I love using math journals. They are such a great way to encourage perseverant problem solving and using different ways of thinking! (Hellooo, Common Core!) I'm linking up with Throwback Thursday to share a post from June of last year. Don't forget to pick up the freebie!
(P.S.- Keep in mind that the photos, etc. are from when I taught a 2nd grade class, although I did something very similar with my 3rd graders.)
I'm guest blogging over at
Second Grade Math Maniac today about one of my favorite quick math activities for building number sense:
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? :)
