going to now take a breath of there I'm going to turn things back over to sherry thank you dr. Pfeiffer that was wonderful and your depth of knowledge of the why students struggle in math really sharpens our understanding of your students needs as well as helped us to fine-tune our intentionality with planning we really appreciate all you had to share a couple of questions I'd like to start with half to do with the actual fam so we'll start there since you just discussed that one question is how do children keep their place on the fluency test how do they keep their place on the fluency test well they're supposed to they're supposed to work the problem just left to right it is a quick test it's only 30 seconds they are allowed to send their finger and fill it to help them anchor and keep your place I thought the question would be more as an examiner how do you keep your place because sometimes the kids are just rattling off those answers at work feed actually that tends to be quite a challenge to stay up with them but we did a little birthday a few different versions of the test and the one we settled on we think is the most comfortable way for both examiner's to keep your place as long as examinees thank you another question about the test was what about the students with slow processing speed and is this has cater to them in any way I think the students with the slow processing speed will certainly be hindered by before means Melissa - and then there are many other timed test on the fam there is no doubt that slower processing speed is is going to be a hindrance but that opens up a larger question ask - what do you mean by slower processing speed and and what it's a wonderful question because this was one of the debate I have with my college quite often at lunch I think processing speed is academically and situational specific and what I mean by that is you might have wonderful reading speed of lousy math speed you might have wonderful speed in one area but not in another I think it tends to be more situational in specific so yeah there are kids that have some global processing speed issues but it tends to be highlighted by the specific tasks that they're doing so I'm seeing slowness here in math whether they came to me with the processing speed issue or not and they're really slow and doing this task it's still I'm doing the same intervention studies - thank you again here's another one this is more specific to a student a student displays an average range of cognitive and math abilities on the Woodcock Johnson four but no SLD diagnosis yet they consistently fail the curriculum based tests and quizzes the student reports they memorize steps however they're unable to apply the steps would you will argue that the student actually has a disability and if so what category would you put them in can you repeat the last part of the question they they mess up on the actual steps it's a report that they memorize the step however they're unable to apply the step so there's a couple of so the answer to that question is is is very straight forward I'm not sure and here's why this could completely be an anxiety issue it has nothing to do with math they do pretty well in your one on one testing with the Woodcock Johnson with an examiner's that the social skills they're comfortable in that testing room not a problem if we have issues with the skill is there you measure this with the Woodcock Johnson this skill is there what's not there is the ability to perform that skill under pressure in an inability to perform a skill with a couch so to me I want to rule out some anxiety or non neuropsychological factors if it's not an emotional issue or other issue getting in the way they except they can't remember the series of steps to problem-solve now you're getting more into subtype to the procedural discount Lea subtype but for that particular example sounds like the skills were there according to attack Johnson couldn't perform it under pressure I'm thinking anxiety Q here's another one what is the best way to help a student develop automatic fax retrieval when they don't already have it nor do they seem to have a strong number sense so the follow-up question of that is do you need to stay with building the visuospatial first or combine that with fact drills great question um I would not even get into any fact drills and that does include those dreaded flash cards until we built in the digital spatial pattern recognition first I think the flow of bath always needs to go from non symbolic to symbolic one in fact that the national mathematics advisory panel which was convened in 2008 a lot of map researchers mathematicians curriculum specialists in math and one of the things they talked about if they felt we were premature in introducing the symbol side of math we were teaching and we are teaching numbers and finds and symbols without the students having a good conceptual understanding or feel of the magnitude with which they represent and one of the things they argued is you need to always start at the Nanshan Maalik level and then superimpose or layer the symbols on top of that so I think some of the games that we talked about with an arch distillery are geared to help build out to teach some of the fill of the automaticity I think one of the games we talked about was that bingo the multi bingo game and that's also helpful it's more for later elementary early middle school kids from Egyptian to two fractions and decimals but I think the best way to teach automaticity good non shambhala to symbolic and do it in the form of games and activities thank you so much what step should an educator cake when implementing estimation of the quantity of items with their students like an estimation jar well I thought I hope I understand the question correctly but what I think that I like to see this games that teachers can can do and many of them do quite frequently is to play games from the classroom where everyone has a fishbowl on their desk or the teacher and the fishbowl on the desk in each week she's going to fill it up one week with popcorn one week with starburst skittles whatever put it in there and you have games where kids have to guess be about then whoever wins they get it all begin an ice cream at lunch on Fridays or something along those lines I don't think and this is this is a dr. Pfeiffer opinion not necessarily a fact even though I like to think my opinions are back they're not but my my opinion is we're so geared into getting answers and not geared enough into doing more estimation activities as part of our curricular day and I think they're important because they teach magnitude representation skills and they teach that non symbolic or visual spatial sided map that I think will facilitate the symbolic stuff but we don't give it enough time and I think it's an easy thing to incorporate within our lessons there's lots of different games and estimation games and things of that nature that we can that we can certainly do and and once again you're going to find activities like this with it with an Rx as well thank you one additional question just pops about your test the fan test they're asking you if they were to invest in it which kit would you recommend the comprehensive kit or the screening test depends what your role is with kit if you are part of a formal assessment team and part of what you do is a diagnostic workup I would do the whole kit no question about it if really what you need is just a little direction you have to keep in mind this screener is three shot test and you would be fine with that but that screen are those three shot tests that make up the screener 30 those exact three shut down on the whole kit so what I'm saying is you can get the whole kit and you could use it for screener and just get those same three or you can do the whole thing now if you use it for a screener to me it's a little bit of a waste of a protocol but it doesn't matter you could do it that way but I think it depends what your role is and how much information you're looking to screw but if you are part of any diagnostic team I would do the whole thing a question and good information so the final question is what is rx discovery what is ni OB discovering that I want to kick that one back to you baby I thought you might not that okay I can do that Rx for discovery mass is an intervention program that's designed to be implemented in a small group setting twice a week 25 minute sessions it can be and I personally use it also on an individual basis as well it has a lot of the elements that dr. Pfeiffer introduced today it does layer the symbolic and the non symbolic throughout it's very explicit and systematic and planning is a because the thinking of what you need to pull from you just base it on the students needs and all of that done for you so it becomes an easy program I find to plan for whereas the niño be educational therapy has over two dozen techniques that we pull from based on the students processing perceptual and cognitive needs one of the techniques this basic is math block and there are two levels of math locksmith block one that's block to and they contain a lot of different activities and dr. Pfeiffer also introduced us to some of those type of activities that we would implement in an educational therapy program during the math block segment so it depends on the students actual difficulties and abilities actually which program you would choose you can think of it as a multi-tiered a you know one-on-one very intense would be the educational therapy versus kind of just they need more of a small group or they need some help with their number sense development and that's more that middle tier kind of intervention that would be our extra discovering that we are just so grateful to you dr. Pfeiffer your depth of knowledge of the why students struggle in math really sharpens our understanding of student needs and it has has helped us and all of the opportunities you had to educate us sharpen our intentionality as well with our planning so we appreciate all you have to share thank you for having me today and by the way great explanation of arts discovery and it sounds like perhaps there might be need to a future webinar to go through that in a little bit more detail I think it's an excellent resource for your therapist oh thank you thank you very much well this concludes our webinar for today thank you everyone for joining us we really appreciate our investment thank you [Music]