{\rtf1\ansi\ansicpg1252\cocoartf1404\cocoasubrtf460{\fonttbl\f0\fmodern\fcharset0 courier;} {\colortbl;\red255\green255\blue255;}\margl1440\margr1440\vieww10800\viewh8400\viewkind0 \deftab720\pard\pardeftab720\partightenfactor0 \f0\fs26 \cf0 \expnd0\expndtw0\kerning0hello.\ i am sherial mckinney. \welcome to the apples \ magazine video.\many people wonder what does \ math look like in a pre?k \program.\ meaningful math activities in \pre?k, part one, will provide \ a clear picture of what math \activities and skills are \

developed in pre?k.\in this two part series, \ sally moomaw, an assistant \professor in early childhood \ education at the university \of cincinnati will address \ math standards and concepts \that young children will need \ to develop a strong \foundation in math.\ she mentions common core \standards that are currently \ developed nationally for \grades k?12.\ some states are developing \their own common core \ standards for pre?k.\using the latest research, \

the national association for \the education of young \ children and the national \council of teachers of \ mathematics have developed a \joint position statement \ called "early childhood \mathematics promoting good \ beginnings."\in this position statement, \ they have pointed out that \all young children should \ experience high quality, \challenging and accessible \ mathematic experiences.\the position statement also \ points out that young \children need a variety of \

hands?on materials and the \time to manipulate and \ explore what the materials in \their play.\ this play can promote \numerous math concepts. we \ know children come to our \schools or programs already \ knowing many math concepts.\researchers have also found \ math skills are a better \predictor of future school \ success than language and \literacy skills.\ let's listen as sally shares \ideas that will impact the \ development of early \mathematical skills that will \

create a framework for school \achievement.\ >>\for many years in pre?school \ classrooms we have had a very \heavy focus on literacy.\ but with the coming of the \standards movement, which \ includes standards in \mathematics, many states \ adopted math standards for \pre?school and i am sure many \ teachers are aware of this.\that's been going on for \ about a decade.\but now we have something new \ coming on the horizon or it \maybe there for some of you, \

and that is common core \standards.\ those have been nationally \developed in many states are \ adopting them.\standard movements are looked \ at in a variety of ways by \teachers.\ but one of the positive \things that i think it has \ really shown us is that there \is a vast amount of \ mathematic learning that goes \on in ages 3?5, and that \ there is a real breadth of \math learning we need to \ provide as teachers.\so it has really i think \

helped us realize that even \very young children are not \ only counting and finding out \how many of things they have, \ but they are also beginning \to add and subtract and \ divide things up so they can \share them, and they are \ measuring things in the block \area.\ they are looking at not just \looking at shapes, but \ actually putting shapes \together to get bigger or \ different shapes.\they are sorting things and \ beginning to create patterns.\there is a tremendous amount \

of math that we need to be \facilitating in the earliest \ years.\ there are actually five \content areas in mathematics, \ and all five of these content \areas should be heavily \ reflected in the pre?school \classroom.\ let's talk about those for a \little bit.\ the biggest area is the area \of number and operations.\ in the pre?school classroom, \that means that young \ children are trying to figure \out how many of something \

they have, can they get as \many as their friend, how \ many more does somebody have.\this actually is happening \ throughout the day if \teachers can capitalize on \ it.\so, for example, in terms of \ number, if i am at the snack \or lunch table, i might say, \ "best, how many grapes do you \want me to put on your \ plate."\if she gives me a number, say \ she says four, i can put some \on and say "did i give you \ the right amount.\check and see sometimes i \

make a mistake or maybe one \fell off my spoon."\ then she can use whatever \strategy she has to figure \ out if that was enough or if \children are playing in the \ sensory table, i might say, \"how many ducks swam over to \ your side of the table.\do you have as many ducks as \ ben has?"\if you and ben put your ducks \ together, i wonder how many \ducks that would be.\ can you find a baby duck for \each mommy duck?"\ that would also be \encouraging number \

operations.\this can really go on \ throughout the classroom.\the second area of math \ content in pre?school is \algebra and that sounds \ ridiculous.\no three year old can \ possibly be doing algebra, \but actually they are because \ when they sort materials into \different groups, that's \ actually algebra.\let's say they put all the \ blue teddy bears together.\little teddy bear counters \ together, that's sorting by a \particular rule.\

when you make a particular \rule in math, and then \ generalize it, algebra.\when they say i am putting \ all the reds together, it \actually formed a rule, and \ that would relate to algebra, \and they are following that \ rule as they sort the teddy \bears. so we can give them \ lots of fun things to sort \and classify.\ they can put them into \categories based on rules \ they developed or we \suggests.\ furthermore, they can then \begin to pattern once they \

understand what an attribute \is oh, we can sort things \ based on color, or based on \size.\ we can put them in another \relationship, which is a \ pattern.\we will say we will have a \ red bear, blue bear.\a red bear, blue bear.\ can make it into a chant, red \bear, blue bear.\ red bear, blue bear!\as soon as we begin to put \ that in a rhythmic context, \move with it, they seem to \ catch on really quickly to a \pattern.\

that's extremely important \because, as they go on into \ first, second, third grade, \they will be expected to make \ patterns, and then apply \those to the number system.\ beginning to get a feel for \what a pattern is in that \ repeating element is \something very important that \ we can do in ages 3?5.\then we move onto geometry.\ of course, we all think \shapes.\ we do that.\we have shape sorters.\ we have shape puzzles.\we do that.\

it is a lot more than that.\first of all, in terms of \ shapes, most of those \materials we can buy will \ have standard shape.\triangle pretty much always \ looks like this.\but triangles can be long and \ pointy or they can be flopped \on their sides.\ as long as they have three \straight sides that connect, \ they are still triangles.\so if we make our own teacher \ made materials, we can show \them shapes that are not \ always and precisely the way \their little shape box looks.\

we can make bingo games, and \those sorts of things so they \ can see shapes in many \different positions.\ furthermore, and this is \something we often don't \ think about, a lot of \geometry relates to \ positioning and location.\so when we are using terms \ with children like "above, \below, inside, behind, next \ to, to the right of," that's \geometry.\ let's say they built a barn \in the block area.\ i can say "here comes my cow.\he kind of doesn't want the \

horses to see him.\he is going to go, and he is \ going to hide behind the \barn.\ if i get him behind the barn, \can the horse see him where \ he is standing?\what if he moves to the side \ of the barn, can the horses \see him now?"\ we can just play, but do it \intentionally, because we \ know what we are really \trying to do model them in \ terms that is meaningful to \the children, if it is part \ of their play, then it is \meaningful.\

then we go on to measurement, \and measurements is a very \ interesting concept for young \children.\ at first, it is mainly, well, \my mommy is taller than my \ daddy or i am taller than my \little sister, or they looked \ at two things that are next \to each other, and they say \ this is the big begin cone.\this is the little pine cone.\ eventually, though, they \begin to maybe want to \ measure some distances.\i had one little girl who was \ four who was determined to \measure the distance to the \

ceiling.\of course, she couldn't reach \ the ceiling.\none of us could.\ she starts putting some \little manipulative cylinders \ together, this kind of thing \that hooks together and then \ stick it up.\no, doesn't reach.\ put some more on.\stick it up.\ doesn't reach.\put some more on.\ she worked at least 40 \minutes on this major project \ because she so wanted to \touch the ceiling.\

eventually, she did.\once she did that, the joy \ was all over her face.\this is a really tough math \ problem, and she just solved \it.\ then we sat down together, \and we counted all of those \ little pieces, all of those \little blocks, and that was \ how tall the ceiling was, \something like 45 little \ cylinders tall.\when children engage in this \ kind of activity, they are \learning really important \ measure concepts like we need \to use the same size unit.\

we couldn't use some little \cylinder, sol big, because we \ wouldn't know exactly how \many to use the next time we \ went to measure.\they have to touch each \ other.\if we have gaps, then we \ don't know the exact \measurement.\ these are all important \concepts we can begin to \ explore through play with \children, especially things \ that they are really \interested in.\ in the block area, most of us \have had the experience of a \

little conflict breaking out \because somebody took all the \ long blocks, and now i can't \make my fence or i can't make \ my house big enough.\that's when we can move in \ and say, "well, look at these \medium length blocks. i want \ to put two together and see \what i get.\ oh, my gosh, they are the \same length as jeremy's long \ block.\even though he is using all \ the long blocks, if we just \put these two together, we \ can go ahead and make our \building as big as we want \

it."\we can go further and say "by \ the way, if we look at these \that are even smaller and put \ one, two, three, four of \those together, we now have \ one that is the same length \as his long block.\ he can have all the long \blocks.\ we can still do our building \and make it really cool."\ these are some of the really \important ways that \ measurements come about \especially in the block area.\ then finally there is an area \called data analysis.\

when children are sorting \their toys, that is their \ data.\their data is stuff that is \ something they are interested \in, they can touch, that's \ right there in front of them, \and it is also things they \ can vote on like are we going \to have oranges, bananas or \ pears for lunch?\let's figure out which one \ has the most votes, and then \we will let the cook know.\ we can make a small bar graph \and put that on there.\ if their names are or their \voting tag, they can say "oh, \

look at this, we all voted \for apples, but a bunch of \ the boys voted for pears.\which one had the host?\ which one had the fewest?\which one we will tell the \ cook we will have for lunch \this week?"\ those are five important \areas in mathematics that all \ kind of intertwine, and that \we should specifically \ support through our \interactions and planning \ with children in the \pre?school.\ a very important question for \teachers of pre?school \

children is where do we start \in terms of these numbers and \ these games and counting?\we know that even many \ toddlers, and some people \even think infants, \ understand one and two.\if they see one object versus \ two objects, they can tell \that they are not the same.\ many three year old's can \look at one thing and say \ "that's one, two, things," \and say that's two of we also \ have research going all the \way back to the 1950's that \ shows that young pre?school \children tend to first \

understand one, two, three, \and after that it is just a \ lot.\original research was done in \ france.\so it was \ (speaking in french) \one, two, three and a lot!\ with our children, often what \we like to do is make our own \ dice or cards, limb the \amount at first to three.\ so i would take a one inch \cuban use some round folder \ stickers and put, one, two, \or three on each side. these \ are numbers that young \children can grasp so they \

will be more quick to be able \to use a more logical \ strategy like matching a dot \to an item.\ then if we gave them a card \that had ten things on it, \ which is just a lot, or even \six, which is just a lot.\ at first, we almost always \start with simple games where \ you have a dice or a card \that has one, two, or three \ dots.\very quickly you will be able \ to tell if this is too easy \for the child.\ as soon as it is too easy for \the child, then you can move \

to a one to six dice.\still only one dice, still a \ dice with dots because we are \not expecting them to \ recognize the numerals at \this point and to know what \ they mean.\later, we are going to find \ maybe our four year old's who \have had some experience a \ one to six is duck soup.\we will give them two dice or \ two cards to draw.\you know what?\ when we do that, we move them \right into addition.\ yeah, they are still four.\they begin to add.\

so let's say they draw these \two cards.\ we can expect two at first, \they may think of them as \ separate. they may go, one, \two, three, and take three \ things or move three spaces \on the path of a game, and \ then one two, and move that.\but then they begin to \ realize, i could put them \altogether, and at first they \ go, one, two, three, one \two ?? one two three, four, \ five.\but i have found that \ children who have a lost \experience with playing games \

move very quickly to \immediately just combining \ them.\one, two, three, four, five, \ and that's addition.\so because they have the \ concrete objects they can \count, they have already \ moved into arithmetic \operations, even if \ pre?school.\now at some point, we are \ also going to model numerals.\when we have a counting song, \ maybe "five little ducks," i \might put that on a chart and \ have a numeral five when \there are five.\

each time we take a duck \away, we might change the \ numeral, four, three, and i \am going to expect children, \ as they get older in \pre?school to begin to \ associate a numeral, a symbol \that they would use, might be \ three circles or three hash \marks.\ we would use a more complex \symbol of five or a numeral, \ and hope they understand that \that means five objects.\ research indicates that young \children still need many \ opportunities to be using the \actual dot dice because when \

we switch and use a numeral \dice, they can't move forward \ into addition.\they may think that all of a \ sudden that numeral only \means one object, even though \ they just told you it was \five.\ for this reason, it is \important to introduce \ numerals gradually.\at first mainly modeling \ them.\then still give children the \ option of using the dice with \the dots on them.\ it is important in terms of \their learning.\

as a teacher, it is also \important to consciously plan \ to integrate math with other \curriculum areas.\ we know that we can put \counting books out, but we \ can often put manipulative \materials out so children can \ model math and not just \counting books, but \ storybooks as well.\so a book that many teachers \ are familiar with is the \"very hungry caterpillar."\ if i have a bowl of plastic \fruit out, then the children \ can actually model how many \strawberries he eats through, \

how many apples he ate \through, how many oranges, \ but i like to trick them a \little bit.\ i don't want to just put the \exact amount in because then \ all they have to do is find \all the oranges.\ they don't have to think as \much about the math.\ i like to put in maybe more \things than the caterpillar \ actually eats.\so they have to look to the \ book and make an association \between what is on the page \ and what is read to them and \how much the caterpillar \

really eats.\>>\ another thing i think \teachers have to be aware of \ is sometimes we may be \misinformed about what the \ child means in response to a \question we ask.\ so, for example, let's say i \have some little dinosaurs \ out for children to sort.\some of the children do it by \ color, and some do it by type \of dinosaur. i come over to \ johnny, and johnny has got \some here and some here and \ some here, and they are all \mixed up.\

i see nothing.\so i see nothing that links \ any group to the other \objects in the group.\ i am very likely to think, \well, johnny doesn't know how \ to sort and classify yet.\let me write that on my \ checklist.\i will have to carefully make \ sure we address that, and \maybe i will ask him to do \ the red dinosaurs tomorrow, \etcetera, etcetera.\ actually this happened to me.\instead of doing, that, i \ said, "johnny, i see you have \groups of dinosaurs.\

i am wondering how did you \decide which ones went here, \ which ones went here."\johnny said to me, "well, \ first of all, i wanted five \in each group so i looked a \ little more carefully, and by \golly, five were in each \ group.\he said "i wanted all five to \ be different types of \dinosaurs."\ i looked, and, my goodness, \this was so much more complex \ than what i was thinking, any \of the children could do, and \ i was about to write him down \as somebody who couldn't even \

think of sorting and \classifying.\ i remember one child who was \special needs who was in my \ class.\would no not go near a math \ game.\now, look, i make really cool \ math games.\everybody likes to play my \ math games.\well, maybe not.\ this child didn't.\i couldn't get him near one \ to play it with me.\but what he did like was \ dramatic play.\so, finally, i decided, look, \

lady, meaning myself, you are \not succeeding with this \ child.\you better move your stuff to \ dramatic play.\so what i did was take a \ cookie sheet and some plastic \tape, and i made it into \ boxes.\i guess i could have just \ used a muffin tin, but i \actually made it into boxes \ like a bingo game, and got \magnetic cookies, and i put a \ bakery over there.\next thing i knew, this child \ was running over, grabbing \the cookie sheet, and i was \

playing bakery with him.\i could then ask all the same \ things i would have asked if \we had been using an actual \ math game.\but because we were in the \ bakery, he wanted to play.\so we would fill up a row of \ cookies.\we would count the cookies.\ i would say give me one more, \and let me see if i have as \ many as you do or you have \got these many cookies, how \ many more do you need?\let's count them.\ we did this for three weeks.\at the end of three weeks, \

this child surprised me.\he came and got my hand, and \ he led me over to an actual \math game, and still makes my \ eyes tear up, and he said, \"can we play this now."\ he taught me one of the \biggest lessons of my \ teaching career, he needed to \do what was hard for him in \ an area where he felt \comfortable.\ we are all like that!\once he felt comfortable with \ the same math concepts, in an \area where he could achieve \ and felt confident, then he \could move them to the area \

where he felt less \comfortable and apply them.\ that was one of my biggest \teaching lessons.\ and it is why i am so opposed \to only looking at children \ in a snapshot of a formal \assessment.\ i think we need to be looking \at where children can perform \ best and then helping them \generalize it to other \ situations.\at home, we might have them \ help us with the laundry.\can you put all of your socks \ in one pile, and all of your \sister's socks in one pile?\

can you match them up so one \pair of socks is two socks \ which is a big deal when you \are three!\ yeah, one pair, two socks.\can you make sure that \ everybody has a full pair of \socks there, and that would \ really help me out and we can \put them away really fast \ when we are done.\when we are driving in the \ car, we might play a game \like "let's count how many \ red cars we see before we get \to the grocery store."\ "i see one.\do you see that one."\

that's one.\there is one, that's two.\ keep your eyes on the road!\things like this integrate \ math into children's daily \conversations.\ if they are taking a walk \with their children, and they \ see some flowers growing.\they might want to talk about \ how many of the flowers can \we count that are yellow, how \ many are red.\do you think there are more \ red or more yellow?\maybe we are walking by \ aquarium, maybe at a pet \store or a museum, and we \

might want to compare other \more big fish or more little \ fish, are there more redfish \or more whitefish, whatever.\ i'd like to end by talking \about math and how many of \ us, as teachers, may feel \about math.\ frankly a lot of adults do \not like math.\ they did not like math when \they were in school!\ they may have even decided to \work in the younger grades \ because there wouldn't be \much math.\ but as we can see now, there \is a lot of math, even if you \

are in the toddler class.\here is what i want to say, \ math is important.\we need to think about it.\ we need to plan for it.\and we need to tip our toes \ in the water and start doing \it.\ this is what i have found, \the more you talk with \ children about math, the more \you discover that they like \ math.\they think math is cool.\ and they think you are cool \because you can do math they \ can do, you can sing songs \about math.\

you can show it with finger \puppets and little items, and \ they think you are a rock \star when it comes to math.\ i found even with myself \personally, as a pre?school \ and kindergarten teacher, the \more i did math and the more \ i allowed children to use \their own thinking \ strategies, with me helping \just enough so they can use \ their own thinking \strategies, the more i begin \ to realize we can think about \math in many ways.\ it is very creative.\i, too, can now allow myself \

to think about math in many \different ways instead of \ seeing a problem that i \think, oh, this is going to \ be hard, better go have \somebody tell me how to do \ it, i now find it is quite \fun to sit there and think \ about it!\i also find when i do that, \ chances are i can work the \problem.\ it is interesting because \this is exactly the same idea \ that math educators are \working now in elementary, \ middle and high school, how \students feel.\

there is not just one way to \do any kind of math.\ we can all do it, and we can \share a strategy.\ as teachers, we need to start \having fun with math.\ if we are not, we need to at \least act like it!\ if we act like it, we may \actually convince ourselves \ that, hey, this is kind of \fun!}

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