Reflecting on What I Have Learned- Final Math Blog

     As I finish attending my final mathematics education class for the year I end an enriching learning experience and begin to create new ones as I continue to develop in my growth as a teacher. However, when I finished the last class I got the opportunity to reflect on what I have learning and how I have grown as a mathematics education teacher. The concepts and strategies that I learned about are too numerous to write in one blog post, so I would like to focus on the big ideas that I learned and how I can use this in my own instruction.

     The first big idea that I learned about that drastically altered my approach to teaching math was having a growth mindset which believes that anyone can be successful at math. I remember how many of my teachers when I was in school telling students that some people are naturally good at math and some are not. While there may be students who excel at math with little effort, there is no research to show that some students do not have the possibility at doing well in math. As a teacher I know it is important to instill this into my students and help them believe that with hard work any student can be great at math. This also meant that I needed to change my mindset from thinking that I would never be good at math to believing that if I work at it then I can be successful.

     Before this class I believed that math was about using specific formulas and algorithms to get to a solution. I was always taught that there was only one way to arrive at an answer and the formulas will help you get there. I have come to learn that this is horrendously false. Often in many problems there are various ways to get to a solution with a variety of algorithms to get there. As teachers I have learned that we not only need to recognize this idea, but also have the ability to anticipate how students can arrive at a solution. Teachers need to do this in order to know if this process makes sense and if it can be applied to all similar problems. To do this, teachers need to be thorough in their preparation by creating multiple ways to arrive at an answer to a problem. All in all, I have learned about how I should encouraging students to be able to get the same answer in different ways and not confining them to one particular algorithm.

     Perhaps the most important role of a math teacher is developing effective questions and creating open problems to develop the math knowledge of each student. One thing that I learned about open problems is that they should have a wide base and a narrow ceiling. This means that problems must be simple enough so that every student can begin to work on it, but hard enough so that every student is challenged. As the classes went on we got numerous examples of what this looks like by performing questions that every student would be able to answer, but can be difficult enough for those who want to challenge themselves. By doing this, no student feels like they are not able to participate and every student can be engaged with the lesson.

     On top of creating open questions, teachers must also ensure that these questions get students to go deeper in their thinking and challenge their knowledge on the concept. One interesting way to do this that we learned about in our classes is creating open questions with little information to get the students to ask for the information they need in order to complete the task. For example, if a question asks how much can fit inside a square then a student should ask for the dimensions of the square to calculate the area. Instead of students always being handed the information and asked to solve, teachers should get students to develop their ability to question problems in order to find a solution. Questioning is also a way to lead students who are struggling to figuring out math concepts on their own. One piece of pedagogical knowledge that I have learned to apply in my teaching is guiding students to a self-revelation or self-discovery rather than simply giving the answer and showing the process to get there. Questions are a great way to accomplish this goal because the right questions can direct students to think about different aspects in order to get to the right path. I remember too many times in my own education that my teachers often taught me by showing the answers and teaching how they got there. I have realized how ineffective this method and that teachers need to educate students by leading them to learn on their own rather than just being the only source of information.

     Finally, the final big idea I want to discuss is that learning in mathematics should be interesting and interactive. This means that problems given to students should be relevant to real life, but also should include something that students can relate to in their lives. For instance, during this time teachers could ask questions that are connected with the holiday season. I also learned that math should be taught in a way where students can interact with what they are learning. This can be done by using physical manipulatives that students can use to explore. For example, in class we got a chance to use various manipulatives that can be used to teach fractions including cut up plates, clocks or shapes. This can help the students visualize what they are learning and use it to apply to problems while making the learning much more interesting than traditional drill and practice methods. It is well known, that students retain much more when they are interested in what they are learning.

     Although this short blog post only begins to explain my development as a mathematics teacher it does present my reflections on the big ideas that I have learned. I have learned that teachers need to be the guides directing students to their learning rather than just telling them how to solve problems. I believe that everything I have learned in this class will help me be a better teacher which directs students to be as successful as they can be. 

Data Management and Probability

     Data management and probability are perhaps two of the most practical yet sometimes forgotten topics in math, but this became the focus of my mathematics education this week. We learned about how to teach students to understand the probability of situations and how to take this information then plot it on a graph. In order to understand these two topics we performed an activity which combines the two. We first estimated the number of Oreo cookies in a jar, wrote down our estimate, then placed our estimate onto a stem and leaf plot. With all the estimates laid out onto the plot we could determine the mean and mode of this data set. This interested me because I did not really understand the purpose of a stem and leaf plot, but this activity demonstrated its practical uses. I believe that when teachers do this it grabs the attention of the student and helps them remember what they learned because they can trace the example back in their memory in order to remember this topic. I know that when I was student I learned at my best when teachers provided me with practical examples of how what we were learning being applied to real world scenarios.

     We also began to perform some activities to exercise our knowledge of probability. For example, we rolled dice until we got to every number on the dice in one set. This demonstrates to students how many variations can come in this particular situation as one group only needed 12 tries while another needed 36. Games are an excellent way to get students’ attention and can be an excellent starting point for an educational conversation. For instance, if I was doing this activity with my students then I would discuss with them the odds of receiving a certain number. The textbook reading also provided a number of interesting ways to teach this topic using manipulatives. One was a spinning wheel labelled with various colours and the students would have to predict the probability of landing on a particular colour. Cards are also another fun way to teach this task, as the textbooks shows us, because it allows for discussion on different scenarios and the probability for each. I think that this would really grab the attention of the student because it is an object that they have seen frequently, one that is familiar to them.

     One deep idea that truly resonated with me this week is that we need to teach our students skills that will help them in everyday life. One of these skills is estimation, a skill that many teachers tend to neglect. I remember how so many of my teachers taught me about formulas and how important they were to memorize, but let’s face it, this is not what we are doing in our everyday lives. Students need to learn how to estimate and predict certain scenarios in order to make educated decisions. As teachers, we need to show students how to perform this process and how to analyze a scenario to make the best decision.