After all my years of teaching the whys of maths..

[Laura Corin]

.... it turns out that Calvin does better just learning the hows. I've always used programmes like Singapore Maths, to ensure that he really understands what he is doing. He's never been a great maths student - he isn't interested and tends to get lost in the whys.

 

So now he's going to school in August and, due to a grade skip, has to spend the summer catching up with the class by studying fourteen chapters. He's doing so much better with this curriculum, which just says: 'Here's this kind of problem and this is what you do with it.'

 

I have to wonder whether the years of learning the whys actually did him any good - he might well have been happier, and learned more, just working by rote. He has a phenomenal memory for rules, and really enjoys them. Sigh.

 

Laura

[siloam]

.... it turns out that Calvin does better just learning the hows. I've always used programmes like Singapore Maths, to ensure that he really understands what he is doing. He's never been a great maths student - he isn't interested and tends to get lost in the whys.

 

So now he's going to school in August and, due to a grade skip, has to spend the summer catching up with the class by studying fourteen chapters. He's doing so much better with this curriculum, which just says: 'Here's this kind of problem and this is what you do with it.'

 

I have to wonder whether the years of learning the whys actually did him any good - he might well have been happier, and learned more, just working by rote. He has a phenomenal memory for rules, and really enjoys them. Sigh.

 

Laura

 

Laura,

 

I really wish we both knew the answer, because I suspect my oldest is this way, if not all my kids. I was when I was young, just loved numbers and could care less why. I have only enjoyed the why as I have gotten older.

 

I really wonder some days...

 

Heather

[Daisy]

I don't know which is better but I agree with you. My daughter is the same way and I wish I hadn't detoured for 2 years into a math that focused on the why's. We've just spent the summer going back to rote math and trying to catch her up. She is doing so much better now with this math curriculum and is motivated to get caught up.

[Country Girl]

.... it turns out that Calvin does better just learning the hows. I've always used programmes like Singapore Maths, to ensure that he really understands what he is doing. He's never been a great maths student - he isn't interested and tends to get lost in the whys.

 

So now he's going to school in August and, due to a grade skip, has to spend the summer catching up with the class by studying fourteen chapters. He's doing so much better with this curriculum, which just says: 'Here's this kind of problem and this is what you do with it.'

 

I have to wonder whether the years of learning the whys actually did him any good - he might well have been happier, and learned more, just working by rote. He has a phenomenal memory for rules, and really enjoys them. Sigh.

 

Laura

 

Interesting observation. I've often wondered if teaching the whys can also be lost on young kids just because their minds aren't really designed to make those connections yet. I've learned so many "whys" teaching my kids that I never really understood until now. But I don't know that I was never taught them or if it just took a more mature mind and thinking process to really be able to grasp them. Maybe the idea of teaching rote and rules first follows the classical method better and once students master the rote and rules (the grammar) of the math concepts, then they can be taught and understand the whys (the logic)????

[Laura Corin]

I firmly believe that understanding is the key to education. It just seems wrong to me that he does better not understanding why he is doing something.

 

Laura

[Daisy]

Interesting observation. I've often wondered if teaching the whys can also be lost on young kids just because their minds aren't really designed to make those connections yet. I've learned so many "whys" teaching my kids that I never really understood until now. But I don't know that I was never taught them or if it just took a more mature mind and thinking process to really be able to grasp them. Maybe the idea of teaching rote and rules first follows the classical method better and once students master the rote and rules (the grammar) of the math concepts, then they can be taught and understand the whys (the logic)????

 

You know, you might have something here. It makes sense.

[Guest Cheryl in SoCal]

I firmly believe that understanding is the key to education. It just seems wrong to me that he does better not understanding why he is doing something.

 

Laura

Is he able to solve word problems, especially complex word problems? The why's of math is important for applying it to real life (word problems). One of my sons has an excellent memory and could "do" math excellently (100% on everything) but was not good at word problems because he didn't know what he was doing so he couldn't apply it to real life. He could work complex equations but apply math to real life, which made the math he could do useless to him.

[siloam]

I firmly believe that understanding is the key to education. It just seems wrong to me that he does better not understanding why he is doing something.

 

Laura

 

Yes, you hit the nail on the head!! I am the same way.

 

My current High School math plan is to allow her to do a more rote plan at grade level, then slowly work through Singapore Discovering Math behind grade level. I just can't quite give up on the why, but I also realize that if I try to use it as our main program she will get really bogged down and never finish her High School sequence.

 

The added problem is she is an auditory learner, and refuses to read the problems out loud to herself. We will go back and forth on a CWP problem, for example, 3 times; I give her hits to try to get her thinking in the right direction, or help her draw a diagram correctly. She still won't get it. If I sit down and read it aloud to her about half the time she will have the answer in 30 seconds. She just needed to hear it. Drives me batty.

 

Heather

[Laura Corin]

He does well at word problems at the current level - beginning 'high school'. When I see him working, it's as though the rules are his scaffolding and he inserts them like a skeleton within the boneless problem, making it conform to the structure that he is comfortable with. It's difficult to express - he makes the problem take the shape of one of the many algorithms that he has memorised, whilst I would try to understand the particular problem and construct a bespoke solution.

 

He's not going to end up going into a technical field - he has 'language arts' running through him like 'Brighton' through a stick of rock - otherwise I would worry that his new-found methods would be too limiting. As it is, I'm just glad that he's found his groove. But sad too. Time to let go.

 

Laura

[Perry]

Interesting observation. I've often wondered if teaching the whys can also be lost on young kids just because their minds aren't really designed to make those connections yet. I've learned so many "whys" teaching my kids that I never really understood until now. But I don't know that I was never taught them or if it just took a more mature mind and thinking process to really be able to grasp them. Maybe the idea of teaching rote and rules first follows the classical method better and once students master the rote and rules (the grammar) of the math concepts, then they can be taught and understand the whys (the logic)????

:iagree:

 

This is why I don't like so many of the math curricula used in ps (Everyday Math, Investigations, etc). They spend way too much time on the why, and too little time on the how and practice.

[Earth Angel_79]

Interesting observation. I've often wondered if teaching the whys can also be lost on young kids just because their minds aren't really designed to make those connections yet. I've learned so many "whys" teaching my kids that I never really understood until now. But I don't know that I was never taught them or if it just took a more mature mind and thinking process to really be able to grasp them. Maybe the idea of teaching rote and rules first follows the classical method better and once students master the rote and rules (the grammar) of the math concepts, then they can be taught and understand the whys (the logic)????

 

Very interesting thread and interesting thoughts above! My oldest is only in the first grade and doing well with math, but he hates it. He doesn't really seem to get excited by the shortcuts that are created when you know the why. He does like problem solving though and enjoyed word problems :confused: (I think it may be the fact that it is words over numbers), but give him one of his Miquon worksheets and all I ever heard was groans. I'm fascinated by the whys, but I was wondering the same thing the other day...if it was because of my age.

I'm getting Simply Numbers in the mail in the next few days and I'm going to see if doing something more rote with a sprinkling of Miquon will work better for us.

[kokotg]

DH teaches high school math and always says that the kids are not at all interested in the whys and get very frustrated when he tries to teach them. They want to know the formula so they can plug the numbers in. He doesn't teach any of the advanced track math kids, though; I imagine it would be different there. This will be an interesting year because it's his first year teaching the new math curriculum in our state, which is very much focused on the whys.

 

I guess what I would wonder, if you're just learning the hows, is...what's the point? It may be much easier for a lot of non-mathy kids to punch the numbers in and get good grades in math, but it seems like it would mean ensuring it had all been wasted time as soon as they graduate and forget everything.

[Ellie]

I am just like him. :)

 

After I know the hows, the whys make sense to me. If you explain all the whys first, I'm just frustrated and want to punch in your face.:tongue_smilie:Tell me the how, let me work with it until I own it, *then* I will understand the why.

[Laura Corin]

 

I guess what I would wonder, if you're just learning the hows, is...what's the point? It may be much easier for a lot of non-mathy kids to punch the numbers in and get good grades in math, but it seems like it would mean ensuring it had all been wasted time as soon as they graduate and forget everything.

 

I think it's definitely worthwhile teaching the whys for as long as possible. There was always the possibility that Calvin would develop an interest. By now though..... he just wants to do maths in an easier way and spend his time on the subjects that he enjoys.

 

Laura

[kokotg]

I think it's definitely worthwhile teaching the whys for as long as possible. There was always the possibility that Calvin would develop an interest. By now though..... he just wants to do maths in an easier way and spend his time on the subjects that he enjoys.

 

Laura

 

Yeah, and I definitely get that. I was like that, too :). I just wonder if there's much point in teaching upper level math to kids who aren't interested in math in that case, you know? I mean, I'm just thinking aloud--I don't know the answer. I know kids have to do it, if they're going to graduate and go on to college, I just wonder if the system makes sense.

[Laura Corin]

Yeah, and I definitely get that. I was like that, too :). I just wonder if there's much point in teaching upper level math to kids who aren't interested in math in that case, you know? I mean, I'm just thinking aloud--I don't know the answer. I know kids have to do it, if they're going to graduate and go on to college, I just wonder if the system makes sense.

 

It is still possible to drop maths at 16 in England and go to university - we specialise early. I did well in maths all the way through until maths became just too much for me - I started to get bad marks and dropped it. I didn't do any maths again until i had to do statistics for my MBA ten years later - it was quite a shock at that point.

 

I like the IB system for ages 16-18: you take subjects at higher or lower level, depending on your interests/talents. So, a child like Calvin would be on track to go to a good university, but still do a practical life-skills maths course, rather than anything more esoteric. He would already, between ages 14 and 16, have done the equivalent of algebra one and two and geometry.

 

Laura

[Lovedtodeath]

.... it turns out that Calvin does better just learning the hows. I've always used programmes like Singapore Maths, to ensure that he really understands what he is doing. He's never been a great maths student - he isn't interested and tends to get lost in the whys.

 

So now he's going to school in August and, due to a grade skip, has to spend the summer catching up with the class by studying fourteen chapters. He's doing so much better with this curriculum, which just says: 'Here's this kind of problem and this is what you do with it.'

 

I have to wonder whether the years of learning the whys actually did him any good - he might well have been happier, and learned more, just working by rote. He has a phenomenal memory for rules, and really enjoys them. Sigh.

 

Laura

I have often wondered this.:)

[kokotg]

So, a child like Calvin would be on track to go to a good university, but still do a practical life-skills maths course, rather than anything more esoteric. He would already, between ages 14 and 16, have done the equivalent of algebra one and two and geometry.

 

Laura

 

That makes a lot of sense. DH's school used to offer a "money management" class, but it was specifically for non-college prep kids. This always seemed dumb to me; kids who are going to college certainly need to learn money management skills, too!

[skueppers]

Interesting observation. I've often wondered if teaching the whys can also be lost on young kids just because their minds aren't really designed to make those connections yet.

 

I think this depends very much on the child. I was always interested in the "whys" as a child, and thrived on the "new math" supplementary activities we sometimes had in school.

[Mom0012]

This is encouraging to hear as I have just decided to drop using the Singapore IP books for my son. He's used R&S all along and with all the negative comments about the lack of conceptual learning, I've felt pressured to add in more conceptual math. This is a child that started out in Rightstart and we were both miserable, and then when we found R&S, it was like we'd struck gold. I find he needs to learn how to do something and then he does understand. Maybe not on the same deep level as someone who focuses so much more on conceptual math, but still, the understanding there.

 

Lisa

[Carol in Cal.]

DD is like this. My approach has been to use Saxon with her, as that is the only program that seems to cement in the knowledge that she needs, but to also torture her by talking with her about why things are the way they are, and blathering on and on and ON about the 'general case,' a phrase which I have driven her to loathe. However, every once in a while, she will realize that this has actually been helpful. Sometimes she will even tell me that. :)

 

I am a bit concerned about this coming school year. She is going to take geometry at a local Catholic high school, and the approach of the textbook is very constructivist--'cut this shape out, and measure it, and notice the relationship between the different measurements, and, based on that, predict what this measurement would be in this other case, and check it.' Yeah, right. I figure that either she will love this or hate it, but that she won't learn very thoroughly this way.

[ScoutTN]

By now though..... he just wants to do maths in an easier way and spend his time on the subjects that he enjoys.

 

I don't think this is bad thing at the high school level. I was allowed to do so at a very competitive New England prep school and I can remember my joy at being able to load up my schedule with History, Latin and English!

[Laura Corin]

I don't think this is bad thing at the high school level. I was allowed to do so at a very competitive New England prep school and I can remember my joy at being able to load up my schedule with History, Latin and English!

 

For the next two years he's taking maths, physics and chemistry, but also English language, English literature, history, geography, Latin, French and Mandarin. He would normally 'only' be studying two foreign languages this year, but we got biology out of the way before he started school, which means that he can squeeze in a third language instead of a third science.

 

Laura

[KrissiK]

Well... on the other hand... I started the boys with A Beka math and last year in first grade DS1 was miserable. He hated math, though I know he's got a mathematical mind. Then, I decided to do a Singapore/A Beka hybrid this year with him and we started with Singapore and he's completely engaged. We had a 35 minute math session today and he could have done more, I was just tired.:D I think I'm going to drop the A Beka altogether and just do Singapore with him because he's eating it up and I don't have to fight him anymore to do math. Go figure.

[Laura Corin]

Well... on the other hand... I started the boys with A Beka math and last year in first grade DS1 was miserable. He hated math, though I know he's got a mathematical mind. Then, I decided to do a Singapore/A Beka hybrid this year with him and we started with Singapore and he's completely engaged. We had a 35 minute math session today and he could have done more, I was just tired.:D I think I'm going to drop the A Beka altogether and just do Singapore with him because he's eating it up and I don't have to fight him anymore to do math. Go figure.

 

Hobbes has been completely happy and engaged with similar maths to that which I used with Calvin. I don't think Hobbes is a maths whiz - it's just a style that suits how his brain works.

 

Laura

[abrightmom]

Interesting observation. I've often wondered if teaching the whys can also be lost on young kids just because their minds aren't really designed to make those connections yet. I've learned so many "whys" teaching my kids that I never really understood until now. But I don't know that I was never taught them or if it just took a more mature mind and thinking process to really be able to grasp them. Maybe the idea of teaching rote and rules first follows the classical method better and once students master the rote and rules (the grammar) of the math concepts, then they can be taught and understand the whys (the logic)????

 

:iagree: with this thought process . . . I have had this same thread running through my mind in trying to figure out math. UGH. I have hated the choosing process, the cost, everything about it. This very issue is plaguing me even today as I hold Math Mammoth and CLE (gasp) in my hands . . .

 

I think this thread is the start of an awesome discussion and I'm excited!

[abrightmom]

I am just like him. :)

 

After I know the hows, the whys make sense to me. If you explain all the whys first, I'm just frustrated and want to punch in your face.:tongue_smilie:Tell me the how, let me work with it until I own it, *then* I will understand the why.

 

This makes sense to me . . . and is kinda how I'm seeing my kids . . . I do hope they don't resort to punching me in the face though :D. Hee Hee. I know how you feel because math was always over my head.

[melmichigan]

Maybe this is why we now use SM and CLE for my youngers? :D Hopefully something will stick...:lol: My older DD is doing well with Dolciani so fingers crossed there.

[Mandy in TN]

Interesting observation. I've often wondered if teaching the whys can also be lost on young kids just because their minds aren't really designed to make those connections yet. I've learned so many "whys" teaching my kids that I never really understood until now. But I don't know that I was never taught them or if it just took a more mature mind and thinking process to really be able to grasp them. Maybe the idea of teaching rote and rules first follows the classical method better and once students master the rote and rules (the grammar) of the math concepts, then they can be taught and understand the whys (the logic)????

While all children are different (my three sure have been), I do think there is a need to teach elementary math (1-8) in two or three different sittings. We separate phonics/ spelling, reading, and grammar. This is the same idea. Right now here is how math looks at my house.

Teach math as rote learning. This would be the phonics/spelling of math.

Little ds primarily uses Kumon math for this, but I also have the Key to books sitting around.

My extra student is working on her multiplication tables with materials that I am creating for her.

Teach math through a variety of problems where a child can apply all the skills he has learned thus far. This is the reading of math.

Little ds and my extra student both use Saxon- just the hardback book- for this. We don’t use the Saxon drill, because we use other drill material. We don’t use the tests, because frankly I sit with them and know where they need work.

Teach math as discovery and concept development. This is the grammar- the why this works and this doesn’t- of math.

Last year little ds used Primary Grade Challenge Math and some Making Math Meaningful. Currently, we are using The Adventures of Penrose the Mathematical Cat, but I also have Creative Problem Solving in School Mathematics for this year.

My extra student is using Making Math Meaningful Level 5. I hope to use the multiplication section this fall and division in the spring.

Just as I don’t have my 7yo sit down and do all of his Language Arts all at once (or even everything we have every day), I also don’t have him sit down and do all of his math all at once. Kumon is the only math that is completed daily. Right now I am shooting to do Key to Decimals 2x/week, Saxon 4x/week, and Penrose the Cat 2x/week.

My extra student is 10yo and she prefers to stick with math until it is done, so the 2x/week I have her she likes to do drill, then MMM, and then Saxon. It is the order she prefers, so that is how we do it. Then, she just does one or two more Saxon lessons at home. I am thinking I need to send drill work home with her in a couple of weeks after we get settled into the fall schedule.

 

Just how we are doing it-

Mandy

[SamanthaBea]

I think the "how" and the "why" of math question is similar to the different learning styles (audio, visual, whole to parts, parts to whole, etc.) Some people probably just need to learn the process first without trying to understand the reason behind why it works, while others are just the opposite.

 

If the "why" is trailing behind the "how," perhaps the word problems need to be pulled from topics that the "how" has already been fully mastered instead of what is currently being learned.

[LizzyBee]

I firmly believe that understanding is the key to education. It just seems wrong to me that he does better not understanding why he is doing something.

 

Laura

 

:iagree: And I have to say that I don't think you wasted time explaining the whys. You've laid a foundation that makes him better at the hows even if it's not obvious.

 

I was one of those kids who could intuitively figure out the hows of math, but I couldn't explain the whys. I thought that's just the way math is - you either get it or don't, and it's easier to do than explain. Even my college math teachers were horrible at explaining why the algorithms work. When I took college trig, I managed an A, but felt like I'd hit a wall. My major didn't require calc, so I never had to take anything beyond trig. When I started homeschooling, I realized that I'd known how to do math without understanding why, and that's why I hit a wall at trig. I've tried to do better with my kids, explaining why even if they don't care why. :tongue_smilie:

 

ETA: I think it's fine if the "why" follows after the "how" has been mastered, as several pp's noted.

Edited August 10, 2010 by LizzyBee

[Laura Corin]

Resurrecting this with a new thought. It may just be that Calvin has grown into maths. I was watching him doing geometry this week - always difficult for him in the past - and his spatial perception was so much better than in the past. It was very much more obvious to him where to place the protractor, for example, in order to measure the angle. It may not be the curriculum that has improved his maths but just puberty/maturity.

 

I'm starting to think that Stanley Schmidt of LOF has a good point: no serious algebra until the child has hair under his arms.

 

Laura

[ummof3]

Laura

 

I know you used Galore Park Maths and Singapore. I'm using Rightstart and considering something to go along with it. I hated maths at school. I was put in a lower class and the teachers were uninspiring. Now, as a grown up, I enjoy some aspects of it. I'm good at real life maths and I guess that's because I understand the why's of it. In school, the books and teachers didn't offer that. I'd like to know your evaluation of the curriculum you used to get to where you are now.

 

Anyone else, feel free to add :)