Blog #2

Use real-life examples and applications to make math concepts more relatable and relevant to students.  This has been an area that I have worked on a lot in the past seven or so years.  My favorite way to approach this is through mathematical modeling.  Mathematical modeling is NOT just word problems where all of the values are provided and the student is just expected to come up with the right combination of operations.  Word problems have their place and can be useful in certain situations, but I don't think they truly get to the heart of this teaching tip.  If students are faced with real-life problems that require them to use math, it will be very unlikely that all of the values will be spoon-fed to them.  So why not give them opportunities to practice this type of thinking in the math classroom before they are required to do it in the real world?

Mathematical modeling is a much more open-ended process than solving a word problem.  Here are a few reason why I love it:

• Mathematical modeling focuses more on the process than the outcome.  It gives students the opportunity to try different approaches to see what makes the most sense.

• Mathematical modeling requires students to make assumptions.  One of my colleagues once described assumptions as, "Questions you must answer for yourself."  To make assumptions, students must consider the factors involved in the problem and which factors need (and do not need) to be represented in the mathematical equation that gets set up.  For the factors that are needed, students must decide which ones they can find reasonable values for (possibly by making assumptions), and which ones they are trying to solve for.  Answers can vary depending on the assumptions students make.  But if they can reasonably explain why they made those assumptions, then their answer is a reasonable possibility, even if it is different from what the teacher "intended".

• The key to mathematical modeling in the classroom is for teachers to choose a context that is familiar to students so that they can make reasonable assumptions.  This also provides an entry level for ALL students to participate and contribute.  Choosing context that is relevant to students' lives allows all students to have an opinion and offer suggestions for how to solve the problem and what assumptions to make along the way.

• Although it is not a required part of the mathematical modeling process, I often include an intended audience as part of the problem.  Who is the solution for?  How will you communicate your solution and why it is a reasonable solution to that person or group?  How will you help them understand your process and convince them your answer is "right"?  These kinds of questions emphasize the importance of mathematical communication in addition to the mathematical computation required for the problem.

If you are interested in incorporating mathematical modeling into your curriculum, here are a few suggestions.

• Start small.  These types of problems, when done well, can take time to prepare.  Consider adding one problem in each quarter, trimester or semester.  Then each year, add to your library of modeling activities until you have several that you can pull out and use at different times throughout the year.

• Modeling tasks do not have to coincide with the current material being taught.  Just getting students to think and communicate mathematically using ANYTHING in their math knowledge "toolbox" is a great way to engage students and show them the relevance of the math they learn.

• Teach students how to do modeling.  They are NOT going to be naturals at this.  Teach them how to determine factors involved in the problem, how to make reasonable assumptions, how to communicate for specific audiences.  In my precalculus class, I spent the first 3 - 4 class periods teaching modeling with a couple of "easy" modeling tasks.  This gave us a foundation of knowledge and vocabulary that we could refer back to whenever we did a modeling task throughout the rest of the year.

If you would like to see a mathematical modeling task that can be used for any high school class, check out my 100 Years Ago task on Teachers Pay Teachers for FREE.  Other "pre-made" modeling tasks will be added to TPT in the coming weeks and months.  If you have any questions, please contact me at kathy@gordonglobalmath.com.