I Think We’ve Been Cheated


I just finished reading an article that is absolutely incredibly mind-boggling.  This article (Click here  to read it) states that a rather large experiment was performed in schools, back around 1930, which showed that children who had no formal math training before sixth grade actually caught up with their peers in math by the end of the sixth grade year, showing that when the brain is developmentally ready, math is learned very quickly.  The children were able to learn in one school year what their colleagues had spent six years on.  The even more surprising things is that the children who were part of the experiment FAR surpassed their peers in language.  These children developed more interest in reading, a better vocabulary, and greater fluency in expression than their peers who had spent so much time trying to learn math in the earlier years.  Not only had math study been largely unproductive, but it had cheated them out of time for other activities which would have benefited them more.

I have long suspected that math is shoved onto kids too soon, and this article made me sort of angry.  If it has been known for all these years that this system works very well, and the children enjoy school a great deal more, then WHY for crying out loud, have we all been forced to struggle with teaching/learning math in the early grades?  Just think, thousands of American children have been taught that math is hard and hateful, when the real problem was that their brains simply weren’t ready to assimilate it.  All that time…wasted!  And when I think of all the wonderful learning they have sacrificed because they had to spend a great deal of time on math, it’s just terribly frustrating! 

Makes me wish that I could start all over, and have the courage to go against the status quo, trying this method of teaching.  And it makes me very angry that this method was not adopted nationwide after its success.  It is just WRONG that young children are pressured to so that learning becomes a drag.  And I suspect that children who struggle with math in the early years often give up, feeling that they will never understand it, so when they actually reach the age where they are developmentally ready for it, they no longer have any desire to try.

I have lamented many times the fact that my children generally want to just “get done with” school, rather than enjoying the process.  It is a sad thing that many people see the learning process as a necessary evil, and completely unrelated to their lives.  I have enjoyed so much all the things I have learned by homeschooling my children, and now I can’t help lamenting the fact that we could have made it infinitely more enjoyable for them.  But, having been brought up in the traditional school system, I simply didn’t know any better.  I can only pray that God will be able to bless my efforts anyway.


And I can’t help thinking that this is a good example of how our government works, too:  If something has been proven not to benefit the people, go ahead and keep doing it anyway…

Yeah, call me cynical.




About dayuntoday

I'm a wonderer. I spend a lot of time mulling, pondering, and cogitating. This is just a place to park some of those thoughts.
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33 Responses to I Think We’ve Been Cheated

  1. mrcolorful says:

    My problem with school in general was not that I was taught math too soon or that other subjects were neglected.  My problems were that there was too much busy-work and non-educational stuff happening (I wanted to learn) and that I never picked up on the unwritten and unspoken rules that other people did but it was assumed by everyone that I knew them so a disastrous cycle of fighting and hatred was continually running.With math in specific, my problem was that not enough time was focused on the word problems.  I know everyone else hates that type of problem but that is what we need to know since rarely in life is information going to be laid out in a handy 3+4= format.

  2. medelamom says:

    thank you for this! just confirms what i’ve been doing with my daughter…weighing her readiness for a subject and if she’s just not ready, i don’t force her to learn it. then i sometimes feel guilty because i’m not doing exactly like public school…then i remember duh, that’s part of why we homeschool in the first place!a mother who is in tune with her child’s needs makes a far better teacher, i believe, than one who is following some set of guidelines that ‘all’ children must learn at the same age. that just doesn’t make sense if you really think about it…not all kids develop the same way or are ready for certain things at the same time. but when they are ready, they learn it so much easier! and enjoy it more too.

  3. MrTrololo says:

    @mrcolorful – Word problems are the best… however even at school when I took some college classes at Liberty, they still just blew through the word problems part. Another thing… the whole psychology of math is wrong… it focuses on “problems” since when is an equation a problem? It’s an exercise, even an opportunity, but not a problem.

  4. firetyger says:

    Thank you for sharing this…definitely something for homeschooling families to consider.I’m one of those who became frustrated with math at an early age and pretty much gave up on it.  It was my only weak subject but nonetheless, I wish I could have learned it better.  I plan to homeschool my daughters, so perhaps we will wait longer before starting math…  I’ll have to do some more research on that.

  5. moritheil says:

    That’s a very good point – why aren’t we experimenting to verify this, if we’re supposedly using scientific methods to teach people?

  6. mrcolorful says:

    @Happily_Married_Guy – That is very true!  Between the focus on “problems” and the avoidance of word problems we are never teaching kids to think mathematically.  When they don’t know how to think mathematically it makes upper level math darn near impossible.  I also believe that mathematical thinking goes a long way towards furthering scientific thought and logic.  Though, these thought patterns I’m mentioning here do go a long way towards improving problem solving abilities.I’m a firm believer that if we improved math education every other area of education in the US would improve as well.

  7. MrTrololo says:

    @mrcolorful – The unfortunate thing is the math in my state is getting more and more dumbed down so that the student is unable to learn upper level math. Myself I had to study pre-algebra with an old book I got from halfpriced books, then I was able to get it…. took a lot of work though.

  8. mrcolorful says:

    @Happily_Married_Guy – I believe that.  I really lucked out in that I had a couple of teachers in pre-algebra and algebra who’d been teaching for decades and refused to dumb anything down.  That refusal did turn a few more people against math since they’d sort of fallen in love with easy, memorization based math that we’d been taught but those who were willing to work on it and learn it usually really got it and went on to do well in higher level math classes.I think a lot of people have the idea that improving math education is simply a matter of getting better grades across the board.

  9. That is why waldorf schools do not even introduce the alphabet until 1st grade.  I’m not sure when they bring in math. 

  10. homefire says:

    @mrcolorful – I, like you, loved to learn and actually loved math, but I have taught four children, three of whom do NOT love to learn, and two of whom have really struggled in math.  So this article was pretty upsetting to me.  Btw, busywork is one of the big reasons to homeschool!  All schools must have busywork, since all children work at a different rate.  Another reason to homeschool is that you can find the curriculum that works–we use Singapore math in the early grades, which focuses heavily on word problems.@Happily_Married_Guy – I love your thought of not calling an equation a “problem.”  Good thought!  Maybe the old term “exercise” should be resurrected?@medelamom – @firetyger – I just hope that this information will help you to deal more wisely with your children than I have with mine.  I am wishing that I had read this about ten years ago!  @moritheil – That’s what I’d like to know.  WHY has this very important experiment been completely ignored?  When our national test scores are dropping at a horrific rate, you’d think they’d be trying everything.  Sigh.@the_Coley_he_seeks – It would be interesting to know.  I’ve never looked into Waldorf.

  11. MrTrololo says:

    @homefire – Yep, exercise is much much better… it’s not a negative “problem”, but something that makes you stronger, exercise šŸ™‚

  12. MrTrololo says:

    @firetyger – The biggest thing is to fully understand the associative, commutative, and distributive properties and the rest is ok after that. I always tried to learn it without doing that so it was just a jumbled mess. The book I usd to prepare for beginning algebra was “Basic Mathmatics” by David Novak. It’s kinda old but the only one that I could trust.

  13. BooksForMe says:

    It would be interesting to see if they could replicate those results.  Really interesting, and disturbing.

  14. LydJaGillers says:

    A study needs to be conducted for a long period of time, usually at least 20 years, before it can be considered conclusive and meritible. I disagree that math is being taught too early. Nothing is taught too early, it’s the patience of the teacher that needs to be considered. One child may grasp things quicker than another based on that child’s learning ability and based on the way the subject is being taught. This doesn’t mean we should wait for all children to wait until they are older before learning something vital like math. I think you have jumped to this conclusion way too quickly.

  15. quilt_cats says:

    When I think of all the frustration and tears that we have gone through (in homeschooling and in the regular style schools) because of math- I wish we’d known about this study.  I wouldn’t have been so critical of my own kids during their times of totally being lost when it came to math.  Math was always my own weakness too… so I already felt inadequate once my children reached about 8th grade math and above.

  16. homefire says:

    @LydJaGillers – Just out of curiosity, did you read the whole paper?  The study had been going on for about ten years at the time of its writing, with quite excellent results.  And the findings in the study coincide perfectly with what I have concluded in teaching my own children, plus talking with many other homeschooling moms.  The way that this paper proposes to study math is a much more natural way, using the child’s own experience to make it meaningful rather than the abstract way that math is usually taught.  They learn many mathematical concepts, but aren’t expected to put it on paper in abstract form until they are older.I would also disagree that “nothing is taught too early.” It is probably a fact that nothing is learned too early, but there are many times when a child is pressured to learn things they cannot yet assimilate.  It seems that math is the most obvious example, but I think that many children are plunged into a “schoolish” environment far too early.  In my experience, children are so very different in their readiness that many, many children are being pressured to learn things they are not ready for.  Since I have one child who was reading quite well at 4 and one who didn’t learn to read until 8, I have some experience with wanting to push a child who is “behind schedule.”  I know for a fact that my son was not ready to read when the world thought he should be.  I also know that even with all the patience in the world, he simply didn’t get it.  And I am thankful that I didn’t push him harder, because I think that would have been the very best way to teach him to hate reading.  As it is, he now reads constantly and has a huge vocabulary.  Which brings me to the thing that is most upsetting in that article–the fact that early math drill seems to actually decrease language and thinking skills.  Language is one thing that probably can’t be taught too early, but it certainly can be too late.  The neural connections made at an early age simply can’t be duplicated later on in life.

  17. homefire says:

    @quilt_cats – I know, it is upsetting to think of all the wasted effort, but we really can’t look at it that way.  We did the best we knew.  But it’s sad that even when I felt the truth of this, I was still too intimidated by peer pressure to let it go.  I think one of my sons would have been very much better off if I had.  He struggled mightily in math, and spent all his school years convinced that he was lousy at math, probably based mostly on his experience in second grade. 

  18. homefire says:

    What kind of crap gets featured on top blogs. That study is almost 80 years old. Show me some recent study that shows that. You can’t. There are too many variables to control, like who’s stronger in what, and whatever. Different people learn different things at different rates. We’re all naturally good and naturally weak at some things. I’m a mathematician/math educator, and I have had math training from an early age,@mathematicalbagpiper – Sorry I had to delete your comment.  I re-posted the relevant part above, but I don’t allow profane or vulgar language on my site. So you didn’t think the study was interesting?  Did you read the entire article?  And the fact that the study was so old is one of the things that makes me angry, btw.  With results like this, there should have definitely been more similar studies made.  Why don’t you do one to disprove it?  To me, the fact that there hasn’t been more research on this shows a reluctance on the part of the educational community to pursue excellence.

  19. @homefire – Yeah, you don’t allow profane language because you’re a Bible-thumper who believes in a fictional deity. Lovely. I know how your kind thinks, and I can promise you that you fell for this study because you believe that public education is for the purpose of indoctrinating children with the Christian faith. I thought the study was garbage and now we know better. Your comment just goes to show that you have no idea on anything relating to pedagogy. Ever heard of multiple intelligences? I don’t guess you have. There are too many variables involved. Also, prime example, look at Japan where the kids literally are taking math equivalent to a first-semester Calculus course in their equivalent of 8th grade, and they start learning math from a very, very young age. Modern educational theory, if you’d bother to learn something about that, completely debunks this study. 

  20. homefire says:

    I’m very familiar with multiple intelligences.  If you read some of my other comments, you’ll see that I have taught children with varying gifts.  Some kids do wonderfully with math early–I did myself.  For many young children, though, math is nothing but gobbledygook.   They learn to go through the motions, but really don’t have a clue why they do what they do, because the usual methods of teaching don’t get through to them.  Sure, there are many variables involved, which is one reason I educate my children at home. Every child is very different, and to say that all children should be able to understand abstract mathematical concepts at 7 years old is as absurd as expecting all of them to read equally well or excel in the same sports.  I had one child who loved math and was very advanced in math before he could read.  And that was fine for him.  However, I have another child who never ‘got’ math at all, and still struggles with it as a senior in high school.  I regret that we wasted so much time on it in the early grades because we could have been using that time for other things, rather than reinforcing his idea that he was ‘dumb in math.’  I think it is very possible that had we waited he would have had more success.  I’ve seen it happen in other areas–why not math?I’m not sure where all your anger is coming from, but I’m sorry.  Btw, I’ve never thumped a Bible and I don’t know exactly what you mean by “my kind,” but I’m pretty sure you don’t have any idea how I think.    I don’t allow bad language because I like to keep my blog family-friendly.  And public education is certainly a tool for indoctrination, but I’m pretty sure that it was never for the purpose of teaching the Christian faith.  What modern educational theory exactly are you referring to?  Are you saying that you know of a study that disproves the theory in this article?  There have been many ‘modern’ theories that were nothing but nonsense–the look-say method for teaching reading is nearly worthless for the average child, for instance.

  21. homefire says:

    @mathematicalbagpiper – And do you really play bagpipes? 

  22. @homefire – Well, here’s a perfect example. I did an experiment for awhile where I taught real analysis to 6th graders (real analysis is a college-level math topic). They took to it quicker than I took to it when I took it as a junior in college. If a child doesn’t get math right off the bat, it’s no different if said child wouldn’t get linguistics, science, or anything else. There are way too many variables involved for any studies of this kind to hold any water. Do you think we should wait until 6th grade to teach someone basic syntax? Something tells me you don’t want to do that. There’s a real problem if you have junior-high aged children who don’t know how to do simple addition and subtraction. I have no problem with the fact certain children are better at certain things than others, however, children are too different to say that waiting so long to learn a concept that gets harder to learn as you get older, as with anything (you might be able to teach an old dog new tricks, but it’s harder to do). 

  23. Wow, quite a good discussion going here! I agree with most of what you say homefire. It is always better to wait until a child is ready before you teach. But remember, there are lots of sloppy homeschool moms out there. The important thing is that you DO teach your child math at some point. And I’m not sure every 6th grader (12 year olds??) will be into doing drills every day, which is really the only method of truly learning the math facts. (Which, incidentally, can be memorized before you understand all the concepts and which will come in very handy all of your life) Actually, I am friend to a family right now whose 10 year old still doesn’t know his math facts. So you think he will learn them when he is 12? I guess we will see.

  24. homefire says:

    @Sunriselearner – That’s a really good point!  And the system outlined by this guy does advise teaching math facts early, I believe by skip-counting.  The child may not really know what they’re used for, but they will have them imprinted on their brain.  I wish I had emphasized that earlier, actually, because you are so right that the younger they are, the easier that memorization is!  My youngest has really struggled with learning them.

  25. homefire says:

    @mathematicalbagpiper – Did you read the article??  Because it certainly didn’t say not to teach mathematical concepts.  It sounded to me more like real-world exploring type math learning rather than sitting them down with a workbook.  And some of these kids were great in math when they finally were introduced to “normal” math lessons. They already knew how to do basic math–they learned it in the course of their normal lives, at times when it was meaningful and natural.  In fact, many were able to do fairly complicated problems very quickly.  Children don’t wait to learn what they want to learn!  This article is NOT endorsing holding kids back–it’s simply saying not to push them and to teach to their strengths.  And math is the area where kids are usually pushed unwillingly the very most.  It’s also the most widely hated subject, which I honestly think is probably a direct result of introducing it too early.Your sixth grade experiment sounds cool.  That sort of thing is wonderful and great way to encourage kids who are interested in pushing further or are bored with their level, but it would be a huge mistake to say that just because some kids did very well with it, that all kids should be expected to learn those things in sixth grade!  And I believe that is what has happened with early math.  But of course, the foundational problem is that every child is different, and any system that tries to push them all into the same mold is ludicrous.

  26. mcbery says:

    I wonder if that’s why I hate math? Humm…I always knew children learned better at their own speed.

  27. deyoderized says:

    Wow, this is an interesting post and an interesting discussion following.   We have 5 children, and have homeschooled almost from the beginning.  Our oldest was in a private school for the first half of 1st Grade, and we homeschooled from then on.  I definitely agree that Math can be taught too early, and in our experience the curriculum can make a huge difference as well.  I finished out that 1st year with the same curriculum he began with in school, and Math was his most hated subject.  I switched curriculum the following year (from ACE to BJ) and Math became his favorite subject!  With that being said, the rest of my sons never did 1st grade Math.  They learned all that in real life situations, and then 2nd grade Math was no problem at all.  Now I wonder what had happened if I would’ve waited even longer.  I can easily believe the part about catching up with their peers in one year, but what was so intriguing is the part about those students surpassing the others in language.  How can I redeem the time wasted now?  My youngest is 12.

  28. homefire says:

    @deyoderized – My youngest is 12, too, and I feel the same way–like if I had known everything then that I know now, surely we could have had more fun and learned more…oh, well.  Our first son went to a private school in first grade and managed to bluff his way through math.  The next year we started homeschooling and I discovered that he was not getting it at all.  (I blame CLE–the lousy math program the school was using at the time–for some of that)  We spent about the next three years doing first and second grade math over and over with different curricula.  Needless to say, that was really frustrating to both of us, and I’m pretty sure it set him up for hating math and feeling totally inept at it.  He’s now a senior and finally getting Algebra (I think) but it’s still very hard for him.  Just makes me sad to think of all that time wasted.  Maybe if we had just taken a year or two off math, he would have gotten along better when I reintroduced it?  No way to tell now, but I can’t help wondering.

  29. I really don’t know much about homeschooling, but I’m going to jump in anyhow.  I think you’re beating yourself up a little too much, you did the best you could with what you knew at the time.  I’m sure of that.  Furthermore, I don’t think God blessed very many people with the ability to excel in everything.   I’ll even go out on a limb and say that probably no one excels at everything.  I’ve also noticed  that those that are really creative and artsy are more likely to dislike math.  I agree that basic math skills are critical, but don’t think that everyone needs to know calculus.  I admire those that are creative and am thankful God created us all differently.

  30. homefire says:

    @RebornLovingHim – I’m not really beating myself up, but I am wishing I could try it again!    And I don’t expect them all to excel in everything–I know every kid is different, and it’s very likely that no matter what I did, my son would still far prefer to play guitar rather than do math.    It’s just that we have had an awful lot of not-very-fun times through the years, and it always makes me so sad when they say they “hate school” etc.  I feel like I contributed to that attitude by making math such a huge deal.  Yes, I did what I thought I had to do, but it’s sad to think that a lot of unhappiness could have been averted.

  31. Janelle says:

    This is the first time I visited your blog, via resolved2worship’s… I am tickled to read this post, as it confirms what I am experimenting with, homeschooling my kids. My 9 year old is a voracious reader, but doesn’t have a big interest in math yet. However, she loves games. For instance, she beats both her dad and I at Mancala, which is all calculating… I have been daring to hope/believe that when the time is right, she’ll take off in Math like she did with reading. I realize, after reading these comments, that word “problems” (we called them story problems) might even be a sneaky way to hook her on math. Meanwhile, I am encouraged! Thank you, all!

  32. homefire says:

    @Janelle – I’m glad this post encouraged you!  I just happened to look back and noticed your comment–missed it at the time–but I’m just really glad to hear of someone who is teaching in the way I wish I had.  Thanks for sharing! 

  33. dissertation says:

    I have been visiting various blogs for my thesis writing research. I have found your blog to be quite useful. Keep updating your blog with valuable information… Regards

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