>> Today's webinar is entitled Alternate Eligible Content: Essentialization Samples, Math. If you are new to Alternate Eligible Content, we would recommend that you visit our PaTTAN website at
www.pattan.net. Click on the Educational Initiatives tab and look for Students with Significant Cognitive Disabilities. Previously recorded webinars are available, outlining the details of the
alternate eligible content and the essentialization process for your viewing at your convenience. Thank you very much; let's get started.
For any content questions, please contact us at AlternateAssessment@pattan.net and reference today's date, December 16, 2015. If you are watching this during the recorded session, please feel free to
send us your questions as well, and reference the date of the webinar, December 16, 2015. During the live presentation today, if you are in need of Tech Support -- and I could be in need of Tech
Support -- it would be support@pattan.net. Thank you very much. Let's take -- let's keep going here.
Our Learner Outcomes today. We're going to identify the steps of essentialization. We've been reviewing these through many webinars over the past year, and looking at the process and teaching you the
process. We're not going to teach the process today, but we're going to review it and look at its application in the area of math. We'll look at alignment to the alternate eligible content at various
levels of complexity.
As a quick walkthrough, the alternate eligible content is only for students who are eligible for the Pennsylvania Alternate System of Assessment, or the PASA. It is aligned to grade-level Core
Standards. The number of pieces alters by the grade and PA Core Standards. There is not a one-to-one match. And it represents the highest level of achievement for students who take the PASA. Again,
students who are eligible to use the alternate eligible content are students whose IEP teams have determined they're eligible for an alternate assessment.
Our focus today is going to be examining essentialization samples in math. So very quickly, the process; how we get to essentialization. We code, we determine intent, then we make a decision based on
student data and the content of whether or not complexity needs to be reduced further. And then meaningful and attainable targets are determined.
You're all familiar with this coding process. We circle what students need to know, box what they need to do, and underline the context. All three pieces of information are going to inform you when
you determine to reduce complexity -- if you determine to reduce complexity. Things can be altered within all three of those areas.
Determining the intent is also a critical piece. How do we do that? We look for common threads between the alternate eligible content, eligible content, anchor and standard. Being familiar with those
threads helps us understand what that conceptual learning is about. When you think about the intent and you think you have the intent and you run through different scenarios in your mind, ask
yourself, is it broad enough to meet the needs of all the students within the range of students eligible for the PASA?
So we determined intent, we've coded it, we have our content information...it's solid. What do we do next? We have to determine whether or not that content can be used as an instructional target and
students can master that. Or, if not, based upon our student data and what we know about the student in relation to that content, do we need to make a decision to essentialize? And data is going to
be your key. I got the question the other day from a teacher who said, "Do we need to be looking at developing new kinds of data collection?" You might, but I would always start with all the
information you have in regard to that content in regard to that student. Even no information is information because that may mean that you may need to gather some information. So it all informs us
when we think about the content and think about our students' current levels of performance.
So generating meaningful targets is really important. But there are some very critical pieces we want you to think about as targets are developed. Number one, is the target challenging? It is not the
idea to develop targets that we know students already can know and can do. What we want to do is we want to increase learning. We want to push students forward. We want to make sure that things are
meaningful when we're asking students to learn and what students need to know and do. Is it aligned to what the alternate eligible content is asking students to know and be able to do? We have to be
very careful we don't get off into the weeds. And is it an increase of the performance from a student's current level performance?
So today we're going to give you examples in three, kind of, buckets. Or three different levels thinking about the targets if the student was going to reach or work instructionally to reach the target
the way the alternate eligible content is written. Then we're going to kind of back it up into a mid-level of complexity knowing that there are so many levels in between what we may write at the
fullest and what we may write at the mid-level. Only because our students provide us with lots of different levels of performance. And then we'll also look at the very least -- or what we would
consider maybe -- around the least complex level. And you may come up with other ideas of how to even reduce the complexity further. There are no right answers -- there are no... Lots of right
answers, I should say. Lots of right answers when we think about writing targets. We just want to make sure that we don't get off into the weeds with instructional skills that lead us to those
targets.
So let's dig into math. Our first thing we need to think about with math is math considerations. Thinking about universal design; how students are manipulating and demonstrating their understanding of
the concepts. Pairing the objects and representations with digits instead of digits all by themselves. Do students really demonstrate they understand what they're being asked to do? Vocabulary is as
important in math as it is in ELA. So making sure students understand the language and making sure we reduce the complexity of that vocabulary to ensure students are familiar with what we're asking
them to know and be able to do. Use your glossary. And we're also going to add another great resource as you consider essentializing in math, is that across the grades view, what's happening before
and after. We're going to reference that a lot today, so stay tuned.
The samples we're going to look at today are in grades five, seven, eight, and 11. And this time, instead of going across different strands, we're going to stay in one strand for you today. We're
going to look at math across the grades. We're going to look at geometry. The right hand corner of your screen you see an Across the Grades view of geometry and alternate eligible content. If you
look at the highlight across the top of your page, we're going to walk you through grades five, seven, eight, and 11 in that particular strand. We'll reference three and four because what happens in
three and four greatly impacts what happens in grade five. Subsequently what happens in grade five greatly impacts with what happens in grade six, and so on and so forth. So leaving grade three and
four right now, thinking about identifying similarities and classifying shapes, we're going to move into some of the more complex content of this strand. And we're going to start with fifth grade:
identifying a two-dimensional figure with specific attributes.
Another consideration as we move into this strand is to think about the vocabulary and language considerations. So isolating vocabulary occurs with coding. It's a great way to determine intent and to
identify and designs align targets. So what can be reduced? What is some other meaningful language that could replace the terms, but still be familiar common vocabulary for students? Checking the
glossary is a good way to help us think about that. Thinking about students being part of learning this underlying language is going to be the most meaningful -- or one of the most meaningful --
parts of math instruction that's going to have students demonstrate what it is that you need to know. So pay attention to the vocabulary and the language. So, for example, if you look up polygon,
polygons in the descriptor in your glossary could lead you to describe those as "shapes with lines that come together at points." Attributes, we could use some reduced complexity and refer to that as
maybe "these are things that are part of" or "things that belong to." Whatever the student may understand. A two-dimensional figure, you could use pictures to help students...of a flat picture,
that's another way to describe a two-dimensional figure. A three-dimensional figure could be an object, picture, real-life... Rotation, a turn-around. A reflection is a flip. A translation could be a
slide, push, pull... And corresponding we could use words like "is like" or "lines up to." Whatever is familiar to the student. But very critical when we think about math instruction.
So back to grade five, identifying a two-dimensional figure...or a flat shape with specific attributes. How would we code it? What do students need to know? They need to know a two-dimensional figure.
What do they need to do with it? They need to identify. And within what context? It's within the context of specific attributes.
And if you remember, step two is thinking about the intent. And in this slide we're going to walk you through thinking about intent. By looking at the document where the content lies on the PaTTAN
webpage, if you pull out the document or look at the document in regard to geometry, you can see it leads back through the eligible content and the descriptor and the Core standard. And we're looking
for students to understand the properties of the figures. Not just to say, "I know that that's a triangle." But what makes it a triangle? We're going to go a little deeper here. So when we think
about the intent of this particular piece of content, is it to recognize, name a two-dimensional figure? Or is to be able to use the basic attributes to identify the two-dimensional figure? So we
could -- knowing a rectangle has four sides that aren't equal, though two (pairs) of the sides are equal, would be a complex way for a student to identify a two-dimensional figure. Understanding a
square has four sides would be another higher level of complexity -- four equal sides would be a higher level of complexity. If we wanted to take it down a little bit we would be thinking about
knowing a square and a rectangle each have four sides. Less complex. We're not talking about how those sides are related. And at its very basic level, knowing a square has sides as opposed to a
circle is round, is even less complex.
So whether or not to essentialize. Of course we have to look at our student data. And first and foremost you always want to take a look at the input of the receptive language and the modes of
expressive language, thinking about how the student interacts. Do they demonstrate imitation skills? What's their frequent familiar vocabulary? Do they even interact with two-dimensional figures?
Think about third and fourth grade...if they've been through that content. And understandably our content is new this year, but as the years go on, you're going to want to reflect on how did they
interact with the two-dimensional figures? Did they classify them? How did they classify? What figures were they classifying? Can they recognize two-dimensional figures when given a picture? Can they
draw it when given a command?
Here are some samples of complexity. Thinking about at the most complex that the student would be able to identify a two-dimensional figure as it's written, you know, comparing multiple attributes.
And some of the attributes are the same, like equal sides. Two sides that are the same in a four-sided figure. At the middle complexity we would be identifying two-dimensional figures with specific
attributes and we would have dissimilar choices. Really some things that are obviously not the same. And at the least complex we would have very basic attribute recognition. Show me the figure that
has sides.
Let's look at some examples of this too. We're going to take a look at some sample student data that might lead us to taking it to the most complex level. This could be a student who already
identifies and is classifying some simple two-dimensional figures. Counts to four. Sorts figures based on similarities. Instructional ideas, you would teach through direct instructions, specific
attributes such as sides and angles. Ensure the students through errorless learning, shaping, error correction, and through data collection that they understand what these attributes are. And you
don't even have to use the language. You can say instead of angles, "points where lines connect or come together." You could have this -- teach the students to draw. Again, most complex level. Model
first, cue in attributes. Lots of different ways you could teach this before you would be assessing for mastery.
If we were assessing for mastery, we might ask this question: which of these has four sides that are equal or exactly the same? Now we're going to use a lot of examples today. We would strongly
recommend that access to examples would be given through pictures, objects, shapes that are textured, raised; however the student may need to access the materials. However you would -- I would be, as
a teacher in the classroom -- and I have been -- I would be manipulating things. Students would be touching it and holding it, moving it... So but today, because we're doing this via webinar we have
to kind of do things... The PowerPoint you're going to see our attempt to draw, to make things look 3-D. You're going to see attempts to see things drawn. But think in your head how I would be having
students not looking at pictures on a piece of paper, I would have them manipulating these objects and these shapes.
So which of these has four sides? Are they equal or exactly the same? The student would demonstrate mastery by being able, through this set, to select the square.
Let's look at this same piece of content at middle complexity. Here are some examples of student data. Again, based upon what they have done previously, what they've brought to the table initially...
Maybe if they're not matching two-dimensional figures that would be part of our instructional skill-building towards mastery of this piece of content.
Instructional idea, you would maybe directly teach. Not just give them activities to do, but directly teach and shape learning to understand different attributes such as sides. Have student trace a
two-dimensional figure. Have them overlap, match, use a T-chart... Build their learning through errorless learning, shaping and error correction.
An example of what this could look like: Which of these has four sides? And remember we're giving them dissimilar choices. So between the circle, obviously wrong, a triangle, obviously wrong because
it only has three sides, and another polygon, they're able to select the one that has four sides. That would be mastery and show proficiency of this particular piece of alternate eligible content.
Least complex. Here's an example what student data might lead us to this. Maybe the student is imitating. Maybe the student is just emerging with imitation. These would be students that you would be
maybe building some skills towards matching simple two-dimensional shapes and then building towards understanding basic attribute recognition. You would, again, explicitly teach. Maybe the attributes
you would use would be straight and round. Think about your students. You know, have them tracing with their finger or with some part of their body touching a raised texture so they understand the
difference between rounded, sides, and use shapes. And engage their learning. Ensure that they understand the vocabulary of sides and round using errorless learning, shaping, and error correction.
So a way you could look at assessing this to determine if this is mastery: Which of these is round? Well that's obviously probably something they've not seen. There is something that's round and there
is something that's not round. Again, just samples. Out in the field, you all are working with kids every day. And our intent is also to get you to be thinking and generating. Maybe you can reduce
that complexity even further and still stay within the intent.
Okay, let's take a look at seventh grade. We're going to move past six. Six was just classifying three-dimensional figures. So you would be doing a lot of sorting to determine if students could know
the difference between some different types of three-dimensional figures. And the complexity would change based on the students that you would be using and their performance data. And then grade
seven we would be identifying three-dimensional figures with specific attributes. Very similar to what we just did in fifth grade. And I think what you're going to see is a pattern of across the
grades you're going to see some very similar ways to write your targets across complexity levels.
So step one, of course we code. What is it that students need to know? They need to know a three-dimensional figure. What do they need to do with it? Identify. And within what context? Well, by the
attributes. So identifying the figure is not enough to meet the intent of the alternate eligible content. So you've got to think about somehow bringing in the attributes.
Again you would be using your documents and your resources to help you think about the intent, locating your alternate eligible content and then working it across to look at the common threads with
the eligible content, your anchor and your standard. So what would be the intent? Would it be to recognize/name a three-dimensional figure? If we did that we would miss the context. Or is it to use
specific characteristics to identify the three-dimensional figures?
So whether or not to essentialize. Let's think about some questions related to student data. As always, think about how the students are taking language in, how they're expressing what they know...
What is the familiar frequent vocabulary? Do they demonstrate imitation skills? Do they interact with three-dimensional figures? Well, if they were classifying them through grade six, what
three-dimensional figures can they classify? Which ones have they demonstrated success with? Can they recognize three-dimensional figures when given a picture? Can they identify three-dimensional
figures in real life? So there are lots of things, again, that you can check into and see what is it that my students know and where is the reality of where I'm starting instructionally?
Again, look at your targets. They're very similar to what we saw in grade five, only this time we're looking at three-dimensional figures. Changing the complexity with multiple attributes. But some
attributes are the same. But we're going to be comparing them at most complex. We're going to look at really some comparison of dissimilar choices in the middle complexity. Or we can reduce the
amount of figures that they're showing us different attributes. But we want -- and that could be somewhere in between the middle and the most complex. Or at the very least complex, can they give us
any kind of basic attribute recognition? Something about that that makes that figure different than others.
So at the most complex, some sample student data that could lead us to possibly selecting this as a target might be identifying -- the student is already identifying some common three-dimensional
figures when the figure is present. They can count up to six because we know cubes have six sides. So perhaps that is something. Identifies two-dimensional figures by specific attributes, because
that's something that's kind of been building up across the grades. Demonstrates understanding of concepts of same and different. So we recognize, with the content being new, that some of this
skill-building might need to be embedded as we task analyze to get our students to these targets. And that's okay. That is okay. But we have to begin where the student is currently demonstrating what
they already know and can do in regard to this content.
Some instructional ideas could be to teach three-dimensional figure attributes. You would directly instruct these. You would use effective instructional strategies, errorless learning, shaping, error
correction... You would teach what a surface is. "This is a surface; this is not a surface." You can do it in the cafeteria, in your classrooms, your desks...you know, anything that you come in
contact with. Same thing with the edges where surfaces come together. Explicitly teach that so they understand what that is, and transfer it to some other 3-D objects. Use three-dimensional figures
that we know are familiar to the student. Use the background knowledge that the student is coming with. Build on that. Build on their knowledge of two-dimensional figures. "This side is like a
square." "Show me the side that looks like a square." "How many squares do you see?" Have them count them.
A way we could assess this to see -- for mastery, a way we could think about assessing is if the student, when we give them this question: which of these has only square surfaces or square flat sides?
Or square flat sides... Which one of these is made up of -- or we could say "Which one of these is made up of squares?" if we know the students' performance levels that they're coming with us
demonstrates that they know, understand what the square is. We could give them -- again, we would give them objects, not pictures. You're looking at pictures on your screen because I can't give you
3-D objects, which I wish I could; it would be so cool. But I can't but let's pretend these are 3-D objects. And I would on the table a cylinder. I would put this cube on the table and I would put a
prism. And I would ask the student which one is made up of squares?
Middle complexity...again, sample student data based upon what we looked at. Maybe they're already identifying some common familiar two-dimensional shapes. Maybe they're able to identify some common
attributes like sides.
Some instructional ideas. Again, explicitly teach. Activities are part of that explicit instruction, but we need to do some explicit instruction with errorless learning, shaping, error correction...
Teach them flat sides. "Show me flat sides." You know? Or, again, "This is a surface; this is not a surface." Have them touch things. Have them see it. Touch them around the school, around the
community... Find edges. Talk about edges...what things come together. Have students match figures that are similar. Build on their background knowledge of what you know they know about
two-dimensional objects. Could be a good place to start assessment if you're not sure what they know. You know? Put some shapes out in front of them. And good way to build towards three-dimensional
figures.
Middle complexity. Again, here's a way we can assess if we were thinking, "If the student has mastered this, what would that look like?" If I asked a student which of these has flat sides that meet at
points, or which of these has flat sides that come together...? Really shaping your language so it gets to the concrete level of what the student understands. And again, these are pictures but I
would never use pictures with students. I would always use real objects. So you could have a ball, you could have a cube or a box...something where the student could show you that.
At the least complexity level, some sample student data that might lead us to picking this as a target... You know, maybe the student's matching one common three-dimensional shape using a template to
another. Or with other conditions. Maybe they're identifying one two-dimensional figure with mastery. Or an attribute of a figure. Maybe they're imitating some matching or imitating matching
two-dimensional figures. They might even be emerging. So our task analysis might be a little bit longer getting to where we want to get with this target.
Some instructional ideas. Again, you would explicitly teach attributes such as sides and round... Have students touching them, feeling them if they can, with some part of their body. If they can't use
their hands, can they use their face or their arm or something where they can touch and feel and make -- put texture to it so it really stands out to them. So they understand that using errorless
learning, shaping, error correction, data collection to ensure that the vocabulary is understood by the students. Use figures or real objects so they're familiar to the student. Build on their
background knowledge.
So, for example -- and again, I would be using a real object here, not a picture -- which object is this shape? Or is the same as this shape? And we could put some real-life objects there in front of
them to touch and feel and put next to each other. And ensure that they understand what that is; that the attributes are aligned and remain aligned so that they can show us that they know that.
Moving along to grade eight. Grade eight geometry. Identify a rotation, reflection, or a translation of a two- or three-dimensional figure. We've talked about this one before. And we talk about this
one in trainings. It's an interesting piece of content that really has great implications for our kids. So if we think that we've already worked them through -- and over the years as we're working
with this alternate eligible content, we know students have been identifying, classifying, using attributes for two- and three-dimensional figures...now we're going to take them to a place where
they're going to manipulate these figures.
So using this content, we think about coding. So if we're going to code this piece of content, what do students need to know? Well if you said a rotation, reflection, or translation you're absolutely
correct. And what do they need to do with it? They need to identify it. And within what context? Of a two- or three-dimensional figure. So based upon what the student's current level performance and
what their data shows us, you know, we can pick or choose which one is going to most effectively help the student learn this particular concept. And still have the student be proficient with this
piece of content.
Again, step two you would determine the intent. You should find this -- and this again, thinking about the intent and when you're working within one or two or three grade levels consistently over the
years -- this is not an exercise you're going to have to do every time. It is something you are going to -- once you wrap your brain around this and once you are confident and comfortable with what
you see as the intent, this is something that's going to just be applicable throughout the years. So again, you would look and see what is it that we really want students to know? And if you look at
the anchor and the Core, it's really -- the Core standard is looking at understanding transformations.
So for determining the intent, is it to recognize and name objects regardless of position? Well, I would say recognizing and naming objects is nice. But really in the big scheme of things, being able
to say that's a triangle no matter how you look at it is good, but associating that language is not nearly as important as being able to say, "That's the same shape." Because I could still work in a
job and be able to manipulate and sort things and stack things and I can still fill a dishwasher and manipulate objects, and I might not know the names of them. But I could still do that and do it
well. So it's something to think about. Not saying that language isn't important and we should always try to scaffold that, but it also -- in the big scheme of things, we can still teach some of
these mathematical concepts using vocabulary that is much more common to the student.
So some questions about student data. If I want to decide whether or not I'm going to essentialize this. Again, I'm going to be looking at their interaction with two- and three-dimensional figures,
I'm going to be thinking about their communication -- how they take language in, how they express themselves, their imitation skills... Can they recognize two-and three-dimensional figures when given
a picture? Do they know what they are? Can I put things in front of them? Can they tell me what they are? Can they manipulate them? These are things... Can they identify attributes? Attributes...they
might be able to identify things by the way they look and the sides before they can tell you it's a square. And that is okay.
So here are some examples of what some targets could look like at the most complex. We could be identifying a rotation, reflection, or translation of a figure. Comparing transformations. And those are
all considered transformations of the same shape.
At the middle complexity we would be identifying -- we could identify rotation, reflection, or translation. We could reduce it. Somewhere in between there we might have students just maybe only a
rotation or reflection. Remember rotation is a turn-around. A reflection is a flip. A translation is a slide...push or a pull of the same object. But we would use dissimilar choices. We would
definitely reduce the complexity there as well. But you could really limit whether it's one or two or all three of those.
And at the very least complex, could they identify translation, which is a slide or a push or a pull? That this is the same shape here on this side of the table as it is if I move it over. It's still
the same.
Some sample student data that could lead us to determining this target at the most complex level. So our student is identifying familiar two- and three-dimensional figures. They're using attributes.
So not only are they classifying them and sorting them, but they can use attributes to know which is which. So they're identifying these figures when the figure is present; they can talk about them
when they're not present. Perhaps. Again, sample student data.
Some instructional ideas. Again, explicitly teach this rotation, reflection, translation. Explicitly teach a turn-around, a flip, a slide... Have the student manipulate object. Draw it to demonstrate
it. If I was teaching this class, my kids would have an object in front of them and I would be teaching -- I would model it and they would do it. Then I'd check for understanding. Then they'd do it
with a partner. And then I would have them do it, you know, by themselves. Manipulating the objects themselves. You could have, you know, the large objects, you could have small objects, you can have
2-D -- two-dimensional objects, three-dimensional objects... You know? Use multiple trials and really explicitly teach this vocabulary. Use -- definitely use the figures that are familiar to the
student. And use your errorless learning, your shaping, your error correction to scaffold understanding. I would not be giving this student workbook sheets to try to figure out if that looks the same
as that. I would have them do it. Because that's what they're going to be doing in real life. That's what's going to be meaningful.
So again, I'm just going to caution you. We're using pictures because our medium to translate with you is through this PowerPoint. However, you would definitely want to be doing this with actual
figures, actual objects in front of the student to be able to make it meaningful and generalized. And then you would be doing it with things on a shelf in the classroom. You would be doing it in the
cafeteria with, you know, silverware or whatever. You would just be definitely reinforcing it everywhere you go. And having students be able to manipulate this and make that determination.
But here's an example. You could ask where the rotation is. You know, which one of these is a rotation? Which one is a turn-around? For middle complexity -- and again, we're using 2-D objects. You
could use 3-D objects. I would be doing two- and three-D probably with the most complex level. But it would, again, depend on your student performance data.
Middle complexity. Some of the student data could include, you know, identifying common two- and three-dimensional figures when it's present. Maybe they identify some two-dimensional figures by
specific attributes. Maybe they -- they might even know one 3-D figure by specific attributes. And with all -- you know, take a look at your data. Data is going to be so important.
So instructional ideas. Teach that specific vocabulary. Definitely, you know, drill that vocabulary. Practice that vocabulary. Or the reduced vocabulary. Have students match figures if you need to.
Use manipulatives. Make it a game. Use errorless learning, shaping, and error correction.
And again, we're using 2-D, but you could use 3-D. I would have students manipulating this. So which of these is a translation (slide, push, pull) of this figure? I could have this figure out there
and I would maybe turn -- I would have a triangle there, another kind of polygon, and then... I could actually where the X is, I would have one there and I would move it over and say, "Which one did
I show you a slide?" You know? Or most definitely give the student the object or the figure and have them do it.
Least complex. Some student data. Again, basing it on what you know the student has already done.
And some instructional ideas. Again, explicitly teach two- and/or three-dimensional figures using those real-life objects, using manipulatives; use the Core words that are specific to the student.
Again, this would all be manipulatives. I would have students moving objects around, using strategies such as errorless learning, shaping, and error correction. I would -- we want students to slide,
push, pull, and understand that it's the same figure.
So which one of these shows a slide (push, pull) of this figure? So here we are. In this particular one we're going to move a couple figures. And at the very end we could use -- or we could put it
anywhere in that order and ask the student to show me, "Which one did I just push/pull?" Or again, I could ask the student to show me that translation. Just push it, pull it, slide it...to
demonstrate mastery.
So finally grade 11. Matching. Corresponding two-dimensional and three-dimensional representations. Are you seeing how this is building across the grades? Are you seeing how the repetitions of -- and
the similarities of the data we're looking at and the way that we're building the student's skills and knowledge in this conceptual realm, in order to be as independent as possible -- as they can
when they leave school. So let's take a look at grade 11, step one. We're going to determine what is it that students need to know. Two-dimensional and three-dimensional representation. So there's no
"or" in there. So we're looking for students to know both, although we can reduce the complexity within that. What do they need to do? Well, they need to match them. But here's the piece -- the
context -- that's most important when we think about reducing our complexity. Corresponding. What's that going to look like? We're excited; we're going to show you three different ways to think about
corresponding two-dimensional and three-dimensional representations.
So then we have to look at the intent. And remember in 11th grade we don't have the eligible content because we did not go from the Keystone eligible content -- the Keystone Standards and Eligible
Content for end-of-course. We went from the PA Core, so we have to look at the PA Core. And it's about analyzing. So this -- matching this corresponding is a type of analysis I would offer. So what
is the intent? Is it to know and identify shapes? Well you and I both know that as we just walked through the grades, the identifying shapes is -- while it's a part of it, it's really drawing
conclusions about what makes a shape the shape it is, is what they're really going for. Or is it to be able to connect various shapes and objects in both two and three dimensions? How do they go
together? How's that going to work for a student?
So at the -- we would have to think about student data if we're thinking about whether or not to essentialize. So again, and no surprise to you, communication first. Thinking about familiar, frequent
vocabulary, interacting with two- and three-dimensional figures, what two- and three-dimensional figures? Can they recognize the figures when given the picture? Can they manipulate them in real life?
You know? What have they seen in real life? And again, are you seeing some commonalities here with our most complex, middle complex, and least complex? Really doing some basic recognition at the
least complex level, though they're still going to be matching two-dimensional and three-dimensional. Middle complexity, we're going to have some dissimilar choices again. And at the most complex,
they're going to be -- have some given attributes.
So some sample data that could lead us to the most complex. Think about what they've learned. What have they been able to do with translation, reflection, and rotation? Because manipulating things is
going to be really important when we look at how two-dimensional and three-dimensional figures relate.
Instructional ideas. Teach your specific attributes. Flat sides, flat sides coming together...where sides connect and come together... You're going to use magazines, pictures online, common visuals,
actual objects in your classroom to make connections between the two- and three-dimensional figures.
So here's an interesting twist thinking about the most complex when you think about three-dimensional and two-dimensional figures. Now you would say Sharon, you've been using, kind of, something like
this to demonstrate three-dimensional. And I have. But I want to stretch your thinking here and I want you to think about this application for real life. If I get -- buy something -- and I have to
put it together, and I get all the pieces and I get the directions...the directions are flat. The directions are flat and sometimes -- and in this case we're giving you an example at the very most
complex -- it might have some dimensions to it because you might get a lot of pieces that look the same, but they're different dimensions. So can the student, from looking at a flat picture like
that, be able to find the corresponding piece that is three-dimensional? So you could have three objects out, only one meets the dimensions of what you're looking for in that flat, two-dimensional
model.
Middle complexity. Some sample data. So thinking about what they've learned, how are they able to translate using push, pull, or slide an object? You know, thinking about two-dimensional figures with
specific attributes; three-dimensional figures with specific attributes.
And instructional ideas that would go along with this. Build the background knowledge. Use real-life objects as students are looking at shapes that kind of match with that using errorless learning,
shaping, error correction...
So here's our idea of what it could look like at the middle complexity with a comparison of dissimilar choices. So if we provide the student a piece of square cut paper, we would ask them which figure
will the paper fit in based on its shape. And we could have three figures in front of the student and ask them to -- based upon -- again, you could use the attributes, which way is the same...? And
this would be a way for us to assess student's mastery with dissimilar choices of matching a two-dimensional model with a three-dimensional figure.
Least complex. Again, emerging imitation skills. Maybe they're imitating matching two-dimensional and three-dimensional shapes.
What are some instructional ideas? Again, you would explicitly teach using direct instruction, multiple trials, the attributes of three-dimensional figures and two-dimensional figures...raising sides.
Having students touch and feel and identify through Core trials the differences, and being able to show you that they have mastery of those pieces. Using two- and three-dimensional figures that are
familiar to the student or the student has demonstrated across the years to be familiar. Use a physical area where the student can sort these shapes. Use errorless learning, shaping, error
correction...
And here's our idea at the least complex of a student matching a two-dimensional representation to a three-dimensional figure. So if you hand the student a square box of tissues and you provide the
student with three shapes, match to the shape of the box. This could be a very challenging skill to be taught, but think about the real life application of partial participation with assembling an
item, access to potential work using templates, being able to partially participate in putting together a project or something that you're building within the house or in the work area or for
home-living... So a student could be a participant just by being able to know these shapes and participate with seeing what goes with that three-dimensional object.
So that was our tour through geometry, looking at that strand in five, seven, eight, and 11. And we hope that that was informative and gave you some information that's going to help stimulate your
thinking to even more ideas. They were samples. I'm just going to say it again: samples. And we know that there are so many other different right ways that those ideas could be done.
I want to remind you about the resources that are available to support the use of the alternate eligible content that are out on our PaTTAN website right now. If you need more information, you want to
review more information on essentialization, you want to think about how to use the alternate eligible content to write IEPs, they're all sitting out on our website. A Closer Look at Math. Different
ideas. We looked at addition and subtraction I think last year. We're trying to give you lots and lots of variety as we look through and walk you through these webinars.
Our fall/winter series, October and November are posted. So if you want to go back and review that Across the Grades View and some information about those documents, you want to take a look at the ELA
reading.
And today's webinar will be posted following today as soon as we possibly can. So take a look for it. Once it gets close-captioned we will have it up there for your review if you want to go back and
rethink through some of the pieces we talked about today. If you have questions please send them to our Alternate Assessment at pattan.net site and we will be sure to get those answers together. And
we'll put a -- if we get lots of questions, we'll put them together in a FAQ for everyone to see.
Our next webinar will be January 20, and we're going to dig a little deeper in Expectations and Intent. What is that long-term learning? And we'll take some samples of content and really, kind of,
think that through in math and ELA.
I'll remind you please, please, please if you haven't already, sign up for our Listserv. Sign up to volunteer. We are always looking for folks to help us as we think through additional examples and
get ideas of what's working in your classroom. If you -- please contact me. We'd love to have someone, like, co-present one of these webinars with us to really talk about how the application in the
classroom has been effective for students that are eligible for the alternate assessment.
In today's webinar our participants, again, we asked you to kind of -- we reviewed the steps of essentialization, but looked at some of those examples and thought about how we reduce the complexity
through those, what the students need to know, how they -- what they need to do with the know, and then within what context. So all of those pieces can be reduced in complexity to meet your student
to set targets -- challenging targets -- starting with their instructional level and moving them towards those targets.
My contact information, Dr. Machella's contact information, and Audrey Kappel at PaTTAN Pittsburgh. We're all available if you have some additional questions that you would like to send to us. If you
are interested in receiving a certificate of completion, please stay on for the code for today, and be sure to complete the questions that were included with your directions for getting onto the
webinar and accessing the handouts.
Thank you very much for your attention today and for your participation. We greatly appreciate it.
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