Curriculum in the Homeschool: What We Have Used for Our APD Daughter for Mathematics

So this post is a day later than I had planned, but I finally have time to sit down and write it.

Mathematics is one of those things that I have found people think about in very different ways.  It sometimes amazes me the way that people can solve a mathematics problem in a way that seems so bizarre to me, but it works.  The reason is because our brains don't all solve problems the same way.  Therefore, I find that mathematics must allow for each child to discover what way works best for his/her brain.

Also remember that  children with APD (auditory processing disorder) need to have visuals and/or kinesthetics to help due to the difficulties with auditory processing.

So keeping all this in mind, I have been very eclectic with mathematics.  All of my children think differently about it and solve problems in their own ways.  My sweet girl Hailey (who has APD)  is very visual and so conceptualizes as well as solves the problems really by picturing things in her mind. For this reason, we have done a lot of hands-on, real world learning with mathematics as well as used manipulatives and pictures.

The Early Years:
When Hailey was a little one, we played with math like we would play anything else.  We counted objects and we shared by dividing up our spoils.  We bought enough apples for each family member by counting.  We found out we are the second house on our block.  We subtracted how many cookies we ate from the total we had to find out how many we had left.  We would cook together and get 1 cup of milk or 1/2 cup of milk.  You get the point; we just incorporated mathematical thinking and language into everyday life and made it fun.

I also liked to read aloud mathematics stories like Measuring Penny and 12 Ways to Get to 11. There are a ton of great story books that introduce math concepts and really get kids interested in trying to "do math".  Hailey's twin brother absolutely adored books about money!

Introducing Numerals and Paper Problems:
At some point, we started writing the numbers down on paper and making written math problems. We used the objects we were adding and wrote them down so there was a one-to-one correspondence with the manipulative (what we were adding) with the numeral associated with it.

Sometimes I would write them as a problem like 2+3=5 and sometimes I would write them on a number line.  Othertimes we would draw them as pictures or stick figures.  This way, the kids would have seen a variety of ways to write it.

Having the Child Solve a Written Problem:
After having done the above for many times, then I would ask my sweetie to solve a problem by giving her the written problem.  She would have access to objects, which was her preferred method at first. Then later, I would not have the objects out and she would have to decide what way she could do it without the objects.  This generally led to using her fingers as objects.   Her fingers then didn't become an obstacle until she got to numbers higher than ten and she needed to implement other ideas.  As she would get stuck, I would show her options like the number line, counting up, counting down, drawing pictures, drawing stick figures, etc. I would only show one at a time to see if that made sense to her.  If it did, then great.  If not, then I'd try another one.  However, if I had to do more than two, then she was frustrated and it was time to stop and try again another day.

Introducing New Concepts:
As we were doing mathematics for everyday living all the time, new concepts were usually not completely new.  So when I wanted to add them to her written abilities - mathematics on paper - I would reintroduce it as "remember when we.......(ex. baked the cake and had to measure 1/2 a cup)". Then we would discuss what 1/2 meant or whatever the new concept was.

I would always be sure to have visuals and manipulatives as needed.  So for fractions, for example, we would have measuring cups and spoons; we would have something to cut into equal pieces; we used fraction blocks (a plastic manipulative you can buy); we drew pictures (half the people are wearing hats).

I always taught Hailey the concept and its practical use before how to solve any problems.  This is the way her brain best stores information: she needs the "why is this important and how does it all make sense" first.

Then she could start to solve problems both in real life and on paper.

Don't Make it Hard or Complicated:
Mathematics can be easy and it is best served in small chunks.  I never spent too much time working any mathematics problems or concepts. If it started to become frustrating and we couldn't fix the frustration quickly, then we stopped and did something else.  We could always go back to it another day.

My biggest concern was that Hailey would get frustrated with math and then decide she wasn't good at it and just shut down.  I did not want that to happen, so I made sure to make the steps small enough for her to always feel successful.  I really felt there was no rush to learn anything at any particular time and her perception of her skills was more important than any race to do things quickly.

The Workbooks We Used:
Mostly I made up my own mathematics curriculum and used the state mathematics as a guideline to make sure I covered everything she needed (but not at the time frame set by the state - at her pace).

I did use workbooks as ready made problems to solve as she got a little older.  We also did some Time 4 Learning, but she found she liked the workbooks better.  Here are some I liked:

School Zone Publishing Company Math Basics:  These are organized by grade level and you can see how the skills are repeated but with a little more added to each year.  I tended to use them without regard for the grade level.  So I might do a multiplying fractions unit and use the Grade 4 to introduce them and then do Grade 5 and Grade 6 the next few days.

Educators Publishing Service Attack Math:  These are books all about addition, subtraction, multiplication, and division. They are the basic skills only, but worked well for repetitive practice.

Educators Publishing Service It's Elementary! 275 Math Word Problems: This is workbook filled with word problems.

Singapore Math Practice:  These are something that I just found this year and she has been doing well in them.  She is technically a 7th grader and she is currently working in the 7th grade level workbook.  I decided to mix up the flow of this workbook as it makes more sense to me to do the geometry sections all together and since we haven't done as much geometry before, I am saving them for last.

Algebra:
Hailey has not taken algebra yet, but she did do an app on her iPad that really taught her a lot about solving algebraic equations.  The app is called DragonBox and the basis is that whatever you do to one side of the equation, you have to do to the other side as well.  The point is to solve for x.

After completing the app, I gave Hailey some paper algebra equations and she could do the problems easily.  So I guess it worked.

In her Singapore Math workbook this year, there is a small algebra section but it is even simpler in that they give you a value for x.  However, the writing algebraic expressions from word problems was tricky.

So Hailey and my plan is for her to take algebra next year. (Remember she wants to take community college courses as a high schooler, so she is wanting to get prepared for that.) We probably will use the homeschool classes that she is enjoying this year as they have an algebra class.  However, if they go about it in a way that makes it seem complicated (as sometimes classes and people make math more complicated than it needs to be), then I'll take her out and do it with her at home.

Perseverance, My Daughter with APD, and Her Latest Goal

"Perseverance: steady persistance in a course of action, a purpose, a state, etc., especially in spite of difficulties, obstacles, or discouragement." http://dictionary.reference.com/browse/perseverance

I love this definition of perseverance from FreeDictionary.com and it totally describes the go-getter, never-let-anything-get-in-the-way nature of my sweet Hailey.  I don't know if it is her auditory processing disorder which has made life so much more difficult for her or just her nature as she is, but Hailey has always persevered.

Recently Hailey (who is 12 1/2 years old at the moment) has decided that rather than being an artist for a living or opening a bakery or any of the other thoughts she has had about a future career, she will be an occupational therapist.  She wants to help children who have disabilities or special needs and she is particularly interested in working with sensory processing disorder.

If you knew Hailey, you would know that she doesn't just decide something, but she makes a commitment to her decisions!  She insisted that we immediately find out all we could about occupational therapists and exactly what she has to do to become one.  So we found out that one of our local community colleges has an associates program in occupational therapy and the college accepts students as young as 14 years old (although perhaps not in the associates program per se). Yup! You guessed it; Hailey wants to go when she is 14.

So she made the decision, found out the path is to go to the community college (and later to a university for her masters degree), and has decided her current plan of action.  She wants to take a few classes at a local homeschool co-op in order to get comfortable being in a class; put a large emphasis on improving her writing skills; learn higher level math (we're going to try pre-algebra); and learn sign language. These are all her goals that she came up with! She told me that she wants to be sure the community college will accept her at age 14 as someone capable of taking their classes.

She really does put a lot of pressure on herself and so I try to be supportive and yet help her to realize that she doesn't have to accomplish everything right away and she doesn't have to go to college at 14 years old. (My plan is for one class at a time at the community college, but she insists she will handle two at a time.) Yes, she is determined!  As she put it to me, "I want to DO something with my life and I'm tired of waiting!" (Hmm.... this makes me wonder about our society's lack of opportunities for teens to do more.)

Anyway, I have no idea if she will go to the community college at 14; we'll have to wait and see. What I do know is that she has perseverance and she will accomplish all she sets out to accomplish in life, or change her mind along the way and set her sights on new goals as she sees fit and then accomplish those.

So what do you think?  Has APD made you or your child more perseverant?

How Mathematics are More Difficult For My Child with Dyslexia, APD, and VPD

It may be obvious how reading would be more difficult for a child with Dyslexia, Auditory Processing Disorder, and Visual Processing Disorder but have you ever thought about mathematics?  There are four areas of difficulty when doing mathematics that my child has to pay extra special attention to. 

1. Word problems:  The most obvious way Dyslexia, APD, and VPD trip up a child when doing mathematics is in the word problems.  Whether they are written or spoken problems, the child has to read or listen to them correctly and understand them correctly in order to know what to do. 
2. Reading the numbers:  People don’t think about the fact that written numerals are a language in which specific notations represent a specific number.  A child with Dyslexia, APD, and VPD can read the numerals incorrectly; 26 may appear as 62 or 56.  If a number is read incorrectly, how can the correct answer be found?  Also, if a number in a sequence is skipped, again the answer will be wrong.
3. Writing the numbers:  Just like reading the numbers, the Dyslexic, APD, and VPD child may write the numeral incorrectly; 26 may be written as 62 or 56. (This one is a common difficulty for my child and she has to pay extra attention to whether or not she is writing the correct numerals in the correct place.) If the wrong number is written or written in the wrong place, the answer will not be correct.
4. Remembering how to compute correctly:  The child who has short term memory problems (common to Auditory Processing Disorder) will have difficulty remembering how to do something until it is finally stored in the long term memory. This is especially true for multi-step processes that are common in mathematics.  Therefore if how to multiply multiple digits was taught yesterday, and even though the child managed to do it correctly yesterday, does not mean the child will remember how to do it today.

Knowing that these four aspects to mathematics may be a problem for a child with Dyslexia, Auditory Processing Disorder, and Visual Processing Disorder, what can be done?

1. Give more time:  The biggest help for a child with APD, VPD and Dyslexia in doing mathematics is to have more time to do each problem.  With more time, the child can carefully reread problems and numbers to make sure he or she is reading, interpreting, and writing correctly.
2. Reteach concepts and practice consistently:  Do not assume just because the skill was mastered yesterday that it will even be remembered today.  Reteach the skill without condemning the child for not remembering.  Reteach the skill until the child does not need to be retaught anymore.  It will happen; the skill will eventually reach the long term memory and the child will be able to do it without help and reteaching one day.  Be patient.
3. Use visuals and/or kinesthetics when teaching mathematical concepts and skills: Children with Auditory Processing Disorder have poorer auditory processing skills and are usually much stronger with visuals and kinesthetics. (My dauthter's VPD is very mild and pretty much limited to letters and numerals.  We have used a lot of drawings, hands on work with objects, Cuisenaire rods, place value blocks, and movement when she was younger for things like basic addition.)
4.  Teach in small chunks:  Smaller pieces of information will be better retained by the short term/working memory and thereby be more usable to the child.  Too much information will simply be overwhelming.  

Given the right circumstances and the time to learn mathematics, my daughter has proven that she is very capable of doing well.  She can grasp the concepts, memorize the processes over time, and use mathematics in her every day life.

* For more information on how to help children with short term memory difficulties, visit the National Center for Learning Disabilities: http://www.ncld.org/types-learning-disabilities/executive-function-disorders/how-to-help-child-with-weak-working-memory

* Here is an article by the Yale Center for Dyslexia and Creativity about Math Struggles:  http://dyslexia.yale.edu/math.html

* Here is a really inclusive article about dyslexia and mathematics from Dyslexia Scotland via Oban High School:: http://www.obanhigh.argyll-bute.sch.uk/Websites/SchSecObanHigh/UserFiles/File/dyslexia%20materials/3_9_19HelpWithMaths.pdf

Personal Notes and Feelings About this Piece:

Since I cannot pinpoint exactly which one of her diagnoses (APD, Dyslexia, or VPD) is the culprit of these problems, I have decided to include them all.

I also have to put in a caveat here that my daughter does have short term memory problems for things like language and mathematics yet her short term memory for things like pictures, feelings, physical movements, and events is incredibly strong.  She has also grown very strong at quickly memorizing the spellings of words via her understanding of phonics and utilization of chunking common spelling patterns.   I suppose all this tells me is that each child is unique and the definitions cannot apply straight across the board and/or she has learned compensatory strategies for some things.