Thinking this through--using a calculator?

[sbgrace]

My son's mental stamina for math is very low. We struggled today to stay focused for just one problem that involved finding common factors of two numbers. It's not an ability issue, but an attention issue (sustained attention, attention to detail, etc.)

 

I'm wondering if I might allow a calculator use for much of his math.

 

My idea would be to spend daily time reviewing memorized math facts. He would work a problem of computational math, such as long division, out on paper paper  so that he doesn't forget how to do the actual computations. Then I would allow a calculator to use for his main math lesson.

 

I'm thinking calculator use would take one cognitive load off (computation, paying attention to accuracy of detail) so that he can focus his energy on mastering both concepts and procedures.

 

 

Thoughts?

[Heathermomster]

Have you given him a multiplication chart yet?

 

You are scheduled for testing later, correct?  Do you think he's on the spectrum?  I'm sorry, but I do not remember.

 

My son has a terrible time with factors.  He will be 14 in a couple of months and factors are still a challenge...DS uses the chart mainly; however, the calculator is available for things like 3 by 6 digit multiplication...Definitely give him a chart and a calculator...Keep math facts review brief and separate from the regular daily math work.   

[Julie of KY]

I think there is a point that you give kids a calculator because their learning disorder interferes with learning math. However, I would be very reluctant to do it with elementary math. I do think you have to take each situation individually and decide what is best for that child. I also realize that others recommend heavy use of calculators early on for kids that have difficulty with math - in my opinion, I think this is overly recommended.

[Pen]

Personally, if I thought it might help, I'd give it a trial for a certain period of time (and tell the child what I was doing) and then reassess whether it seems to be helping or harming.

[sbgrace]

Have you given him a multiplication chart yet?

 

You are scheduled for testing later, correct?  Do you think he's on the spectrum?  I'm sorry, but I do not remember.

 

My son has a terrible time with factors.  He will be 14 in a couple of months and factors are still a challenge...DS uses the chart mainly; however, the calculator is available for things like 3 by 6 digit multiplication...Definitely give him a chart and a calculator...Keep math facts review brief and separate from the regular daily math work.   

 

He's completing school provided cognitive testing this week. I know the results will have qualifiers. She told me he was very distracted in the testing and that the actual scores themselves  aren't going to be reliable. He is on the spectrum (dx'd).

 

He's pretty solid on multiplication (at least until he tires, and then he can't even add!) The issue seems to be about staying mentally with the material for any length of time.

 

Factoring something like 72 takes quite a bit of sustained attention. He just doesn't seem to have it. It takes forever due to loss of focus (so he has to refocus /mentally retrace his steps and restart over and over). He also starts to make tons of mistakes as math time goes on. These aren't ability or understanding mistakes, but lack of attention mistakes (ie writing 3, but multiplying by 2 instead, subtracting incorrectly, etc.) This isn't math he can't actually do when focused/when he first starts.

 

We are struggling just to complete 2 problems a day now. It wouldn't be an issue for me if this was needed for concepts to sink in or similar. But this isn't a problem with conceptual  or even procedural understanding. It's an issue related to lack of ability to stay focused on math long at all. Or at least that's what it feels like!

 

I don't want to mess up with him. Today he said he was bad at math twice. He really isn't bad at math. He was just making mistakes due to loss of focus. 

[geodob]

The problem with him using a calculator, is that he might forget that he is bad at math?

He might come to see his way of doing math on a calculator as normal.

Also he might not learn to feel anxious when doing math?

 

The way that we do math is really arbitrary?   The ability to do math as a life skill, is the real concern.

 

[Pen]

...

 

Factoring something like 72 takes quite a bit of sustained attention. ...

 

How exactly does he approach factoring 72?   And how would he do it on a calculator?   It isn't the sort of thing that I usually think of a calculator as helping.

[sbgrace]

How exactly does he approach factoring 72?   And how would he do it on a calculator?   It isn't the sort of thing that I usually think of a calculator as helping.

 

Well, he's doing it the way the book modeled.

 

They have him start with 1 X 72 , 2 X ?, 3 x ? and so on.

 

So my son wrote down 1, 72 (actually on opposite sides of the board so his answers were least to greatest).

Then he wrote 72/2 and divided it out by writing a 3 above the 7, subtracting to get 12 and so on (not mentally, his twin does it mentally but this one needs to see things)

 

Then he wrote 72/3 and did the same written math.

Then 72/4, knew 5 wouldn't work, 72/6, then he just knew 8X9 is 72.

 

He had actually already factored 12 (mentally/easier). So, after finding the factors of 72, he was to find the greatest common denominator for the two numbers.

 

He was mentally done by 72/3! So by the time he got to whole point he was largely mentally disengaged.

 

So in this case he would be doing that division computation on the calculator. My hope is that a 20 minute problem (due to constant refocusing) would be more like 5? I don't know!

[mom2bee]

Well...how does factoring on a calculator work? It usually requires a lot of short-term memory and attention, doesn't it?

I think that a trial run with the calculator may be in order, like someone suggested earlier. I didn't see your latest post detailing how he factors, so I don't know that a calculator will or wont help.

 

But...have you tried showing him a factoring tree.

 

72

2 * 36

2 * 6 * 6

2 * (3*2) * (3*2)

2 * 2 * 2 * 3 * 3

 

Seems a good deal more straighforward than writing out 1*72, 2 * ?, 3* ?, etc...

 

Why not let him practice factoring on smaller numbers so that he can learn the concept behind prime vs composite numbers, talk about rules of divisibility and then factor with a tree? Seems like it would be much easier, no?

[Pen]

Well, he's doing it the way the book modeled.

 

They have him start with 1 X 72 , 2 X ?, 3 x ? and so on.

 

So my son wrote down 1, 72 (actually on opposite sides of the board so his answers were least to greatest).

Then he wrote 72/2 and divided it out by writing a 3 above the 7, subtracting to get 12 and so on (not mentally, his twin does it mentally but this one needs to see things)

 

Then he wrote 72/3 and did the same written math.

Then 72/4, knew 5 wouldn't work, 72/6, then he just knew 8X9 is 72.

 

He had actually already factored 12 (mentally/easier). So, after finding the factors of 72, he was to find the greatest common denominator for the two numbers.

 

He was mentally done by 72/3! So by the time he got to whole point he was largely mentally disengaged.

 

So in this case he would be doing that division computation on the calculator. My hope is that a 20 minute problem (due to constant refocusing) would be more like 5? I don't know!

 

 

That sounds exhausting.  And also confusing to have the pairs apart from each other.    What book?   Maybe he needs a different book.

 

Factor trees, or factor grids, or factor cakes...there are various ways I've seen to make sense of factoring, but the above looks especially daunting.

 

If he knew 8 x 9 = 72,  that is where I would start.   I'd show him that 9 is 3^2 and 8 is 2^3   (3 squared and 2 cubed), and with those primes one has the whole thing as one might need to make use of it.  Or if he had to generate a whole table, then how to use the primes to work that out, and at that point, a calculator could help just to do the multiplying.

[Heathermomster]

Enlarge, print up, and laminate the multiplication chart that I linked. Have your son go down every row, looking for and then circling the number he is factoring with an erasable marker. Review the numbers circled with him to determine the factors and jot down the answers for him. The largest number he will be able to factor is 144.

[Pen]

Enlarge, print up, and laminate the multiplication chart that I linked. Have your son go down every row, looking for and then circling the number he is factoring with an erasable marker. Review the numbers circled with him to determine the factors and jot down the answers for him. The largest number he will be able to factor is 144.

 

If it is a 12's chart up to 12 x 12 is 144, then I do not understand how it would help him to factor 72.   How would he get:

2 x 36  

3 x 24  

4 x 18  from a chart?

 

 

I think it would only have 8 x 9 and 6 x 12.     ?????

 

If he knows something like 8 x 9. and how to find the primes in 8 and in 9, or uses a calculator or a chart to find the primes that are factors of the factors he knows, then he can derive all other possible combinations.

[Heathermomster]

If it is a 12's chart up to 12 x 12 is 144, then I do not understand how it would help him to factor 72.   How would he get:

2 x 36  

3 x 24  

4 x 18  from a chart?

 

 

I think it would only have 8 x 9 and 6 x 12.     ?????

 

If he knows something like 8 x 9. and how to find the primes in 8 and in 9, or uses a calculator or a chart to find the primes that are factors of the factors he knows, then he can derive all other possible combinations.

 

so true...

[sbgrace]

I will look for a bigger chart too. I imagine I could make one. I'd have to go pretty large to work on this stuff.

 

If I can do this, would you just let him have it for all his math?

 

I will also work on the alternate way of factoring. But he's moving onto other material soon. His issues are beyond just factoring. This issue is affecting nearly every single lesson.

[Pen]

If he is able to understand the mathematics of math, then you may find he actually does better with a program considered "mathy" and more rigourous, rather than one that is computation heavy.

 

Personally, I would not try to find a bigger chart.  I would try to have him understand the math behind the process.

 

So if he knows or can find 8 x 9 on a regular chart, then let him find factors for 9, and factors for 8.  Once he has fully taken apart each number to its primes, he can recombine the primes to get all the factors.

 

2 x 2 x 2 x 3 x 3 ... can be regrouped and rearranged via commutative and associative properties of multiplication.

 

so there is always a) 1 times the number itself,  

b) then in this case 2 x (2 x 2 x 3 x 3)

c) and  (2 x 2) x (2 x 3 x 3)  

d) and (2 x 2 x 2 x 3) x 3

e) and (2 x 3) x (2 x 2 x 3)

etc.

 

and a calculator could help work those out.

 

factoring is mainly needed in elementary math to figure out common factors for fractions, and if that is so, going ahead and knowing how to use the primes could save effort in the long run.