The Finale

               As our time in our first math course comes to an end, it is easy to look back and see how much better I feel in regards to my how I view my competence as a math teacher. Truth be told, I do not think I ever thought about being a math teacher, at any grade level, but that has changed. So much so that as I write this, I have a lesson plan entitled “Introduction to Grade 7 Data Management: Key Terms” beside me, of which I am teaching tomorrow in my placement. Saying I was very nervous about having to teach math in my placement is an understatement, I was basically a wreck for a short time. However, slowly but surely I began to feel more and more confident as a math teacher, with a little help from my friends, but mostly because of the help provided from my instructor.

                Like me, most students dread math, they often walk into math classroom with what I like to call “poor vibes”. The amount of fun I had during hour three hour classes not only made my learning easier and showed me that I could have fun in math class, (quite possibly the first time ever), it taught me about the importance of making math fun. I think educators in general should try to create an environment that create “rich vibes” for their students. An environment that is fun and engaging. Fun and engaging are defiantly two things that I believe describe and effective teacher. Fun in the math classroom is easy to do if your plan ahead, as being prepared allows you to make changes on the fly but also interact with your students in a more natural way.

                The best way to create a fun math classroom is by incorporating manipulatives in your lessons and activities as much as you can. We worked with a massive amount of manipulatives throughout our time in math class. Not only did it make it fun but also it engaged us much more than if we just sat there and listened on how to teach math. It was routinely stated, but also observed, that the use of manipulatives in math class allows for more comprehension for the students. Pictured below are some manipulatives we used throughout our time in class, which helped us learn. Particularly useful are the pattern blocks and connect blocks for the strand of Pattern and Algebra because it allowed us to display linear equations using a physical tool. When students are able to use their hands to learn, to be able to use their knowledge and understanding via physical manipulatives, it allows students to touch and feel what they are learning about, not just read and write about what they are learning.

                  To my recollection, most of the problems we worked through in class were open based questions. We were taught about what makes a math question great or not, the main factor in my opinion is whether or not all students can get started right away, what was dubbed “a wide base”. Having a wide base for your questions is crucial for creating an activity that engages all students easily. Another aspect that I find very important is whether questions have a “high ceiling”, meaning whether or not the question you asked allows for students who excel, are able to continue to learn and expose new aspects about the question. Another aspect that is a key ingredient to making good math questions, especially open ones, is creating questions that allow for more than one response and more than one way to find an answer. We conducted a great question that involved many pathways to finding the answer. The problem, titled “Joel’s Kitten Problem” asked us to determine out of 2 stores what had the better deal for kitten food, one store selling 12 cans for $15 or the other selling 20 cans for $23. We were asked to find the better deal without using division to simply find the unit price. Even within our group, we had differing ideas on how to do it. What made this question great was that everyone could start it (Wide Base) and that each group basically came up with a different method to determine the better deal. The pictures below, display how a group determined that the way both stores sold their kitten food enabled them to buy 60 cans of food. By doing that, they could compare the two stores prices for 60 cans and determine the better deal. Two of the solutions groups completed in the group can be seen below. 

In my first blog post, I presented the myth that many people think they are inherently bad at math, that they “just didn’t get that gene like their parents”. I use to say a very similar thing, my mom works for Revenue Canada as an accountant and saying that she is good at math is a severe understatement. I always use to say, “Well my mom is an accountant, but that did not get passed down to me”. The notion that math is an inherent trait is seemingly ridiculous, that you either have it or you do not. Now that is to say, I do not view myself now as a mathematician, but I feel like I have an almost brand new view when it comes to math, specifically in regards to my competence as a math teacher in the future. I am excited to teach math to my students this year, and I know that if I focus on creating a fun environment in class with the use of manipulatives and open questions I can make a lot of headway to becoming an effective math teacher.

Thank you J      

You Manage to use Statistics and Probability, Probably Every Day

               It is easy to forget how much statistics effect the decisions we make every day. Even without statistical data, we often chose one thing over another based on past experiences and what should or ought to happen. I don’t go to my regular coffee shop on Wednesdays, because that is when they have their specialty donuts making it very busy all day. I leave for work most days 30 minutes before my shift starts, but not on Friday’s or Saturday s, because I know that on average the roads are much more congested and it takes longer to arrive compared to the other days in the week. Statistics, and specifically the management of data and knowing what it tells us allows us to make better decisions throughout the day.

                This week in our math class, we focused on data management and probability, our final strand and a strand that I have struggled with but have much appreciation for.  I really like the idea of how organized the process is and how much information one can draw from various variables. In data management, the data is not the most important aspect. You can collect all the data you want, but it is how you use it and organize it in different ways to show what is really happening is what is most important. When it comes to teaching student’s about data management and probability, it is easy for educators to give each pair of students a coin and ask them to flip it 100 times and record the results, but that is not very fun. As I have stressed in the past about the other strands in math we have covered, when it comes to data management and probability, it is very important to structure your activities so the data that is being used engages the students. Not only can the data they are using in their questions and activities be about topics they like, sports, music, art and popular culture, a great tactic to use is to ask students what they would like to know about their school and have them collect the info through a survey. This type of activity not only exposes them to the collection of primary data, it exposes them to the fact that most questions you ask result in some sort of categorical data, and if you have enough of it, you can make assumptions based on the data.

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                Illustrating how data should be collected and organized from start to finish is a crucial skill for students in grades 7 and 8.  I believe students need to practice their surveying methods early on in their schooling because it is very hard to understand the difference between good survey questions and bad survey questions and how easy it is to be biased even if you are not trying to be.  In the text, Making Math Meaningful to Canadian Students, K-8, they identify the common  error of creating questions that are unclear or vague as the most common misconception when students begin to collect data. Students may ask in a survey, “How much do you look after your pet?” which could result in a huge number of varied responses. Instead, educators should have students test out their question on friends and family, so they avoid the answer of “please explain the question”. A better way to ask the same question could be “How many times a week do you look after your pet?” which would most likely result in more specific responses.

                We go through our lives collecting data without even knowing it, it is important for students to realize just how useful it is to be able to make decisions or discover trends about things they would have never found in the first place. I like collecting data, I like it when after everything is organized you can discover certain things you were looking to prove, but also expose other aspects I was not considering before. My favourite way to use my data collection skills is while I am coaching football. It is often said that football is 50% a mental game, a claim that is backed up by how much film is watched on your opponents in order to discover team tendencies. Every week I would sit down and record how many times a team did a certain play, type of play in certain situations, what plays they call most but also what specific things certain players do in certain situation. I collect all this data so we as coaches have an idea of what the team will do come game day. Although math had never been my strongest subject, the fact that one of my favourite parts about coaching is the film study and team data collection, is proof of how meaningful and useful math skills are when you get older, which is the key message  I intend to teach my mat students in the future.