## Coffee and Mathematical Understanding

I spent the majority of this past week visiting with friends and family.  My destination ended up being in snowy and icy northern Michigan.   The house that I was staying in lost power for five straight days.  Thankfully the house had an efficient fireplace and a small gas-powered generator that ignited a few space heaters to keep one of the rooms fairly warm as outside temperatures hovered around 20 degrees.

In normal circumstances, the first person that wakes up in the house starts to brew the coffee for the family.  Since we had no power the coffee machine wasn’t an option.  You see, my family definitely enjoys their coffee. Being official coffee addicts my family has a decent understanding of the integral parts of the coffee-making process: hot water, filter, coffee grounds and cup. The one missing ingredient in this process was the hot water.  One of the family members found a pan and began to boil water on top of the fireplace.

The water was then used to complete the coffee making process.  Success!  All of the family was able to sit around the fire and drink our coffee.

As you can imagine or already know, they’re many ways to make coffee.  My family knows this and that understanding led us to a solution that was adequate.  We substituted a different process in the coffee making flowchart and arrived at decent tasting coffee. Regardless of the process used, the user ended up with the same solution.  In the end some type of hot coffee was served.  Understanding the key components of any process allows opportunities to substitute yet arrive at the same solution. Because my family knew the process in-depth we we’re able to substitute the missing item and still have the same result.  I feel like this type of thinking applies to the classroom.

Having a limited understanding of place value and number sense can limit opportunities for students.  Students need to be exposed to an array of methods to complete problems, not just shortcuts.  Only understanding the formula/shortcut doesn’t necessarily show mastery of a particular concept.

At the upper elementary level students are expected to find the product of  3+ digit numbers.  If students have been exposed to using only the traditional method to solve these types of problems they know how to multiply large numbers using one method.  Although that process might be effective for them, it doesn’t cement a deep understanding of multiplication.  Students often have problems when decimals are introduced when finding the product of these types of problems.  Having a more in-depth understanding of place value and multiplication can give students the tools to solve more complex math problems.

On the other hand, if a student has been given opportunities to use repeated addition, partial-products, lattice and traditional methods, students might have a better understanding of the role that place value has in the multiplication process.  Having that understanding of place value will help students when they approach decimal computation and throughout their academic career.  Having multiple tools/strategies also encourages students to be independent and choose the correct method to find a solution.  Even more important, students that are then able to apply their mathematical understanding to practical situations (beyond the test) can often immediately see the benefits.

In the end my family used the tools that we had (fireplace, metal pot, water) along with other materials (coffee filter, ground coffee, cup) to create coffee that we all could enjoy.  If we were fully reliant on just the coffee maker and electrical power, we wouldn’t have had coffee to drink.  Understanding the details of the process and that there are multiple ways to find a solution is an important skill to have as adults and as students in the classroom.

The power came on and I believe we all found a newly acquired appreciation for the electrical grid in Michigan.  Our coffee story is unique and yet I feel as though it’s mathematically relevant as teachers will be back in the classroom to start the second half of the school year.  Enjoy the rest of 2013 and I look forward to a successful 2014.