Teaching Intentionally

Each time that the topic of division comes up, memories of minute quizzes make me cringe. I know that I am not alone in this feeling either, so why were “Mad Minutes” so terrible? I’d like to think that it might have been the mad scramble to write an answer to each problem. Maybe it was the frustration of forgetting an answer to a problem that you had seen on a flashcard what must have been a thousand times. I remember my parents testing me the night before until I completed each fact without hesitation. I also recall thinking, why am I doing this? We have talked in class about the importance of fluency and efficient methods. There is no doubt that straight memorization of facts provides fast recall, but as a kid was I fully understanding what each fact represents? Honestly, I believe that I was more focused on memorizing facts of one category so that I could move onto the next the following week.

Last year I volunteered at Wyoming West Elementary School in a kindergarten classroom and a fourth grade class. The majority of my time spent with the fourth graders was holding up flashcards for them to tell me their best guess at the answer. It is true to say that many of the kids really were guessing. Most of them did not understand how to estimate, so when I asked 3 x 5= ? they did not understand that they could count by 5 three times in order to get the answer they need. This poses a major problem to them because they are failing to understand what multiplication is and they are failing to make connections.

We have been talking in class about the importance of connections in math. Without them, students are failing to make sense of math and solve problems in a way that is meaningful to them. From class the last few weeks, there is one phrase in particular that has stood out to me.

Be intentional.

This may sound simple and obvious, but I have recently become more aware of the impact elementary math has on people. All of the foundations students learn are typically followed with memories of frustration, thus turning people away from math as they grow older. In my opinion, math should be supported by real-life problems that prompt problem solving skills and persistence. Too often math is seen as memorization of facts and equations, while understanding how they can be applied is less frequently known. As a recent assignment, I asked two of my friends to complete a long division problem. Both remember the steps and arrived at the correct answer. However, when I asked specific questions about why a certain step was important, they responded with, “Because that is what you do.” If we only know the steps to an algorithm but cannot understand why they are done, are we really improving our knowledge of math?

So, as a future teacher, I hope to encourage understanding with a variety of methods that we have discussed as a class. I want to provide students with methods that make sense to them. It is a clear fact that all people do not learn the same way, so teaching in different ways will support more students in a class. Creating lessons and activities that challenge all students and also give them the new knowledge they need to gain better mathematical understanding are essential to promoting long-term learning. When I think back to my own elementary experiences and how I wondered why we memorized countless math facts, I now know that we need effective strategies. However, before efficiency and speed comes understanding. I see a great importance of teaching realistic division problems, estimations, and easier to understand methods before long division. Yes, long division is effective but students need to understand why we need the algorithm. More importantly, we need to give them a why in math. There should be less “It is just what you do,” and more “I am doing this because…” As teachers, we need to be intentional in a way that we have more than just the next test in mind. We should be considering the importance of providing students with tools and understanding that will benefit them for their entire lives.



  1. Kalyn Overweg · February 12, 2016

    Sarah, I really enjoyed your blog. The story of the 4th graders really stood out to me. With all that we are learning about math and how to teach it, it is sad that so many students are struggling with the whys and the hows. I would love to hear more about the math in the kindergarten classroom and see if any connections could be made. Math and almost every other subject builds on what they were taught in previous years and I would find it really interesting to trace the math from kindergarten to 4th grade from your example. What a great post, thanks for sharing!


  2. goldenoj · February 14, 2016

    Stories of real students are powerful. Sad how math stripped of meaning only leaves one way, which is often memorize.
    You’re probably set for completeness/content, but this section “I now know that we need effective strategies. However, before efficiency and speed comes understanding. I see a great importance of teaching realistic division problems, estimations, and easier to understand methods before long division.” begs for expansion/examples. Maybe break that big paragraph into 3?

    5Cs: 4.5


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