Here is a little introduction, if you're just now joining me!
I'm guest blogging over at Second Grade Math Maniac today about one of my favorite quick math activities for building number sense:
|Click on the photo to read all about it!|
When I was little, we learned strategies for "word problems." Usually, we would practice two or three that followed a certain pattern to solve, and then we would have an assignment that followed the same pattern. Sometimes we learned "clue words" that would tell us, supposedly, which pattern to follow. But they were inconsistent- "more" could mean adding, but in the case of "how many more" it could also mean subtracting. And I didn't know why I should subtract when it said "how many more"- it was just an arbitrary thing I had to remember.
I hated math.
Everything else came pretty easily to me, but math took some work, and Elementary Jenny did NOT like that.
And then I got to middle school, and took pre-algebra. My teacher, Mr. Wall, was phenomenal. He was an old-school teacher with high expectations, but he also put more time in with his students than just about any academic teacher I ever had. If you ever needed help, or wanted his help studying for a test, he would come in before or after school to help you. And every Wednesday morning, he hosted MathCounts in his room. If you came, more often than not he would bring donuts.
If you've never heard of MathCounts, it's a program specifically designed to challenge kids with tough problem-solving questions. But- Mr. Wall knew how to make it fun. He'd give us a page with 15 impossible problems, and if you got 2 or 3 right, that was a good day! And somehow, he made us believe that. These weren't problems that followed a pattern- no, these were problems that you might have to try 3 strategies to figure out, and you still might not get it. He would always let us try it (even if it was the wrong way), and after awhile might give hints to get us going in the right direction, but he never gave up and told us how to do it. And if someone else in the group managed to solve one we were stuck on, that student could tell us how they figured it out. They were puzzles, using all different kinds of math, and we would spend an hour pushing ourselves to figure out the puzzles.
Because they were so hard, and there was no formula, and we were doing it without the help of the teacher, when you did get one, it was the most amazing feeling.
And, that year, I realized that maybe I wasn't so bad at math.
Yep- puzzling away at tough problems and getting maybe 3 out of 15- and that's the year I realized I could do math.
Mr. Wall was that teacher who changed me as a learner. We've all had one. But here's how I take that and make it change me as a teacher.
Once a week (or, at least, that's the goal!), my students get out their math journals. (Next year I'm thinking of stepping it up to at least twice a week- possibly daily!)
We made our math journals during the first week of school. I cut construction paper to the size of a composition notebook cover, and then walked them through the steps. I was very detailed so that the title would be easy to read (or because I'm a control freak- not sure).
First, you write "So-and-So's Math Journal" in the middle with red.
Then, you use blue to make a cloud around the words.
Finally, you use different colors to write what you think of when you hear the word "math." I show them my example, and I tell them they can be different names for a number, math tools, shapes, math units, symbols, math words, time, money, measurement, ten frames, fractions, base ten blocks... anything that is "math."
And then, we store them in these shower caddy things with our science journals (so that when math journal time, one kid goes to get the bin for his group). The first few times, we work through problems together and I model multiple strategies.
When we get out the journals, I have students glue in the problem with a gluestick and write the date. Then, they have to visually represent the problem in some way. This really helps with those students who "don't know how to solve it" because it gives them somewhere to start. (And sometimes, helps them discover a way to try.)
Then, if they used a math equation, they have to write it with a box around it so it's easy for me to see. After that, they need to write how they solved the problem (which could be done all verbally to save time, or with younger students). And finally, they write their final answer in a sentence. (This really helps to make sure they answered the correct question.)
We don't do "word problems" in my class. We do problem solving. Problem solving doesn't have a formula, or a "right way" to solve. I always teach that math is awesome, because you can do things the way it makes sense to you, and still get the right answer. Take this problem for example:
There were 7 ducks and 9 geese at the pond. How many more geese than ducks are there?
Well, some of my students used 9-7 = 2.
Some of them drew ducks in one row, and geese below and saw that two didn't have partners.
Some used 7+2 = 9.
One thought that if you had 9 you would have to take away 2 for the number to be equal.
Another drew two unit bars, one for ducks, and one for geese, before subtracting.
And guess what? They all got the answer: 2 more geese.
Many of us probably have an "author's chair" or time for sharing in writer's workshop- but how many of you have a time for your mathematicians to share their thinking? Even with a simple problem, I like to say, "How did you solve that? Great! Who used a different strategy? What was your method?" (and I make a point of using those words so that they don't startle my students on a test.) A document camera is fantastic for sharing their work. My students start to look for other ways to solve something, because they know a variety of strategies are valued. They're not looking off of their neighbor as often, because they know their work doesn't have to be the same.
My students are much more eager to attack a new problem when they know there isn't a certain "right" way. They will also try something they've never been "taught" before (like multiplication or division problems for my 2nd graders) because they're not afraid to just try. They know I won't get mad if they don't get the right answer, or don't get an answer at all. They know they are "making their brain stronger" when they take on a challenge, and that I will appreciate their effort no matter what.
It's not a perfect method, of course- you'll still have students get stuck, or frustrated, from time to time. But the overall attitude towards math in my classroom became so much better when I started encouraging multiple ways to solve the same problem. And the best part? They're building number sense, skills, and confidence to solve not only problems in the next grade, but problems in the real world.
To get you started, here's a week's worth of math journal prompts. You can get the PDF and keep the cute font here, or get the Word document (and insert your students' names for better engagement) here. All you need to do is print the number you need, cut off the right edge (if you use a composition book, anyway!), and cut into strips.
Do you use math journals? Any tips for me to make mine better? :)