# Singapore Math vs Montessori Math

It is quite overwhelming the sheer number of math programs out there for homeschoolers.  Though we already use Montessori math, I got side tracked into cursory looking at the different programs this morning in my quest for math skyscrapers.

What’s Singapore Math?  The only thing I know about it is the review from Cathy Duffy and the free worksheets I looked through quickly.  What jumps out at me from her review are:

1. It’s a program that teaches children math from concrete, to pictorial, then abstract.  Sounds like Montessori Math.
2. Concepts are taught thoroughly and sequentially rather than in a spiral.  So once a concept is covered it isn’t covered again except in review.  Montessori Math is more a more spiral approach I think.
3. The program requires one-on-one teaching.  Not Montessori at all unless they mean that the concept is taught one-on-one and then the children work on it.  Montessori kind of emphasizes the working and learning by yourself part.

I got a headache looking at the worksheets.  I was reminded of the pages and pages of worksheets I did as a child, which often has NO BEARING on math in real life.  I know people say that Singapore Math’s strong point is in how it relates to real world problems.  But looking at the worksheets, often my confusion is on interpreting what the math question is trying to say.  However, they did illustrate concepts that I don’t see in Montessori Math concrete materials.

From Singapore Math I jumped to this listing of homeschool math curriculum overview.  It’s nice seeing it in one page.  A forum thread I came across elsewhere noted that Math-U-See, Shiller Math, and one more all came out of Montessori.  Apparently the “founders” trained with her or her disciples.  Many of these work with the concept of concrete to abstract. Someone also said that Singapore Math is based on Montessori.  I can see that from the point of going from concrete to abstract.  But this idea of teaching math isn’t copyrighted; I’m sure lots of other people have the same idea.  Except maybe Maria beat them by about 100 years.

Singapore Math is super nice to have because it really lays it all out there for you, the math concepts you need to cover, broken down in specific units.  For example, I saw problems for adding 10,000 to a number, or for learning how one equation is same as another, or adding one or subtracting just one from a number.  Very detailed concepts.  Whereas in Montessori, it’s just divided into addition of 4 large numbers, and memorization of addition.  I don’t know if Thumper understand how easy it is to just add a 1000 to a number in an abstract way.  And these are worksheets for 1st graders.  Speaking of Singapore Math, here is a link to free Singapore math material.

So I think people choose programs like Math-U-See or Singapore Math because the curriculum IS laid out for you, in a workbook format.  You know you’re done when you finish the workbook.  It’s much easier to stick an addition worksheet in front of Thumper to see whether or not she has mastered the concept.  It’s harder having her pull out equations from a drawer or generate her own, even though those are more interesting for her to work with.  In addition, while math is sequential, the freedom of choice and the way multiple materials cover the same concepts or review previous concepts can be overwhelming for people who are used to a very sequenced and ordered way of learning (ME!).  It is only human nature that we want to categorize and order things (curriculum in this case).  But for now I’m going to stick with Montessori math, maybe using Singapore Math workbooks as a supplement to see what other concepts I need to teach.  I know Montessori math doesn’t necessarily cover all state standards.  Part of the reason I’d been searching is I learned through worksheets.

But, if Montessori math is the precursor to many of these other math programs, then why not use it.  There is no reason to use materials that have been redesigned and thus lose some of the indirect methods math is taught concretely.  For example, I see the Shiller math concrete materials don’t color code the place values (unit bead, ten bar, hundred square, thousand cubes).  The only thing of course is cost.  The materials are not cheap for homeschoolers.

I never did find my math skyscrapers, which are these drawers of equations to children to work through.  Onward to the search!

# Small freakout

This morning, I was happily browsing FB and came across pics from a Montessori school on the math their kids are doing.  Looking at the kids working on their addition to the millions reminded me that this was something we’re supposed to be covering already.  Plus all those lovely work cards.  I felt behind.

For the last 2-3 weeks, I’ve already been quite anxious because I’m playing catch up with making materials.  Every day it seems like I find a new work that Thumper and Astroboy might need to work on, and the mad dash to making those materials for them.  I usually only have time to kind of think about what I need to make, then another material pops up and I start researching those.  Gradually a long list of materials to make/buy accumulates and it’s growing faster than the rate I can deal with them.

On top of that, the kids have been dragging their feet in school, especially Thumper, due to the sheer amount of work you “NEED” to cover in Elementary.  I’ve been trying to adjust but nothing is quite working.  I also don’t like having school more than 3 hours a day.  It feels like then we might as well just go to school.  Because the one thing I do complain about school is the children not getting enough free play time.  But at the direction we’re going, we’re slowly doing the same thing.

kind of know my vision of how the children ought to be learning, what our days should look like, I’m just having a hard time trying to figure out how to get there.  The problem with having a vision is that I get quite discouraged, mad, annoyed, when the children don’t want to follow my plan.  I know, I know, you’re supposed to follow the child.  Yet another conflict.

I’m freaking out.  Feeling inadequate.  It’s only a small freak out because my logical brain is saying, don’t be so hard on yourself, you’re doing fine.

This got me to thinking about the recent post from Mandarin Mama about coveting what you don’t have.  Namely, thinking that if you ONLY could have this, this, and that, then your vision of how great your life could be, can be, will be, will magically appear.

It’s a problem I’ve always had.  When Thumper was smaller, I think part of the reason I kept buying ever more expensive “educational” toys was because I somehow thought that it would magically make her want to play with them, or shape her into the self-motivated, independent person I want her to be.  She refused to play with all the toys I got, but just wanted to play with us.  I learned from that and did not ask so much of Astroboy.  And yet the desire of thinking “if only I have this, then life with the kids will go much more smoothly” continues.

This need to make materials is for the same reason.  Subconsciously, I probably feel that if I just have the classroom set up, all the materials made, environment/routines perfectly set up, then the kids will magically want to learn and want to do their work, all by themselves without so much prompting and tempting and work from me.   Every day they will wake up, put on their clothes immediately, make their bed, eat breakfast without whining or complaining about the offerings, do some chores without prompting, and cheerfully say, “I want to go to school!  I can’t wait!”  They will put their dishes away right after eating and brush their teeth and thump thump thump down the stairs to knock on the door of their school room happily.  They will be eager and willing to learn rather than dragging their feet for whatever reason.

Okay, I feel much better now.  Writing down the things that make me anxious somehow make it not so bad.  I will continue to march forward.   Once in awhile, my Type-A, competitive side comes out.   But honestly there is no perfection.  There is only the need to recognize, to understand, as Mandarin Mama said, of what it is that’s triggering the reaction in you, in order to do something about it, or to make peace with it.

# Introduction to Fractions

Last week and this week, both Astroboy (4) and Thumper (7) got their introduction to fractions.

In training, I was told that fractions come at the end of the series and that some kids don’t even get to it.  But reading my album I see that fractions can be introduced as young as 3 since it’s just a Sensorial experience.  For Thumper, we verbally introduced the idea pretty young with half, and half of half, etc.  I’m pretty sure she learned them in school too.

The Fractions curriculum is basically 6 parts: naming, equivalence, and the 4 operations. It appears that fractions are taught like other Montessori math, first manipulating concrete materials and then moving toward abstraction. The main materials are the fraction metal insets, and fraction insets in other shapes, plus lots of cut out fraction pieces, and reference charts. Fraction is something that is introduced in first grade.

I love seeing the difference in development and how that affects the way the children learn. For Thumper, I did the classic first presentation of all 10 fraction metal insets, naming them, and showing her how to name them in both Chinese and English.  In Chinese, you read the denominator first then numerator, 三分之一, for example for 1/3.  The nice thing about it is that you don’t have different names for the numbers like in English: halves, thirds, fourths, etc.  In Chinese the denominator is called 分母 and the numerator 分母.  分 means to divide, 母 is mother and 子 is child.  So super easy to remember.

As an older child, Thumper got the concept of fractions easily. We even started on equivalence. So I didn’t need to spend much time on the IDEA of fractions. But I could tell that she has trouble with the difference between the way we name fractions in English and Chinese. She keeps wanting to flip them when she says it in Chinese. I remember I did the same thing after years of naming fractions in English.  It’s making me wonder if I need to teach fractions in Chinese at all.

Astroboy really wanted the same presentation, so I did it for him.  But after the presentation, he couldn’t really name the fractions. So the next day I pulled out my fraction skittles instead.  These look like little people, color coded inside; compared with the insets which are just all red. It’s meant to be handled and “played” with.