Thursday, November 02, 2006

Numerical Expectations

Sunburst loves computing numbers. Throughout our days there is always something she finds worth counting. Always. Though it's not enough, because if left to her own devices, she devises math worksheets and enlists her dad to play school with her. She's drawn to kids suduko books and other number games. She asks for "math work." Her thirst for number play is ripe.

In putting together our maths block, I recently looked up the mathematical standards for my state and discovered that we've mostly covered their expectations:

Grade 2
  • Counting
  • Fractions
  • Addition and Subtraction of Whole Numbers
  • Estimation of Mental Arithmetic
  • Number Patterns
  • Sentences and Expressions
  • Order of Operations
  • Identifying and Classifying Basic Shapes
  • Congruence and Similarity
  • Measurement (time, length, money, temp, weight, area, volume, etc.)
  • Graphs and Tables
  • Strategies, reasoning, connecting problems
  • Checking calculations

Then I flipped open the Waldorf book, The Educational Tasks and Content of the Steiner/Waldorf Curriculum, giving serious thought to my purpose, my goals, my role as the educational facilitator. Do I really want to tie us into the Waldorf School goals of Grade Two? Last year we didn't even come close to the ones for Grade One. And in looking at them, I have to wonder, how deeply does a class of 30 little kids manage this?

Let me show you:

Class 1
  • Counting up to 110
  • Learning up to the the 7 times table by heart and rhythmically
  • Intro of four processes with numbers up to 20
  • Notation from whole to parts (ie. 7 is 3+4)
  • Number riddles
  • Intro to mental math

Class 2
  • More mental math
  • Using four processes with numbers up to 100
  • Combined calculations
  • Intro to number connections (even, odd, primes, etc.)
  • Up to 12 times table by heart
  • Represent tables in drawing
  • Written calculations, including parts to whole (i.e. 3+4=7)
So in looking at this, the first thing I obviously ask myself is, where is Sunburst at?

Class 1: Can she count to 110? By ones - yes. Without fail? No. She skips a few numbers that end in 4, like 14 or 44. She knows she skips them, and it's not a big deal, I don't think. Does she know her times table up to 7? No. We've worked on it a little bit. Counting by 2's. Counting by 3's. Counting by 4's. By 5's, by 10's, by 100's. If I had to wager a guess, I would say she knows her 1's, 2's, 5's, 10's, and 100's. But only if it's phrased correctly, like 6 groups of ten, rather than 6 times 10. The rest of the list we've done, in small bits.

I'm also thinking about math attitudes. About the relationship of a girl's self-esteem to her math ability, as painted in Things Will Be Different For My Daughter by Bingham and Striker.
"According to the AAUW report, "Shortchanging Girls, Shortchanging America," girls who like math and science have higher self-esteem, aspire to more ambitious careers, cling more tenaciously to those career goals, and even feel better about their appearance than girls who do not like these subjects."
They say that a girl's math ability has everything to do with attitude and expectations. I think that can also be transferred to boys. Attitude is key. Math needs to remain fun and exciting and applicable. I don't want to rush or push or squash anything.

Then the real question for me is this. How important is memorization of the times table for a seven-year-old? What are they going to do with it exactly? How is it meaningful? Sure, it can be made into a fun game. We've worked with it on that end, but is it useful? Can they apply it to anything much in real life?

That's the angle that I shoot from. Application and usefulness, as well as interest. My kids may grow up to be computational geniuses and need this stuff, but right now? Not exactly. Not unless it comes up. Not unless it's meaningful to them to memorize it. For now I'm satisfied with introducing mathematical ideas. Situations. Thinking adventures. Numerical fun. Mathematically themed stories to ponder on. Strewing the path to numeracy, so to speak. And I've got big plans there. Stay tuned.

Until then, my friends, what do you think?


  1. Hi Sara,

    I really like your blog and your very inspired and inspiring posts. I wouldn't worry too much about the times tables, I think she is fine where she is for now. You can spend more time at it in second grade, then really firm them up in third so she is ready for fractions work in grade 4. I think the "rhythmic" part is more important than the actual tables she knows, to my understanding this is what they need at this age.

    So now I have a question for you: in balancing the unschooling and Waldorf aspects, how do you know when to leave it more up to the child, and when to present materials through stories etc.? Do you have a set schedule when you "do school," or do you wait for the children to get interested in something, and then you bring out stories etc. for this? I'd love to learn more about how you make it flow.

    Thanks, Kirsten

  2. Thanks, Kirsten! Actually Sunburst IS in second grade now-- there's no way she'll have the times table memorized up to 12 by the end of the year, especially given that we're not even up to speed with the Waldorf Grade One expectations. Ha! But maybe she'll surprise me... who knows!

    I'm going to answer the unschooling bit in a blog post, because I think it's a great question and my answer is a bit lengthy. Thanks for asking!

  3. Wow, great post on unschooling. Thanks.

    Sorry, I don't think I was clear in my comment above, I meant to say that she has another year after this one to really get solid in times tables, so that's why I wouldn't worry about it too much. The way you are connecting with her, it seems to me that somehow she'll get all the important stuff in when she needs it.



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