My six-year-old son, SA, loves math and does very well with it. My joy and challenge as a homeschool mom has always been not to kill that love of math, but to nurture it and help it grow. We are currently working through second grade math using a program that emphasizes mastery of mathematical concepts. We supplement with a variety of math activities and games. We are moving along smoothly and steadily, but at the back of my mind I'm always wondering...is he being challenged enough? He never seems to find any of it hard. I believe that part of the value of learning math is learning persistence and stick-to-itiveness through problems that seem hard at first, but become clear as you work away at them. SA is not really having that experience, and I'm not sure how much it matters. (Don't be envious of me if your children don't like math. We all have our own challenges and our own joys in homeschooling, don't we? And clearly I'm still finding something to worry about...)When I first saw the opportunity to use and review A+ Interactive Math Adaptive Placement Test and Individualized Lesson Plan, an idea began to form in my mind. This combination of mini tests and lesson plans at specific grade levels promised to "identify and close" gaps in math learning within an intensive three-month period. What if we could just zip through second grade math, skipping the parts that SA already knew, and focusing on what still needed to be learned? Then we would just pick up and start third grade math at the beginning of next school year, and maybe, just maybe, he would finally be challenged.
That was the theory.
In practice, it didn't quite work out the way I hoped it would...
What are the Adaptive Placement Test and Individualized Lesson Plan?
The Adaptive Placement Test and Individualized Lesson plan are offered by A+ Interactive Math as a three-month online subscription for up to ten students. You choose the grade level to test your children at (usually the grade level they've just completed), and they then take a series of mini tests. If they pass the tests, great, they're at grade level. For any tests they don't pass, students can go on and follow an individualized lesson plan which teaches the concepts they missed. Students can also practice with online worksheets.Then, when they're ready, they can retake the tests.How did we use the Adaptive Placement Test and Individualized Lesson Plan?
Left to Right, or Right to Left? The Direction Problem
The problem was one that would be an issue with any math done on the computer rather than on paper. Typically, addition problems are solved from right to left. First, you figure out the ones, you carry any tens, you add the tens, you carry the hundreds, then add the hundreds, etc. The problem is, data is entered into a computer from left to right. First you enter the hundreds, then the tens, then the ones. So when a young child confronts an addition problem (especially one that involves carrying) on the computer, they can do one of two things:
1. Write it down, figure it out on paper, then enter the answer into the computer. (And I ask...If we're going to write it all out on paper, what is the benefit of doing math on the computer, anyway?)
2. Figure out the ones in your head, hold that number in your mind, carry the tens and add them, hold that number in your mind, carry the hundreds and add the hundreds. Type in the hundreds. Type in the tens (if you remember, otherwise figure them out again). Type in the ones (again, if you remember, otherwise figure them out again.).
Obviously, either option has more opportunity for error than figuring out addition problems on a math worksheet, whether during transcription, or whether during the "holding it in your mind" stage.
My son (whose fine motor skills are admittedly slightly delayed...he prints neatly, but not with grace and ease yet) will always choose option #2 if he can. Add to this the fact that the Adaptive Placement Test saves all your previous answers and they pop up when you start typing (for example, if you had a previous answer that was 255, and the current answer is 241, the number 255 will pop up as soon as you type in the 2), and it was no wonder he was making mistakes. (It was quite amazing to me that he was getting so many right, actually!)
Of greater concern to me is the fact that solving problems backwards in this convoluted way becomes a habit if it is done regularly. I don't want that to happen, and so I'm giving serious consideration to never doing math on the computer (at least in this early elementary stage) unless a program has addressed this issue in some way.
In any case, I made sure SA had a pencil and paper the next time he took the test and insisted he write things down if they were at all complicated. He still chose to write very little down, but passed the test.
The Individualized Lesson Plan
Next, SA went on to the subtraction mini-test, and failed it. I realized that a similar thing could have happened, but thought I'd sit beside him on his second attempt just to make sure. It turned out he did have a gap in his understanding. He was having trouble with borrowing when there was a "0" in the tens place.
The next day, we opened up the Individualized Lesson Plan. I was a bit surprised to see a whole series of nineteen lessons on subtraction waiting for us, but realized that this might be helpful for some since a lot of the knowledge builds on previous knowledge. The trouble was, we had a very hard time finding the particular lesson we needed...the one that specifically addressed borrowing when there is zero to borrow from in the tens place. We watched several lessons trying to find it. SA did not enjoy this at all, since he is a child that really dislikes too much explanation when he already understands something. Finally, we gave up for the day. We did find it on a later day. It was the third question in the second-last lesson offered. By then I had already explained it myself to SA.Based on this experience, I felt that the Individualized Lesson Plan was not individualized enough. It was individualized in a broad sense...if a student failed a mini test on subtraction, that student got access to all the lessons on subtraction. I would have liked to see lessons highlighted that dealt with the specific issues the student had within the mini test.
The Terminology Problem
By this time, I'd learned my lesson. I sat with SA while he did the tests from then on so I could assess myself where his gaps were. There were several instances where SA simply did not understand the terminology in the questions. For example, in the Elementary Algebra test there was a question that asked, "What is the common ratio in this number pattern? 1, 2, 4, 8, 16" Once I told him what "common ratio" meant, he figured out the answer immediately. This problem actually came up quite a bit, so I know I need to work on making sure he knows the proper terminology of what he's doing. At the same time, I think terminology is less important than understanding the concepts and being able to solve problems. (I am reminded of a math program I went through when I was a child that had me do a lot of labeling of math problems with the proper terms: a subtraction problem would be labeled minuend, subtrahend, difference. I still don't know why that was considered so important...)
What We Enjoyed
I asked SA if he enjoyed anything about the Adaptive Placement Test and Interactive Lesson Plan. He mentioned three things. He really enjoyed the Elementary Algebra mini test, because the problems were of the sort he likes to figure out. He also liked the Progress Report (and indeed, I found him looking at it quite often.). Finally, he liked the Interactive Q&A in the lesson plan. (I think this had to do with a frog that hops across the screen to collect your answer.)Did the Adaptive Placement Test and Individualized Lesson Plan Work for us?
The answer is...sort of. It worked when I sat next to him and assessed for myself where he had gaps. It didn't work the way I envisioned, and I think perhaps it would work better for older grades than younger grades. I can also see it being useful if a parent is beginning to homeschool and has no idea where their child is at in math. Even in that case, I think parents should sit with their children (or review their answers afterwards, which is also possible with this program), clarifying why they got the answers they did and getting a clear picture of where the child's gaps really are.We did not complete all the tests, and now that our review period is over, we will not be continuing with it. I also should mention here that the quality of the website was not excellent, and that may have helped to undermine my confidence in the program as a whole. There were numerous minor glitches in the programming. SA figured out pretty quickly that pressing the enter key restarted the timer if he was running out of time on a question. Occasionally the review of a test would not accurately reflect what had been done (saying a problem had not been attempted, for example), though the final score would be correct. I saw several spelling errors and typos ("litter" instead of "liter", for one...though of course as a Canadian I would have liked "litre" even better. *smile*).
And my original idea? The one about moving quickly through second grade? I've thought more about it, and realized that if SA has mastered a concept, we can move on. We are free to skip problems in his regular math book if he doesn't need all the practice. We can move on to concepts he doesn't understand yet and work through them instead. That's something I should have known all along. Now I've thought it through and decided to do it, so that's one good thing that's come out of reviewing A+ Interactive Math.
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