## Monday, November 14, 2011

### Inspiration Can Come From the Strangest Places!

Gotta love it when great math content just comes to your inbox!  The image below was part of a GoDaddy.com ad I received recently.  When I saw the ad, I was immediately inspired to write this post.   Guess you never know where you might get inspiration for math content or teaching strategies!!!

The subject line of the email was "Choose your savings, all the way up to 30%".  Here's a screenshot of the GoDaddy.com ad:

Why I like this graphic:

Often times in math, we concentrate our efforts on the topic we're teaching to the exclusion of other questions or topics that could arise from the same problem or situation. By doing this we unwittingly lead our students to become locked in to one way of thinking about the situation. This causes problems for students when they later (usually on standardized tests) experience problems/situations that are a variation of or the counter to the problems they're used to solving.  Or, if the question that accompanies a familiar picture is different than the typical question.  For example, when students see a picture of an aquarium, they automatically think that they're going find the volume.  But, the question could ask how much sand is needed to cover the bottom of the aquarium.  If students have only found volume when given pictures of rectangular prisms, they won't even consider that the question could be asking for the area of the base.  If we don't give students experience in generating questions from given situations, they'll continue to jump to the wrong conclusions even if they do read the problem!  That's the big problem with formulaic teaching rather than teaching students to think and problem solve.

The graphic above is a prime example of this type of formulaic teaching.  Most students would look at the graphic and automatically think they need to find 10% of 50, 20% of 100, and/or 30% of 130 in order to answer the question.  Did you notice that there really isn't a question?...At least not one posed by a math teacher!  "How much do you want to save?" was part of the graphic in the email, so I'm not counting that as the question right now.  But, students may think this is the question.  If so, they'd probably still jump right to the calculations mentioned above.

The beauty of this graphic is that there are many questions that can asked about this sale offer. And, some of them lead to some interesting mathematics and considerations.

Generate Possible Questions:

Have students brainstorm questions that could be asked about this image.  There are many possible questions.  It will be interesting to see what students come up with.  You may learn a bit about what student's know, or don't know, about percents and interpreting information by the questions they generate.  You might want to check out the first post of my Brainstorming series to see some benefits of brainstorming.  Here are a few possible questions that came to mind:
• How much will you save if you choose the 30% option and only spend \$130?
• How much more will someone save if they choose the 20% option over the 10% option?
• Why would Go Daddy make this offer?  What's in it for them?  Which offer do you think Go Daddy wants people to choose?  Why?
• What's the most I can save if I choose the 20% option?  What's the least I can save if I choose the 20% option?
• Which one is the best deal?
• Are the offers proportional?  Why would this matter?
• If I choose the 30% option, am I saving 3 times what I would if I choose the 10% option?
• If I'm planning to spend \$115, should I just go ahead and spend \$130 to get the 30% discount?...At what \$ amount, would it make sense for someone jump to the next level of savings?
Some of the questions above have a correct answer and some are great for discussion because they don't have one correct answer.

There are also some added benefits of having students generate multiple questions for a given situation.  These are a just a few of extra benefits:
• Natural Differentiation --- As you can see from the questions listed above, there are questions at various levels.  Once you've created the list, you can assign students questions based on their level of readiness.
• Built-in Choices --- This is a great way to provide students with choices.  Students can choose which question or questions they find most interesting and really want to answer.  Providing choices is a key component in effective teaching because it gives students a sense of control.   It's also a way to differentiate by interest.
• Teachers Gain Insight About Students Level of Understanding --- When you have students generate questions, you get see where they are with their understanding of concepts and problem solving skills.  In the beginning, some students will only be able to come up with surface level questions.  As they gain more experience with problem solving and generating their own questions, you'll be able see and document their growth.
• Student Attitudes Improve --- When students become more involved in their learning experience, their attitudes generally improve.  If you combine this with differentiation and giving choices, you're likely to see an even greater impact on student attitudes about math and learning.
• Opportunities For Problem Solving Arise --- From the questions above, you can see that some of them would involve problem solving as opposed to rote computation.  And, I would venture to say that many students would much rather answer some of these problem solving questions than the more basic questions.  The best part is that the skill practice we want students to have is automatically built-in to the problem solving experience!
Whether or not you use this particular scenario with your students, you may want to begin having students generate their own questions with other content.  Give it a try and you might just see some unexpected growth in your students.

Hopefully, you've found this post useful.  If so, please pass it on to someone else who may find it helpful.

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