By Sara Finegan

I’ve written about what inclusion most definitely isn’t, and about what special education most definitely should be, and even made some comments about what special education instruction in a general education environment is supposed to look like.

That’s all well and good, if you’re looking to get a taste off of the menu that is Special Education, but it doesn’t constitute a meal, nor, more importantly, does it give you the recipes with which to create one.

What we all really want to know these days is what “Accessing Grade-Level Standards” looks like, whether it takes place in a separate classroom or in a general ed class.

Let me give it a shot, via a hypothetical set of students with IEPs.  Let’s follow this mythical cohort through the fourth and fifth grades, not because those grade levels are the most typical or constitute a more crucial pair of years than any other, but because that’s what I’ve been looking at for the last month, and unless there’s an offer of chocolate, we’re all going to look at things for the next few pages through my eyes.

The Cast of Characters

We begin with the diverse mix of students, whom we encounter at the beginning of the fourth grade:

Matt is a cheerful, restless student with mental retardation.  He knows 50 sight words, can count to 30, and likes to listen to stories.  He has limited social skills, and needs a high level of structure in order to be able to participate in any large-group activities.  Matt, who has limited verbal skills, loves to identify and label things and has an excellent memory for the names of things he’s learning about.  He can copy words and sentences, but does not construct sentences of his own without a great deal of support.  Matt is easily frustrated in a large-group environment and often disrupts class by knocking objects off desks and chewing on other students’ zippers and hoods.

Alex is a highly-functioning student with autism and ADHD.  He has difficulty with visual tracking and this, combined with his attention deficits, makes reading extremely difficult.  He reads reluctantly and is easily distracted from the text.  He has an enormous vocabulary and can dictate complex paragraphs, but the mechanics of writing is difficult for him due to dysgraphia.  Alex has excellent cognitive and reasoning skills and can apply what he’s learned across multiple subjects.  He is easily overwhelmed in large groups, needs a lot of repeated drill and small group, guided work in order to learn new skills, and needs to keep moving.  If he sits for more than five minutes, he begins to “zone out” and gets lost in his own world.

Freddy has moderate-functioning autism and mild mental retardation.  He perseverates on whatever he was watching on television while he ate breakfast.  He is anxious to please adults and, while he enjoys being with his classmates, has few friendships and doesn’t show much interest in others’ needs or likes and dislikes.  He remembers every new word he learns in his reading, and as a result, his sight words vocabulary is enormous.  His decoding skills are less strong, but he is currently reading at about the beginning second-grade level.  Fred loves to take the morning survey in class, and carries his clipboard around to each student, tabulating their responses to the day’s questions.  He can write a sentence describing the results of the survey.

Ben is an English Language learner with expressive and receptive language deficits, auditory memory deficits, and working memory deficits.  He has many friends, encourages people to do their best, but is also easily distracted and can disrupt his table by making faces, tossing paper wads, and chatting when lessons are going on.  Ben’s writing skills are very limited:  he struggles to be consistent with singulars and plurals as well as verb tenses, and uses very bland, generic vocabulary.  His thinking is not particularly organized and he jumps from topic to topic in conversation and writing.  Ben reads at the second grade level and has good literal comprehension.

Martina is the class artist.  She spends hours working on craft projects and can be found drawing and making costumes for paper dolls in her spare time.  She works extremely slowly at academic tasks, which in the past frustrated her general education teachers, and, as a result, caused her to lose confidence in her own abilities.  She reads at the third grade level and has excellent critical thinking skills.  Her writing is less strong, as she lacks organization and structure, and her spelling is poor.  Like Ben, Martina’s primary language is Spanish.  Martina takes three times as long as anyone else to complete assignments, but is thorough and methodical and neat, and rarely makes mistakes.  She excels at social studies and invariably wins the class Jeopardy! Games.

Toby is an excellent reader and thinker who lacks executive functioning skills.  His desk is a mess, his work is all over the room, he loses everything, and he forgets his homework four days out of five.   He is three grades behind in math and reads at grade level.  He rushes through most assignments and pays attention to about 45% of what is going on during instruction.  He is articulate, uses powerful vocabulary in speech and in writing, and participates actively in class discussions.

Amanda is  a very bright kiddo with a bubbly personality.  She struggles with multiple-step tasks and her working memory is extremely limited.  She has low numeracy and, despite years of work, doesn’t know what makes ten, cannot remember her multiplication facts, and cannot do grade-level math.  She reads at the third grade level and, although her spelling is atrocious, writes descriptive pieces about topics that interest her.  When it comes to narrative writing, she exhibits less skills – her tendency is to skip details and important parts of the story, leaving the reader to try to figure out what’s going on.  Amanda is very emotional and struggles with friendship skills – she prefers to play with kids who are 2-3 years younger than she is.  She has severe ADHD and medication helps a bit, but not as much as for some other kids in the class.

Sam has Asperger Syndrome (which is now considered a mild version of Autism Spectrum Disorder) and ADHD.  He also is a profoundly anxious child with limited social skills.  He is easily frustrated by academic tasks and has difficulty paying attention and understanding what is going on in class.  He loves science and sports, and will listen to anyone read stories for hours on end.  Sam needs repeated review and drill on a daily basis in order to master new skills or understand new concepts.  After 20 minutes or so in a large-group, fast-paced setting, Sam often has a melt-down, and either tantrums or cries, which causes his peers to make fun of him.

Grant has moderate-functioning autism with accompanying hyperlexia. He can decode any text but doesn’t understand much of what he reads.  He loves Sponge Bob and The Doors, and marching to his internal beat.  Grant doesn’t do well in groups or cooperative learning activities but is an excellent sight words and spelling coach.   When it comes to auditory processing, you can forget it:  Grant doesn’t process much of what he hears, but has amazing visual perceptual skills and remembers everything he sees.

These nine students can and will learn grade-level science and social studies in the fourth and fifth grades.

Fourth and Fifth Grade Science and Social Studies Standards:

Minerals

In California, fourth grade science includes a unit on Magnets and Electricity, one on Rocks and Minerals, and one on Biomes and the Food Chain.  Social Studies focuses on the history of California.  Fifth grade science involves learning about the human circulatory, digestive and respiratory systems, water and the water cycle and the weather.   In Social Studies, students learn about American history, from the Meso-American civilizations to just before the Civil War.

Whether the kids are in a Special Day Class or mainstreamed into a general education class, they will need differentiated instruction and assignments.  This is what the fourth grade science class might look like:

Rocks, Minerals  and Erosion Unit:

Types of Rock:

• The entire class sings the Rock Cycle Song every day at least once.  The lyrics, sung to the tune of “Row, Row, Row Your Boat”, provide an excellent way of memorizing the facts about Sedimentary, Igneous and Metamorphic rocks.
• All of the kids have the opportunity to work on three hands-on projects:  Make your Own Sediment; Sedimentary Rock In A Bottle; and  Make a Metamorphic Rock.
• Matt, Freddy and Sam read easy-reader books such as “Rocks”, and “Crystals”.  Grant, Alex, and Ben participate in a guided reading group to read “The Rock Family” and “Digging for Dinosaurs.”   All of them gather with the class for a read-aloud of “Dinosaur Hunters” and Martina and Toby serve as table leaders when the class discusses fossils.
• The teacher has prepared two sets of sorting cards with photos of different kinds of rocks (limestone, sandstone, slate, agate, quartz, etc) and cards with the names of rocks.  Every day, kids get together with a partner to match the words to the photos, or to use the cards for a Memory game.  Students use a classroom chart or, in the case of Toby, Ben, Alex, Martina, Amanda and Grant, their “rocks and minerals journal” in which they’ve filled in graphic organizers about different types of rocks and minerals.
  

  Sorting cards

• Freddy, Sam, and Matt like to take the teacher’s collection of small rocks and minerals and sort them, putting them in labeled squares on a 3×3 piece of wood.   Amanda and Martina and Toby often supervise, prompting the three boys to speak in complete sentences about at least three of the rocks they sort.  (ex: “This is a piece of quartz.  It is pink.”;  “Sandstone is a sedimentary rock.”)
• Matt, Sam and Freddy complete a sequencing activity based on the text “A Rock Collection”, which the teacher has copied, cut up, and laminated.  After listening to a peer or an aide read the story, they work independently or together to put the story parts in the proper order.  In the meantime, Martina, Amanda and Toby, having read the story, write a summary of it.  Alex and Ben also write a summary, but they use a word list provided by the teacher and a sentence starter for each paragraph.

Erosion and Changes to the Earth’s Surface

• All of the students listen to several read-alouds by the teacher using picture books about glaciers, volcanos, and earthquakes.
• Freddy and Sam sit with an aide and read “After the Flood” together.  The aide helps them make a list of things that floods and water do to the earth’s surface.
• The kids watch a short film about the San Francisco Earthquake.  A peer or aide reads from the textbook to the kids about earthquakes and the earth’s surface.  The higher level kids work in partners to answer questions from the textbook, while the lower level kids start working on sorting cards and sight words using the vocabulary for the unit.
• Matt, Freddy, and Sam read about what to do in an earthquake.  They work with an aide to make posters to display in the classroom telling people what to do.
• The kids watch a short film about the Grand Canyon.  The higher level kids create a thinking map in their journals about what they learned about water and wind erosion.  The lower level kids get coloring pages about the Grand Canyon to color and, when they’re done, write a sentence about each picture at the bottom.
• The higher level kids complete a cloze activity about glaciers.  All of the kids work on daily review activities, identifying types of events and weather that affect the earth’s surface and whether they are fast or slow influences.
• After a mini-lesson about how water affects the Earth’s surface (weathering, transport, and deposition), the kids participate in a variety of activities in which they identify which part of the process pertains to a photo or event.
• All of the kids do a culminating report on either volcanos, wind and water erosion, glaciers, or earthquakes.
  • The higher level kids work in small groups to complete graphic organizers as a pre-writing activity, and then, once they’ve completed their first drafts, participate in editing and revising activities using a class-generated rubric.  They are expected to type their reports on the computer and use spell check and  any other aids such as a thesaurus and grammar check, if available.
  • The lower level kids use templates which pictures to identify and sentence starters about each of the different things they’ve learned.  All but Matt are expected to write one general statement and give 2 supporting details for each fact about their topic.  Matt gets a set of labels on which the teacher has typed vocabulary words for his topic and he sticks them underneath the pictures on his graphic organizer template.

accessing grade-level · ADHD · autism · decoding · differentiated instruction · dysgraphia · executive functioning · expressive language · grade-level standards · hyperlexia · Inclusion · low numeracy · modifications · receptive language · science · social studies · sorting cards · standards · vocabulary

By Sara Finegan

         An inordinate number of kids are growing up without learning their multiplication facts.  Some of this is due to the prevalent use of calculators.  Some is due to the fact that there’s been an overall rejection of rote learning – throwing the baby out with the bathwater, in this case, I think.  Some of it is due to low numeracy as a result of math disabilities. 

         Many kids with learning disabilities really struggle with numbers and their values.  And, I think, it also has to do with processing memory and retention of information that isn’t used on a regular basis.

         I think there’s a place for rote learning of math facts in a demanding classroom.   The only way to learn multiplication facts and what happens when you add ten to a number is to recite them over and over in some way or another. 

         The way I use is skip-counting.  Skip-counting can be done starting at any age, and should continue to be done if not daily, then at least several times a week once the kids know the routine.

 I cannot stress enough the importance of visual cuing when it comes to math.  In this case, a giant number line, or individual number lines to 100 for each student are  in order.  You can also use individual multiplication charts or a giant one; the point is that the kids have to have the numbers 1-100 in front of them when they are skip-counting, at least during the first few months.

           A lot of teachers practice skip-counting with their students through 3, 4, and 5 multiplication facts, and then stop.  As a result, many kids know their multiplication facts through five, and can’t go higher.  Don’t let this happen.

         It can be a part of your daily routine to start with 3, and have the kids skip-count to 60.  Move to 4, then 5, and 6.  Once they know those, move to 7 and 8.  Practice them religiously.  I like to point at the numbers on a chart or number line with a pointer or a yardstick at first, but later it becomes a favorite reward for a student to be allowed to stand at the front of the class and cue the numbers. 

         It doesn’t take long for kids to internalize the facts as they continue to skip-count regularly.  But here’s the deal:  You can’t stop here. 

         One mistake I’ve seen over and over again is special educators working on skip-counting with their students and then never extending the skill into actual math problems.  And when I say “actual math problems,” I don’t mean a standard multiplication worksheet.  I mean math problems that require critical thinking.

         There’s no point in rote learning unless the information learned by rote is applied in complex situations.  Skip-counting alone, in a vacuum, has little meaning.  We need our students to be able to use the math facts to solve word problems, to reason through division problems, to figure out the value of x, and to  calculate prices and amounts. 

          So teach the multiplication facts by rote, but then require your students to use them, and use them in a variety of ways.  Only in this way will they truly be learning.

          In a demanding classroom, rote memorization has a place in supporting mastery of facts to be used in deeper-level situations.

critical thinking · demanding classroom · high expectations · learning disabilities · learning disabled · low numeracy · mastery · math fluency · math language · multiplication · Nimble with Numbers · processing · rigor · rigorous instruction · rote learning · skip counting · special education · standards · visual cuing

By Sara Finegan

         If we knew as much about math disabilities as we do about reading disabilities, we’d be in far better shape in this country. Great Britain, Australia, and New Zealand educators and researchers have been exploring all aspects of difficulty with numbers for a long time. I don’t notice a whole lot of interest among American researchers, and as a result, we are unfocused and less-than experts when it comes to math instruction in the special ed classroom.

          I’m the first to admit that I don’t know a lot, and that I am slow to educate myself. This is probably because I wasn’t much good with math myself as a student, and I still have the residue of my frustration and insecurity flowing through my veins.

         Still, I’ve come to actually like teaching math, and have lately been having more success than failure in developing strategies that work in my classroom. In my school district, kids take benchmark assessments every 6-8 weeks in math to ascertain their progress and status with regard to the standards.

         For the first time last year, most of my students scored at Basic level or above after the first math benchmark exam.  We also made our way all the way through the fourth and fifth grade math standards – in our own time, and in our own way.  This year, 12 of 14 of my students are in general education math at their own grade level.  I’m not sure yet how well it’s working, but at least we’re giving it a try.

My two mentors. 

         I owe pretty much everything about my approach to math to two skilled colleagues. 

          Greg Roy, the sixth grade teacher at the elementary school that has been my home away from home for the last five years, introduced me to “friendly numbers” and “decomposing big numbers” and base tens. Leading our staff development in math, he taught me how to think about numbers and operations in a new way.

          He continues to give me simple explanations for concepts that seem too complicated for me to teach. And he trusts me enough now to have handed over half of the sixth grade general education class to me for math this year.

         Leatrice Roberts was for many years a District Math Resource Teacher in San Diego Unified School District until budget cuts eliminated her position. She’s now in her own classroom and doesn’t have as much time to help guide my thinking about math, but I can always reach her by email. And before the financial meltdown forced our district to wipe out the entire math department, she spent hours in my classroom learning about learning disabilities and brainstorming with me about ways to teach new concepts and skills.

         If not for Leatrice, I would not have overcome my fear of teaching kids about decimals: she walked in and did a one-hour lesson that opened up all of the doors for us and jump-started a comprehensive unit in which the kids became inspired by math.

Just another brick in the wall.

         I envision (and I’m sure this is not an original train of thought here) math as a long brick wall. (when I was in school, I think I bruised my head on it more times than not). Each brick is an important skill. The more loose or missing bricks we have, the more unsteady the wall. Most students in Special Day Classes are missing a lot of bricks, and the ones that are in place are precarious, at best.

 So what are these bricks?

         The bottom row is all about math facts.

• Knowing what makes ten and what ten minus any number is.
• Knowing what makes twenty and what twenty minus any number is.
• Knowing what makes one hundred.
• Multiplication facts.

         Math facts fit into an area of math reasoning called numeracy, which has to do with understanding the value , use, and place of numbers.

         Low numeracy is a highly-prevalent math disability that is pretty much unspoken in the U.S. In England, they know all about it and are developing ways to help kids and adults with coping strategies.

         We don’t really know why so many people don’t grasp the basic math facts. And it really doesn’t matter why, now, does it? What’s important is how we teach those facts or, if a student cannot internalize them, what strategies we can teach him or her to use to move on: what mortar, so to speak can we use to strengthen this level of the math wall?

         Another row of the brick wall has to be the language of math. There’s a whole vocabulary of math that one must know in order to be able to do things like set up a numerical equation from a word problem, or just figure out what a word problem is asking.

         This vocabulary is part of math reasoning, and you can bet that math reasoning is yet another skill set that is tenuous, at best, in kids with learning disabilities.  I’m just starting to explore the language of math. Well, not the language itself, but how to blend it into my instruction and get my students to embed it in their skill sets.

         Part of the reason that understanding the language of math is important is that it helps us to visualize what’s going on in a problem and grasp what the question is all about. Consider this word problem:

Ms. Finegan bought 92 Halloween pencils – the kind with sparkly purple and orange ghosts on them, and erasers in the shape of skulls. She wants to share them equally with her 18 students. How many will each student receive?

         If you don’t know that the words “share equally” mean that each student is going to get the same number of pencils, you aren’t going to be able to draw a picture or diagram of the problem, which I think is really important, though not crucial, to developing math reasoning.

         And if you don’t know that “share equally” implies division, you, like most of my students last year, you aren’t going to have the foggiest idea how to proceed with this problem whether you can draw or not.

         So many of our students not only don’t know the basic math vocabulary but have receptive and/or expressive language disorders that sometimes math instruction seems incredibly daunting. It’s much easier to throw a worksheet in front of students and teach them the rote solving strategies we learned growing up than it is to force the language through the lesson, to talk and talk, and model, model, model. But it’s that talking and talking that is going to develop math students.

For my next few posts about math instruction, I’m going to focus on these basic numeracy skills. We’ll move on to higher-level reasoning later in the year.

demanding classroom · high expectations · learning disabled · low numeracy · math disabilities · math language · number sense · rigor · rigorous instruction · special education · standards