Trying to Make it Stick

Math was causing a lot of stress in our home this week.  Last year I struggled to find a good fit for JT when it came to math instruction.  Around February, I made the decision to move him into something less structured for a bit.  That seemed to allow him time to renew an interest in math again.  Before I made the plan for his math for this school year, I asked for his input on curriculum.  He liked the look of the Key Curriculum Press Algebra series.  In the past, he used some of their other books and liked the way new ideas were presented.  We started the year skimming through book one, Operations on Integers, as that was mostly review work for him.  We completed that book by mid-September and moved on to book two, Variables, Terms, and Expressions.  This book started out being easy, but somewhere along the way, JT missed something essential and started to struggle.  I am not sure if I failed to explain a concept fully or if he just wasn't listening when I did.  Lack of attention is becoming a more common problem in our daily routine.  I know this is true, not just because I am experiencing it, but also because my husband has been frustrated by JT's lack of attention on several occasions lately when they are working together on computer programming instruction. It is maddening to spend an hour explaining something in great detail only to ask JT to generate some simple bit of work from the lesson and hear him say, "I don't know how to do that."

But that's a frustration we can deal with at a later time.

So, last week book two introduced the concept of like and unlike terms.

3xy and 2yx are like
3x and 2xy are unlike

He answered every one of those problems correctly.

Next lesson- Combine like terms.

8a + a = 9a

No problem!  He got all of those right.

This week- Simplify the expressions, just add like terms.

3x + 6y +2y + 8x = 11x + 8y

But that's not what JT did.  He answered it like this.

19xy

So, I asked him how he came up with that answer.  He had NO memory of learning about like and unlike terms.  We reviewed.  I did lovely sample problems on the white board showing how his answer and the correct answer would not result in the same number if we gave values to the variables.  He stared at me blankly and said, "I don't get it."  I explained again.  I had him write out the problems on the board as I talked him through it.  I thought he was starting to understand.

I gave him more problems to do.  ALL WRONG.  I banged my head on the desk a bit and questioned my ability to ever get through to this kid.

Then I turned to the best tool any homeschooling mom has...homeschooling mom friends.  The first friend suggested substituting tangible things, like silverware, for the variables.  So we did.

2forks + 3forks +knife/fork + 3knives +knife/fork
2a + 3a + ab + 3b + ab

  

Simplified 

5forks + 3knives + 2knife/forks
5a + 3b + 2ab

This visualization seemed to help him a bit.  So I sent him back to work on another set of problems.  A little better, but still a great deal of confusion, especially when negative numbers were in the problems.  So I asked another mom friend for suggestions.  She recommended highlighters to make it easier to see the different components in the expression.

Free highlighter from a conference pays off!

This idea, combined with the cutlery computation, finally made the difference.  He only had one mistake on this set of problems.  

I know this is not the last difficult week I will have on our homeschooling journey.  But I also know I am not in this alone.  There is such a wealth of been-there-done-that knowledge in the homeschooling community.  I need to remember to draw on it when I am struggling.  

And maybe someday I'll have opportunity to give back to those who have so graciously shared their ideas with me.