How much "teaching" do you actually do? (Math)

[nov05mama]

I am struggling to find a good balance between how much independent work he as vs how much is actually me teaching him, in several subjects, but most specifically MATH. I feel like his math is nothing but review, review, review at the moment, and I don't want him to hate math like I did.

 

So, how much do you actually TEACH? Should it be where he's doing his exercise in Singapore math and just completes the work even though he completely understands the concept? Should I be skipping these sections or is the constant review beneficial? I am sorry to sound stupid, but I don't want to stress him out either by making it too challenging...at the same time, don't want to have it too 'hum-drum' and have him HATE math (which is currently his favorite subject).

 

To give a general idea, he's on Unit 2 of 2A and working on 3 digit addition with regrouping (339+104+40=, etc). Today, he completed the exercise independently and got only 2 incorrect (and was incorrect only b/c of not paying attention to what he re-grouped and was off by 1 digit - typically he gets them ALL correct on the first try), and when I asked him to re-check the 2 incorrect, he found the mistake immediately.

 

Should I be skipping this portion and call it mastery?! I just feel like I should actually be 'teaching' him more than I am...I don't want to sound like I am bragging about his ability b/c I am NOT - I am really just not sure what to do. Math didn't come easily for me like it does for him...I can explain a concept to him once and he just GETS it...but I don't know what to do with that?! Maybe set aside those chapters and then revisit them for review periodically?!

 

PLEASE HELP!

[2smartones]

I find that I've never really taught my kids much. I've introduced, elaborated, and corrected, but there have only been rare occasions when I've lectured something from scratch and TAUGHT something new. My kids are self-taught in most areas. They learn better by trying something new and having me correct them than by listening to me show them how it's done and then practice it.

 

My tendancy is to bump things up a notch. If they roll their eyes, I bump it up another notch. If they struggle, it's perfect. If they get frustrated, I back up.

[Halcyon]

I rarely teach my older. He reads the textbook, goes through the examples, does the workbook and then works in the IP or CWP. We occasionally will work together through the CWP or IP challenge questions. He likes to be independent. We are also working through Lial's BCM and there are parts that he needs a little help on, but really, he'd rather just sit there and stare at it til he gets it :) What I've done for him (because, like your son, he gets things quickly but I am wary of moving too quickly) is to simultaneously work on challenging topics while moving quickly through "the basics". For him right now, that means Alcumus, Lial's BCM, lots of challenging math puzzles and challenge math (like Zaccaro and Olympiad questions). That way, he gets the pleasure of "getting" his grade-level math quickly, and the challenge of higher level math all at the same time. You don't want him to get to a place where he feels "math is so easy" because when he does hit harder stuff, it's more likely he'll give up--he needs challenge now, but also needs confidence building. A two pronged approach might work.

 

For my younger, my involvement is mostly in the form of thinking of fun games and playing them with him. We are doing a bit of MM 2A along with SM and he definitely doesn't need my help with that.

[nov05mama]

Thanks so much to you both! I am definitely weary of moving too far ahead, so I definitely like the idea of continuing to add the challenge elsewhere and continuing with the material he does know as well. I think to help balance, I will just make sure it's not TOO much of the "easy stuff" so he doesn't get burned out on it...that's my biggest fear in that respect.

 

For my younger, my involvement is mostly in the form of thinking of fun games and playing them with him. We are doing a bit of MM 2A along with SM and he definitely doesn't need my help with that.

 

That's a great idea and I need to find some more challenge things to continue with. We went through Logic Safari book 1 and he liked it, but wanted a little more 'variety'...one I recently added (that he LOVES) is Solve It! Challenges - I found this free download on the TpT website for November: http://www.teacherspayteachers.com/Product/SOLVE-IT-November-Math-Logic-Problems-Using-the-100-number-Board

and he's done the first one so far and LOVES it!! She has some others also available that I might have to get for him (or at least come up with something similar for him to practice).

[AK_Mom4]

I almost never teach math. There have been a handful of lessons I had to walk DD10 thru in the last few years. Multiplying/dividing negative fractions was one - swapping the signs was eluding her. Setting up word problems was another. Mostly she reads the lesson on her own and *gets* it.

[acurtis75]

I find that I've never really taught my kids much. I've introduced, elaborated, and corrected, but there have only been rare occasions when I've lectured something from scratch and TAUGHT something new. My kids are self-taught in most areas. They learn better by trying something new and having me correct them than by listening to me show them how it's done and then practice it.

 

My tendancy is to bump things up a notch. If they roll their eyes, I bump it up another notch. If they struggle, it's perfect. If they get frustrated, I back up.

 

:iagree:I was just telling dh the other day that if/when we have another child it might be a serious shock to me as a teacher because I don't really have to teach dd much. She pretty much just gets things and reads and teaches herself. I'm more of the scheduler and the supervisor than teacher. The only things I feel like I "teach" her are about social skills, having great character, developing a good work ethic or life skills in general.

[nov05mama]

Thank you all SO much for your responses :D I feel SO much better knowing that it's "normal"...I really was feeling like I was doing something WRONG b/c I just don't feel like I am teaching...I feel like I just supervise and answer questions when and if they come up. Don't get me wrong, I am thankful...just worried I was messing something up and/or not doing things right, LOL!!

[Crimson Wife]

I teach new concepts, but if it's a review section, I maybe take a minute to just verify that the child remembers what to do, and then have him/her do the exercises.

[Whereneverever]

Wait, we're supposed to teach math? :tongue_smilie::lol:;)

 

Honestly, my DD reads the lesson to herself, works it out, and often will grade it as well. If she can't suss it out herself I will happily help but that doesn't happen often.

[MissKNG]

Wait, we're supposed to teach math? :tongue_smilie::lol:;)

 

.

 

My thoughts exactly!! :D

[Tigger]

Wait, we're supposed to teach math? :tongue_smilie::lol:;)

 

 

Who knew?

[go_go_gadget]

I teach new concepts, but if it's a review section, I maybe take a minute to just verify that the child remembers what to do, and then have him/her do the exercises.

 

This is what I do as well. I will depart from the general theme in this thread and say that I think skill subjects, especially math, should not be self-taught. It's very easy in math to form false associations that work for now but won't work later, and to go through the motions without true understanding of the underlying structure. It's also essential that students learn multiple ways of approaching problems instead of using the same method each time. As I math major, I see students in higher math trip up again and again because of these kinds of problems, and have experienced the same myself.

[boscopup]

I teach math a little bit, but I had to accelerate him to a point where I *needed* to teach the math. We skipped things that he was proficient in. For example, we did 2-digit addition/subtraction with regrouping. He understood the concepts quickly and was able to apply the concepts to larger numbers immediately (5+ digits). So when we came upon the 3-digit chapter, I skipped the chapter completely. I had him work some word problems in Singapore's IP and CWP on those topics, but I didn't do the actual chapter in MM where 3-digit addition/subtraction is taught. It was unnecessary. He was continually demonstrating proficiency in the topic, and would be using the topic in later math (multi-digit multiplication, for example). It wasn't a topic that we'd never see again.

 

I skipped several chapters in MM1 and 2 (we did one tiny section of one chapter of MM2B, and skipped the rest of that book). We skipped a little bit in MM3. We have not skipped much in MM4. Some topics we have done a few problems to review and then moved on, but we don't dwell on topics if it's obvious he fully understands them forwards and backwards.

 

My son is not independent with math, mostly because he doesn't want to be. He's perfectly capable of reading the material and understanding it, but he's 7. I don't expect to hand him the workbook and let him learn it. Besides, I think there is a lot of value in discussing math with your child. We often go off into the weeds, discussing higher level topics that aren't what we're learning in the book, but stem from what we're learning in the book. It's fun to watch him start thinking about the numbers and discussing them. If I were just handing him the book to do independently, we wouldn't have that exchange of ideas.

[LittleIzumi]

I finally skipped an entire book and flew through another half until I found something that needed teaching. Then we had no idea how to handle that. :lol: Dd was very displeased with having something that was hard for her, esp with the ADD (too many steps). So we stepped back for a bit. I still do some instructing, but not much. Once it's explained she takes off, and I just have to remind her a little the next time on hard things and off she goes. I like Miquon for the new concepts, as it helps her to truly understand & manipulate the math with her VSL style.

[zaichiki]

I can explain a concept to him once and he just GETS it...but I don't know what to do with that?! Maybe set aside those chapters and then revisit them for review periodically?!

 

Yes: that's what I do.

 

We go through fits and spurts. Some things seem to come so easily: it seems as if they already knew the skill on some level. If not much review is needed for a particular topic, we forge on (but I try to add in one of the review problems from that chapter each day until we run out of them).

[zaichiki]

I had him work some word problems in Singapore's IP and CWP on those topics, but I didn't do the actual chapter .

 

We do this, too. IMO the problems in the IP are more worthy of our review time than the problems in the workbook are... so we do sometimes ditch the workbook completely and hang out in the IP. It just depends on the topic/skill.

[zaichiki]

My tendancy is to bump things up a notch. If they roll their eyes, I bump it up another notch. If they struggle, it's perfect. If they get frustrated, I back up.

 

I've found that my older kids, especially dd right now, will roll their eyes and complain that it's too easy, but then jump right to being frustrated (it's too hard!") with no stop in between. I don't know if I'm just bumping up the challenge level too much or if that's just their dramatic personalities. The funny bit is that they will often go from "it's too easy" to "it's too hard" and then back again in five minutes! (Makes a mama crazy!)

[wapiti]

I think there are several aspects of a situation that will affect independence, including but not limited to: (1) age of the child, (2) difficulty of the material in relation to ability and past experience, and (3) the child's unique combination of personality, strengths and weaknesses.

 

For instance, my dd was pretty independent with MM5. After that, I bumped her up to AoPS Prealgebra (on purpose, for the challenge). Since then, she's been much less independent. Part of that is the amount of challenge, and part of that is her personality/learning style. She gets a little anxious or something, self-doubting, when things are challenging, even when I know she can do it if she puts her mind do it and even when she yearns for the challenge. In contrast, one of her brothers will probably not be that way when it's his turn - he just "sees" stuff and really feeds off the challenge, and I expect he'd move along through that book much faster if it weren't for his glacially slow processing speed when it comes to writing and such :glare:.

[LMD]

We skipped some of that in 2A, it was literally boring my DD to tears. I'll try to push doing as many exercises as possible, but once it's clear it is doing nothing but annoy I'll skip to the review section - if she aces it then we move on. Once we got to the next topic (measurement?) she loved it again and finished the workbook that evening. :auto:

 

What boscopup posted sounds similar to us, DD is still so young that she needs me there, and we enjoy discussing the questions, coming up with other ways to think about them etc.:

I teach math a little bit, but I had to accelerate him to a point where I *needed* to teach the math. We skipped things that he was proficient in. For example, we did 2-digit addition/subtraction with regrouping. He understood the concepts quickly and was able to apply the concepts to larger numbers immediately (5+ digits). So when we came upon the 3-digit chapter, I skipped the chapter completely. I had him work some word problems in Singapore's IP and CWP on those topics, but I didn't do the actual chapter in MM where 3-digit addition/subtraction is taught. It was unnecessary. He was continually demonstrating proficiency in the topic, and would be using the topic in later math (multi-digit multiplication, for example). It wasn't a topic that we'd never see again.

 

I skipped several chapters in MM1 and 2 (we did one tiny section of one chapter of MM2B, and skipped the rest of that book). We skipped a little bit in MM3. We have not skipped much in MM4. Some topics we have done a few problems to review and then moved on, but we don't dwell on topics if it's obvious he fully understands them forwards and backwards.

 

My son is not independent with math, mostly because he doesn't want to be. He's perfectly capable of reading the material and understanding it, but he's 7. I don't expect to hand him the workbook and let him learn it. Besides, I think there is a lot of value in discussing math with your child. We often go off into the weeds, discussing higher level topics that aren't what we're learning in the book, but stem from what we're learning in the book. It's fun to watch him start thinking about the numbers and discussing them. If I were just handing him the book to do independently, we wouldn't have that exchange of ideas.

[Alte Veste Academy]

I've found that my older kids, especially dd right now, will roll their eyes and complain that it's too easy, but then jump right to being frustrated (it's too hard!") with no stop in between. I don't know if I'm just bumping up the challenge level too much or if that's just their dramatic personalities. The funny bit is that they will often go from "it's too easy" to "it's too hard" and then back again in five minutes! (Makes a mama crazy!)

 

Oh my word. It's like you're at my house! I think I'm starting to figure DS8 out. He cries too easy if he knows something, because it is immediately extremely boring and a waste of his time. He cries too hard if he doesn't immediately understand new material, because it is rare and that is a terribly uncomfortable feeling that he's not used to having. I'm trying to find the sweet spot where he sees the unknown as intriguing challenges. I'm also wondering if there is some kind of fast track curriculum or some fabulous test that will make it easier for me to figure out exactly where he is because half the time, I feel like I don't have any idea what he knows and what he doesn't. :001_huh:

 

Help? :lol:

[nov05mama]

Thanks everyone! I am really glad to hear that it's common...I was really concerned that I SHOULD be having to teach more to him. We have fun with math challenges and such as an extra bonus, but his regular Singapore 2A has just been something that I can literally hand him and he just completes....didn't seem "right" to me ;) He doesn't necessarily mind that it's review, but I can definitely tell the AMOUNT of review matters (otherwise boredom sets in), so I will definitely make a point to keep the review in the mix, but skip ahead if necessary too.

[zaichiki]

Oh my word. It's like you're at my house! I think I'm starting to figure DS8 out. He cries too easy if he knows something, because it is immediately extremely boring and a waste of his time. He cries too hard if he doesn't immediately understand new material, because it is rare and that is a terribly uncomfortable feeling that he's not used to having. I'm trying to find the sweet spot where he sees the unknown as intriguing challenges. I'm also wondering if there is some kind of fast track curriculum or some fabulous test that will make it easier for me to figure out exactly where he is because half the time, I feel like I don't have any idea what he knows and what he doesn't. :001_huh:

 

Help? :lol:

 

As my oldest has gotten older it has gotten easier. He has found a middle ground... unless the number of math pages is more than 2 (doesn't matter if that is only 6 problems with large graphs). Even though he *sometimes* still gets overwhelmed and thinks something will be too hard, he controls his reaction better. Most of the time. Heh. He's 12.

[regentrude]

This is what I do as well. I will depart from the general theme in this thread and say that I think skill subjects, especially math, should not be self-taught. It's very easy in math to form false associations that work for now but won't work later, and to go through the motions without true understanding of the underlying structure. It's also essential that students learn multiple ways of approaching problems instead of using the same method each time.

 

There are programs that are intended for a student to self-teach: Art of Problem Solving for instance. It is not just self-teaching, but based on discovery - so not even the book tells you what is going on at first, but lets you figure it out yourself. And when the material is presented and you get to the practice (using different methods for each problem), there is no way to make it through the problems until you have completely understood the concepts and have several different strategies ready - otherwise you don't even get through the normal ones, and have no chance on the challenge problems. So there are checks and balances built into the program that take care of your concerns.

[Beth in SW WA]

There are programs that are intended for a student to self-teach: Art of Problem Solving for instance. It is not just self-teaching, but based on discovery - so not even the book tells you what is going on at first, but lets you figure it out yourself. And when the material is presented and you get to the practice (using different methods for each problem), there is no way to make it through the problems until you have completely understood the concepts and have several different strategies ready - otherwise you don't even get through the normal ones, and have no chance on the challenge problems. So there are checks and balances built into the program that take care of your concerns.

 

Thanks for this explanation, Regentrude. It is for this reason that I doubt aops prealg will be a good fit for dd. She loves a visual presentation. If she sees something once she usually has an imprint of it and it sticks. The wordy text of aops will not appeal to her. I hope to add elements of aops. I know things can change but I am foreseeing a more traditional approach to alg with her. She loves TT prealg currently. The up-front lecture is quite effective with her.

 

As to the OP's question, I teach dd from the SM HIG & we work through the text. I help w/ problems as needed. With TT, the video lecture does the teaching while I sit beside her. We pause often to discuss. At this point I am with her during the whole lesson explaining these new concepts as we go.

 

I teach all our HoE lessons. It's my latest guilty pleasure. :) (Did I mention how much I LOVE this program??)

[go_go_gadget]

There are programs that are intended for a student to self-teach: Art of Problem Solving for instance. It is not just self-teaching, but based on discovery - so not even the book tells you what is going on at first, but lets you figure it out yourself. And when the material is presented and you get to the practice (using different methods for each problem), there is no way to make it through the problems until you have completely understood the concepts and have several different strategies ready - otherwise you don't even get through the normal ones, and have no chance on the challenge problems. So there are checks and balances built into the program that take care of your concerns.

 

Right, and those are reasons I plan to use AoPS with mine when they get to that point, but AoPS is (until Beast Academy is released) only for older students who have a solid foundation to begin with, not lower elementary students who are just starting out, which is what the OP was about.

[boscopup]

Right, and those are reasons I plan to use AoPS with mine when they get to that point, but AoPS is (until Beast Academy is released) only for older students who have a solid foundation to begin with, not lower elementary students who are just starting out, which is what the OP was about.

 

Yeah, I wouldn't skimp on teaching in the early elementary grades. I'm fine with my child using AoPS independently when he's mature enough to do so. They do eventually grow up and are able to study something independently and learn from it, just as we adults do. But a 5, 6, 7 year old learning the basics of early math... I don't trust that to self-teaching, even though many of the kids on this forum often learn the things before we get there to teach it, we still end up needing to fill in holes in their knowledge. ;)

[Alte Veste Academy]

As my oldest has gotten older it has gotten easier. He has found a middle ground... unless the number of math pages is more than 2 (doesn't matter if that is only 6 problems with large graphs). Even though he *sometimes* still gets overwhelmed and thinks something will be too hard, he controls his reaction better. Most of the time. Heh. He's 12.

 

I'm hoping this will come. I think me relaxing into his way of learning instead of being a worried wreck would be helpful. Not shocking. :tongue_smilie:

 

This is what I do as well. I will depart from the general theme in this thread and say that I think skill subjects, especially math, should not be self-taught. It's very easy in math to form false associations that work for now but won't work later, and to go through the motions without true understanding of the underlying structure. It's also essential that students learn multiple ways of approaching problems instead of using the same method each time. As I math major, I see students in higher math trip up again and again because of these kinds of problems, and have experienced the same myself.

 

Right, and those are reasons I plan to use AoPS with mine when they get to that point, but AoPS is (until Beast Academy is released) only for older students who have a solid foundation to begin with, not lower elementary students who are just starting out, which is what the OP was about.

 

Laura, I suspect part of the reason so many are saying they don't teach is not that their kids are self-taught so much as intuitively understanding. I have tried to teach my DS8. Really, I have...still do. But it's sometimes like I'm sitting him down for breathing lessons. I might say, "OK, first you breathe in. OK, try that. Now, breathe out. That's called exhaling." And he's looking at me like I have three heads because, seriously, duh. That's as close as I can come to explaining what it's like "teaching" math to my oldest. :lol: So, I go for exposure and try to find stealthy ways of making sure he understands it perfectly and, yes, from all different angles.

 

Even when he doesn't immediately understand something (and is shocked and offended by that :001_huh:), he doesn't respond best to me teaching the material. He responds best to me giving it to him as a puzzle to solve, then getting out of his space while he plays with it. Obviously, I have to make sure that he understands it, and I do. Ultimately, that is the goal of teaching, right? In the end, understanding as demonstrated by execution is paramount, regardless of the specifics of the process. You are right about not letting them form (or proceed with) false understanding (although we haven't had that problem yet). Not formally teaching does not necessarily mean removing yourself from the process entirely.

 

Believe it or not, not teaching makes my life much harder, not easier. I expend way more energy worrying about botching it up than I would doing a prepared lesson every single day. Heck, I could throw in a full-on overhead projector experience and still be expending less energy than I do obsessing. :lol:

[go_go_gadget]

Sure, sometimes "teaching" is instruction, sometimes it's just close observance to make sure no false associations are being made. Dialogue is important, whether it's instructional or just mutual musing. Observance of the thought process is essential, regardless of whether the material needed to be talked over before being worked through; it's the same as showing your work. However, if a concept is understood intuitively, to me that suggests a need for a few challenging problems that utilize that concept, not an immediate moving along to the next concept.

 

I'm pretty sure we're agreeing here; I think the problem is just different ideas of what "teaching" means. I tend to approach things in very Socratic way, so to me "not teaching" perhaps means something different than "not teaching" means to others.

 

 

eta: I think what I'm trying to say is that the level of interaction should not be lower for students for whom concepts come easily and intuitively (they do for my kids as well) than it is for kids for whom the concepts are more difficult. There isn't less work for the teacher/parent to do, it's just different work (the work of finding a way to present the material in such a way as to present an appropriate level of challenge for the student).

Edited November 11, 2011 by go_go_gadget

[Alte Veste Academy]

Sure, sometimes "teaching" is instruction, sometimes it's just close observance to make sure no false associations are being made. Dialogue is important, whether it's instructional or just mutual musing. Observance of the thought process is essential, regardless of whether the material needed to be talked over before being worked through; it's the same as showing your work. However, if a concept is understood intuitively, to me that suggests a need for a few challenging problems that utilize that concept, not an immediate moving along to the next concept.

 

I'm pretty sure we're agreeing here; I think the problem is just different ideas of what "teaching" means. I tend to approach things in very Socratic way, so to me "not teaching" perhaps means something different than "not teaching" means to others.

 

I think you're right in that we are agreeing, especially as you described what teaching looks like to you. We absolutely move from understanding the easier concepts to folding them into more challenging presentations of those concepts.

 

I do sometimes wish I could take a little flashlight and look into DS's brain through his ears at night while he sleeps. I could make a little map, maybe an outline...something to make me feel better. :D

[Beth in SW WA]

 

I do sometimes wish I could take a little flashlight and look into DS's brain through his ears at night while he sleeps. I could make a little map, maybe an outline...something to make me feel better. :D

 

:bigear:

 

Speaking of sleep...and math....

 

Dd8 dreams nightly about Fred (from LOF). He is now interacting with Rochester (Jane Eyre) in her vivid dreams about math. Her wind-down time is cuddling up w/ LOF and a flashlight in bed.

 

Pardon the digression..... :)

[Whereneverever]

OK, to clarify- I don't send my child out into the void sans interaction. I don't teach the stuff we're doing in math right now because she gets it- but I also am constantly checking that by presenting problems in different ways and discussing various ways to get an answer.

[gracyomalley]

I teach math.

 

I do have one child who asked to do saxon this year, skipped 3 levels, and is mostly doing it on her own...but that is an experiment, as she is my most verbal/visual learner....and thinks she doesn't like math....we'll see how it goes....and I do still go over new things with her. She just needed her math to be different from the boys, and to take some ownership and pride in it...as she stuggled with long division but naturally "got" all the other concepts up to level 8/7 on the placement tests....

 

With both boys I teach. If they get something easily, I move on some, but I also DISCUSS the how and why of the math with them....especially with the older one who is doing MM6/LOF pre-algebra...and because we've been elaborating on his math with "pre-algebra" and scientific applications since about saxon 3 level, its not new stuff....Now, he is 2E, with significant dyslexia and a bit anxious if he doesn't know exactly how to approach something, so much of the "teaching" isn't the actual problems, but rather cross application of concepts to help him ease up on his rigid approach, and really own the concepts....many gifted kids wouldn't need this.

 

I do think that there are kids who intuitively get math...my youngest never had to memorize facts, never had to be taught place value, and hasn't struggled at all with multiplication and division so far....but we still teach....again to make sure that he really understands the underlying problem solving....I am expecting that with MM4 and up he will need more, but I don't know....maybe not.