We started home schooling about four years ago. The biggest struggle for me over that four years has been trying to understand how my kids think about elementary school math. Take fractions, for example. Before we started home schooling, I’d guess that I’d not given 10 minutes of thought to how to understand fraction math in 30 years. The lack of any detailed thought about how kids think about fractions means that there’s a really steep learning curve for me when we started covering that topic. Well . . . assuming I’m aiming higher than “how can you possibly not understand this?”
In an effort to learn about teaching young kids I started reading a bunch of teacher blogs and following lots of teachers on twitter. There’s an incredible amount of information out there ranging from detailed writing that focuses on education theory to much more conversational writing about day to day life teaching math. One of the teachers whose writing has influenced me the most is Fawn Nguyen.
Fawn has an amazing gift for writing. She can take the terribly difficult topic of teaching math to kids and break it down in to bite size pieces that seem easy to understand. Her writing is also filled with example after example after example about how her students have approached problems in the classroom. Many of these examples are cataloged on her “Math Talks” site:
On this site you get to see first hand different ways that kids approach problems from pre-high school math. It is an outstanding resource for me, and if you want to do some fun math with young kids I’m sure you’ll find it to be really useful, too.
I’ve linked her set of problems from Febuary 15th, 2014 above and went through these four problems with both of my kids this morning. A few are a little above the level of math that I’ve covered with my younger son, but I still thought it would be fun to see how he would approach them. Here are our attempts at each of the problems:
(1) What is 0.48 x 650?
I would have guessed that my oldest son would have just jumped right into the multiplication, and was surprised to see that he converted 0.48 to a fraction first. His first step helps him avoid some of the pitfalls that come with decimals, and having converted to a fraction he then charges ahead with the multiplication. At the end of the video we talk through one step he could have done before multiplying.
I have not covered decimals with my younger son, though he’s probably seen them in a few problems here and there. I’d hoped that he would be able to recognize that 0.48 was close to 1/2, which he did. That was all I was trying to get out of this problem with him.
(2) Counting toothicks
This is the first of two problems in this set that focus on recognizing patterns. Fawn has an entire site dedicated to these pattern recognition problems:
These problems are great for getting kids to understand how to move from the concrete (seeing the specific pattern at each step) to the abstract (writing a formula for the general pattern). I personally think that both understanding patterns and being able to describe patterns are an important part of learning math, so I’m always excited to try out Fawn’s pattern problems with my kids.
For this particular problem, both kids approached it the same way – first counting the number of triangles and then figuring out how to write down the formula for the pattern. Both kids were able to write down the number of triangles in each step and struggled a little going from that list of numbers to the general pattern. That struggle is such an important part of learning.
(3) It is 2790 miles from Los Angeles to New York City – how many inches is that?
I work with a guy whose arithmetic skills are so incredible that he can do problems like this in his head. For the rest of us, learning how to estimate is a really useful tool. It is a useful skill way beyond arithmetic, too. I remember being absolutely amazed at the way my undergraduate physics adviser could draw solutions to various differential equations on his chalk board. Problems like this one help kids get some useful practice at basic estimation.
As with the first problem, I’ve not spent much time with my younger son on this topic yet, but still wanted to see how he’d approach it even if it meant I’d have to help out more than I’d normally want to:
(4) One more pattern problem
Not much more to add from what I said on probelm #2 – these pattern problems are great ones for kids:
So, I’m happy my attempts to learn more about teaching math to kids eventually led me to Fawn Nguyen’s writing. If you are interested in learning about teaching math to young kids, I’d encourage you to follow her, too.