Patterning and Algebra: The Perfect Pair

     It seems to be that every week I attend my mathematics education class I have those “aha” moments that I know will alter my approach to teaching a particular topic, and this week was no different. This week our focus was on patterning and algebra, if you are like me that word algebra can send shivers up your spine. However, I believe this is only a reflection of the way I was taught and not my true feelings. When I was learning algebra in school I was always taught to memorize the rules and apply them to the equation in order to solve them. I had no idea what the variables meant, but I was able to get the answer. As a result, I had a very shallow understanding of algebra until I learned about the relations between patterning and algebra in class. Below you will see a picture of a table of numbers that follow a particular pattern. We learned that an algebraic equation is simply just a way to express this pattern, this was my “aha!” moment. I learned that I can teach my students that algebra is just a way to express patterns and if they think about it that way then it is easy to express it in many forms. Below you will also see a picture of an activity we did where we had to arrange the cards in order to match its equation, grid, table, and blocks. I believe this is an effective activity because it allows students to see the pattern in various forms and see how they connect. I remember when I was first learning this topic I always thought of these forms as separate, but they all fit in together. As shown in the textbook, there are various ways that students can display these equations. It shows how it can be displayed using manipulatives (like blocks), it can be solved using opposite operations or guessing and checking, but one way I found interesting was thinking of the equation as a balance. This means that what is done to one side must be done to the other to maintain a balance.

     At this point in my education I am learning a lot about lesson planning and what should be incorporated. This class also aided me in my learning of constructing a lesson not only through demonstration, but some of the things that were said have really stuck with me. In mathematics education especially, mistakes should not be put down, but the effort should be rewarded because through struggle deep education occurs. I believe this is very important for students to learn in order to stay motivated and engaged in math. I would argue that many students who disengage from their math education only do so because they treat their mistakes as failures, but it is the role of the teacher to let that student know that their failures are the best opportunity for learning. This was truly a revelation for me and one I know I will take into my own teaching because I believe that this is the secret to keeping students motivated in math. Let’s face it, nothing worthwhile in life comes easy, like knowledge in math for example, but with work there is reward. I believe as teachers we need to teach our students not to focus on their failures, but to focus on their progression and the growth in their own learning.