Truly Understanding Mathematics and Your Learners

Introduction

     Hello again to my readers! Once again I am excited to share with you my growth and development in math education with another week of knowledge into my brain. As I normally do, I like to break down what I have learned each week into themes and this week I have separated into two. The first deals with knowing your learners and creating a diverse instruction that can benefit different types of learning styles. The second looks at teaching math in a way that promotes understanding rather than speed.

Know the Learning Styles 

     It has been proven that people learn in different ways based on their senses and that reflects how they approach their own education. The three main ones are visual, auditory, and kinesthetic. Not only did I learn more about what each learning styles entail, but also what pedagogical decisions can be made to support them. In my teaching block experience I had a lot of students who were visual learners who received the benefits of when I used tactics like attaching visuals to math problems, using colour in my presentations, or encouraging them to draw out diagrams to help them with the problem. My auditory learners learned best when I explained each new concept in detail to them and when there was small group discussion about the problem. These are just some examples of tactics you can use for your own students with these learning styles. Finally, I believe that kinesthetic learners have the most difficulty in school because many teachers do not instruct in a way that helps them. I remember having a conversation with a friend of mine who has a negative experience attached to education. He is the type of person that works great with his hands, but does not benefit from lecture style teaching. For these students you can manipulatives that they can hold in their hands in order to help them learn more effectively. For instance, when I taught addition/subtraction of integers I allowed the students to use blue and red tiles to represent a positive and negative integer.

Here is a link to help you determine the learning style you have. 

http://www.whatismylearningstyle.com/learning-style-test-1.html

Speed vs Understanding

     As I worked through the online modules this week I was once again reminded of the importance of having students struggle with deep questions that provoke their understanding. Too often in my experience as a student do I remember doing math drills and games where you compete with other students as to how fast you were at solving a math problem. Even today many online math games focus on the student being able to answer an equation quickly rather than provide a difficult problem. I remember one of the most effective math classes I taught in my practicum was when I had one challenging problem for the students to solve in small groups that took the whole period to complete. Here the students had to incorporate everything they learned and apply it to a scenario that really challenged their understanding of the concept. It was here I learned that students benefit more from open questions that really challenge their thinking rather than repetitive math drills. Math is not about speed, it is about true understanding! 

Success through Failure: Try, Try, and Try Again

     As I continue throughout the weeks to learn more about how people view Math and how I can influence my students to be successful in Math. I received confirmation this week that it is important for me to teach my students that mistakes are a part of learning and failure is the first step to success.

Challenging Your Students

     I found it surprising when I viewed a video by renowned Math education expert Jo Boaler when she said that sometimes students should not be praised for correct work because it may encourage them to continue to seek that praise the easy way rather than challenging themselves. While I may not completely agree with this premise I do believe that we need to encourage our students to challenge themselves by increasing the level of difficulty. There is plenty of research to show that brain growth only occurs when it is forced to think hard about new ideas and struggle with them. If students do not continue to push themselves, they will not become better, just like in sports or music or any other activity. I remember in my teaching block having a student that clearly demonstrated that he was a level 4 student in Math and could exceed the expectations set for his grade level. It was clear to me that he was not being challenged with the work provided for him and he was losing his passion for Math because it became boring. I realized that as a teacher I should not just be comfortable with him meeting grade level expectations, but that I should push him to become better. I accomplished this by getting him to think about other scenarios than what the questions were asking and providing him with difficult, meaningful, real world problems that he would be interested in doing. What I learned from this experience is that once you learn where your students are at, you must adjust your instruction so that it is challenging for the student, but not beyond their reach.

Know Your Students

     Learning about your students is crucial to effective instruction, as I have learned through my experiences, because students view Math in different ways. For instance, in the picture below you see a set of black dots organized in a particular way. On the right hand side you can also see how different students in the class memorized the number of dots in their head through their own pattern. This shows how different we all are and the importance of differentiating your instruction to suits the needs of all your students.

Process Over Results

     Perhaps the most interesting idea I took away from this week was that students need to struggle in order to learn. Too often teachers only praise their students when they arrive at a correct answer. Instead we should be praising our students for going through the process and providing them with the necessary feedback to improve. We need to realize that struggle brings success and the process of working through the obstacles is what makes us better. This means that teachers should be instructing in a way that teaches students that mistakes are a part of learning and continuing to challenge their knowledge in order to gain a deeper knowledge on the subject.

Here is a video by Jo Boaler discussing the idea of learning from mistakes. 

Welcome Back! September 11, 2017

     Welcome back to my readers! It has been some time since my last Mathematics blog post, but as I continue to learn in my teacher education about different aspects of Mathematics education I feel the need to reflect on them in my writing. 

     This week in class and in my weekly online module I had the chance to review as well as reflect on the mentality that people have towards Math. One major theme that I noticed this week was about the stereotypes and myths that are attached to Math. These stereotypes are important to know about as teachers because they greatly influence the way our students perceive Math.

     The one myth that was discussed which influenced my career as a student was that many people believe that some people are genetically better at math, while others are not. However, this is simply not true and we got a chance to watch videos that point out the research on this. As teachers we need to instruct our students to truly believe that they are capable of success in Math and that with hard work comes success. In fact, research shows that people who do not believe they are capable of learning Math cause chain reactions in the brain that are detrimental to their learning. As one video pointed out, those who are successful at Math were not necessarily born with this ability, but have just been exposed to it more than their peers. As a student, others reinforced this myth which led me to believe that I was not capable of success in Math, but that I could succeed in athletics. I know now that this was not true, but this belief caused me to spend more practice time in athletics and less on Math. As a result, I became more successful at one more than the other.

     As a teacher you might be asking, what can be learned from this and how can I prepare my students for success? I would argue that this most important step is to demonstrate to your students that these kinds of Math myths are false. Instead, lead your students to believe that they can succeed with hard work and dedication not only in Math, but in all aspects of life. Secondly, teachers must teach their students to embrace the mistakes and challenges they face in Math. Throughout this week I heard testimonials from people who dislike Math because of their struggle with it. We as teachers need to show our students that these struggles will help them become better. Many students understand that there will be struggles when they learn a sport or an instrument or a new subject, and are usually ok with that, but why not with Math? We need to show our students that the brain is like a muscle that needs to be trained and exercised to get stronger.

     I am excited to continue my Math education journey this year with a substantial amount of experience now to reflect on. I understand that there is much more to learn and I am thrilled to have the opportunity to grow as an educator. I take it as my mission to show my students that they are capable of success in whatever they put their mind to as long as they are dedicated enough to endure the challenges.