Brain dump on Arithmetic

I actually wrote most of this post about a month ago - yes, even the quote below! I tend to give myself a few weeks before I publish almost anything but recipes and random pictures of the kids - time to edit and make sure I really want to put stuff out there forever and to give Craig a change to look over it. This post has been sitting even longer than normal because as I state below, I was worried about how it would appear and if it would be of use to anyone but me. But no sooner had I finished writing it, than I started hearing all about the Common Core and I do not like what I'm hearing. My plan was to use the types of things below until first grade then start Saxon. I love Saxon and used it as a kid (note that I did not say I loved Saxon as a kid - but I learned a lot from Saxon as a kid and therefore I love it as an adult!) I even have the exact same Saxon books I used in the upper levels (7/6 through AM) in the basement already. I had briefly considered selling it since we won't need it for a long time but now with all the CC changes infecting homeschooling curriculum, I think I'll keep it. And the resources below are looking better and better. So publishing time it is!

It has become somewhat the fashion to adopt new and fanciful ideas in teaching, and many young teachers are misled into thinking that unless a method is new it can not be the best. It should be borne in mind, however, that change is not necessarily progress. Rays' Teacher Guide

Lucy loves math and working with numbers.She taught herself to count to 10 and what the number symbols were last summer and then I was left wondering where sorts of things we should be "playing" with next. In theory I agreed with the idea that basic arithmetic is best learnt with hands-on experience and manipulatives but I couldn't get a grasp of what that meant in real life and every homeschooler's example seemed to be cooking. Lucy loves to cook with me but there had to be more.

So we counted. And counted. And counted. I didn't really want to count much higher than 10-12 because I think it gets very abstract for a preschooler. We also had fun with shapes and patterns and that is math too, but it doesn't seem to fulfill her need for number fun.

Enter some really neat resources. They are all pretty similar in one regard especially - they are old (1800s, early 1900s for the most part), mostly textbook style, and show how basic arithmetic used to be taught. Simple, easy and fun!

I use them mainly as parental resources, not textbooks. I can see the types of questions I can be asking her when we are playing with manipulatives/toys. And they are all pretty similar but there are some variations so I thought I'd like to them all - and for purely selfish reasons, I don't want to lose them later on.

Arithmetic for Young Children - My favorite of these. It's basically a series of questions/requests that get progressively harder. This is the only one I have actually sat down with her and read through, just to get a feel for it. And she had a really fun time. Once I got the concept though, I started applying it to other situations but looking over it again, we might try working straight from the text again once a week or so - as long as she has fun. (And I've heard that the curriculum Right Start is basically the same thing!)

Everyday Number Stories

The Arithmetic Primer

Ray's New Primary Arithmetic

Ray's Teacher guide: Piney Wood's Homeschooling Blog has done a wonderful service is putting together a document with the Ray's teacher guide in a legible format! This is my other favorite resources and the section for young children is only a few pages long but it had so many lightbulb moments for me.

Most of the direct usefulness of these books will come into play later as Lucy gets up towards 6-7 years old and beyond but they really helped me understand what arithmetic really encompasses and how children's learn math so they did change how we are approaching the subject now at age 2.5.

Before learning this, I was working with Lucy on correlating the number 1 with one object, 2 with two objects, etc. We aren't doing those types of activities anymore and have even taken away her sandpaper numerals (I've left out her homemade Montessori spindle box because she really loves to pretend with the sticks but she never really uses it as intended). I want her to be acquainted with what numbers really are and how they act before bringing in symbolism.

 Instead, we are working on recognizing sets of items without counting (she's pretty good with 1-3 but 4&5 is hit or miss), determining which groups have more/less and even adding and subtracting.  I would never have thought to even attempt addition and subtraction but because it is displayed right in front of her and done oral, she has no problem with these types of questions.

Now she likes to ask her own. It is not uncommon for her to spend lunchtime quizzing me on how many boys are at the table, how many girls, how many ears, what about when Jonah is big enough to eat, how many will there be then, etc. And just yesterday I overheard her playing with two toy giraffes, asking herself outloud "How many horns? One, two and one, two. How many is two and two. One, two, three four. Two and two is four!"

At this point, I'm a little worried this post is going to come off as obnoxious.  I'm writing this neither to illustrate how incredible talented my child is and how we are starting her on Kindergarten math (we aren't!) nor to tell you that to teach your 2 year old to count you need to read a bunch of books (you don't!) and it's not like I really know what I'm talking about (see the purchase of sandpaper numerals and making of the spindle box to begin with :-) so so hopefully it is taken in the spirit it is intended - just my excitement over what I'm learning and desire to share some neat things with you.

Update - I've found a few more interesting math things lately.

Here's a very interesting article on "late start" math which I understand is somewhat ironic of me to post given that I'm talking about what I'm doing with my not-quite-3 year old, but still, I do agree with a lot of it.

And here is what looks like a fun pre-Miquon cuisinaire book printable. I already have a set of cuisinaire rods, passed on from my mom, but we haven't done anything with them yet. This might be something fun to consider for a year or two down the road.


  1. I haven't read anything about the Common Core because I don't need something else to be frustrated about. I know from the education I did (and did not) receive training to be a mathematics teacher that anything influenced by the National Counsel of Teachers of Mathematics and other teacher unions is going to be a mess.

    My most consistent frustration teaching high school algebra and geometry was that the kids had no idea how numbers really worked. How in the world can I teach the segment addition postulate when students don't recognize that 2+1=3 without the help of their calculator? And forget trying to do it with x and y! I had students that couldn't tell me the basic identities without, again, a calculator. I think it worth mentioning at this point that all this calculator dependency was not only condoned by NCTM but actually advocated. Why waste time memorizing math facts? Just go straight the higher level reasoning.

    Stepping off soap box. Zuzu has just started counting everything, so I'm really excited about reading these resources. When she starts school, I'm tempted to use two or three curricula because I know the strengths and weaknesses of each, but we'll probably use Singapore with supplemental drills, if needed. The students at my private school have an excellent understanding of math concepts thanks to Singapores spiral approach and lack of hand holding.

  2. I tried to tuned it out for a while but now that it appears to be affecting homeschoolers, I can't seem to avoid it. It's all over my favorite blogs!

    Is Singapore considered a spiral curriculumn? I had always heard it was more on the mastery side but perhaps that is only in relation to Saxon which is probably as far on the spiral side of the scale as you can get.

    I understand that temptation. I'm less enthused about lower level Saxon (although I have enough experience with it as a recurring sub that I feel like I could easily change the real negatives as a homeschooler (remove practice questions when I see my kid doesn't need them, edit "the meeting," ignore the script). I go back and forth about which and they all sound good - and bad. It will be interesting to see what I end up with :-)

  3. The CM school my younger two are attending beginning in the fall uses Right Start Math. From what I have seen, I am a fan. I've been using some of the ideas at home already with E about grouping to get to 10.

  4. I'm so excited your kids are going there, I will definitely be picking your brain come fall.

  5. I'm not sure if we are using "spiral curriculum" in the same way. I'm referring to the Asian model of reintroducing topics again and again at a different level each time. For example, instead of having a course titled "algebra," students get sections on algebra spread out over many years with each one progressively harder.

    I'm also not sure what you mean by mastery. What definitions are you using for mastery and spiral?

    The main thing I appreciated about Singapore was that students were shown just a few examples and then expected to extrapolate how to solve very different problems with the basic information. I loved watching the gears turn in my students until the solution clicked.

    Which school blogs are you reading? I haven't really explored that topic much because I'm afraid I'll end up even more opinionated and obnoxious about education. ;)

  6. That's my definition of spiral too. You learn part of a concept, practice it but keep reviewing it and other topics but later on down the line, you spiral back and add to it.

    I've always heard Mastery to mean that you work on one specific topic, master it, then move on to another. I've heard others (probably spiral fans since nobody wants to be known as "anti-mastery") refer to it as sequential too but more commonly mastery. I'd never experienced that until college and was not really impressed (although to be fair, I'm not sure any method of teaching would have made Math 141 impressive but BIMS wouldn't let me go up to a higher math despite my already having taken calculus - stupid BIMS department!)

    But interestingly enough, I did a quick google to see if I was using the terms correctly and on three different lists, I saw Singapore listed as three different things (one put it as a mix of spiral and mastery) and Saxon as two (spiral and mix). So apparently the difference is often in the eye of the beholder!

    I'll try to post some of the education blogs I read soonish.

  7. Still not sure what mastery means other than the public school definition which I never could figure out how to implement. Oh well, probably won't affect how my kids do home schooling.

    Interesting article about how difficult it is to overcome an early deficit in number sense and what parents can do to help their preschoolers.

    Math Skills: What Scientists Can Teach Parents About Kids' Developing Minds: http://www.huffingtonpost.com/2013/03/25/math-skills-first-grade-number-sense_n_2950383.html?utm_hp_ref=tw