November 11, 2013

Third Grade Math

In this previous post, I gave a brief overview of A+ Interactive Math.  At that point, I hadn't yet successfully installed it, so here's what's going on now!

I was not able to get the software installed on my Mac, even in Parallels, so I put it on the old Windows laptop that's been kid-abused.  It works just find on that one.  (There is an online option, as well that I plan to use for fourth grade.)

A+ exam 3; Addition table to help him out
As  my readers know, we follow the Charlotte Mason method's in our homeschool, so this time I'm going to discuss how this program can be used in a CM way.  AO has created a new topical CM Series, making it easy to research by subject - here is Math & Arithemetic!  So very handy.  The first quote that strikes me is the first sentence.
Of all the subjects a young child learns, the most important one might be arithmetic. It's not so much that he needs to be able to add that makes it important, but using the skills he needs to come up with the sum has a beneficial part in the rest of his education.                     -Vol 1 p. 254
Then the following paragraph begins with
We don't need to say how arithmetic has practical value for everyone, no matter what their station in life. But arithmetic's practical value is the least of its benefits.
Hmmm.  These thoughts do not often occur in modern public education, do they? I always thought of math as a mostly practical skill, like using a hammer.  As I read more CM, however, I can see what she means - math is a brain exercise, useful for learning to problem solve and logical thinking.  For those with a biblical worldview, math is yet another subject that points us to God.
Children should approach math from the perspective of that unalterable law. They should understand how impressive it was when Euclid said that two and two equals three or five is an absurd possibility, as absurd as a man claiming that, on his tree, apples fell upwards. It's absurd to think that apples would break the law of gravity. Figures and abstract lines work just like an apple falling. They are confined to an unchangeable law. -vol 6 p 152

Adding and multiplying with marshmallow manipulatives
A+ is computer-based, but has many printable worksheets and exams.  When I was a kid, I would have loved this!  My son, though, does not.  He likes the computer interaction, but not the worksheets.  Except on days he likes the worksheets better.  Yeah, its like that around here. :)  So, I find that mixing it up and following his lead works well for him.

We do a couple lessons on the PC one day, then some worksheets to review the next day.  About one day per week, I forgo A+ completely and use Graded Work in Arithmetic (free online, a book for each grade), which is a lot of math facts and oral work, and old-fashioned word problems.  (I think GWA is more CM, but we hit a wall there sometimes, too.)  For us, variety in math is important, so that when he gets stuck one place, I just move away from it for a while and change the focus, even moving back to 1st grade workbooks to build confidence when necessary.
The main value of arithmetic and higher math is the way it trains reasoning powers, habits of understanding, quickness, accuracy, and being truthful intellectually.  -vol 1 
In the younger grades, CM recommends using many manipulatives (household objects to count and add with), so that the child has concrete understanding before moving on to using symbols.  Questions should be asked orally and worked out physically until the basics are mastered.  She gives examples of word problems that make the child work through the correct processes in order to get the answer.
Now the child is ready for more challenging word problems, such as 'A boy has two baskets of ten apples. How many bags of four can he make?' He'll be able to work with a bigger variety of numbers, like 7+5-3. If he needs the beans, let him use them. But he should be encouraged to use imaginary beans as a way to get him closer to working with abstract numbers.  -vol 1

I think A+ fails at this.  It aims for the child to learn the appropriate definition of addition, multiplication, etc., and the practical application - ie, system - to determine the answers.  Its a straight-line, follow the rules and you'll get the right answer sort of program.  It teaches the process but doesn't make him think about which process to least not at this point in the curriculum.

In order to make A+ "fit" us, I don't print out all the worksheets.  In fact, I only print 1 or 2 of the 4-5 pages per lesson, and sometimes don't print any at all.  I do like that there are only 4-6 questions after each lesson on the computer - if he struggles, then I know to print out something for the next day to work with him on.
Problems should be chosen carefully. They should be easy enough for him to do, but challenging enough to require a little mental effort. -vol 1
Some second grade work
On the other hand, Graded Work in Arithmetic really does make one think.  There are a lot of oral questions - every other lesson is done aloud.  There are word problems at least every 5 lessons.  He still has trouble with them. Determining the correct process is really tough for him, even though we've done manipulatives, oral work, and word problems for so long.  Could be this...
No other single subject benefits as much from good teaching as arithmetic, and no other subject results in such damaging results if it's taught wrong.  -vol 1 in, teacher error.  Hopefully, we have plenty of time to fix this problem!  I believe, like reading, there will be times when intellectual leaps will happen, regardless of the teaching time-table.  So, we'll keep plugging along, using GWA and A+ in tandem for the foreseeable future.  I don't want to be a curriculum hopper, especially in math, where future skills are built upon all the previous skills.

I do believe, after reading a bit more CM and writing this post, that we need to go back to "counting beans" for awhile before coming back to "imaginary beans"and A+ Interactive.

This post was submitted to the Charlotte Mason Blog Carnival!  Hosted this week at Aut2BHomeinCarolina.