I've got a first grader of my own, and I shepherd her math learning. I watch her figure out how numbers work and relate to each other and I observe her make observations and formulate questions while experimenting with shapes and other manipulatives. So, I really liked looking at the CCSS to put all that work into perspective. The content standards were all pretty straightforward but I immediately started trying to figure out how I could really know if those words meant things my kid knows. What does her understanding look like in action?

Luckily for me, it turns out that a great way to assess a lot of what a first grader knows and can do, mathematically speaking, is to look inside my purse!

We were having a late lunch/early dinner at our local co-op. The plan was to eat a nice balanced meal and then hit the bulk bins for chocolate coconut candies after that. I was digging around in my purse to make sure I had enough money to get the promised after-dinner treats.

Digging...digging...and finally finding a handful of coins. That's when inspiration struck.

"Hey! Let's figure out if I have enough to buy dessert!"

Unfortunately my camera was at home with battery charging, but the following photos are a faithful re-creation of the independent thinking that followed.

Showing no hesitation she went for the quarters first. Lined them up, counting by 25, dollar by dollar. Got the dimes in line counting by ten, and finished out that dollar with nickles (by 5's) and pennies (by 1's). Added it all up in her head, no fingers (you go, girl!). The grand total? $5.07.

"Which coins make the highest stack?" I wondered.

*almost*be 'one thin penny' by a hair. You'll also notice that putting them thickest to thinnest lines them up biggest coin to smallest coin. Hmmm...I wonder how that happened?

What did all this dinnertime inquiry show me about my daughter's math skills in relation to the CCSS?

First, it's important to remember that using money is just one of many ways to represent numbers and understanding of numerical relationships. As an instructional tool, I think that using money is one of the best ways to develop numeracy. You're working with a whole unit of 100, for one thing, and anything less is a fraction of the whole. Also, the random sizes -- a dime is worth more but smaller than a nickel -- is a fabulous conceptual challenge, and think of all the different kinds of skip counting! Plus, money amounts are always changing depending on what you save, spend, or find on the ground, so there's always something new to figure out.

So, she can represent her numerical understanding through money and mental calculations, but although she likes to write out simple equations, we haven't done much with adding larger numbers on paper. After reading Peggy Kaye and Constance Kamii (which I've written about here and here), I'm fine with it that way for now.

As for the standards, most of 'how much money in the purse' challenge was related to numeracy skills but, overall, the activity showed me that my daughter is gaining mastery in multiple content ares in three of the four content domains:

**Operations & Algebraic Thinking:**

*"Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20."*

**Numbers & Operations in Base Ten:**

*"Developing understanding of whole number relationships and place value, including grouping in tens and ones."*

**Geometry:**

*"Reasoning about attributes of, and composing and decomposing geometric shapes."*

The other half of the CCSS for math is the Mathematical Practices section. The change in my purse also illustrated these goals in action at the first grade level:

*"...adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy)."*

In this case the mathematics was most certainly 'sensible, useful and worthwhile'! Although the change in my purse did not asses

*everything*in the practices section

*,*of course, it was helpful to have a spontaneous moment to see up close not just what she knows but how she goes about using what she knows. On the whole, I feel confident things are going in the right direction.

And, in case you're wondering, the chocolate coconut clusters were delicious!

Malke, I have been enjoying how you are working with your daughter as you are doing your own exploration. You are seeing in the standards what has always derailed me, the separation of skills listed in such a way that makes it easy to test, it is all conceptual ideas. You two are having contextually meaningful experiences which generate ideas through the curiosity of engagement in your play. The thing about standards is they are just that, standard. Each student is not standard and the fit is never quite right.

ReplyDeleteNext time you two are in your purse playing with coins, see if you can use them to show a circular flat representation of the polygons and polyhedra you made with the straws and pipe cleaners. The number representation of the coins can also be played using pattered arrangements of the circles. Once you've figured out something with the flat coins, then the question will come up about if it will work the same way with balls of the same size.

Are you going to the Midwest Home School conference April 19-21 in Cincinnati?

Thanks Brad! I love learning math this way. As I figure out how to support the math my daughter uncovers and plays with, I am deepening my own understanding of those topics. Most of all, I especially enjoy watching my daughter discover new things and make connections, find the patterns.

ReplyDeleteAnd, yes, the standards are broken down into pieces and testing is one reason for that, but I know from reading other teachers reflections on their work that they look for and use more comprehensive ways of assessing their students understanding as well. I think the 'what's in the purse' activity I described above is a pretty good example of an assessment that takes into consideration that skills are best tested in context. What's better than asking someone to use what they know when it's actually needed in a real-world situation? I had a conversation with an astro-physics professor who was bemoaning that none of her students could do the necessary math in her 'real world' of phsysics because they didn't know how to do math outside the context of a textbook. Anyhow, I digress...

I really don't want to defend OR decry the whole standards thing, but as they say, 'the map is not the territory' so it stands to reason that the standards are not the education. The real challenge is in not confusing one for the other. ;-)

Definitely in the right direction even though I tend to think that math standards for K-1 are way too simple for majority of the kids I know.

ReplyDelete