Attn: Math teachers/experts ... how do you know?

[alwayslearning]

Hi all! I could really use some insight on math knowledge/comprehension. I am an English teacher and can assess a student's knowledge in language pretty easily; almost intuitively, right? But in math ... I just don't have that skill. I feel comfortable teaching math and understand what I am doing, so it's not intimidation. I just don't have the experience in teaching math enough to know when he truly has a concept down.

 

He is 9, and we are working on 7th grade math. I am using the sequencing from a public school book - no formal curriculum.

 

Here is my issue. We are moving into this abstract math and he absolutely gets it. He absorbs concepts like they are water. He understands, he can teach them back to me, he can create and solve his own problems. This is easy for him, and we move along at a quick pace. He may forget vocabulary, or after a few weeks, forget what he is supposed to do - but a quick review snaps him back before I can finish a sentence usually.

 

However. We are having some difficulty in basic math operations. Addition, subtraction, multiplication and division. They are like torture to him. He does his math the loooooonnnngggg way because he wont just suck it up and memorize his facts! He understands these operations ... he just hates doing them. But it is getting to the point where his math stinks because of his attitude.

 

We are getting into math where the facts need to just be known because the focus of the problem is on other things. Like reducing fractions or multiplying negative integers. How can he do those problems and understand them ... yet struggle with 9+7? Is it sheer laziness? Is he being difficult?

 

He says sometimes he will look at a problem like 2+3 and see the answer, but forget the word. Huh? He does this often.

 

I told him that the math we are doing now relies on his knowing these facts stone cold. That they have to just come to him, so he can focus his energy on the other portions. He sees it, and gets it. But there is like a block or something. Long division brings us both to tears ... yet he can explain it, show it, demonstrate it and create/solve problems of division ... but make him write out a long division problem and you'd think I was killing him. And he will not get the right answer. He will shrug and say he doesn't know. It's maddening, I tell you!!!

 

So my idea is to do a Basic Operations Boot Camp. A week of addition, subtraction, multiplication and division. From the beginning. Place value, carrying 1s, associative property. I think he understood the concept of addition but was never able to learn in his public school because of other issues (behavior, boredom, anxiety...). It's like he missed Math 101, but managed to get through because he understood.

 

Is this a common problem? I feel confident he understands the concepts we are working on this year. But when he has to do the basic operations, it's like he shuts down. How can a child do prime factorization, but struggle with simple division???

 

If I were a math teacher, I could probably pinpoint the issue and fix it. But this isn't an essay... and I am feeling a little clueless.

 

Do I let him do these problems the hard way? Do I keep going forward with new concepts, but continue to do basic operation review each day (this is what I have been doing ... there is small improvement doing this but it is very, very slow going)? Do I stop all current learning and go back to basics? (He would hate this... and be bored out of his mind, but if it is necessary... then I will).

 

Thanks all! :)

[mathwonk]

i think you are on top of it. my grand daughter has similar issues. off the charts problem solving skills but forgets what 7 times 9 is. i don't know the solution, but agree with your ideas with one caveat, I would not "stop and go back to basics" as that would deaden the process for the child and bore him to distraction, in my opinion.

 

in my younger son's case, who was similar, his school used saxon math, whose repetition helped his basics, but bored him so much he lost interest in math altogether. that is the problem with "back to basics and stop all creative learning".

[kiana]

"How can a child do prime factorization, but struggle with simple division???" Because division is boring and prime factorization is interesting. Frankly I did not have my multiplication facts down myself until I was in Calc III.

 

Under no circumstances would I stop ALL learning and go back to nothing but facts. This would be like taking a child who is reading well but struggling with spelling and sending them back to read nothing but Hop on Pop until their spelling improves.

 

I would keep doing what you are currently doing and provide high levels of encouragement for math facts improvement. (stickers etc.?)

[alwayslearning]

Thank goodness - I was hoping you guys would say that. Because I think *I* would be bored to tears going back to basics... haha. I think we are going to begin working on multiple solutions to the problems we work on. Sometimes he gets so stuck on figure out a problem in one set way, that he has trouble extending outside of that. We'll keep on keeping on.... thanks!

[La Texican]

I like the free online game Sum Dog. It's like flash cards, but not. It's like a video game. It's for making facts automatic and the difficulty is easily adjustable. I recommend mixing it up. My kid's "got" the four operations. We're introducing using the operations on fractions and decimals right now. I told him, "A boy gave 2 cents for a marble and six cents for a top, how much did he pay?" He disappeared under the table (so I wouldn't see him counting on his fingers). He came up and said, "What's 3 + 5?" I said 8, he said, "that's how much he paid." Yeah, so I like to throw in the Sum Dog game some days so he remembers the facts faster.

 

Just keep doing what you're doing but some days say, "Go play Sum Dog" instead.

Other options are cards, dice, and dominoes.

[kiana]

Good point. I have heard really good things about Timez attack for multiplication as well.

[Mukmuk]

Not an expert or a math teacher, just a mom who's also feeling her way around :p. A few things that helped:

1. Manipulatives. DS actually never liked it (Rightstart failed for us), but I demonstrated a lot of these concepts with c-rods, cubes, sticks, anything. I got him to work with it too, and the facts stuck better that way. In ds' case, he's a kinesthetic learner and has good visual memory.

 

2. Moving on to higher level math. Please do move your son on so he can fall in love with these concepts! Ds loves them and plays with them in his head. These all require the basic operations, so suddenly, practicing them isn't work at all. He was telling me that the difference of consecutive squares is the sum of their bases which led to circles blah blah. Moving on to advanced concepts helps whole-to-parts kids (which is what your son sounds like) understand the why of what they're doing. The motivation is the beauty of it all.

 

3. Feed him with loads of math literature because they illustrate the beauty of the concepts. I'd recommend the Number Devil and the Murderous Math series. There are lots more down the pipeline, but these are great for the middle/junior high levels.

 

It takes awhile to change the mindset, but for some kids, it works.

[dbmamaz]

i totally get the 'see it but dont have the word' lol

 

Timez attacks i think now has addition and subtraction too. We did some free long division worksheets and some kaleidoscope math from scholastic for multiplication practice. we arent quite as advanced as you, but also more conception and less practical!

[Esse Quam Videri]

Wanted to mention Math Wrap-Ups as well. They may seem "babyish" to him, but then again, he may enjoy the hands-on route. You can time him and make a goal for each set of facts.

[EinsteinBlueprint]

Ah....the math facts...yes they are indeed very important. I can pretty much assess how well my students will do on standardized tests (AMC, SAT, etc.) by simply how long it takes them to verbally answer a multiplication problem like *8 times 13*.

 

THE cure for math fact weakness is, IMO, learning mental math and left-to-right computation and VERBALIZATION. No more carrying. No more borrowing. Have them skipcount all the time. Have them factor the numbers 2-100 every single day (no factor trees!) until they can do it in less than 7 minutes.

 

 

Yes, I am a fan of the online math fact reinforcement too. I used Math Rider a little bit with my second child.

[alwayslearning]

i totally get the 'see it but dont have the word' lol

 

 

 

Really? What is this all about?? :)

[alwayslearning]

Ah....the math facts...yes they are indeed very important. I can pretty much assess how well my students will do on standardized tests (AMC, SAT, etc.) by simply how long it takes them to verbally answer a multiplication problem like *8 times 13*.

 

THE cure for math fact weakness is, IMO, learning mental math and left-to-right computation and VERBALIZATION. No more carrying. No more borrowing. Have them skipcount all the time. Have them factor the numbers 2-100 every single day (no factor trees!) until they can do it in less than 7 minutes.

 

 

Yes, I am a fan of the online math fact reinforcement too. I used Math Rider a little bit with my second child.

 

That is incredible. The little boy did them faster than I could. :)

 

Can you break down this left-to-right computation? For someone who was taught strictly on paper and pencil, I don't know the methods of it - but I am intrigued. Verbalization definitely seems the way to go; especially for my son. Even for me, I have to "see" the problem... even if I am using my finger in the air, or a chalkboard in my head. How can we learn this left-to-right thing?

 

I have been making an extra point to make him figure out the math problems of our day as we are out and about, trying to train his brain to do it mentally. He has a hard time stepping out of his math box ... he is set that there is one way to do a problem, with a textbook in front of you, and just getting it over with - I'm trying to open his windows a little to let that fresh air in, haha. And to show him math isn't just a chore you have to get over. So we are trying to branch out a bit.

 

Thanks so much!!

[kohlby]

Could you explain the why's? My oldest is normally a terrible memorizor. He's 9 and still can't tell you the months of the year in order. He only learned the days of the week in order last year. Yet he can handle AoPS Algebra. We used MUS before that. And though it was easy for him, it taught it in a way that explained the why's very simply. My oldest raced through MUS, but he managed to memorize since he understood why. I'm not saying that I'd go back to first grade and do a formal curriculum, but if you have a friend that has MUS, then get the disks and watch how the lessons are taught and use some of those skills. (Or even have your child watch them. Though MUS suggests the parent watches and it's not used as a primary teaching tool for the student, we did just that and it worked great). When my oldest got stuck, he could reason out the answer. (Like 6 x 7 would be 5 x 7 + 7 initially). Reasoning out helped his weaker memorization, but he eventually sped it up on his own.

 

As for oral math, could he give you problems? He would need to figure out the answer too to see if you got it right or not. If he's testing you, maybe he'll fight it less - and try to come up with more challenging questions to trip you up. Both of my older two kids are constantly asking us math computation questions at the dinner table trying to see if they outsmart us.

 

For skip counting, I played a game called ping pong with my students. (I used to be a math teacher). This worked even with honor level kids to get them to start listening better. We would count, starting at 1. When you got to the multiple of one number, you said "ping" and for another "pong." For example, let multiples of 3 be "ping" and 4 be "pong." Go back and forth with you and your child each saying a number. So "1," then "2," then "ping" then "pong" then 5 . . . when you get to 12, it will be "ping pong." With two people, the game ends when you miss one. Try to see how high you can go. (With a class, the person who missed is out and then you start over again at 1).

[kiana]

Left-to-right is how I naturally compute. The numbers come out in the correct order for writing them down, and estimation is more natural this way as well. This is nothing I was ever taught but simply the way that made sense to me. I think this is also partially because I started algebra so young that I tend to apply algebraic algorithms -- and when adding polynomials, it tends to be taught to combine the highest order terms first.

 

Side note -- when I was first taught long division, I was taught it as an algorithm (by the PS math teacher), and I just did NOT get it. I could neither remember the steps nor get them in the right order. When my algebra teacher taught long division of polynomials, it was as though a light bulb went off in my head. "Oh! THIS is what they were trying to get me to do before! It's just all the x's were 10s!"

[jenbrdsly]

To the OP. Are you familiar with teaching math from a Constructivist approach? Info here on my blog. It is what Kiana is describing.

[Reya]

You don't have to do ALL the numbers 2-100 every day for factoring, but your kid should be able to do any number 2-100 quickly.

 

Most math facts can be seen, not memorized, but drill is necessary for speed and fluency for ALMOST every kid.

[mathwonk]

As a mathematician, I find this focus on rote repetitive manipulative skills a little scary. Please don't try to make robots out of your bright curious kids. I recommend trying to interest them in math, not beat them over the head with it. Would you teach reading by having them diagram sentences, the same ones over and over? A gifted math kid is not necessarily one that can factor three digit numbers quickly in his head, but more likely one that notices that he always gets the same result no matter in what order he factors the number. or maybe one who notices that a number whose digits add to a number divisible by three is also itself divisible by three, or maybe even one who notices that a number like 1331, whose digits have alternating sum zero is divisible by 11. mathematical thinking is not calculation, it is observation, and conjecture, and verification. of course opinions differ.

 

In my own view, if this statement is correct:

 

" I can pretty much assess how well my students will do on standardized tests (AMC, SAT, etc.) by simply how long it takes them to verbally answer a multiplication problem like *8 times 13*."

 

then it is an argument for the utter triviality and unimportance of those tests.

[alwayslearning]

As a mathematician, I find this focus on rote repetitive manipulative skills a little scary. Please don't try to make robots out of your bright curious kids. I recommend trying to interest them in math, not beat them over the head with it. Would you teach reading by having them diagram sentences, the same ones over and over? A gifted math kid is not necessarily one that can factor three digit numbers quickly in his head, but more likely one that notices that he always gets the same result no matter in what order he factors the number. or maybe one who notices that a number whose digits add to a number divisible by three is also itself divisible by three, or maybe even one who notices that a number like 1331, whose digits have alternating sum zero is divisible by 11. mathematical thinking is not calculation, it is observation, and conjecture, and verification. of course opinions differ.

 

In my own view, if this statement is correct:

 

" I can pretty much assess how well my students will do on standardized tests (AMC, SAT, etc.) by simply how long it takes them to verbally answer a multiplication problem like *8 times 13*."

 

then it is an argument for the utter triviality and unimportance of those tests.

 

I really appreciate this insight. After getting some validity in moving forward vs regressing back to basic operations (torture for both my son and myself), we went onward to negative integers. He loved them - and we never cracked the book. We actually learned about these in the car, during discussion. Later when we put a number line on paper, I asked what would happen if we subtracted a negative number from a negative number ... he knew intuitively what would happen based on the direction of the number line and how negatives cancel each other out. He nailed it. He told me he likes math now that we are past the boring parts ... and fractions. :p He will like the next few chapters, and then I think we will revisit fractions. I am just going to make sure he is doing some warm-ups each day using the basic operations. I appreciate all input here.

 

PS - he is even trying to figure out math in stores while we are out without cringing or putting up a math wall. He has never initiated a math question in real life but today figured out 20% on his own, because he wanted to know the price after a sale. This is not major math here but in regard to his attitude - night and day. Love it!!! :p

[quark]

I've found that giving a child a valid reason to memorize facts makes the whole process not only easier but also infinitely more fun. Memorizing in order to win a game, for example, or introducing x as a factor so that he can solve an equation, e.g. 13x = 169 so x must be...what? Substitute x with apples, ninja turtles etc. if necessary. Games like these are fun played in the car. Or sum all the numbers in a license plate. Too easy? Multiply the numbers and see who can do them faster.

 

When you allow the child to experiment with higher level math, he eventually realizes how much more useful it is to know his facts. You are giving him a reason to learn them and you are telling him, showing him that you know he can do it. He sees that you trust him and most kids usually want to rise up to that challenge.

[quark]

As a mathematician, I find this focus on rote repetitive manipulative skills a little scary. Please don't try to make robots out of your bright curious kids. I recommend trying to interest them in math, not beat them over the head with it. Would you teach reading by having them diagram sentences, the same ones over and over? A gifted math kid is not necessarily one that can factor three digit numbers quickly in his head, but more likely one that notices that he always gets the same result no matter in what order he factors the number. or maybe one who notices that a number whose digits add to a number divisible by three is also itself divisible by three, or maybe even one who notices that a number like 1331, whose digits have alternating sum zero is divisible by 11. mathematical thinking is not calculation, it is observation, and conjecture, and verification. of course opinions differ.

 

In my own view, if this statement is correct:

 

" I can pretty much assess how well my students will do on standardized tests (AMC, SAT, etc.) by simply how long it takes them to verbally answer a multiplication problem like *8 times 13*."

 

then it is an argument for the utter triviality and unimportance of those tests.

 

:thumbup: Eloquent and so true.

[Dmmetler]

The World Maths Games have been the impetus for DD to learn her facts quickly-she did well, but not wonderfully, last year (and completed fewer questions in math, despite them being "Easy" than in any other area-it was the one area she didn't make it on the high score table), and discovering just how fast kids her age could be at that easy stuff was a challenge she picked up. I figure the Mathletics.com subscription has been worth it just for that-because before then, any effort at getting her to practice only seemed to lead to digging in heels and slowing her down. Her goal, now, is "Human Calculator" on all live mathletics levels (she'd managed it on the old format, and then they changed it and added more ;) ).

 

I will also say, though-that was right about the time she really, really accelerated in math in general, so maybe it was just coincidental and she made a great leap in understanding all at once?