Tell me why I'm wrong about math

[Lilikoi]

This is my first post, but I’ve been reading here for about 2 years; I hope to get your advice on my math plan.  My DD just turned 5, so is now ‘officially’ being homeschooled.  We completed Miquon last spring.  Loved it.  We moved into BA and did the parts of each of the four books (3A-3D) that she could realistically handle, given her age, maturity, and math skills.  She was probably able to do about ½ the program, typically the first half of each chapter.  Now I am considering what I want to do next.  My problem with continuing to work on BA as a standalone curriculum is twofold:  1) It moves very fast for a five year old, and I find myself “filling in†too much – Googling tips for teaching long division, for example.  (I work full time, and I don’t have hours a week to plan new math lessons.)  2) My goals are not to challenge her to death for the sake of challenge, and sometimes that’s what BA feels like to us, when using it as a standalone curriculum.   

So what to do next?  It seems that many of you would suggest more game-type stuff and/or other “challenge math†at her level.  We’ve done some of this… Things like Sunshine Math and Math Kangaroo problems.  I am inclined to move into MM, 4^th grade.  My rationale for this decision:  1) It’s the appropriate placement for what she already knows.  2) It will allow her to continue to build on her knowledge with a more manageable level of challenge.  3)  Most important reason:  She will “get something†out of the hard work she puts in.  I want to continue to challenge her at her level; she is capable of it, and I believe it will build in the appropriate character skills needed to succeed later in life.  However, I want her to get something out of the challenge.  And if she can master 4^th grade math now, while also building character and being reasonably challenged, that seems much more valuable than just being challenged with overly complicated story problems, and not “getting†anything tangible for it. 

In simplest terms:  My thinking is that 4^th grade math is good for her brain, and it accomplishes the goal of learning 4^th grade math.  Doing more challenge problems is “only†good for her brain.  Is this bad logic?  Another option would be to continue with BA, with me doing more teaching, but I feel like MM does a great job of filling in the steps – much better than I could do, given my prep time constraints.

Last few notes:  1) Not doing any math is not an option.  Both parents are STEM types and think math is important.  Once she completes calculus, she can do other stuff if she prefers.  2) Math only consumes 30 minutes a day, and we think that’s reasonable, so please don’t think that we’re torturing her with hours of math every day.  3) I am not looking for curriculum advice; I can compare the options myself.  I am more looking for what the hive thinks about moving forward into the next level (4^th), instead of going sideways, given the rationale and circumstances I’ve laid out. 

[regentrude]

Let me preface this by saying that, a physicist, I love and value math and understand its importance. We have given our children a rigorous math education and love AoPS.

But this said: your child is five. I see no need to make even an accelerated five year old work on 4th grade math for the sake of character building.

BA is an advanced curriculum for strong math students and intended to challenge students in grades 2-5. It is supposed to be a challenge for a studnet who uses it on grade level, and thus is most likely not a suitable curriculum for a five year old, even if she is smart - you having to suplement and direct teach is a strong indicator.

Unless the student is craving and demanding this math challenge, I do not consider it a sensible path to push her to work five grade levels ahead.

Edited September 11, 2016 by regentrude

[wendyroo]

I LOVE Math Mammoth.  I currently have two kids working through the program.  I think it is a great fit for my accelerated learner.

I also LOVE Beast Academy.  My oldest is currently working in 3b.

 

In your situation, I think Math Mammoth would be a better fit than Beast Academy.  BA is an advanced curriculum meant to be started with advanced 3rd graders.  Yes, I think there are many advanced 2nd graders who can tackle it, and probably even some advanced 1st graders who can handle some of it, but I think, as you mentioned, it is just too big of a jump for most kindergartners even if they are strong in math.  My oldest had the math skills to do some of the BA problems several years ago, but he is getting a lot more out of it now that he can focus more on the logic and strategy and problem solving without simultaneously having to learn all the new math concepts he encounters.  For this reason I purposefully placed him "behind" in BA so it is a challenging, out-of-the-box review of concepts he has already learned through MM.

 

As for starting at Math Mammoth 4...well, if you're sure.  MM4 is what my oldest is currently working through and it is...a lot.  A lot of precision calculations, a lot of pages, a lot of writing in small spaces.  It definitely has a more mature feel to it with less illustrations than the previous books.  DS is finding it a lot less fun and more of a slog than in the past.

 

OTOH, there are a lot of meaty concepts in MM3, many illustrated with pictures of animals:

Roman Numerals

Order of Operations

The Array Model of Multiplication

Multiplying by Zero

Elapsed Time

Currency and Making Change

Measuring Length, Weight, Volume

Comparing Equivalent and Non-Equivalent Fractions

Charts and Graphs

Lot of Word Problems and Puzzles

 

Best of luck with whatever you decide on,

 Wendy

[EKS]

Have you looked at Singapore math?  It is easy to accelerate, it teaches conceptually, and it isn't as hard core as BA.  I'd give her a placement test and start where she places.  Then you could give BA another try when she's a little older.

[Sarah0000]

My four year old just started BA 3, and mostly does it at will. Its a fun puzzle book to him, not a math curric. For math work he's been doing Key to Fractions book 1 which is considerably easier than BA and he can do it independently. Its a lot like Miquon.

[quark]

I mean this in the nicest way possible. I really do so please don't be offended. Why does your title begin with "tell me why I am wrong"? Is it because you want:

• answers that challenge the way you think about how a 5yo should be taught?
• answers because your intuition is telling you that while you certainly know a lot about math and are a STEM-type, something might not be right about approaching math teaching this way, especially since you are including plans for calculus now, when you have a 5yo?
• both?

I can tell you what can go wrong because I know this first hand. Your child can burn out completely. Even if you had not intended to cause that burn out. Your child can be turned totally off of math. I don't read anything in your description about your DD wanting this level of math out of sheer joy/ passion/ delight/ because her whole world would go dim if you stopped teaching math this way. I see a lot of words about hard work and appropriate placement and getting something out of challenge.

 

I wouldn't give up BA if she loves it and yes, I would still expose her to 4th grade math because if she really likes the challenge I wouldn't want to risk boring her with too much easy stuff but I would definitely reconsider goals about getting her to calculus and letting her do stuff she prefers after that.

 

There's a reason why we suggest games and going sideways on these boards. Taking a different path from time to time or alongside standard/ challenging curriculum often introduces different types of critical thinking (vs just slogging through the critical thinking) in a very age appropriate, gentle, fun, connecting the dots sort of way. I also understand not wanting to let go of or changing the way you do math (because that might be the way you know best or how you were taught math yourself).

 

How we did it was to teach math in strands -- at age 5, that might have looked like 10 minutes of curriculum (BA came out too late for us -- in the early years we used MEP, SM, a bit of Right Start) + 10-15 minutes of whiteboard you teach me what I taught you (or you teach me new things you thought about) math + maybe 10 more minutes after dinner of puzzles/ logic problems/ living math (but if it was very fun, my son would ask for more than 10 minutes). We increased the time as appropriate when he grew older.

 

It didn't slow him down or teach him bad habits one bit. He finished calculus at 12 and this was *after* taking him through algebra and more algebra, geometry and more geometry, logic and more logic, group theory and abstract algebra and more group theory, etc. So many bunny trails. Lots of hard work and good attitude. But no, at 5, it wasn't about *teaching* grit or resilience. I think deep down, I was scarred by the way I had been taught so I wanted him to keep loving math, to make it something he would turn to for fun and not just for school.

Edited September 12, 2016 by quark

[maize]

I'm also missing any sense of "my child loves learning math this way and is begging for more" in the original post. 

 

I see more of "this is a smart capable child and I'm going to get her to calculus as quickly as possible"--and that approach worries me.

 

What math would your daughter enjoy doing this year?

[SeaConquest]

Echoing the sentiments of Regentrude, Quark, and Maize. I would also add that I'd have mutiny on my hands if I tried to do MM4 with my son after completing BA3. We found MM to be a total slog, even skipping half the problems. We are waiting on our BA4 books to come in from our charter, and have been skipping around in the Singapore 4A IP. Sacha, my compliant child, is grumbling, asking when BA will be here.

 

When I find that I have to do a ton of handholding with him, it's usually a sign that he's just not ready for something. Rather than feel like a salmon swimming upstream, we set it aside. Invariably, we come back to it later, and it is smooth sailing.

 

Unless she is begging for more math right now!!, I agree with moving sideways. Read living math books, watch math documentaries, if she is interested, and play math and logic games. Move into BA4 when the time is right for you both.

[Arcadia]

Both my hubby and I are engineers. However my DS11 wants calculus for his interest in physics and reach calculus at his own pace :P DS10 is also going at his own pace and his interest is more on chemistry so he is happy to go slower :)

 

Regardless of what the subject is, going in a "straight aim for the finish line" way when a child is not driving the need can lead to resentment and burnout. My DS11 learned violin when he was 3 when he wanted cello. We stop violin lessons after six months. Recently he took out his violin and played it like a cello.

 

Math only consume less than 10 minutes a day of assigned work until my kids reached AoPs Prealgebra. My kids did explore more at their own free time.

 

As for grit and resilience, I can honestly say making a child practice his/her musical instrument for hours at 5 years old would work but whether the child becomes a virtuoso or someone who is music phobic is hard to foretell.

 

ETA:

For grit and resilience using math, maybe read elmerRex long thread on how she use Saxon math

"An In-Depth Review of Saxon Math 54 -- LONG *little update*" http://forums.welltrainedmind.com/topic/547570-an-in-depth-review-of-saxon-math-54-long-little-update/

Edited September 12, 2016 by Arcadia

[slackermom]

hmm...  I guess I don't see "the goal of learning 4th grade math" as a particularly meaningful goal for someone who is capable of doing such a thing at the age of 5. Around that age, my daughter asked for more "complicated" math, so I spent time covering all of the elementary math topics in a logical progression, using whatever materials seemed appropriate as we went along, at a variety of levels and from different perspectives. 

I am not sure what you mean by "overly complicated story problems." Math is a great tool for understanding lots of things, both simple and complex. When dd was 6, she told me, "math is life."

[ebunny]

I agree with the previous posters about your strategy not being optimal to raise a math 'loving/liking' child.

Having said that, you know your child best. if you're already set on moving her on to MM..A few suggestions. I think Maria Miller has placement tests on her site to correctly place a child into the appropriate grade. Use those. I would focus on the content rather than grade number.

[ebunny]

Dp

Edited September 12, 2016 by ebunny

[SanDiegoMom]

Singapore Math Intensive Practice starts at grade one, is a very solid program that stretches without being quite as intense as BA. My son started it in grade 1 and we compacted it and he finished grade five (with a lot of compacting!) by grade 2. He started PreA in grade 3. But in K we played math games, strategy games and read books about math. It was those things that really fueled his love of math. Books like Penrose the Mathematical Cat, DK books like Why Pi and Go Figure, the Number Devil, all of the Murderous Maths books... He didn't really start doing more than 10-15 minutes until he was in 3rd grade. And Math Mammoth would have killed him. Repetition is the surest recipe for disaster!

[Mike in SA]

To the OP:

 

On this board, you'll find that most parents with accelerated math learners have students of the "can't be slowed" variety.  What I mean is, the kids aren't accelerated because the parents decided to accelerate.  They are accelerated because the kids decided to accelerate.

 

You may sense some frustration with the expressed desire to force accelerate.  Part of that is because we are constantly assaulted with accusations of robbing our children of their childhood through forcible acceleration - by individuals who have no comprehension of what it means to give an EG or PG child a happy childhood.  The other part is because we definitely do understand what it means to encourage, instead of push.  When a child is pushed before being ready, the child is likely to burn out and hate a subject.  When a child is encouraged through appropriate challenges, the child will grow to love the subject.  You will find out if and when the child is ready to take off.  It may not be a gradual process - it could be sudden and surprising (our 4th grader didn't know basic arithmetic at the start of 1st, and you can see he isn't struggling or lagging).

 

Don't ditch a curriculum your child enjoys because it is challenging.  Allow them to set their own limits, and establish their own challenges.  If, on the other hand, the curriculum is not fun, it's a bad time to force the issue.  Be patient, and keep it fun.  We'd all appreciate seeing another math lover.

 

Please do stay engaged - this is a very active and supportive community.

 

[Guest]

Usually 'filling in' means the student is missing pre-reqs or number sense.

 

Our experience with word problems was that most were trying to use language subtleties to confuse the student, or require multiple steps that the student couldnt keep track of, and the student was really learning to state assumptions, detangle multiple parts, or figure out grammar. The exception was Singapore IP ...the challenge section there had some interesting problems...and some Problem of the Day material from Houghton Mifflin that could be solved figuring out things using number sense rather than wag&check. The value there was stretching the mind out of cookbook mode, learning problem solving, learning to play, and presenting solutions ('proof'). I would also suggest trying Ed Zaccaro...he was fun and some of his questions were good for warm ups.

 

As far as 'get something'...you are better off not putting math in level boxes. Just go thru the strands. The student should feel that they 'get' value out of each problem; if the satisfaction of solving isnt there, one needs to question and adjust. Our decision was to let the child select the problems that he felt were not obvious and encourage multiple solutions.

In your situation, with 30 min a day, I would recommend Singapore Math plus fun in the form of games and real life. Learn probability and stats and logic hands on with card and board games. Garden, cook, measure and build. Study music and perform...handbells, violin, piano...whatever is the interest and available in your area.

Edited September 12, 2016 by Heigh Ho

[wapiti]

My two cents - OP, I think I get what you are trying to do - I am kind of having flashbacks LOL.  You want to keep her challenged for all the usual reasons, for intellectual development and for avoiding perfectionism.  Where your thought process went awry for me was connecting that to character, which is unrelated in my perspective. I'd throw away the notion of involving character in math decisions for anyone, let alone a young Ker.  On the one hand, generally I think it is good to strike while the iron is hot, and yet on the other, obviously there is no rush.  There is plenty of time to explore and no need to adhere to a straight sequence.  I would emphasize exploration.  It's hard to say more not knowing what your dd's behavior is like, whether she eats it up, gets annoyed, is quietly compliant, etc.

 

BA is an odd mix IMO because the concepts may be accessible to younger kids but some of the challenge level isn't.   Many kids have already accelerated through some of the 3rd gr concepts by the time they are in 3rd, though it's probably worth going through the other topics later, maybe skipping the known ones(?).

 

MM4 can get tedious.  It's very solid, but that level is a bit of a slog.  Maybe Singapore or MEP would be a better fit for this age, for a more playful feeling, though I don't know about placement in MEP.  SM has a placement test and the area to watch there would be possible asynchrony between language and math skills; the language of the SM word problems sometimes comes across to me as a little awkward.

 

Also keep in mind how quickly and easily some bright students can absorb concepts and make leaps; there is no need to keep on the standard sequence at this very young age to still end up where you want to down the road.  Explore, enjoy, wallow, follow the child - offer her a rotating banquet and she'll get what she needs and get where you want her to go.

Edited September 13, 2016 by wapiti

[Dmmetler]

Have you looked at Life of Fred? The Elementary books weren't out yet when my DD was that age, but she's loved them, and has borrowed most of the elementary ones. They have basics, but they also have a lot of really neat concepts worked in, and don't have long, writing intensive problem sets (which a lot of 4th grade math curricula have). And they go through math beyond Calculus (we have Real Analysis on the shelf-my math major DH couldn't resist it), so she's not likely to run out any time soon.

 

I don't know your DD, but mine reallt needed/wanted cute/fun stuff

[Paige]

There is so much value in things being fun at 5. I would not do MM4 w/ any 5yr old who wasn't pulling it out on his or her own. It is not fun at all. I like MM a lot. I think it prepares kids really well and is a good combo of challenging for the student and easy for the teacher. It's boring, though- a just get it done kind of program. I see no reason a 5yr old needs to get it done. I'd also hesitate to put anyone in MM4 unless they could independently pass the placement test or end of year 3rd grade test. It's about the writing as much as the math. 

 

Maybe she'd like to read through Life of Fred's younger kid series for fun, play challenging games such as Prime Climb or Equate where you can manipulate numbers at whatever level she is comfortable, play some Speed for times tables, and do a lot of logic puzzles and games. Logic skills are so important to higher level math and most kids don't have enough time to spend on logic. Practicing fun logic games now would be a very valuable use of time and she won't even know she's doing math. 

 

As for why you are wrong, it's because she's a baby. 5 year olds are so small, and so sweet, and so cute, and fun, and they will never be 5 again. She has plenty of time to learn to work, to push through boredom, and to learn to be serious later. The emotional health of our kids is worth a million times more than any academic achievement. If you push her now, you may not notice any emotional damage until she's older and it's too late to go back. It's not worth the risk. Let her be 5 and happy. 

 

If she's happy to do MM4 and she's saying, "Please, can we do this?" That's different. I don't think that's wrong as long as you let her quit if she wants. 

[pkbab5]

"1) It’s the appropriate placement for what she already knows.  2) It will allow her to continue to build on her knowledge with a more manageable level of challenge.  3)  Most important reason:  She will “get something†out of the hard work she puts in.  I want to continue to challenge her at her level; she is capable of it, and I believe it will build in the appropriate character skills needed to succeed later in life.  However, I want her to get something out of the challenge.  And if she can master 4^th grade math now, while also building character and being reasonably challenged, that seems much more valuable than just being challenged with overly complicated story problems, and not “getting†anything tangible for it."

 

I am Chinese, and I am going to let my tiger mom come out here a little because I think you can handle it.

 

1)  If she couldn't finish 3rd grade math and could only do the 1st half of each section (albiet in an advanced curriculum), then no, I don't think 4th grade math is the appropriate placement for what she already knows. 

 

2)  True.  A more "standard" curriculum will be a little bit more manageable than a "challenge" curriculum like BA.

 

3)  What on earth makes you think that standard 4th grade math is something worthwhile to accomplish for a kid who is gifted in math.  Any regular 4th grader can do 4th grade math.  It is not special.  Yes, your kid would do it early, but so what.  If you go this route, you are not giving your child "more and better math" than a standard student, you are giving them "standard math, just quicker".  Which is really pointless. 

 

What makes someone really successful with math related endeavors as an adult is not that they got through to adult math quicker than everyone else.  It's that they did the standard math PLUS all of the extra breadth of tricky math that they can handle.  The logic problems.  The over complicated story problems.  Learning how to diagram math problems, how to hold them in your head and manipulate them and extract new information, or a different perspective, or a novel approach to how to solve a problem.

 

This is the stuff that you get from the math games, from the Singapore Intensive Practice / Challenging Word Problems books, Challenge Math, and yes Miquon and Beast Academy.  And all of the other terrific suggestions on this thread.

 

If you go your way, then after Calculus, the only math your child will know is the standard math sequence, but she will be younger.  So what?  Give everyone else 3 more years, then they will catch up.  3 years is nothing to an adult.  No, what you want is more breadth.  So that when your child is an adult, she will have had the same math as everyone else, PLUS all of the enriching-teach-you-how-to-think math that they others didn't get.  That's where the competitive advantage is.  Not age.  No one cares about age when you are an adult, only skill.

 

Think of it this way:  there are two approaches.  1)  Release a kid with the same education as everyone else out into the world at age 14.  or 2)  Release an 18 year old into the world with a higher degree of brain development than everyone else resulting from the extra challenging out-of-the-box cram-as-much-breadth-as-you-can curriculum.  I don't see any advantage at all to number 1.  Not one iota.

 

Just my opinion.  :)

[quark]

More resource suggestions -- we used this as part of our "math conversations/ whiteboard math" sessions:

Good Questions for Math Teaching

And book 2.

 

Edited September 12, 2016 by quark

[Clemsondana]

One thing to keep in mind with young kids is that sometimes they can understand complicated math concepts but there are other things that may slow them down. For my son, his handwriting in K wasn't good enough to keep his numbers in a row when doing multiplication or long division. I ended up making grid paper with big boxes to help him. He also doesn't have as much attentioin to detail as an older child should be able to manage. In complex problems where he has to combine like terms or deal with exponents, he's more likely to make careless mistakes than I'd expect from an older child. Sometimes this can make it hard to tell when he doesn't understand vs when he's not paying attention. Because he's actually more interested in history than in math, we do an advanced program (AoPS) but don't push to move at a faster pace (he's in 5th grade now). It's always hard to separate the idea that the child is good at something from the question of whether they actually like it. It's a fine line keeping them challenged without pushing them - too much struggle in an area that they're not interested in can cause them to hate the subject.

[raptor_dad]

 And if she can master 4^th grade math now, while also building character and being reasonably challenged, that seems much more valuable than just being challenged with overly complicated story problems, and not “getting†anything tangible for it. 

 

 

Long division is terrible procedural math, hardly a tangible benefit for a 5yo... I would choose Singapore CWP3 story problems over any 4th grade curriculum at this point. You could do 3 hard but rich problems a day for the next year. It would build invaluable problem solving and algebra skills. If that's too easy move on to 4th grade in MEP, MM, or Singapore. If it is too hard move back to 3rd grade MEP, MM, Singapore.

[Black-eyed Suzan]

Welcome to posting! :)

I don't have much time, but wanted to post this link as a reason why you might consider continuing with problem solving instead of jumping into a standard curriculum. 

 

http://mathprize.atfoundation.org/archive/2009/rusczyk

 

My advanced DS1 did the LOF elementary series when he was 5. It was the perfect fit for him. The books start out VERY easy, but he enjoyed following the story from the beginning. We just flew through, sometimes several chapters per day.

 

Best wishes!

Edited September 12, 2016 by Black-eyed Suzan

[chocolate-chip chooky]

Lilikoi, there's a lot of wisdom here for you to take the time to absorb. 

 

Really, Quark, if you wrote a book I'd buy it. I'm always soaking up your wisdom.

 

A lot of us here have quite accelerated maths learners (mine is now 10), so there are many, many combined years of experience to draw on.

 

 

At 5, we were doing the following:

 

- playing LOTS of games (both commercial games like Monopoly, Yahtzee etc, but also print-and-laminate educational games, such as fraction dominoes, decimal bingo etc). We played because she wanted to and not because it was 'time for maths'.

 

- following my child's interest - if she wasn't asking for it, we weren't doing it

 

- lots of real-life maths applications eg cooking, shopping, playing with measuring cups, weighing and comparing things, building paper planes and comparing the distance they went etc etc etc.

  Lots and lots and lots of hands-on stuff. Lots of embedding maths concepts in fun, real stuff.

 

- we used NO textbooks, NO curricula at all at that age. In fact, we didn't until about age 7ish.

 

- if I'd known about Life of Fred then, I probably would have read it to my daughter for fun, not for 'now we're doing maths' time. We love LoF.

 

- we read fun mathy books like Sir Cumference.  Again, for fun.

 

 

 

And welcome to the boards, lilikoi  :001_smile:

 

 

[Lilikoi]

Thank you to everyone who took the time to comment.  I asked you to disagree with me, and I am not offended by any disagreements.  Your thoughtful comments have allowed me to reconsider my program, clarify my goals, and revise my thinking… slightly.

 

First, I would like to address some of the common comments:

(Paraphrasing):  ‘Finishing math early has no intrinsic value, but going deeper and broader does.’  And/or ‘There is value in going deeper – learning to think about problems, finding creative solutions, applying what you know, is all important.’ I agree.  More on this at the end of my post.

 

‘4^th grade MM is “a slogâ€.’  Thanks for the warning; I have only seen online sample pages. Of course I agree that “fun and cute†is better than dry and boring.   The “fun and cute†suggestion of LOF was a bomb here.  Child prefers higher quality fiction and found the math problems uninspiring.   On trying Singapore:  We did some CWP already, and I will reconsider looping back there.  Thanks to those of you who mentioned other possible resources.  I’m still researching them.

 

‘I was scarred by someone pushing me too hard as a child.’  I’m sorry to hear that.  I know that happens.  I was somewhat scarred by nobody challenging me, which is also a problem.  I am well aware of both ends of the stick and am doing my best to find balance.

 

To the “We just let our child play†comments:  Our kindergarten curriculum consists of 30 minutes of math and 30 minutes of reading a day.  That’s it for school requirements.  This is on the “light†end of what most people on WTM currently do for Kindy.  Comments about “pushing†are misguided, in my opinion.  I agree with Paige that emotional health is important, and it’s a focus here.  I suppose that I disagree that 5 is too young to teach the value of consistent effort.  (Isn’t that the message of The Little Red Hen?  And The Little Engine that could?  And The Tortise and the Hare?)  30 minutes of math a day should not crush anyone’s soul.  30 minutes of frustration a day might.  30 minutes of mind-numbing repetition might.  So I am trying to find the optimal curriculum that (a) is not too hard (b) does not repeat what she already knows.  My calculation was that MM4 would fit those parameters.  Of course, if I had a “play†based curriculum that covers new material that she doesn’t already have down, I’d be the first in line to buy it.  But I really need “a curriculum†to follow, since I work full time.  I can’t just come up with interesting lessons that build in math every day that are appropriately challenging etc.  

 

Let me try to rephrase my original post in another way, and see if you all still think I’m nuts:  I have a very capable five year old who enjoys math but doesn’t beg for it.  I do not want her to get overly frustrated with BA problems that are designed for children with a much larger working memory than my five year old has.  I don’t see her getting anything useful from working problems that require more critical thinking skills than she is ready for.  My thinking, therefore, is that if we slightly redirect our current efforts and move forward more with “algorithm†type work – building the mathematical toolbox, so to speak, that would free up time later, say in a year or two or three, where we could spend more time focused on applying the tools she has acquired onto challenging problems.  So my thinking was to continue with our 30 minutes of math instruction by focusing on something that 5 year olds are better at – following the steps of an algorithm.  And in a couple of years, “apply what you know†can then be the focus.  Personally, I don’t think it’s highly appropriate to ask a 5 year old to look at a problem with no obvious route forward, study it for a period of time, and “try to figure out how to do it.† This is what I feel like I am asking her to do when we do the starred problems in BA.  “Building the toolbox†seems like a better path for us right now.  And, honestly, it feels more developmentally appropriate.  Do you still disagree? 

In retrospect, my original post did not acknowledge the value in abstract thinking and advanced math problem solving skills.  So, assuming we all now can agree that these have substantial value, what about the approach of moving forward with “building the toolbox†and solidifying the basic tools of math, and waiting on deep dives into challenging thought problems until a riper age?  (Again, all are welcome to disagree.  Please just don’t mischaracterize me as someone who is trying to push my child to do math that she is not capable of doing.  If that’s what you’re thinking, you’re misunderstanding my whole post.)

[Ravin]

Honestly? In your shoes I would throw out the math curricula and just focus on reading and fun for now. Maybe get some living math resources or, at most, Life of Fred. Then, re-visit BA in a year or two, or better yet, Miquon, because if your child cannot yet 'look at a problem with no obvious route forward, study it for a period of time, and "try to figure out how to do it."' then you have missed the entire point of Miquon and much of the point of BA.

[Arcadia]

What is your definition of “Building the toolbox� Mental math, getting the multiplication tables down, other skills?

 

As for "ask a 5 year old to look at a problem with no obvious route forward, study it for a period of time, and “try to figure out how to do it.â€", some kids enjoy being puzzled while some kids get frustrated. It really is kid dependent.

 

There are lots of living math books that are "high quality fiction". My kids have enjoyed The Number Devil at that age. Quark has a good long list.

[Paige]

30min is a long time for a 5yr old. A curriculum is just a plan. Your plan could be as simple as "buy these games and puzzles and rotate through them."  If you really want to do book work, maybe 1 page of something like a MM topical book instead of 4th grade or even one of those cheap Spectrum books. It would expose her to the algorithms and practice without too much complex thought required. 

 

Maybe buy some good math and logic games, a logic puzzle workbook on her level, and do 1 page of whatever book work you pick. 10min book work, 5min logic puzzle, 15min game, and done. Rotate the games and your good! I'd recommend skipping the book work and just rotating another game in, but 10min if she's not complaining won't hurt. We also really liked the Kumon workbooks at that age for cutting, folding, mazes, crafts, etc. and a different publisher of huge dot to dots. 

 

For reading, again, 30min of sustained work is a lot, but 5-10min of rotating stuff is more fun.

 

FWIW, my 4th grader old is not super advanced but always has been good at math. She hates slogging through workbooks and official math, however. She likes board games, computer games, and apps like Dragonbox. I've found it works best to take it really slow on the official book work. She would only do about 5-10min a day and consequently is officially only a year ahead in MM. But when she tests into computerized game-like curricula, she works on a 7th and 8th grade level. That way, she gets exposed to the harder stuff in games and while having fun, but practices her work on a lower level that doesn't stress her out. I did the curricula just to be sure she doesn't have gaps and she gets practice. 

 

I also have 7th graders working at a 7th grade level so I know what's really expected in 7th and 8th grade, and I think the computerized placement is pretty accurate. I know by talking to her and giving her random harder problems for fun that she "could" do her sisters work, for sure, but without the interest, it's not worth the push. She hates it. But she likes 1 or 2 AOPS's alcumus questions a day. 1 or 2 is fun....a whole day is hell for both of us. 

 

 

[wendyroo]

Personally, if I had a 5 year old who was even remotely in the vicinity of placing into Math Mammoth 4 then I would not spend one minute teaching her the algorithms.  Algorithms are short cuts; they are a crutch for those who don't really understand the math and a convenience for those that do.  

 

My accelerated learner spent a year adding numbers of increasing difficulty before I showed him the addition algorithm.  By the time I sat him down and introduced how to "officially" put numbers in columns and add them he had pretty much figured it out on his own and along the way he had also discovered all sorts of other tricks for manipulating numbers and he had phenomenally strengthened his working memory as he mentally took apart larger and larger numbers in order to reorganize, regroup, reconnect and generally make them dance for him.

 

If a strong math student truly understands the concept of multiplication and how numbers work then she will naturally figure out many methods for multiplying multi-digit numbers.  I see a lot more value in that journey of discovery than in rushing to the destination in order to have a soulless algorithm in her toolkit.

 

Wendy

[Jackie]

I'm hardly a voice of experience, as my child is only a year older than yours. Looking quickly at the MM placement tests, she would have easily placed into MM3 last year, but probably not 4. We tried BA3 and it was a total fail at the time. She had no desire to puzzle out problems, she just wanted to get it right. I did consider both MM and Singapore about a year ago, and ultimately decided against them for the time being.

 

My daughter loves conceptual math. There's lots of math that she can explain how to do even though she can't compute it yet. I decided to spend some time solidifying what she knew while expanding her conceptual math. I did not use a curriculum, nor did I invent new fun math daily. I did research twice during the year, and then bought a stack of living math books, math puzzles, logic resources, and games appropriate to where she was. I also bought a couple of Kumon workbooks of stuff she knew but couldn't do easily yet, and gave her 1-2 pages a week. From the math stack, I would be able to grab what I wanted any given day for math.

 

The result is that my daughter, who would love to have thrown out the BA practice books at age 5, is not struggling with them at age 6. Today, she was talking about how easy multiplication was - she had figured out tricks for most multiplication problems on her own, and only had to memorize about half a dozen facts. Same is true when we talk about fractions, division... she now just understands them from all the reading we did and they simply make sense to her. We still sit down together with the really hard problems in BA, but mostly so I can gauge when her frustration tolerance has hit a tipping point and move on, as she can now do the actual work involved in the problems.

 

So, we did move ahead, but with "fun" conceptual math, not so much on the paper and pencil math.

 

I'm not saying that one way is better than another. I'm saying that my daughter had lost her absolute love of math, and a year of nontraditional resources completely brought it back, and improved her math abilities by more than a year of any curriculum would have.

[Guest]

Yes, I still disagree. Following any algorithm other than the problem solving steps (first understand the problem, etc) is inappropriate at this level. Build number sense and logic, probably some visualization skills, and then the algorithms will become obvious and fun. Worse thing I have seen was a 6 yr old who had memorized the times tables. Poor kid couldnt prevent 'the answer'from coming out, and never came to understand the array model of multiplication, much less the properties. Factoring was a nightmare as he never came to see part/whole relationships. You will get a larger roi out of free play with a box of legos than with teaching algorithms.

[Clemsondana]

I kind of had the same philosophy with my K kid - whatever we could do in 30 min - and I had to adapt that because 30 min was indeed enough time for my child to get frustrated and insist that he didn't like math.  In the same way that kid interests are unpredictable at that age, math interests were also quirky.  My kid was fascinated by negative numbers at 4 and perfect squares at 5, but incredibly frustrated by the details of 3x2 multiplication...although he could mentally deconstruct the multiplication and do it in his head.  We did Singapore because it gave several different ways to do each type of problem and explained why the standard algorithm worked, which also meant that there was no need to follow any particular method if he could do it mentally.  At 5, he didn't do well with repetition, so we skipped over a lot of practice once he understood something.  He's now 10, and we're still working on not getting frustrated when things get hard, and he'll now tell you that he's good in math but doesn't particularly like it.  I don't know if it's because of early frustration - there are days when he thinks that figuring out the puzzles of math is fun and I often find him reading ahead in his math book - and I don't know if the frustration could have been avoided because at some point he would have to learn to be a little more meticulous, but I kind of feel like I got lucky with something that didn't completely turn him against a subject that he was good at.  On a different note, I have another vote for Singapore's word problems books.  He loves ratios, so he enjoyed the challenging ratio problems even when frustrated with other parts of math. 

[wapiti]

 You will get a larger roi out of free play with a box of legos than with teaching algorithms.

 

Well that would explain a lot of things  :laugh:

[quark]

You said she could do the things she prefers after she finishes calculus. That's a long time to wait to follow the learning style that suits you best and the interests that truly stir your heart. And for a parent to think that when a child is 5 would naturally get a lot of people who hear about that a little worried don't you think? :001_smile: 

 

By setting up a "toolbox" if you are talking about drilling math procedures/ algorithms for 30 minutes, it might depend on the child really. Maybe your child *will* appreciate having a store of knowledge to pick up on later for the more fun problems. Or maybe your child will start resenting math. We don't know her and even if we did, I don't think any of us can tell you 100% whether this will work or not. Maybe just be flexible? As mentioned, we did math in strands and one of those sections usually contained about 10 minutes of math fact practice.

 

I know you said you can research offerings yourself but I am not sure if you looked at MEP and nrich.

 

MEP  is free! I used to think 5yos didn't have a toolbox for solving problems until I saw MEP. We started I think in Year 2 or maybe it was 1b, then dialed back and forward according to need/ whim-fancy/ gaps/ fun etc. My son hated using the teacher's scripted lessons so we didn't use them. But they are there if you need them. We just used the very puzzle-like worksheets. Really well done. We compacted a lot. I don't think we ever finished anything as written. You can easily follow as written too if you need a very set plan.

 

nrich maths (also a British site) has excellent problems for all ages. Good luck!

[ebunny]

Thank you to everyone who took the time to comment.  I asked you to disagree with me, and I am not offended by any disagreements.  Your thoughtful comments have allowed me to reconsider my program, clarify my goals, and revise my thinking… slightly.

 

  So my thinking was to continue with our 30 minutes of math instruction by focusing on something that 5 year olds are better at – following the steps of an algorithm.  And in a couple of years, “apply what you know†can then be the focus.  Personally, I don’t think it’s highly appropriate to ask a 5 year old to look at a problem with no obvious route forward, study it for a period of time, and “try to figure out how to do it.† This is what I feel like I am asking her to do when we do the starred problems in BA.  “Building the toolbox†seems like a better path for us right now.  And, honestly, it feels more developmentally appropriate.  Do you still disagree? 

In retrospect, my original post did not acknowledge the value in abstract thinking and advanced math problem solving skills.  So, assuming we all now can agree that these have substantial value, what about the approach of moving forward with “building the toolbox†and solidifying the basic tools of math, and waiting on deep dives into challenging thought problems until a riper age?  (Again, all are welcome to disagree.  Please just don’t mischaracterize me as someone who is trying to push my child to do math that she is not capable of doing.  If that’s what you’re thinking, you’re misunderstanding my whole post.)

 

Now that you've shared more details, the approach seems reasonable. But, I'm curious about your repeated request? need? for validation of your plan (evidenced by the bolded) as the disagreements are consistent in the message: Your approach is high risk for math-dislike or academic burn out.

[quark]

Personally, I don’t think it’s highly appropriate to ask a 5 year old to look at a problem with no obvious route forward, study it for a period of time, and “try to figure out how to do it.† This is what I feel like I am asking her to do when we do the starred problems in BA.  “Building the toolbox†seems like a better path for us right now.  And, honestly, it feels more developmentally appropriate.  Do you still disagree?

 

Are the starred problem in BA geared towards a 5yo? The problems were written for bright, older kids right? You probably have a very capable young girl there but you are still using a book that was meant for very capable older children vs a capable young girl getting stumped by a book for just older children. I think you might find MEP much easier to customize challenge wise (or SM, we used MEP more often and why I don't think to suggest SM as often as I do MEP).

 

Try Year 2, if it's too hard, go back half a year or if too easy go ahead half a year (similar to raptor-dad's suggestion). You might find that MEP has problems that stretch her just enough for her to solve and that will build confidence. Once she is confident she *will ASK* to learn procedures to solve even harder problems. Keep stretching her, dangling the carrot in front of her in stages. BA might not be as accessible right now but it will be soon! Just hang on a little while more!

[Arcadia]

As for BA, a friend kindly gave me a BA 3D workbook spare she had. My kids did the pages they like for fun. For a five year old, maybe just let her use the BA workbooks as fun puzzle books that can be completed later. So she can do those she is able to and shelve the rest for later.

 

While my DS10 is not weak in algebra, it was the geometry topics that gave him joy.

 

The Oliver Byrne version of Euclid Elements is something a young child can peruse and enjoy as a fun read. Link below

https://archive.org/details/firstsixbooksofe00byrn

 

We use Lego as math, physics and genetics/DNA manipulatives.

 

I think you might find MEP much easier to customize challenge wise (or SM, we used MEP more often and why I don't think to suggest SM as often as I do MEP).

MEP is a lot more customizable in terms of topics and levels than SM :)

I had download all of MEP pdfs and just let my kids pick what MEP pdf they like on their ipad to do for hotel entertainment. It is very portable and my kids enlarge the page on their iPads so it is easier for them to read when they were much younger. Sure beats bringing SM books on a road trip.

[lewelma]

Hi Lilikoi,

 

Welcome to the boards! It sounds to me like you are a hard working mother looking to do the best by her child, and finding that there is no clear cut best path forward.  I have so been there. It's hard to get it right, and you won't really know for years, so there is no way to adjust the program as you go in any way that feels proven. You are flying by the seat of your pants. I have felt this way for a decade. But let me say, that at age 5, you can't really get it wrong. Kids are shockingly resilient, so we can muck up and yet still get it right.  But I will add one big however.  If your child learns to hate math for whatever reason, you have a problem.  And a big one that is hard to turn around (BTDT with my younger).  At ALL costs, you Must Must Must make sure that your child LOVES math. Do whatever it takes.  Children that are gifted at math are more than accelerated. They *think* differently. In my experience they make unexpected connections between math concepts and discover ideas before being taught. They just do MORE than accelerate. So is your daughter accelerated or gifted?  I would really stop and ponder this.  If your daughter is accelerated, then the standard curriculum is well suited but just a few years ahead. However, if she is gifted, then the standard curriculum is tedious because of the WAY the material is presented and practiced.  Differentiating between these two categories may help you to find a way forward.

 

My older boy was in a gifted one-day school at 6, and there was a 6 year old school kid who had been put in 8th grade math. He hated it. After a couple of months he asked to be put back to 6 year old math.  He said he would rather learn to add and subtract with the class than be doing the math that was *at level* for his cognitive abilities.  Clearly, he was gifted not just accelerated, and the 8th grade math attacked math problems in a routine way for 13 year olds.  But a highly gifted 6 year old is absolutely NOT like an average 13 year old.  To suggest that you can give them the same math book defies logic. 

 

Given that you have read these boards for a couple of years, you must have followed my older boy's adventure as I have posted frequently.  At this point he is ranked 3rd in NZ at age 16.  At age 5 we were playing shop.  At age 6 we were estimating numbers of cars or birds or mushrooms. We were each taking turns making up difficult word problems to challenge each other.  We were playing with probability and chance.  We were having FUN with math. I don't mean to say that you can't do the program you have envisioned for all the reasons you have outlined, but I do want you to know that there are those of us out here who have the high-level outcome that gifted kids seek, that did not go the way of accelerating math instruction.  My son is completely self taught, in fact he has discovered any math he has ever learned.  At age 6.5 when we started his first formal math program (singapore), not only did he consider my instruction to be cheating, he considered any and all textbooks to be cheating.  He *discovered* all the rules of primary school math, don't even ask me how.  It took him 2.5 years, and then he started AoPS algebra at age 9. I tell this story, because there are two pieces of mathematics -- the algorithmic skills and the problem solving skills.  It is easy to accelerate the first and very difficult to accelerate the second.  MM4 will accelerate the algorithmic skills, MEP1 will train a 5 year old in problem solving. They are two different things, and in my experience if the algorithmic skills far outpace the problem solving skills, students lose patience and confidence as they try to back up years to learn the problem solving skills that had been underdeveloped.  DS has virtually met a number of students on the AoPS boards who are in this pickle, and it really becomes a pickle. They can only use math that has been taught, and cannot seem to creatively apply it or develop it.  It leaves them in a quandary, because they know that in a few years that they will have nothing special, but will be just like everyone else even though they started out as something special.  Just the other day, my ds's problem solving helped him solving a programming problem.  He is not much of a programmer, but he was trying to make a prime number identifier to run more efficiently.  After he adjusted the program, he looked on line to find out how to save more time, only to find out that he had independently developed an advanced level sieve for prime numbers, one that he had never seen or read about even though he does olympiad level number theory.  This is math in action.  My ds does not need to be a human calculator, he needs to be a creative problem solver. 

 

So over the past decade, I have never known what I was doing or if it was the right path. In the end, I simply followed my ds's lead because I wanted him to maintain his love of mathematics and his playful and creatively approach to it.  All through primary school, he wanted to play and to discover, and he needed to do things *his* way.  Because of this, I struggle to advise how to guide a strong (gifted? or accelerated?) student.  But I will stress again, you must must must maintain the passion, the love of mathematics, or you have lost. My one suggestion to you is to put that at the front of your priority list.  With a strong math student, you can easily accelerate at any time, but if you lose the love, the road back is long, slow, and painful. 

 

Good luck to you in this search.  I hope you find a path forward that leaves you confident and at peace.

 

Ruth in NZ

Edited September 13, 2016 by lewelma

[Guest]

Well that would explain a lot of things :laugh:

I have no clue what you mean, but if it brings you joy, that is great.

Edited September 13, 2016 by Heigh Ho

[luuknam]

I am inclined to move into MM, 4^th grade.  My rationale for this decision:  1) It’s the appropriate placement for what she already knows.  2) It will allow her to continue to build on her knowledge with a more manageable level of challenge.  3)  Most important reason:  She will “get something†out of the hard work she puts in.  I want to continue to challenge her at her level; she is capable of it, and I believe it will build in the appropriate character skills needed to succeed later in life.  However, I want her to get something out of the challenge.  And if she can master 4^th grade math now, while also building character and being reasonably challenged, that seems much more valuable than just being challenged with overly complicated story problems, and not “getting†anything tangible for it. 

 

If she likes to check boxes, feel like she's accomplished something, and get gold stars (or badges, or w/e), then I'm thinking Khan Academy.

 

Personally, I think it's more character building to struggle with complicated problems where the answer is not obvious than to just learn some algorithms, but she's 5, so I'm not too concerned about the character-building merits of one vs the other.

 

FWIW, I'm from a country where kids don't start math at all until 1st grade (I'm sure that in preK-K they work on counting some, but no arithmetic). So, I have no idea where "30 min of math/day in K" comes from. 30 min is quite a long time. You say you only do 30 min of math and 30 min of reading as your entire K curriculum. Why not add in some other subjects (history, science, etc) and drop the math to only 10 min a day?

 

Need to go, will probably write more later.

[Spy Car]

I'd look at MEP (Mathematics Enhancement Programme) as several other posters have suggested. It offers a good dose of problems that work the noodle while building conceptual understanding. Then you could add challenge work like Intensive Practice or Zaccaro books, and other resources.

 

The key at his age IMO is to spark the fire. Make problem-solving and reasoning fun and rewarding. Nothing wrong with drawing on a mix of resources to provide depth and breadth.

 

Bill

[wapiti]

I have no clue what you mean, but if it brings you joy, that is great.

 

Sorry I should have explained :).  My neglected middle child, ds10, placed higher in math than I expected at his new school even though we never really did much afterschooling.  It isn't that he knows all that math he skipped, but apparently he knew how to figure it out in an untimed testing situation.  He's a lego-maniac, a maker/inventor kind of kid.  There is a back corner of the family room that is perpetually covered in legos.

 

ETA, this just reminded me of something about playing and problem solving that might be nice to tie in.  Back before BA existed, in Rusczyk's 2009 problem solving talk (p.8) at the Math Prize for Girls linked above in Suzan's post, he talked about elementary level and the importance of play:

 

All the great problem-solvers are very playful people. They spend a lot of time playing even now, not just when they were little kids. When I was a little kid, my dad called me Mr. P, and it wasn’t perfect, it wasn’t punctual. Whenever there was work to do, I was off playing, so I earned the name “Mr. P.†It’s just critical. You’re learning a lot when you’re playing. You’re creating problems and solving them. That never goes away.

 

(or video starting around 19:53; perhaps this a good time for me to listen to it all again as I reflect on each of my kids' current situations.  I'm pretty sure the video sound is much improved from what it was originally.)

Edited September 13, 2016 by wapiti

[pkbab5]

 

To the “We just let our child play†comments:  Our kindergarten curriculum consists of 30 minutes of math and 30 minutes of reading a day.  That’s it for school requirements.  This is on the “light†end of what most people on WTM currently do for Kindy.  Comments about “pushing†are misguided, in my opinion.  I agree with Paige that emotional health is important, and it’s a focus here.  I suppose that I disagree that 5 is too young to teach the value of consistent effort.  (Isn’t that the message of The Little Red Hen?  And The Little Engine that could?  And The Tortise and the Hare?)  30 minutes of math a day should not crush anyone’s soul.  30 minutes of frustration a day might.  30 minutes of mind-numbing repetition might.  So I am trying to find the optimal curriculum that (a) is not too hard (b) does not repeat what she already knows.  My calculation was that MM4 would fit those parameters.  Of course, if I had a “play†based curriculum that covers new material that she doesn’t already have down, I’d be the first in line to buy it.  But I really need “a curriculum†to follow, since I work full time.  I can’t just come up with interesting lessons that build in math every day that are appropriately challenging etc.  

 

Let me try to rephrase my original post in another way, and see if you all still think I’m nuts:  I have a very capable five year old who enjoys math but doesn’t beg for it.  I do not want her to get overly frustrated with BA problems that are designed for children with a much larger working memory than my five year old has.  I don’t see her getting anything useful from working problems that require more critical thinking skills than she is ready for.  My thinking, therefore, is that if we slightly redirect our current efforts and move forward more with “algorithm†type work – building the mathematical toolbox, so to speak, that would free up time later, say in a year or two or three, where we could spend more time focused on applying the tools she has acquired onto challenging problems.  So my thinking was to continue with our 30 minutes of math instruction by focusing on something that 5 year olds are better at – following the steps of an algorithm.  And in a couple of years, “apply what you know†can then be the focus.  Personally, I don’t think it’s highly appropriate to ask a 5 year old to look at a problem with no obvious route forward, study it for a period of time, and “try to figure out how to do it.† This is what I feel like I am asking her to do when we do the starred problems in BA.  “Building the toolbox†seems like a better path for us right now.  And, honestly, it feels more developmentally appropriate.  Do you still disagree? 

In retrospect, my original post did not acknowledge the value in abstract thinking and advanced math problem solving skills.  So, assuming we all now can agree that these have substantial value, what about the approach of moving forward with “building the toolbox†and solidifying the basic tools of math, and waiting on deep dives into challenging thought problems until a riper age?  (Again, all are welcome to disagree.  Please just don’t mischaracterize me as someone who is trying to push my child to do math that she is not capable of doing.  If that’s what you’re thinking, you’re misunderstanding my whole post.)

 

1)  30 minutes of math a day for a 5 year old does not sound too harsh.  My kids did/do 20 minutes of math at 5 (plus 20 of reading, and 20 of fine motor skills like writing or coloring or cutting).  So that's not the issue.

 

2)  Your kid enjoys math, but does not beg for it, and you make her do it anyways.  Yeah, I do that too.  Math is important.  That's not the issue either.

 

3)  Your kid is not ready for critical thinking skills, so you want to pass the time by teaching her all of the algorithms ahead of time.  THAT right there is the problem.  If your child is really gifted in math, then if you do this, you will CRIPPLE HER.  Teaching critical thinking teaches someone to THINK.  Teaching algorithms ahead of time before they can be reasoned out by the child REMOVES the necessity for the child to think, and teaches the child how to regurgitate.  How to copy.  How to follow.  How to only know how to do what someone else has already showed her.  How to not know how to think for herself.

 

There's not a whole lot of opportunities for a young child to be able to discover how to reason for themselves, because so many things are done for them, are directly taught to them.  Math is one of the only areas where you can really teach a child how to THINK.  That's why math is important, and why I think it's important at an early age, because it teaches you how to THINK.  But you seem to be intent on skipping that part for some reason.  Your child is terrific at regurgitating algorithms, and not so great at critical thinking. Help her with what she is struggling with, which is critical thinking.

 

Back up the math to where she is critical thinking-wise.  Get those early grade logic books.  Teach her THAT.  Get that caught up to where she is algorithm-wise.  THEN, after she has been evened out, proceed on to the next grade.  Then you'll be able to do all of each section, instead of the first half.  And you will teach your child how to think.

 

[wapiti]

 in my experience if the algorithmic skills far outpace the problem solving skills, students lose patience and confidence as they try to back up years to learn the problem solving skills that had been underdeveloped.  DS has virtually met a number of students on the AoPS boards who are in this pickle, and it really becomes a pickle. They can only use math that has been taught, and cannot seem to creatively apply it or develop it.  It leaves them in a quandary, because they know that in a few years that they will have nothing special, but will be just like everyone else even though they started out as something special.  Just the other day, my ds's problem solving helped him solving a programming problem.  He is not much of a programmer, but he was trying to make a prime number identifier to run more efficiently.  After he adjusted the program, he looked on line to find out how to save more time, only to find out that he had independently developed an advanced level sieve for prime numbers, one that he had never seen or read about even though he does olympiad level number theory.  This is math in action.  My ds does not need to be a human calculator, he needs to be a creative problem solver. 

 

So over the past decade, I have never known what I was doing or if it was the right path. In the end, I simply followed my ds's lead because I wanted him to maintain his love of mathematics and his playful and creatively approach to it.  All through primary school, he wanted to play and to discover, and he needed to do things *his* way.  Because of this, I struggle to advise how to guide a strong (gifted? or accelerated?) student.  But I will stress again, you must must must maintain the passion, the love of mathematics, or you have lost. My one suggestion to you is to put that at the front of your priority list.  With a strong math student, you can easily accelerate at any time, but if you lose the love, the road back is long, slow, and painful.

 

Ruth's entire post is a font of wisdom.  Truly outstanding.  OP, we are glad you posted because then we get to read gems like this one :)

[wapiti]

1)  30 minutes of math a day for a 5 year old does not sound too harsh.  My kids did/do 20 minutes of math at 5 (plus 20 of reading, and 20Your kid is not ready for critical thinking skills, so you want to pass the time by teaching her all of the algorithms ahead of time.  THAT right there is the problem.  If your child is really gifted in math, then if you do this, you will CRIPPLE HER.  Teaching critical thinking teaches someone to THINK.  Teaching algorithms ahead of time before they can be reasoned out by the child REMOVES the necessity for the child to think, and teaches the child how to regurgitate.  How to copy.  How to follow.  How to only know how to do what someone else has already showed her.  How to not know how to think for herself.

 

I'm really glad that you and Ruth are fleshing this out so nicely.  I hadn't really thought of it this way.  In particular, with regard to educational philosophy, e.g. the Trivium focus on memorizing or the focus of certain more-heavily traditional math programs on procedures, I hadn't thought about this idea that some programs might not simply be lacking a component, but may be ill-suited to a point of detriment for certain students, especially some gifted ones.  (Not sure about that last part?  Thinking out loud.)

Edited September 13, 2016 by wapiti

[quark]

Hi Lilikoi,

 

Welcome to the boards! It sounds to me like you are a hard working mother looking to do the best by her child, and finding that there is no clear cut best path forward.  I have so been there. It's hard to get it right, and you won't really know for years, so there is no way to adjust the program as you go in any way that feels proven. You are flying by the seat of your pants. I have felt this way for a decade. But let me say, that at age 5, you can't really get it wrong. Kids are shockingly resilient, so we can muck up and yet still get it right.  But I will add one big however.  If your child learns to hate math for whatever reason, you have a problem.  And a big one that is hard to turn around (BTDT with my younger).  At ALL costs, you Must Must Must make sure that your child LOVES math. Do whatever it takes.  Children that are gifted at math are more than accelerated. They *think* differently. In my experience they make unexpected connections between math concepts and discover ideas before being taught. They just do MORE than accelerate. So is your daughter accelerated or gifted?  I would really stop and ponder this.  If your daughter is accelerated, then the standard curriculum is well suited but just a few years ahead. However, if she is gifted, then the standard curriculum is tedious because of the WAY the material is presented and practiced.  Differentiating between these two categories may help you to find a way forward.

 

This is child-rearing + how to work with gifted kids + how to teach any subject 101 all rolled into one. Just substitute "math" with "learning". :001_wub:

Edited September 13, 2016 by quark

[SarahW]

OP, just weighing in to say I do understand your frustration. I was in a similar pickle when CP was in 2nd grade. He understood "2nd grade math" in a few days (because if you already really understand place value, you have the majority of 2nd grade done), and then.... what was left to do?

 

I did try to start BA with him then. But yeah, the starred problems do require working memory and/or processing skills which just need to develop on their own time. He could do it, but wasn't getting all the value from it, so I dropped it for a while. We did logic puzzles and similar things for a while. I tried some math books, but he hated Sir Circumference, he thought LOF was funny but didn't like the math in it (LOF basically teaches algorithms, though in a more convoluted way), other math books from the library were too simple or not interesting. 

 

He responded positively to the BA guide books, and reads them obsessively. But our completion rate for the Practice books is abysmal. :o  We've done a few other things the past few years as well, and some international moves, so those hold part of the blame. But honestly, the amount of "math problems" done has been quite small.

 

Other than the BA guide books, which he's read so often that he practically has them memorized, I've found value in just sitting him down with some good math videos and a handing him a blank notebook. Maria (author of MM) has some videos on her website. AoPS has Pre-A and Algebra videos. There's some other good videos I'm sure people here can recommend. He watches them, sometimes talks to me about them, and jots down equations in his notebook. He's sort of all over the place with this, which drives me completely  :willy_nilly:  :willy_nilly:  :willy_nilly: . But he definitely "progresses" and learns a lot, and he's definitely loving math doing this (I really don't think this approach would work if he didn't love math, a lot). If he comes to me with questions ("how does dividing negative fractions work?") I try to answer them. If he tells me he wants to work on factoring I try to believe him and give it to him. It's totally out of sequence (even for BA) but I think it'll work out okay in the end.

 

And fwiw, MM made my kid cry. I've tried it with him off and on, because there are good things about it, definitely. But he considers doing it to be utter torture. I don't know why.

 

I am not a math person. I have to really study to understand major portions of BA. I totally understand the appeal of just scheduling a straightforward A to Z math curriculum. Unfortunately, that just hasn't proven to be possible here. I think the other responses you're getting is because other people found it to be impossible as well. It's maddening, yes, because I look at MM and see where he could fit into it, and how I could schedule it out and condense it, and if he would just sit and do it, he'd be done with it in no time! But he doesn't see it like that at all, no matter how much I try to tell him. His brain is just different. So very weirdly different.

 

You have to find the path that's right for your kid. Of course. And there's usually not a clear path that you can just pick and do. Sorry.

[Arcadia]

In particular, with regard to educational philosophy, e.g. the Trivium focus on memorizing or the focus of certain more-heavily traditional math programs on procedures, I hadn't thought about this idea that some programs might not simply be lacking a component, but may be ill-suited to a point of detriment for certain students, especially some gifted ones. (Not sure about that last part? Thinking out loud.)

My hubby who missed the cutoff for our country's gifted program does not get the hype about Singapore Primary Math or New Elementary Math and we used those curriculum as public school students from 1982-1988. My hubby lament his math and science education despite our country's high ranking on PISA and TIMSS. Comically he thinks our language arts education was better than California's. My math education in school was enriched beyond the SM books by teachers who aren't afraid to be challenged intellectually.

 

He also lament that he has less Legos than me as a kid :lol: I received lots of Legos as birthday gifts as a kid because I didn't want any dolls and nothing pink.

 

ETA:

I do think memory work has a place. Just not memorize and regurgitate style of learning.

Edited September 13, 2016 by Arcadia

[Spy Car]

Promoting *thinking* is the key IMO. Get the little minds cogitating and those little (or in some cases "big") wheels spinning.

 

It's not so much about calculating at this point as it is about getting those reasoning skills a workout—which for smart kids is fun and rewarding, which gives impetus to learning more about math fundamentals in order to be a better problem solver.

 

Forgot to mention a couple other good resources earlier. CSMP is an archived (free to print) 1960s New Math program with lots of intriguing elements (like the mini-computer) that are outside the box.

 

http://stern.buffalostate.edu/CSMPProgram/

 

The SMSG (School Mathematics Study Group) materials are also archived online. SMSG represents the best of "New Math" (don't let the wrongheaded downing of New Math deter you) and has a lot of ideas for rich instruction on both conceptual and cognitive levels.

 

The good news is there are lots of resources you can use to "turn on the lights." Like others, I'd urge this sort of route (deep materials that meet intellect and age) as opposed to accelerating with standard materials pitched to older but more typical kids.

 

Go deep. Get the kid's mind turned on to thinking and reasoning with well-chosen challenges.

 

Good luck.

 

Bill

 

 

[mathnerd]

OP: "Doing more challenge problems is “only†good for her brain.  Is this bad logic?"

 

I use applied math for my living. Here is why you are wrong about math - learning math is not just about learning algorithms. You can train anybody to learn algorithms. That can only take one so far in a field where mathematical thinking is required. It is very easy to spot a person who approaches a tough real world problem as a challenge as opposed to a person whose thought processes crumble when faced with something that they cannot fathom. If you have heard of the cliche "thinking outside the box", then creative problem solving is what it is about. I have immensely benefited from posters like Kathy, SpyCar, lewelma, quark, Arcadia etc on this board who have generously spent their time helping posters find appropriate resources. Please do read some of their older posts - there are too many to link here. I also want to second (or third) Richard Rusczyk's math prize talk on problem solving that was mentioned before - here is a transcript of that presentation for an easier read - http://mathprize.atfoundation.org/archive/2009/Rusczyk_Problem_Solving_Presentation_at_Math_Prize_for_Girls_2009.pdf

 

No single curriculum met my needs. I have clobbered together various resources and continue to do so. At your child's age, my son was reading Penrose the Cat books, doing Zacharro's challenge math and a ton of logic and creative thinking puzzles from Critical Thinking Company and Prufrock. He also joined a Math Circle and solved problems with other kids in a fun setting. We went to Math Festivals, attended low key math competitions, started programming using a couple of languages and enrolled him in a local chess club. I remember that the main curricula we were using was a combo of SM IP/CWP and MEP. We have also used legos, cuisenaire rods, blocks, origami, Zometools etc to learn math in a hands on way. It was true that we could not get 5 worksheets done in 20 minutes and move on to the next thing when we were using manipulatives to learn multiplication. But, at age 9, my son can do 3 digit by 3 digit multiplication and 5 digit by 3 digit division quite accurately and rapidly in his mind. I cannot take credit for it, because I use a calculator! It is not a useful skill, but, he developed it because of his own unique way of seeing connections between numbers, spotting patterns which are normally hard to see etc. I am pointing this to show you how a child who is exposed to various ways of solving a simple problem at an early age can develop their own methodologies.

 

30 minutes is a lot of math at age 5 - so, yes, you can teach 4th grade MM and then move on to 5th grade MM too if that is what you want. But, I would suggest that you break down the 30 minutes into 2 slots and do some problem solving in one half and whatever you would like to teach (MM etc) in the other half. Good luck.