Impressive! I love these updates.
Aangeles-
Is Ella playing Dragonbox+ on the IPad? Alex has been playing with me and it seems to be fairly intuitive at tha moment, but there are hundreds of levels for teaching Algebra… I am interested in just how far LO could go with it and what their understanding/knowledge would require at the higher levels…
Also, have you seen/used this site:
http://www.algebra4children.com/games.html
Oooh, DragonBox+!!! Ella was obsessed with that app! She finished all 300 levels + the bonus ones within a one-week period. It IS very intuitive and she played with it independently from the beginning, almost always getting 3 stars on the first try. Even now, she would go back and re-do Chapters 4 and 5 for fun. I wish they would make more advanced levels!
I’m not sure how I missed this update in the last week… it perhaps deserved its own thread.
Those algebra equations incorporate some advanced concepts, that frankly, I’m dumbfounded and at a loss of words to describe.
In Bayesian terms, we ought to ask ourselves a serious question…
either Ella is a once in a lifetime prodigy or *our concept of how to teach and what children are capable of needs serious adjusting.
*the term “our” can be viewed in two ways: society as a whole, and the EL community. I’m speaking more of society as a whole, but certainly being able to solve these level of equations at a hair past 4 years old perhaps would indicate that even the early learning group as a whole is far under-reaching our children’s potential in mathematics.
I have to agree with Poker Dad. This is truly amazing, Ella!!! Great job to both Ella and her mom!!!
So what are the rest of us missing?? Is it just the type of curriculum/programs that she has been exposed to? Or the time and effort AAngeles must be putting into her learning? Higher expectations??
Just think what Ella will be doing when she is typical junior high school age!!
If you have any suggestions for the rest of us AAngeles, let us know! 
Oops, sorry for confusing you, mrlee. What I meant in the first post was she had “skip counting 2-12 AND her times tables down pat.” I first taught her the times tables in Chinese and, in Chinese, it typically means 1-9 only (ä¹ä¹ä¹˜æ³•). I HAD been preparing to teach her to memorize up to x12 which is why I taught her skip counting to 12, but I was advised by a teacher in her soroban school to let her memorize only the times tables of single digits because she will be taught x11, x12, and up using soroban and anzan. One of the common obstacles to anzan visualization that they see in their students who have memorized addition, subtraction, and higher multiplication facts is relying on their math facts memory and having a very difficult time visualizing. So I didn’t teach her higher than x9 as I had originally intended. (Although, to be even more precise, she can easily solve the x10s since they are so easy and she figured them out by herself.)
So sorry for confusing you and I hope that clears it up. Blame it on typing fast and not proofreading before I posted. 
Aangeles
Your daughter is truly amazing! Proofreading is a luxury to us parents 
… I was advised by a teacher in her soroban school to let her memorize only the times tables of single digits because she will be taught x11, x12, and up using soroban and anzan. One of the common obstacles to anzan visualization that they see in their students who have memorized addition, subtraction, and higher multiplication facts is relying on their math facts memory and having a very difficult time visualizing…
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aangeles,
My son is currently solving addition and subtraction problems from 0-10 and we are following Singapore 1A as our spine. He can do it with the help of manipulatives and sometimes can visualize. In Singapore 1A, they suggest that at this point the child should memorize the math facts before moving onto further chapters. But I’m in a dilemma whether to make him to memorize the math facts as in future I might introduce Soroban to him. So can you please give me your opinion on this. Is Ella able to solve problems using both Soroban method and Singapore method? If she can solve problems using Singapore method, has she not memorized the math facts?
Thanks.
Oh you will make aangeles too shy to answer!
I do think that yes, we are seriously undervaluing “our” children ( oh yes myself included!) I have a pretty good idea of what IS possible but still I go to work and constantly find myself readjusting my thinking. I am teaching 4 year olds their shapes and half way through it I think to myself " crikey woman why aren’t you showing them an octagon, pentagram and a dodecahedron?" I know they can learn them ( yep my kids all do!) so why do I pull back? Societies expectations! Doesnt make it right but I find myself doing it all the same. anyway I am adjusting and increasing the expectations gradually but we are a long way off what is possible.
Changing the minds of what is possible will be done fastest through today’s early childhood carers. If there are some daycare centers and kindergartens teaching kids amazing things AND THOSE KIDS ARE HAVING FUN AND WANTING TO ATTEND EACH DAY then that will become the expectation for all childcare. Once it is it will filter through to parent training and general acceptability. But boy do teachers hit some walls here! my local family daycare is NOT allowed to show LR to under 3 year olds! I have to do many thing with some “creative” reasoning in order to put it in the curriculum at all!
So for Ella? Well I think the credit goes to aangeles. She is incredibly dedicated to her daughter in terms of time, ( no 1= time! ) understanding and effort not to mention endless hunting and adapting of the perfect curriculum level for Ella. By comparison I spend much less overall time on EL and my results are still beyond societies expectations! So I think clearly the more time you can dedicate the better your results will be. Bearing in mind that it still needs to be fun enough to ensure happy participation. No one can force a toddler to learn! :nowink: They have to want to.
Need to go find dragonbox app now, ever the curious teacher that I am :biggrin: Jaykob needs a new challenge he has finished where’s my water and monster physics…I must say each day I am surprised at how much easier it is to teach an “all believing” curious 4year old to an “are you sure mum” 8 year old! lol
Arvi,
Sorry for the delay in answering your questions.
Unfortunately, I don’t know of any shipping companies that deliver to Europe from the USA. The shipping company we use only delivers to the Philippines.
Regarding memorization of math facts, even though we started doing the Singapore math workbooks before she started learning soroban, I skipped the addition and subtraction math facts chapters until I was certain she was able to visualize using anzan. When she started to demonstrate that she could visualize, I think at around 3.5 years or so, that’s the only time we went back to do the chapters we skipped in 1a and 1b. And I did teach her to solve the equations the Singapore way when we went back because, as I watched her become more proficient in using the soroban and I myself learned more about how it works and the thought processes involved in using it, I saw how a child COULD learn how to solve large-number equations by simply learning how to push certain beads up and down in their heads without ever getting a good sense of numbers or even know what the numbers mean. I wanted Ella to be good not only at computation but, more importantly, I wanted her to really understand numbers, be able to think creatively about them, and be even better at problem solving and thinking outside the box. I think we have been able to accomplish this so far, because Ella is able to do arithmetic using whatever approach I ask of her, be it anzan, Singapore, JG, or even just coming up with her own creative solution to the problem, using both right-brain and left-brain methods. Also, to be able to do algebra, I do think you have to be able to think creatively as well, and she has shown that she can do this. My eventual (very lofty? don’t know if it’s even possible??) goal for her in math is to be like BOTH Feynman and the abacus salesman in this thread :biggrin: :biggrin: :biggrin: http://forum.brillkids.com/teaching-your-child-math/question-(or-hypothesis-if-you-will)-about-anzan/
Oh… and one last thought: We do a ton of right brain activities, 1 to 1.5 hours worth almost daily, and I think this is a big factor in her being able to continue visualizing easily even though she now also knows her math facts.
Hope this helps!
I have to agree with Aangeles about right-brain activities helping in various academic topics. Me and LO have found it very beneficial especially with mental math (anzan) and recently, algebra too!
We carried experiments incorporating right-brain techniques with math (specifically soroban and algebra) such as rapid-flashing and mental imaging.
First with rapid-flashing of soroban values, I would flash 1-2 digits cards and also make them into Little Reader files. In a matter of days, she was reading 3-digit values expertly. We also did the same method with number bonds which are fundamentals in all soroban operations. As of now (LO is 3 years, 10months old), she can mentally solve simple equations such as 4x+3=3x+9 and even some that involves multiplication like 3(3x+1)=2x+1. We combine adjectives and properties to numbers like "those jiggly numbers with letters need to group together and those red-hot plain numbers must stay close with their own kind, any of them who crosses to the other side of equation will shiver and have the opposite value!) It sounds silly that why it sticks on her.
On soroban, we’re visualizing 3-digit addition and subtraction. She’s not yet in the “mechanized” level as we’re just studying soroban for about 6-months with the first 2-months at a soroban school and henceforth only home-schooled.
We also learned the times table the “right-brain way” months before at www.multiplication.com which involves an integration of “silly stories” to the multiplication facts.
Our math curriculum involves:
Soroban
Singapore Math (we skipped all beginning levels bec of the proficiency she gathered at soroban and is currently at 3a)
Planning to start with MEP 3
Language and Vocabulary:
Visual Vocabulary for grades 1-6 (this is a hit! contains intuitive pictures that makes LO think)
Your Child Can Discover
Little Reader (done with 2 curricula but we’re using it for customized lessons)
Right-Brain Training:
Tweedlewink
Wink
Memory Magic
Our frequent “imagination” integration with math (I would shout equations and soroban problems from the kitchen or wherever and she’ll solve it)
I am a big,big advocate of developing the right-brain. It complements any curriculum. It’s also my opinion that it’s the best thing that we’ve doing so far as EL goes.
Silly stories, lots of hugging, games, incorporating humor even in math - I’m sure every successful EL parent does this but it might just be the most potent ingredient for that perfect curriculum! Hope I have helped!
Nadia,
Super impressive.
At what level of Singapore Math did you start with then? You mentioned you skipped the beginning levels. Did you start straight with 3a?
Hi Nee! Thanks Yes we started with 3a as it’s the only copy I have (courtesy of a friend). It’s actually our dilemma how to get the next levels 
Dear aangles
regarding Ella’s Soroban and violin classes, do they allow the parent to be present during the class or they want you to drop her off and pick her later??? and if u are allowed to join in the class how active or passive u will be??
thanks
Rua
For Soroban, I don’t go in with her to class anymore. I used to in the first few months - they didn’t really encourage it but accomodated me because Ella was just 3 at that time. I didn’t participate, though, and was just there to provide “moral support” for Ella. :biggrin:
With Suzuki violin, they actually WANT the parent to attend the lesson and even take notes so she will know how to teach the child during daily practice at home. So I always go with Ella, the teacher teaches her for 20-25 minutes and I just observe. Then, the teacher will discuss with me and show me what to practice with Ella for 5-10 minutes.
Keri, can you please tell me how you are using this livemath software with your toddler. I perused the site and it looks more like an advanced calculator to me.
Arvi-
In many ways that is exactly what is is! You could use this all the way up through calculus, as it is intended, but it will also very simple algebra. We have been using it very simply for her, in the same way that you could use a graphing calculator to show how an equation is related/defines say, a 3D shape…except that you can do all sorts of coloring, shading, rotating, to make it interesting for her that are just not possible on a calculator.
Here was the thing for me: I am not a programmer, and other math programs are very difficult to use as you must first learn the programming to do equations. LiveMath is similar to writing on paper, so I can show her step by step…for now, just simple things like moving variables from one side of the equation to the other…
This is NOT a program that we would have bought had we not planned to homeschool her in math at an accelerated rate, and my hubby can use it to generate exam problems neatly and quickly, at least the math portion…
Here is an activity we recently did that may be more specific…
We recently found a book called ‘The Greedy Triangle’ in the library and Alex fell in love! The book is for young children, and starts out with a young triangle who grows dissatisfied with his lot in life as slices of pie, supports for bridges, etc. He goes to a local ‘shapeshifter’, and asks for just one more side and one more angle: poof, he is a quadrilateral…he keeps going back, asking for just one more side, and one more angle: pentagon, hexagon, heptagon, etc, until eventually he has so many sides and angles that he resembles a circle…you get the idea, very cute. Here is the book:
http://www.amazon.com/s/ref=nb_sb_ss_i_0_10?url=search-alias%3Dstripbooks&field-keywords=the+greedy+triangle&sprefix=The+greedy%2Cstripbooks%2C210
Alex loved it so much that I made her a little wand and a ‘shapeshifter’ hat and let her ‘poof’ the shapes in order (I dug out a set of IAHP bits originally);then daddy had the idea to model it on LiveMath, and while it took a little while, she was able to ‘see’ it happening along with the equations…
It does seem strange! But I think because very young kids are just learning EVERYTHING!, they don’t have the preconceived ideas that adults have on how complicated math looks…is she learning how to use trig functions and advanced math? Of course not! BUT, she is familiarizing herself with how it looks, as well as what it can do. I want her to never, ever fear advanced concepts simply because the ‘language’ looks daunting or frightening!
The funny thing is, it is actually quite easy to show a toddler how sine, cosines, and tangent ratios are made using a triangle and defining the sides! I think she remembers them better than I do…does she know how to divide them, or manipulate them? Nope! But I am hoping that showing her the simple relationships, combined with a step-by-step picture will simply introduce a broad understanding of how math works in the world!
Nee,
After reading Robert Levy’s post in the Moshe Kai thread, I’ve been thinking about the Saxon/JG Singapore/MEP issue. Maybe Manda or someone should pull this out to a different thread, Not sure if you can pull our conversation from the middle of the thread and leave the rest.
David basically was finished with his high school math at about 10. My son started having trouble with Saxon at about the time David was finishing the whole series. I’ve noticed from other kids that have been discussed, that many of the kids are finished with High School math around that time. Assuming you start JG in kindergarten it would take a child anywhere from 2-4 years to complete - or at about 8-10 years old. I originally thought this to be very ambitious for a child. So, about the time the drill, drill, drill of these programs starts to wear on a child they are moving on to application of math - or going to college like David.
I am wondering if the problem with Saxon is the books or the age of the child using the books. I didn’t push my son to move faster - he could have early on. Most people were aghast that we were doing Algebra at the end of 5th grade. I didn’t want to early enroll him in college. I think our problem was that we slowed down in grades 3-5 to accommodate the system. Had I continued to push, he would have finished HS math by 6th or 7th grade. As it was we spent a couple hours a day fighting over math. We switched to AoPS and Khan he was able to move as fast as he could. He is 17 and working on upper college level math. He needed to apply what he was learning as the drill was making him crazy. The funny thing about Khan is that it also drills skills and uses a spiral approach, but because it is taught with a lot of application he doesn’t seem to mind as much. We have not had a fight over math since.
It gets me to thinking if part of the problem with Math in the US is when we teach stuff not just how we teach stuff. Part of it might be that we aren’t moving the kids fast enough and dragging out the early mastery process. The is the joy of JG. He recognizes it is a hard work and there is no way around the drill so he came up with a method to do it quickly and efficiently and to mastery. My son didn’t mind doing the drudgery work of drill when he was little. that might be partly why the soroban works so well also, Basically the first 6 years of Saxon covers mastering the four basic functions of math, fractions and decimals. There is some measurement, time telling and introductory geometry but that is it really the jist. As the Levy’s have displayed - that can be moved along fairly quickly and the same with JG. Perhaps the issue is moving to the stage of application by 9-12 and not so much the curriculum used to get there. If that is the case, I might be more inclined to skip application with my child in favor hitting the mastery hard and moving to application later.
After Mr. Levy elaborated further on the Saxon use in his home (on the Moshe Kai thread), I am going to stand by my original assessment of Saxon. There are better ways to get to Mr. Levy’s destination - it just happens that Saxon the was the best available tool for him at the time. However, young Ella can do much of what Saxon taught in the Levy household (and she is doing it sooner) and I’m betting that aangeles hasn’t had to resort to spanking or fighting. It is not my goal for early education and part of the reason I wanted to educate my second child early is so that I could avoid the pitfalls I experienced with my first child.
The Imafidon children of Great Britian used the books found in this shop: http://excellenceineducation.org.uk/home/eieshop It might be of interest to aangeles and others as their children are getting to the age when the Imafidon children began their high school math work.
Sonya-
I absolutely agree! The point of EL, at least at the baby/toddler/preschool age is to teach them in a manner that is fun and effective at their age. I grew up using Saxon materials, have them now, and the idea of setting my toddler down for a lesson like that is laughable! Not to mention it would utterly and completely ruin her fascination with math.
I have no doubt that Saxon is/can be used very effectively, and the results Mr. Levy and his son achieved are amazing! But I also believe that the program is simply a tool that hard work, perseverance, and dedication to education bring to fruition…
Will we end up using Saxon down the road, in its entirety or as a supplement? Maybe, I think it depends on Alex, her style of learning, and her mastery of math…
Regardless, I truly appreciate your perspective having taken an older child through, and working with a tiny tot again!