When this email promoting a webinar appeared in
my inbox, I was intrigued … and terrified.
What do you mean “reconsider using worksheets”? These are the life blood of math classes. How else are students supposed to practice
basic skills?
my inbox, I was intrigued … and terrified.
What do you mean “reconsider using worksheets”? These are the life blood of math classes. How else are students supposed to practice
basic skills?
Intrigued, I signed up for the webinar. Terrified, I listened carefully.
The webinar “Why We Should Reconsider Using Worksheets (And
What We Should Be Doing Instead)” was offered by Robert Kaplinsky, a math
educator from Southern California. I
follow him on Twitter (@robertkaplinsky) so I had a good sense of his approach to mathematics
education.
What We Should Be Doing Instead)” was offered by Robert Kaplinsky, a math
educator from Southern California. I
follow him on Twitter (@robertkaplinsky) so I had a good sense of his approach to mathematics
education.
In his webinar he presented his concerns with the use of
worksheets:
worksheets:
Full disclosure – I have used worksheets as busy work. I’ll admit it, it’s an easy sub plan. But I also have experienced his other three
points. When students are given a
worksheet, they go into “git ‘er done” mode often without deeply understanding
the concepts behind the problems.
points. When students are given a
worksheet, they go into “git ‘er done” mode often without deeply understanding
the concepts behind the problems.
While there can be a role for traditional worksheets in some
situations, Kaplinsky promotes as an alternative “open middle problems.” Here’s an example:
situations, Kaplinsky promotes as an alternative “open middle problems.” Here’s an example:
Notice that there is not just one solution. There are, in fact, many. This type of problem encourages students to
uncover the mathematical concepts behind the problem. These are best done in groups where students
can talk through the problems. Then,
sharing among the groups reveals the variety of solutions and leads the students
to a deeper understanding of the concept.
uncover the mathematical concepts behind the problem. These are best done in groups where students
can talk through the problems. Then,
sharing among the groups reveals the variety of solutions and leads the students
to a deeper understanding of the concept.
Here are the benefits he sees to these types of problems:
No longer terrified, but fully intrigued, I decided to try this
with my Algebra 2 Trig classes. On
September 25 my Period 5 sophomores would be taking the NWEA MAP test with Sara
Anderson’s sophomores while I would have a block period with our combined 34
juniors! Instead of giving them an 80-minute
study hall (which I’m sure would not have resulted in much studying), I decided
to test out the open middle problems.
with my Algebra 2 Trig classes. On
September 25 my Period 5 sophomores would be taking the NWEA MAP test with Sara
Anderson’s sophomores while I would have a block period with our combined 34
juniors! Instead of giving them an 80-minute
study hall (which I’m sure would not have resulted in much studying), I decided
to test out the open middle problems.
I projected these problems in front of the class while groups
armed with whiteboards went at it:
armed with whiteboards went at it:
While these problems do not reflect Algebra 2
Trig content, I thought that something familiar would be a good way to introduce
this type of problem.
Trig content, I thought that something familiar would be a good way to introduce
this type of problem.
What I found most interesting was that the students very
quickly focused in on the concepts behind the problems. For the inequality, they knew that the first
box had to be a negative number. Instead
of having them practice row after row of “multiplying or dividing an inequality
by a negative number” worksheet problems, this open middle problem brought to
the surface and had them apply what they had learned in middle school: multiplication
or division of an inequality by a negative number reverses the direction of the
inequality sign.
quickly focused in on the concepts behind the problems. For the inequality, they knew that the first
box had to be a negative number. Instead
of having them practice row after row of “multiplying or dividing an inequality
by a negative number” worksheet problems, this open middle problem brought to
the surface and had them apply what they had learned in middle school: multiplication
or division of an inequality by a negative number reverses the direction of the
inequality sign.
I also enjoyed watching them talk about math. So often students just want to write out the
steps without explaining their thinking.
steps without explaining their thinking.
I had found Kaplinsky’s “benefits” to be true.
The following week I had planned to teach piecewise
functions – a challenging topic for many students as it requires them to graph
only a “piece” of a function. And if it’s
a linear function where the domain does not included the y-intercept, well, you can just forget about that!
functions – a challenging topic for many students as it requires them to graph
only a “piece” of a function. And if it’s
a linear function where the domain does not included the y-intercept, well, you can just forget about that!
I did my usual flipped “video the night before” and “exercises
in class the next day” on Tuesday. But on the block period, I gave them my own version of open middle piecewise functions problems:
in class the next day” on Tuesday. But on the block period, I gave them my own version of open middle piecewise functions problems:
What I saw was students referring back to their work from
the previous day, explaining the concepts to each other, asking questions, and
being creative. Multiple concepts beyond piecewise functions were
reinforced: slope, different types of functions, what a function is, how to
restrict the domain, among others.
Success!
the previous day, explaining the concepts to each other, asking questions, and
being creative. Multiple concepts beyond piecewise functions were
reinforced: slope, different types of functions, what a function is, how to
restrict the domain, among others.
Success!
While I will still continue to use worksheets as an optional
review for skills-based problems, I am looking for other opportunities to
integrate open middle problems into the curriculum.
review for skills-based problems, I am looking for other opportunities to
integrate open middle problems into the curriculum.
I am also wondering if this sort of problem could be used in
disciplines other than math. Any ideas?
disciplines other than math. Any ideas?
I love this! Any time students use creative thought to solve problems helps learning.
Mary Beth, what a great way to learn math. Back when I was teaching math, "story problems" were all the rage. They were more interesting, but not nearly as mind expanding as your examples.
We are dealing with such a problem right now in U.S. History. The evidence clearly shows that white Americans have been racist since the beginnings in Jamestown. The question we are tackling is, "Why are people racists?' There are many reasons, none of which are neatly listed in the textbook. It is an open ended problem that really makes students think. They love it.
MBD you are so inspiring. This is awesome! I haven't used this resource before and now my brain is churning about how I can use this in my Algebra Readiness and Financial Algebra classes to continue to build number sense. I agree that it is so important that students see different strategies for solving problems and I would even go so far to say that seeing different strategies in math can help them be more understanding and empathetic in other classes and even outside of the classroom. Thank you for this!
The description of students going into a "get-er done" mode is interesting. I see that mode sometimes, and it is so discouraging.
As a former "math tutor throughout middle and high school and almost failing college math" person, this open middle problem stresses me out! It makes me think that I need to relearn math in a way that you are exactly describing!
I just finished the online course through Stanford for math for math teachers and this is exactly what is being described. I discussed these concepts with Lesley, and these concepts are certainly applicable to Spanish!
A couple of years ago, I gave a worksheet to a low performing student and I could see the sense of relief on her face. When I asked her if she liked a "get-er done" assignment (I didn't use those words), she emphatically responded that she did. I rarely give worksheets, but my point in telling this story is that I think students (people) need variety. I know that the class with nothing but worksheets is a class that is not great; Beau's history class is like that right now and he HATES it.
Ohhhh you are probably all over Malcolm Gladwell's new book… Talking to Strangers… It is in my cue but I have not started it… the interview he did with Oprah has me very encouraged… but yes we have been racist forever…
there was a UCLA study that explained by that was genetically encoded to keep us safe FYI…
I agree with Kate, they do need variety… it is not so much the worksheet that I am aiming at, but I think sometimes they need an easy win… I think sometimes they need the teacher to be telling them a story, and I think they also need to work through and expand what they learned…
if we do anything over and over in the exact same format, it gets tedious…
The weird thing is I feel like they need the perfect balance of predictability and novelty… But I think that is true of us as adults too…
no one said what we do is easy 🙂 but god it is fun figuring it out!
I think there's something to be said for both. I remember back in the day getting worksheets of 40 or so problems practicing the same skill. While cumbersome, I definitely knew how to do that problem type by the end. Did it deepen my understanding? Probably not. But I feel like there's something to be said for practicing a skill you just learned a bit until you get some confidence. I'm sure there's a perfect middle-ground in there somewhere.