Nature You Say? More Like Mathure

                 This is it, the last one, the moment of truth, the big one, the last straw, the big show, the last whoora, the big finale, my last math blog post (for now). There will be no lady singing, but after publishing this I have to say a smile has not left my face. It is not that I didn’t enjoy creating my posts, it is more like a sense of accomplishment, I have made it this far.

                I brainstormed many ideas as to what I wanted to talk about in my last post, but the topic of this week’s online portion of class gave me a lot to work with. It is very easy to find math in our daily lives, highlighting these real world connections to the topics in math class is the ultimate way instructors can promote student engagement. I really liked the videos we watched about how math is the ultimate designer in nature. Nature is math, it’s all about symmetry and relationships based on number patterns.

Retrieved from https://i.ytimg.com/vi/wvAXzlHpSs8/maxresdefault.jpg on October 28th, 2017

                One of my favourite words to say is Biomimicry, which is scientific approach to innovation that aims to crate sustainable solutions to human challenges by imitating designs and patterns we see in nature. The idea behind this is the belief that nature has already solved many of the problems we face, their solutions are time tested (because of time itself). Nature has used this time to do all the math for us, and we as society are starting to take notice of this more and more. Biomimicry.org goes outlines how biomimicry is changing our lives for the better, improving our designs of the innovative things people are doing all over the world. One of my favourite examples is how a bird’s beak made the fastest train in the world, even faster. The Shinkansen Bullet Train in Japan travels at 200 miles per hour, but when it first hit the tracks, the speed at which it traveled produced thunder like claps every time it left a tunnel, making many people very mad. Engineers used the design of the Kingfisher bird’s beak, who dives into water with a minuscule splash, to redesign the front of the train. This change, made only possible because of the things we learned from nature,  got rid of the thunderous clap, improved electricity use by 15% and made the fastest train in the world, 10% faster. 

Examples of Biomimicry

Biomimicry is combining biology and technology, nature can help us help others even more. Behind all types of science and design, there is math. Behind any phenomenon in nature, there is pattern and symmetry, which is math. These realization fuel my belief that students need to be exposed to more and more real-world applications in math class via blended learning designs. Science and math are two subjects that I believe can be symbiotic in the classroom, teaching one with the other. It also makes me very excited to teach math and science in my upcoming practicum, as I have the opportunity to practice these types of strategies in my class.

                Before I taught math, I was not a math person. I didn’t get the math gene from my mother, the accountant, that’s what I use to always say. I never considered myself a math person, I don’t think I do yet either. What I do consider myself is a teacher, an educator who has the opportunity to provide students with an array of experiences in math class due to my lack of a mathematical background. I never want my students to be the only one learning in my class, the best math classes to me are ones based on overall discovery and teaching for all parties involved, me included.  My future students only have two jobs to do in my classes. The first is to try, and the second is to be kind. Whatever they do after that is a bonus.

Thanks for reading,

Mr. Primeau 

Putting Learning into the Blender

Hello Math friends,

It has been a bit of time since my last post. We had a week of flexing, then reading, and now we are back to the grind, the home stretch. This week we continued to focus on new and exciting teaching strategies we can use in our upcoming placement. We focused specifically on blended learning this week, and how we as teachers can use technology better in the classroom.

Our classrooms are becoming more and more connected to the real-world via technology, which is allows educators to extend the reach of their learning past their school walls as well as out of their hands as it is a main way to develop more student centered learning. When it comes to the use of technology in my classrooms, math focused or not, I tend to look at the use of technology as somewhat effective. I believe technology is routinely used as a distraction for students after they have finished their required work. Instead, using technology in the class needs to enrich an improve understanding instead of just take up time.

Retrieved from https://goo.gl/5bzU2F on October 21, 2017 

That notion if woven into SAMR, which is a model designed to help educators infuse technology into teaching and learning. It enables teachers to gauge how technology is utilized in classrooms. The focus is on how technology is changing the learning for students and not the technology itself, which is crucial for using tech in math class. SAMR is an acronym for Substitution, Augmentation, Modification and Redefinition. Each word describes how technology can be used in order to alter how the students learn and execute and activity. I really liked the ideas behind the Augmentation aspect of the SAMR Model, as it focused on how students can use technology to improve how they complete a task, without changing the original task. An example of this would be having students use some of the iPad’s built in tools such as the thesaurus, dictionary or speak mode to augment the classroom task. Allowing he students to alter how they get to their final result of a task could allow for more students engagement as they feel more in control over their learning.

           Below is a helpful link for those who want to know more about SAMR model, and how to approach any lesson across any discipline with this way of thinking in mind.

Transforming Lessons Using the SAMR Model

The SAMR model is just one of the strategies we focused on that taught us how to blend our learning for our students. I consider the whole idea of blended learning as being a great background ideal to have when doing any long range planning. We routinely hear about how our brains are muscles and they get stronger the more we use them, like regular muscles. I can take this thinking a little bit further, focusing on the importance of confusion. When training your muscles, it is important to embrace muscle confusion by completing different variations of an exercise, as your muscles can get bored with a certain way of doing something, which makes the action itself less effective. This way of thinking describes why blended learning is so important. Not that is creates confusion, but it allows students to answer, complete and conduct various activities and tasks, many ways. Blended learning models like SAMR allows me as a teacher to design lessons and tasks that ask my students to use many different skills instead of just relying on one or two.

I will be remembering the SAMR model for long time now, because I think it is a great tool to use while in the beginning stages of unit and long range planning.

Thanks for reading,

Mr. Primeau

Make Math Rich, and Wild

Hello readers!

                Another week has passed, which means we had the privilege of learning more about teaching math more effectively. This week we focused on getting rich in math class, learning about the value and wealth that revolves around question and activity design. Rich Tasks follow guidelines that involve creating activities that encourage the students to work collaboratively, logically and the most important attribute: room for interpretation and discussion. How I would describe the nature of math lessons that I was taught in the past would be rigid and boring. I say rigid because I do not believe there was any goal of making the lessons and the activities “rich”, they were structured so that we were all to learn the same strategies, skills and get all the same answers. My math classes were boring to me primarily because I didn’t excel in the class, but also because they were not very engaging. I value my time in my math classes in the past because my personal experiences are now my clear guideline of how I never want to teach my math classes.

                If we ever want our student's to think math is fun, we actually have to make math fun. I believe that math has an underlying tone of seriousness about it, a driving force that has caused teachers to stay in their lane when it comes to lesson and unit design. The amount of skill-based content math involves, means it takesa very creative mind to take math curriculum expectations and teach them in different ways. Comparatively, subjects like science, geography and history are often littered with lessons and activities that would be qualified as rich tasks. I think the best way to create math lessons based around rich tasks that bolster student engagement is through differentiated instruction and blending other subjects into math. 

               Cross-curricular planning is difficult, but can be the best tool to create rich tasks in math because it. This weekend I took part in the Project Wild seminar day, which focused on implementing outdoor and environmental education across all subjects. I really like the idea of teaching math topics through an environmental lens, because it directly connects math to the real world. One of the activities we did at the seminar involved tracking the population of animals within the same food chain. Part of the activity was the accumulation and organization of the data, through math skills. This activity blended math with deeper thinking in regards to population trends because of human impact. Teaching our students that processes in the real world rely on math operations may bridge the gap for the students between the skills they use in class and why they are so useful.

                Below is a link that takes you to a Webinar made by the Ontario Teachers’ Federation that focuses on bringing math out of the traditional classroom and into the great wide open. The webinar is catered for grades K-6, but involves strategies and activities that can be used in intermediate settings as well.

Taking Math Outdoors!

Math can be as fun as it is useful, exciting as it is challenging, and flexible as it is rigid. It is very easy for educators to rely on the old model of lesson and unit design for math class. It is up to us as educators to try a little harder in order to create a math community in our classrooms that is more about learning for understanding then learning for memorization and repetition.

Thank you!!

Learning Styles, Defining You as Much as You Let Them

Hello all! 

                Isn’t it amazing to be different? I think it is important for us all to realize and believe that we all have unique qualities that allow us to be different, look at things a different way, and learn a different way.  In class, we talked about the three main learning styles. The three general types of learners are visual, auditory and kinesthetic learners. It is important to know that most students are not just one type of learner, most students benefit from various different types of instruction, as differentiation of instruction is the best way to keep students engaged and invested in their learning. It is as important for students to know how they learn best as it is for teachers to know how their students learn. There are many ways one can test what type of learner they are, below is a ink that takes you to a brief quiz that tests what kind of learner you are. Using a quiz like this is a great starting point, but I think it is detrimental to the development of student’s ability to learn if they pigeon hole themselves into one specific type of learner. In addition to a test, personal reflection is a great way for students to realize the many ways they learn best. 

What Learning Style Best Describes You?

After determining how a classes types of learners differs, the best step to take, as teacher should be how he or she will differentiate the instruction and activities. During my placement in grade 7 and 8 math, I prided myself on my ability to involve various different types of activities for my students to do. Compared to my associate teacher, my lessons asked students to work through larger and harder questions in groups instead of using the textbook every day. Using manipulatives in my class, that included many ELL students, was crucial to my success when teaching fractions and even data management. Even though students may identify as a specific type of learner, I strongly believe that majority of students respond well to math with manipulatives or math-based games that are more hands on. In class, we were given the task to go to our school’s resource center and find board game that we could alter to involve math. The game my partner and I selected was BUZZ. The game asks the player to roll a single dice, moving the number of spots the dice lands on. The purpose of the game is to collect tokens as you take your turns, trying to collect six tokens before the bear reaches the honeycomb (the dice has a bear paw on one of its sides, the bear piece moves if the paw is rolled). Our alteration for the game focuses on students number sense and numeration skills. Once a player rolls a number, the person to the left of them must give them a number to divide or multiply their rolled number by. The player may only move the number of spaces if they get the correct answer. Students would be able to answer many different types of questions with this alteration. I also like that this alteration has the potential to be used in most games that involve dice. 

Retrieved from https://goo.gl/z3rN2U September 24, 2017

Be it audio, visual or kinesthetic, your learning style defines you as much as you let it. It is important that students are aware of how they work best so they can provide feedback to the teacher if things are working or not. I view teaching as being very symbiotic relationship, that students and teachers both do their best when they are working together towards better understanding. 

Look Good, Feel Good, Math Good

Oh, hello there. Back again for some Primeau Math tips and strategies? Well you’re in luck, because in this post I will be talking about the most important step everyone needs to take before executing any math procedure ever, of all times, across all flat circles.  The first step is all about positivity.

LOOK GOOD, FEEL GOOD, PLAY GOOD.

                One of my earliest and most fond memories I have while playing football at a young age did not happen on a field, instead it was in the equipment room. My first head coach as a captivating character, a very large man with as much charisma as he had muscles. With the addition of his slight southern drawl, he epitomized the description of “old school football coach”. My coach’s name was Larry, and he taught me a lot of things that really made a lasting impression on me. That first day, in the equipment room, he passed me as I was putting on a football helmet for the first time in my life. He stopped and placed his palm on the top of my newly gigantic head and said “Amazing! Look Good, Feel Good, Play Good”. Our whole team would go one to hear that message at least once a practice, it was part of Coach Larry’s manifesto, and I have taken it to heart.  As simple as that message is, it is all about positivity. Feeling good, feeling confident, will help anyone perform better than they would if they approached their task with a negative outlook. For Coach Larry, the first step he took was all about positivity. 

A short clip from 1963's "Little Engine That Could",  and boy could she ever!.

 Retrieved from https://www.youtube.com/watch?v=Yx9xO98kcBU

              Last week there was a great focus on whether some people can do math because they are “math people” and some people can’t do math because they’re not “math people”.  It was only a few short years ago when I really would have considered myself as being one of the many people who have a general negative outlook towards math. I attribute my newfound confidence toward math to being thrust into a situation where I had to teach math in my placement. When I found out that I would be teaching math to Grade 7 and 8 students, I had to have a “put up or shut up” moment. It was either I take it in stride and believe in my abilities, or perform and negatively affect these kids experience in my class.  I had to alter my view about math; I had to approach with a different mindset. The little engine and I share an origin story, her positivity to get over the obstacles she faced epitomizes the growth mindset. Although she had all the tools to get over the hill, it was only when she exhibited a growth mindset that she was able to do so. 

               

                The topic of having a growth mindset as opposed to a fixed mindset was in focus this week, as well as the difference between teachings for understanding math versus teaching for knowing math. When I look back, in addition to having a primarily fixed mindset when it came to my time in math class, I believe my teachers were more focused on having us as a class be able to just know how to do the math instead of really understanding the math. I remember how obsessed some students were with learning their times tables, and how I struggled with them because my memorization skills were not up to par. This was a common situation for me throughout my time in math class as I got older as the focused remained on the procedural aspects of math in order to get a certain final answer. This way of teaching math embraces a fixed mindset, as it is more focused on arriving at a certain final answer rather than how the student got there. It is refreshing to see that there is a shift occurring in the teaching world, so that there is just as much focus on the journey students take to get their final answer as there is focus on what number they ended up with.

                What I want to embrace in my math class is much more growth mindset focused. Teaching math so that my students are less obsessed with the final answer and memorizing, and more focused on understanding why the math works and its various concepts. I really believe that the difference between knowing math and understanding math is simply having a more positive outlook while completing tasks. If students are taught to approach math as more of an open subject that is still up to interpretation and exploration, I think they will be more positive in their ability to get better and better in class, because their understanding will be deeper and deeper.

                I want to end this post with saying that for anything, having growth mindset in general will only help you. I am not naïve, I understand that being positive about everything all the time is impossible, it would be hard to enjoy a good feeling if you never felt a bad one. But I can guarantee that if your first step is believing in yourself and your ability to learn and get better, than you have already succeeded.

Thank you Larry.

Drive on. 

Guess Who’s Back, Back Again, Primeau Math, Tell a Friend

                 A wise man in a HBO television show once stated that “time is a flat circle”, meaning that it is cyclical, destined to repeat itself. So here I am again, asked to blog about math, but this time it is very different. Following the completion of my first year math course, as well as my time teaching Grade 7 and 8 math during my first year placement, I emerged on the other side feeling very good about my effectiveness of being a math teacher.

                During my placement, I was able to embrace my role as a math teacher and focused on keeping my students engaged via blended learning and more group work than they were use too in math class. I put forward a lot of effort in order to be the best instructor I could be. I wanted to be open with my lack of experience when it came to math in general with my students. I never wanted to give off the impression that I was not qualified to teach them, but I wanted them to understand that the class and I were learning more and more about math together. I think this type of relationship is important in teaching, especially for the later grades as it allows teacher to develop more of a learning community in the classroom instead of an environment that is based on hierarchical order.  I want to continue this way of thinking throughout my time in my year two Math course.

                During the online section for this week, there was a lot of focus on combating myths and stereotypes society and the education system has developed when it comes to math. One of the most important skills I think students need to work on when it comes to math class, is their ability to communicate to the instructor what issues they are having with a specific process. All too often in my placement I observed students ask for help, but they could not communicate what aspect of what they were trying to do that was so hard to them. I attempted to combat this phenomenon by keeping my lesson engaging, but also focused on scaffolding my lessons so all students could learn at their own pace. 

14 Virtual Tools for the Math Classroom

A main goal I have for this year’s math class is to develop more knowledge on the use of virtual learning for math. Last year I was exposed to numerous online math games and platforms, it was as overwhelming as it was useful. I want to use this year to find what tools I really like to use and would be best for constant use for students. All too often I found these online games could only be used as a time filler for students who finished their work quickly. Author Monica Burns complied a short list of what she considers effective virtual math tools, all of which I would consider as being great tools for classrooms. One tool in particular ,an app based tool called Geoboard , allows students to create and manipulate shapes of all sizes and types for the students to gather and develop better understanding of geometric skills.

                I really look forward to the next weeks, as I know I will be exposed to more and more tools and strategies that can make me a better teacher. So let’s do this! 

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