Math Education - interesting

[sonya_post]

Just because we need more conversation about this: 

Lecture on math education by the creator of Jump Math - he makes some interesting points at the very end of the lecture on enriched learning environments.

<a href="http://www.youtube.com/v/hmpVOUrLqq8&rel=1" target="_blank">http://www.youtube.com/v/hmpVOUrLqq8&rel=1</a>

Very interesting paper he mentions in the lecture:

http://act-r.psy.cmu.edu/papers/misapplied.html

[queriquita]

serendipitous.  thank you so much for sharing that.  it's exactly what i've been working on lately.  i am saving for reference   i'm so pleased that he was 1) able to duplicate the success of his initial results, 2) duplicate in larger student classes too, 3) teach other teachers to duplicate, 4) increase the mean and decrease the width of the students' results - yes! i appreciated his analogy of the rungs on the ladder and also his comments on the need to find balance between practice and interest.  the rat experiment is exactly what i've been saying (at least locally), and i'm pleased that people are starting to shy away from thinking that intelligence is so genetic!  math is a language and requires immersion to gain fluency.  my kid's aren't chinese, but you better believe they'll learn to speak the language if we moved to china.  furthermore, i would too, just at a much slower rate - but i would definitely possess the desire and wonder to make it happen.  until we start teaching for fluency, our society's problems will continue to grow. math is essential, as it's the language of the universe.  i relished at how he tied in destructive/violent/physical/poor/bad (choose your word) behavior with lack of knowledge/understanding, and how he wove it to our problems as a society - all while emphasizing that it is neither the good teachers nor the bad students who are at fault, but the result of a biased system who is emotionally blinded to the solution.  and i loved how he compared the beauty in numbers and math and the wonder of the world and 'figuring it out' to the visible beauty in nature, and that 'figuring it out' is so vital if we're going to see and fix the major contradictions that are affecting our ability to survive as a species. loved it. again, thank you so much for sharing!

also, i'm putting pascals triangle, the bell curve, and some waves up on our play area wall this week for the kiddos to admire as they walk by and play. i will be so excited when they start seeing the patters come out! can't wait!  as a matter of fact, in addition to tracking the weather, i'm also going to create an online tally sheet for them to track heads and tails. ... i'll probably incorporate it somehow by having it be a way to choose whether we do this or that first ... not quite sure yet.  but i'll figure it out ;-) feel free to add suggestions.

(and i just have to say - i love being excited about life - and i'm so over natural high on life buzz killers who think that everything should be just boring and bland and that to stray from that sentiment is not cool, not socially acceptable, and the sum of life's experiences. blah, life truly is amazing and if you disagree then that's your body's way of telling you that you're not living to your fullest and that you need to switch up what you're doing until you find what gets you naturally excited.)

[cokers4life]

I just found time to watch this today, and Wow.  It was truly inspiring.  It even brought me to tears.  I am just a little emotional lately about early learning verse the "gifted" mentality.   Just the other day I had someone (not from this forum) tell me her children were born gifted and that she did nothing to provide them with environment to make them so.  This forum of people are quite adamant that all of their children are quite "gifted" and that it has nothing to do with their environment.   The person also proceeded to tell me there is a difference between an accelerated child and a "gifted" child.   Basically implying that you could accelerate a child but that didn't make them gifted.  Well, I had to do some research, and I found this is common ideology for most people.  When I look back on my life, I see it every where.   I have been much protected in this bubble I call "Brill kids" where everyone believes that all children have the astounding learning capabilities in the right environment. 

I still don't even know how I really feel on the term "gifted" through genetics as there are some children who demonstrate amazing abilities but its hard to get a honest look into these children's lives.  Can a parent really say they did nothing?  There are so many factors to raising a child and that is true when it comes to implementing early learning techniques.   We have no real idea how each day is played out for any of the amazing children in this forum let alone in the world in general.  Is it genetics or is it the way in which a parent presented the information and the level of consistency that's performed?  The earlier you start (from day one of birth) might mean the difference between reading at 10 months or 15 months.  For example, I didn't start with my youngest using LR until he was 6 months.  Before that I was using powerpoint slides with no real technique if I was being honest.  Is it reasonable for me to expect the same results as someone who used LR from day one (obviously not from day one of birth but then I could be wrong)?    Choosing the consistency of 3x a day of LR verses 2x day or 5 days a week vs 6 days a week...  Did you flash cards along with LR?   I scour the posts of the best of the best to figure this out, but honestly I don't know how different their day is compared to mine.  Does the education of the parents impact their ability to properly develop the babies cognitive development?  Was the economic ability of the parent to provide the toys, tools and resources for cognitive development a key factor?  What tools did they use for mathematics and how early did they start?   Does the smallest detail of difference mean the biggest difference in results or is genetics the largest factor? 

I am sure everyone has a different view on this.  I will tell you I don't really know yet.   I don't think I will ever know for certain.  I will tell you that the problem I have with the term "gifted" (implying genetics as cause rather than environment) is that it overshadows the capabilities of all children.  It creates an attitude that you are either born smart or you are not or you are born average or born extraordinary.  This does boil me as my children did not exhibit "gifted" capabilities until I created the environment to spur their cognitive development.  I have only been in this for ten months so I will be the first to say my knowledge is limited as well as my experience, but I can't help feeling annoyed by the term "gifted."  Maybe its because its used too casually.  I can't really say that there aren't "gifted" people out there.  I am just saying that it annoys me when a parent will not take credit for the early learning environment that they created.  The underemphasis of environment is destroying the chance of most all children from reaching the potential of achieving amazing cognitive development.   

I needed to most of all be reminded of the plasticity of the mind. That it doesn't end at birth or at your DNA.   I think as parents we often are busy comparing ourselves to more successful parents.   We can learn great things from successful and awesome parents, but we can't torture ourselves with thoughts that because we didn't do this or that or had this or that that we some how failed them.  At the end of the day, I just want to do right by my kids and no one likes to be limited by their DNA because you can't change that.

I needed a little inspiration after a tough week of contemplating this so thank you for posting this.  I am definitely curious to find out more about jump math. 

[sonya_post]

Hey Cokers,

If you think about what he said concerning the bell curve, there will always be kids who are gifted with a high IQ at the top. The thing that is great is that with an enriched environment the distance between the "gifted/high IQ" and the regular Joe is really shortened. So in practice it doesn't matter.

That has been borne out in study after study - so who cares in the long run? And, I'm still going with my long held belief and several studies and personal experience that bears this out is that the children who are truly gifted - unless they are challenged - end up burnt out and lazy. That is why it is better to tell a child that he is a hard worker and not that he is smart. Children who are gifted end up making their way through the system never having to test their mettle - because people are always so impressed with them and they tell them so. They get to college when the rest of the kids have now caught up and they are stumped. The reality is that unless you are profoundly gifted - the rest of the kids eventually do catch up and you aren't a big deal anymore. They have no idea how to manage time, study, and are just plain mentally lazy. They can't hack it and drop out. Statistically, gifted children are less likely to graduate from college than a "c" student. That "c" student has been learning to manage sports, music, work and passing school. These are far better qualities in the long run than merely intelligence alone. Though we need not pit one against the other, we should be striving for a both/and. Those parents who are convinced that their children are just gifted, let them think that , but for the children's sake, I hope they never tell their children that.

In the meantime, keep making your children work hard and don't let them think they are something special. The little boy I have in daycare is now in preschool and his teacher tells him how smart he is that he can read. The little boy is smart, truly smart, but because he didn't have any training is already pretty lazy. I asked him if learning to read was easy - he said no. I asked if he had to work hard to read and wasn't he sometimes frustrated - he said yes. Then I said, "The next time your teacher tells you that you are smart - you tell her Hog Wash! I worked hard to get here." He should be proud of that HARD WORK.

As for Jump Math - I am having a wonderful time going through the teachers material and I think we are going to go ahead and get the workbooks for 1st grade. If you are going to use it as a spine, you really need to get the books for school rather than the Jump At Home books. I've been through Saxon 1 to Saxon Algebra 1. If you look at the review in these it is not exactly the spiral that Saxon has but it is certainly spiralish - they call it scaffolding and I get why. This will take you through Saxon's Algebra 1/2 and will be excellent preparation for AoPS material. There is a lot of mental math built in and plenty of stuff to keep the most "gifted" busy. It covers material earlier than Saxon. Children are doing three and four digit addition at the end of 1st grade you don't see that in Saxon until second grade.

What this guy is brilliant at doing is moving in small steps and making each step understandable to everyone. Which makes it perfect for EL. I am starting my little girl with Downs on this next week. If the child doesn't get it one way he will come at it from another way. And then another. And you don't move on till the child gets it.  I am a big picture person so I don't see things incrementally. I don't know when there are several steps to solving a problem, I just do it. Nor can I explain what I have done. That is a huge disadvantage in math. For other subjects, like literature and history, big picture thinking comes in handy. I'm reading through Jump and realizing what I did wrong and how I can do it better and that even Miss C. would get math if explained properly and given enough repetition to grasp the concept. The charges leveled against it that it is too much like Saxon and no teacher will be able to get all that repetition in - well, there is a lot, but he manages to cover lots of ground while doing so. And the comparisons to Singapore, it's probably as good.  The lessons aren't scripted like Saxon's but there is enough of a script that I even I can teach math out of one of these. That is a huge deal BTW.

[cokers4life]

You make an important point about working hard.  I know that my kids work hard to obtain information.  It takes repetition, lots of practice and this generally means me playing lots of games. 

Right now with my four year old we are working through Mammoth Math 1A, and I find that he can translate manipulative work to worksheets.  I end up taking the problems and turning them into a word problem that we work out with using a manipulative like blocks, cars, animals, rocks, etc.  For example, he has to fill out a problem with greater than, less than or equal to and the problem will be 4+3 ___ 6.  He doesn't get it on paper, but if I show him he has 4 cars in one hand and 3 cars in the other and I have six cars, does he have more than, less than or equal the amount of cars to me?  Or how many do you need to make this true equation true: 5+__>7? 

I have found myself doing this the entire time, and he prefers this.  At age four, I am assuming this is to be expected, but I often wonder if this will translate later down the road when he should be doing book work.  Will he have to learn it all over when he is ready to fill out worksheets?  Right now I just use Mammoth Math as a spine to organize what math concepts to present and in what order.  I just find games or make up my own to teach the concept.   We work out the problems using manipulatives.  He isn't very receptive and gets bored if I don't bring in a manipulative to solve problems.   

You said Jump Math presents concepts in different approaches.  Could you give an example?  I have been thinking about Right Start Math because it uses a lot of different manipulatives which seems to be where my boy is comfortable with.  I am trying the techniques of Jones Genius' with my 3 year old and my 4 year old watches and participates as well. 

My 3 year old girl is very receptive to this technique right now which is saying a lot as she is a very difficult child because I swear she is training to win a grammy one day.  She is acts just to be acting.  I can't ever figure her out.  We play a lot of imaginative games with her.  I can get her to solve any math problem as long as I address her as Milly Patterns from Team Umizoomi and tell that we have to complete these problems so we can save GEO from a shape eating alien.   

That is where I am with math.  The question is how long does one stay in the manipulative world and how far can it take you?  I am just making it up as I go.  Its all very hard work though.  My kids can appreciate that.  There will be know doubt in my kids mind that while learning can be fun.  It also takes practice and hardwork. 

I wonder if manipulative based math learning builds the cognitive skills needed to do the expected "book work" that is necessary later down the road?  Or am I missing a piece that connects the two to make independent "book work" happen sooner?  Right now there is no independence.  I have to guide him through every problem.  He figures it on his on only after I have worded in a way he understands.  Sometimes I don't always word it right the first time for him to get it either.  Does Jump Math provide this assistance?

[sonya_post]

Saxon uses manipulatives until 5/4 I think. MEP all the way through high school. Jump Math - all the way through 8th. Jumps manipulatives are pretty simple - dice, cards, dominoes and printables. MEP's are like that other than gathering all kinds of fun stuff to count.

In Jump the explainations are very clear and you move so incrementally that the concepts are hard to miss. So, let's say you are making groups of ten (for mental math). So, first he will explain it using fingers - 2 up and 8 down. How do we know it is ten? We have ten fingers. So we practice making tens with our fingers. Then we do it again on a 10 block - similar to a ten frame. Then we might do it again playing card games. Then again with dominoes. You only need to do the activities until your child has mastered the material. If your child gets it right away and can master facts that make ten he has additional activities that make it just a little bit harder. Use your fingers find ten with more than one addend. Or use the ten block.

If you haven't looked at the teacher resources, they are free if you get an account. I have all the files for grade one in my dropbox here:  https://dl.dropbox.com/u/60668524/Jump%20MathTeacher.zip

You can also download the first 50 pages of the workbook for each grade free on the website. You could work with it awhile before you decided it is what you want to do. You really don't need the workbooks for the first grade. You can do the work from the teacher's manuals and blackline masters. Workbooks are $22 a year plus shipping. All other material is free on the site.

EDIT: And yes it is normal to be using them. No, he is not going to have trouble translating it to a book as long as he understands that 4 cars plus 4 cars equals eight cars is the same as 4 + 4= 8. WIth multiple children at different levels this is exhausting. But worth it.

[aangeles]

Oh no, Sonya! Just when I thought I had our math curriculum all figured out!!!   

And the comparisons to Singapore, it's probably as good.  The lessons aren't scripted like Saxon's but there is enough of a script that I even I can teach math out of one of these. That is a huge deal BTW.

Can you please elaborate more on how it compares to Singapore Math?

[sonya_post]

aangeles,

You are in luck - you guys can probably stick with what you've got.

If you are a parent who is successfully using Singapore then you should probably just stay. Here are the reasons I would switch:

I am not comfortable teaching math or my child is having a hard time with the concepts.

Jump is as good as Singapore I'm not sure I'd go  so far as to say it is better. What is better about it is how it teaches and breaks down every concept to it's smallest possible step. Great for a 2 year old. I'm not sure Ella needs this. And you can teach math so I'm not sure the true benefits of this program are a good fit for you.

You are going to get the depth that Singapore is great for, you are also going to get lots and lots of review that Saxon is known for. Not spiraling in that kids master the material and move on - just like Singapore, but there is review that goes 2 years back, which is why the worksheets samples don't give you a good idea of what the kids are learning, Do you need all that review for Ella? Probably not. Especially since Singapore is one of many curricula choices you've made.  Do we need it for a 2 year old? Yep. I am not going to buy 10 different curricula for math. We are doing JG and Jump with lots of games and living books.

The worksheets are good, but the teaching manual is the core of this series. If you don't use the teaching material Math Mammon is going to be as effective. You are good. I don't think you need this, but I do.

[akalori]

Very interesting video.  I watched it twice.  You always finds such informative stuff.  I have a kid with learning challenges so it was inspiring.
Thanks again, Lori

[lzp11]

Finally found the time to watch this an it is very inspiring.  I also need this inspiration as my 3.5 year old is quite a challenge to engage in learning, so to see such a narrow bell curve after using the approach is amazing.  I am currently using Rightstart and will be afterschooling once she starts UK reception (at age 4) next year.  I love RS but I also would like additional approaches to teaching maths including methods that will bridge the gap between home and school learning.

I really like the look of Jump Math - Sonya thanks again for highlighting the curriculum and also for helping me understand the differences between the different curriculae - it's so difficult to know what to do for the best and what will be a good fit for my kids.

But I now think that Jump math might be a good fit for us because
 - I'm not confident at my ability to teach math and I don't have masses of time to learn
- I need a really straightforward programme that maps out the stages of learning
- Moving in tiny incremental steps is absolutely necessary to build confidence for my 3.5 year old who has a tendency to give up on anything if it doesn't come easily (we are working on lots of praise for trying hard and for effort but it's certainly hard for her)
- I think we need lots of review and to use different methods for learning the same concepts
- I like the evidence backing the approach and the methodology makes sense to me
- It seems great value!
- It seems like it might complement using the RS abacus

i'm not quite ready to get started as we have a few lessons we need to master in RS but there may come a point where she struggles to move ahead with RS or where we need new ways of looking at the subject and I'm now excited to have Jumpmath as my next step to try.  I'm guessing it will be in a few months.  maybe after Christmas.  But I'm excited 

Cokers - don't worry about the gifted versus accelerated debate.  Whenever I start getting uptight about this issue (usually because my 3-year old is playing up in some way  )  then I go back to that lovely thread about the books Mindset and some others - did you see them?  If not I'll try to post the link.  It seems to me that being gifted is far less of a predictor of how much a person will achieve in life, especially if they fall into the mindset of thinking that it's all about being clever rather than putting in effort.  We all have to stretch ourselves in the end if we want to achieve things and learning to do this is essential so actually learning to work hard and achieve against the odds is wonderful life lesson that can lead to truly amazing and inspiring achievements.  Probably the biggest lesson I have learned from Robert Levy on his thread is how much hard work both he and his son put into learning and how he ensured his son understood that his success was due to effort. 

[PokerDad]

I left a comment about this video in another thread:
http://forum.brillkids.com/general-discussion-b5/what-works-clearinghouse/

"I enjoyed the lecture also, especially the part about normal environments producing wide bell curves with large standard deviations and then enriched or restrained environments producing narrow bell curves with small standard deviations. It made sense, but I had never thought of it that way"

Cokers, my comment goes along with yours. One thing I do from time to time is visit the WTM forum and browse the accelerated learning threads. The people over there are very quick to point out that their kid was "born that way". Well, here's something to consider... if the parent is engaged enough to take part of a forum on LEARNING AT HOME, I find it difficult to believe that they did "nothing" to foster their child's gifted-ness. I think I read one comment about the "gifted" father learning to read early all by himself "even though" he was left in front of the television all day....
LOL....
I laughed out loud because I've done enough research to know that this is how many early readers in the 70s and 80s learned to read. Commercials would come on the television and the voice over would say the words that were flashing in large colored print on the screen... such as "Act Now!".... "Supplies are limited".... "Head On! Apply directly to the forehead" (okay, just kidding about that last one, but the commercial is basically what I'm describing)

Here's another thing to consider. Environmental stimulus can turn a gene on or off. In fact, most of our DNA consist of these "switches". I'm not sure which book it was, perhaps Nutureshock (whichever book talks a lot about Ted Williams), discusses this at some length.

EDIT: Was just browsing over at Science Daily and saw this article that effectively discusses what I wrote in this post
http://www.sciencedaily.com/releases/2012/10/121018123052.htm

[sonya_post]

I've been wanting to post something about this nature vs nurture issue for awhile. In practice, it really doesn't matter whether your child is genetically "gifted" or not. What matters is what Beth Lucy Wellman calls brain building - basically nwhat we are all doing here.

I have been attempting to find hard data on Dr. Wellman's studies on war orphans in the 30's but there are only excerpts online and her books sell for upwards of $125 on amazon last time I checked. Her studies involved early stimulation and brain builidng activities with preschoolers in an orphanage. What she found was the early stimulation caused a 15-35 point increase in the Stanford-Binet test scores. The children were followed until they were teenagers and the benefits lasted at least until then. The children far out performed their peers from intact homes.The younger the children were when they received intervention, the higher the jump on the IQ test.  It was her research that sparked the nature vs nurture debate and was the impetus for the Head Start Program started by the Johnson administration in the US. However, none of her methods were followed and in its current form head start is just a babysitting service.

I also read study about child prodigies recently.  Few of the participants ( a small sample so you can't make too much of this) had high IQ's. Most were in the normal range and a few in the below normal range. Most (something like 90%) of them were on the autistic spectrum or just slightly missing the autistic spectrum. What they all had in common is that they scored in the 94 percentile or above for working memory. It is the autistic fixation tendencies and tremendous working memories that produce children who are so competent in a rule based arena like music or math. While I'm not after a child prodigy it does go back to the 10,000 hours to expertise argument. Time/Training is what produces a competency not IQ. And IQ functionally goes up with early intervention. Whether that lasts is really unimportant - as the effects early stimulation last until at least the teenage years and by then the normal IQ kids are catching up mentally to the "gifted" child anyway. But by the time the normal kids and even the bright ones who haven't had early intervention are teenagers, the  Early Learners have had years and years of education under their belt - they've made a huge dent in that 10,000 hours. And I'm not sure the 10,000 hours is directly relatable to early learners as the earlier they learn the better they learn and subsequently the faster they learn. Hence Dr. Wellman seeing a 35 point jump in IQ for the youngest children receiving intervention. That takes a child from 110 - 145. That is a huge leap. Thus, narrowing the standard deviation.

[Kimba15]

Sonya,

Thank you so much for posting this video. I just did a blog about my biggest regret which was just glossing over maths with my eldest. This video has given me the confidence to go ahead and teach maths and know that even though I didn't start early I can still get my dd well ahead by starting now.

Thanks heaps,

Kimba

[cokers4life]

Sonya,

I just found Beth Lucy Wellman's "A Manual on Nursery School Practice" online to read.  I didn't know if you had seen it.  You got me interested about her and she is not easy to look up on the Internet either. 

http://babel.hathitrust.org/cgi/pt?id=mdp.39015068424897;seq=5;view=1up;num=1

[sonya_post]

Thanks!   

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