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.

Retrieved from http://bit.ly/2gci5do

                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. 

Constant Assessment Is Best

                  Several aspects and attributes are needed to be an effective teacher. You need to know your students, be able to create an inclusive environment, be able to engage students in critical thinking through lesson plans that grab their attention. What is often overlooked when it comes to key aspects to be an effective teacher is being effective at assessment. The OEM document Growing Success is the end all be all when it comes to how educators should structure how they assess their students. I always viewed assessment as its basic form, taking notes of students work, collecting their work and assigning letter grades and commenting on their performance in regards to the achievement chart. That type of learning is what Growing Success and many other educational sources deem as Assessment of Learning. What was relatively new to me is the notion that educators must actively think about incorporating Assessment as Learning within their lesson plan and assessment moves. I was aware that as a teacher, I would want to promote more and more self-regulation and editing for my students. Assessment as Learning is now something that I really want to focus on as a junior/intermediate teacher, especially if I am able to teach grade 8’s. I think focusing on teaching students at that age to self-regulate and continually assess their own works will do dividends for them as they continue to secondary school where there is much less teacher intervention when it comes to checking up on students doing work.

A great example of assessing a student with a detailed rubric but also incorporating personal feedback  that bolsters assessment as learning. Retrieved from http://bit.ly/2gFlGhH.

                   In regards to math, assessment can be easy at times, but also very hard. It is very easy for a teacher to collect work pages, quizzes and tests and come up with a grade based on quantitative data. However, just basing your assessment on those sources is not at all being close to being an effective teacher. In the text, Making Math Meaningful to Canadian Students, K-8, they state that in order to be a good assessor,  I must be able to gather information about students’ knowledge and abilities not only from a variety of sources, but on many occasions to ensure that the information is reliable and valid. The text provides a guide on how to be a good assessor in math, via 8 key paths. I think one of the most important ways the text identifies as areas to focus on is to ensure your assessment is fair to all students. In order for me to do that, I need to ensure that I am able to create strong bonds with all my students, especially students who have accommodations or individual plans that alter their learning. It is key to understand that if the way you teach needs to differ for some students that you allow students to be assessed differently too. Another interesting tactic the text presented was the idea that students benefit greatly when teachers “set high, yet realistic, expectations for students”.  The text argues, based on research that was done, that students respond well when they are presented with high expectations because teachers who do not expect a lot of their students may embrace a more negative attitude in the classroom.

                My ability to be able to create a number of different ways for students to be assessed is crucial to my future if I am presented with the opportunity to teach math. It is easy to base marks only on tests and quizzes in math, but that does not accommodate the various learning styles students have. I must not only commit to being able to different my instruction, but be able to differentiate my assessment, I believe this will result in higher achievement for both me and my students in the classroom. 

Geome-tricky

          The focus again for this past week’s math class revolved around geometry, which somewhat solidified my belief that this particular strand of math is crucial for us as future educators. We focused more on working with 3D shapes, specifically working with cylinders by working through a type of activity that our Instructor called a “Guided Learning Activity”. Like most of our activities we did in class, we were asked to team up with our classmates to take on the activity, but the nature of this type of instruction is slightly different. Guided Learning Activities are supported by a somewhat intricate back-story, a topic with a little bit more substance than usual, and the students are asked to solve a big problem by working through a worksheet. Our activity was based around the task of trying to figure out how many giant metal cylinders could be made out of a given sheet of metal. The questions started simple, asking us to use toilet paper rolls to try and determine the exact measurements of the cylinders that will be built according to the activity. The activity guided us through, gradually, but also asked us to think deeply about what it was asking and what to do with the information we were acquiring while working through the series of questions. This type of learning activity is an amazing tool for an educator. It allows educators to have their students do exactly what they intended them to do in regards to what learning goals they have set out for their class but also allows them to have their students use the key skills in regards to the achievement charts. The assessment criteria for an activity lie this is very multifaceted in regards to how much an educator can assess.

An example of the easy to get manipulatives we needed to complete the activity in class. 

                One of the best aspect about the activity we did was that it would ask students to really be able to have a grasp on the language and terms that emerges when learning geometry. Every strand of math has plenty of new words and terms that students must understand and know when to use, but geometry has so many terms that students can get hung up on and miss use. In my opinion the best way to combat confusion is to focus on having your students use physical manipulative so they can see and feel the difference between shapes, especially when it comes to 2D and 3D shapes. The text, Making Math Meaningful to Canadian Students, they identify how students often struggle with what appropriate language to use when dealing with 2D and 3D shapes. Students may have issues when they start to work with 3D objects, such as calling a rectangular-based prism a rectangle, or calling a cube a square. This misconception is very common, and is often seen when students are first introduced to 3D objects, and their confusion can be seen as them understanding that 3D objects have 2D objects within them.

The struggles students have in the geometry lessons are of course not limited to working with 3D objects. The text, Making Math Meaningful to Canadian Students, identifies the issues that students have in regards to their ability to the common belief that the orientation of a shape is what defines it. The text suggests using concrete shapes like patter blocks to illustrate that it does not matter what orientation a shape is, a triangle is always a triangle and a square is always a square.  How well students grasp the language when it comes to geometry is a good measurement about how well they will understand when they continue to work with 2D and 3D shapes.  I think the language of geometry is the huge base that students need so they can continue to explore, learn and develop geometric skills and thinking. 

Geometry, It's Fun for You and Me

              I consider myself both a geographer and an environmentalist, mostly because I majored in geography and environmental studies for my undergraduate degree. Everything about those two subjects appeals to me; I find it all so interesting. I can also confidently say that one reason why I grew do fond to those specific social sciences is that I am very spatially aware.

                In this past week’s math class, we focused on geometry, exploring the ins and outs of 2D and 3D shapes. One topic we also focused on was how geometry connect to spatial skills, specifically how the development of geometric thinking can have a profound effect on a child’s development in regards to spatial skills and awareness. The text, Making Math Meaningful to Canadian Students, K-8, summarizes the ideas behind Pierre van Hiele and Dina van Hiele-Geldof’s Taxonomy of Geometric Thinking, explain how students go through 5 stages on their way to developing geometric thinking.  Level 0 is what they explained as the “Visualization” stage where students begin to be able to identify shapes based on the fact that they a circle simply “looks like” a circle and a triangle is a triangle is because it “looks like” a triangle. Level 1 is the Analysis stage where students begin to conceive shaped in groups based on their similarities, followed by Level 2, the Informal Deduction stage where students develop the greater ability to develop their own simple logical arguments about shape properties. Level 3 and 4, Deduction and Rigor, apply to students learning at a high school level and beyond where students develop advanced understanding about shapes through traditional and non-traditional axiom structures. I found it very interesting how the stages the van Hiele’s developed, mirror many cognitive taxonomies in regards to students general development as well. This makes me believe that the fact that geometric thinking is s connected to one’s own spatial skills, the development of good understanding of geometric thought is crucial for both math students and math teachers.

                For the most part, I think some of my most favourite activities in math class during my time in elementary school revolved around the geometric strands. I recall making 3D shapes with straws and pipe cleaners. I think that exercise is used today often because it allows students to create the shapes they are learning about through the construction of their own manipulatives. Use of manipulatives while teaching geometric operations at any level is a great idea, but is also simple because there are so many different types of manipulatives teachers can use. Pipe cleaners and straws cam be used to make 3D shapes, students can also construct their own shapes with paper. The creation of shapes by students addresses the first three levels of the Taxonomy of Geometric Thinking, and most importantly, it does this in a fun and engaging way. There are many other activities students can complete with the use of manipulatives, in class we completed some “Tangram Duos”, which allowed us to use different shapes to create specific 2D shapes.

Tangram Fun!

                For me, I think my appreciation of my time studying geometry in my early years of education can be connected to my spatial awareness, but also my appreciation to geography because it is the study of space and how we interact with it. All strands of math are important , but the development of geometric reasoning and thought is somewhat more important because it can shape how individuals use and understand space. It also can be considered as one of the most important stands of math because it follows cognitive development so closely.

Thank you for reading!

Algebra is Pattern, Algebra is Fun, Algebra is Pattern, Algebra is Fun

                Out of all the math units, algebra has always been the hardest for me to complete. Algebraic equations appeared to be strange foreign language to me, and still do to some degree today. So when I realized that this week in our math class we started our conversation about teaching algebra after I completed the reading, I half excited to find out how our instructor was going to approach it through the new math lens we have been practicing but I was still nervous.

                “Algebra is just patterns”, is something that I have heard my instructor say many times already, but I did not really think about how true it way. The notion of taking a simple patter, such as number starting at 3 and increasing by 4 can be translated into a linear equation, is something that is relatively new to me. Sadly, I do not think my math teachers in the past ever taught me this way, and if they did, it certainly did not stick. We began the class by performing a “mix-and-match” exercise where we had to identify what graph, table and visual aid matched with each equation that we were given. This activity was phenomenal at illustrating how linear algebraic equations are able to be compared and visually shown in different ways.

Matching Algebra Activity

                One aspect of this activity that stuck out to me the most was the tangible use of manipulatives. I do not recall using manipulatives at all to demonstrate algebraic patterns. The use of the connect cubes allowed me to really be able to visualize how the equations we were using change as they continue through the pattern. The idea of using two different colours of cubes would really allow students to visualize the patterns they are dealing with. The image below illustrates how the equation (Number of Tiles =2s + 2. Providing manipulatives for the students to be able use the hands to actually build a model of how the values increase would help provide background for the student when dealing with missing variables in the future.

                I never specifically associated algebraic equations with patterns, but even that simple idea has improved my understanding of the subject.  Our text book states that one of the most common mistakes students make is misinterpreting equations, specifically when dealing with equations that use “x” as a variable, students commonly see “x” as the multiplicative process when first exposed to equations. It is important to combat this by not using the letter in equations or by italicizing the parts of the equation, they would appear like this for example T = ab X f.

 I think there is a general consensus in regards to students having negative views toward algebra.  I think through proper planning and structure, educators are able to remove the intimidating vail that comes with algebra by focusing on committing to the use of manipulatives and open questions. Of course, the same notion can be said with any strand of math, and it should be. However, with algebra being the foundation to higher levels of math, slow introductions that really focus on getting students to realize the pattern aspects would result in the building of a better foundation for them to better understand more complex algebraic equations in the future.

Keep on keepin’ on 

The Good, The Bad, and the Questions

              Before I started this class, and my journey towards being an effective math teacher, I would have told you that all math questions are inherently bad, mainly because they are math questions! Like I have stated throughout my last blog posts, I am learning so much about math, and how to teach math that the subject is slowly morphing into something that I no longer fear, rather something that I want to embrace. At first thought, I could say what makes a math question good, is whether or not it is an open question, because that is the kind of questions we have been focusing over the past few weeks. This is somewhat true, as open questions embrace collaboration and the use of students’ imagination to work through the questions. But through further instruction, we have learned about other key points as to what makes a math question good, and what makes a math question bad.

                Obviously clarity in how you are asking and presenting a question is the first step towards creating good math questions, or what is known as the use of “Soft language”. Educators like myself should focus on creating questions with what we can call a “High Ceiling”, which means structuring questions in a way that students that are learning at a higher level are able to continue their learning past what the question is initially asking, questions that allow all learners to get the most out it. Good math questions also have what can be dubbed as a “Wide Base”, another term that embraces the learning of all students, focusing on asking questions that enable all students to get started.  Good math questions should also be relevant to the students, like sticking to themes or interests the students have which promotes engagement. Good math questions normally involve an activity and or manipulatives as well as embrace student collaboration.

                One key aspect that good math questions have is being structured in a way that embraces different ideas and methods in order to solve the problem. An activity and problem that we worked through in class is an unbelievable example of a math question that embraces different methods to solve the problem. 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 picture below, Method #1,  displays 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.

Method #1

 Another method that a group used was to solve the problem by visualizing each can from either store being a standard and easy to work with value. After each can had the same value, they started to divide the remaining money into each can, essentially discovering a unit price and revealing what is the better deal.

Method #2

             Both groups shown in this post discovered that the better deal was at the store selling 20 cans foe $23.  Joel’s Kitten problem exemplifies how an educator can create good math questions. Answering these questions with the use of manipulatives would also be a good idea, also illustrating how this is a good question. Educators have a lot to consider when developing lesson plans, but it is important o remember the key aspects for what make questions good or not, because the quality of the question has a direct relationship to how much every students takes away from the exercise.

A Rational Reflection About My Ratio-based Presentation

                This past week had been one of the most interesting weeks I have had since enrolling in teachers college, specifically in regards to my “becoming a math teacher” journey. I had the task of creating a 8-10 minute lesson for my colleagues in my math class, on the topic of ratio’s. I must admit that when I began the process of putting together my lesson and presentation, I was very nervous. There is defiantly something different when you compare getting in front of colleagues to getting in front of students when conducting a lesson. I have never been shy while in front of a crowd, but because I was getting ready to essentially teach them a subject that I have never been that successful with, I was slightly nervous.

                It was not until I laid out how exactly I was going to teach ratio is when I became comfortable with what I was doing. What helped most was relating to what we have been working on a weekly basis, that is, learning how to teach math in a completely different way compared to how I was taught. With this idea being in my mind, I decided to gear my activity towards Grade 6 students and structure it in a way that would emulate that grades general introduction to ratios by focusing on proportional geometry through the lens of ratios. I also made the commitment to include simple, real-life scenarios while I introduced the topic, scenarios that if those kids were actually going to be in the class, would be very relate-able for them. I decided that my lesson would start with a short presentation that introduced not only the definition of ratios, but  I wanted to include two examples that simply explained what a ratio is as well as how they can apply to comparing two similar geometric shapes. The other half of my activity was based on a worksheet I developed (which can be seen in the image below) that consisted of 5 questions that asked students to explore ratios by comparing similar shapes.

An Image displaying my worksheet for my presentation 

                I can honestly say that I values this assignment greatly for many reasons. Primarily, I now believe that by making sure I am prepared, I can confidently say that I will be able to teach more than just a 10 minute math lesson. This was actually the first presentation I have had to make this year, so not only was it refreshing to get it out of the way, based on the fact that it was in my math class has made me even more confident and excited to be able to teach lessons in the future. This assignment also introduced me to lesson planning, albeit it was on a small scale, I value the experience greatly. While putting together my assignment, I noticed that both the curriculum documents and our text “Making Math Meaningful to Canadian Students, K-8”, obviously included what topics should be specifically introduced but also identified key mistakes and misconceptions students have when dealing with Ratio, percent and proportion. These key items the focused on helped e improve my lesson but also made me think that in addition to knowing the best way’s to teach students math, educators must also be aware of common mistakes and misconceptions students have in order to avoid them and strategize how to help students who are showing signs of struggling.

                My presentation went very smoothly, and I enjoyed my time in front of a class while teaching math. That is a sentence that I would have never thought would come out of my math just 2 short months ago. This week I made great steps towards becoming confident in my ability to teach math in the future. I look forward on continuing my education when it comes to math, but also telling you all about what I will be learning in the future as well!

Thanks for reading!

Often Less than 1, But it Doesn’t Fracture the Importance of Teaching Fractions

It is safe to say that fractions may be often over-looked. Early in their lives, students grasp the simple aspects of fractions; but as educator, we must illustrate to them that they have many functions. Quickly think about how many uses fractions have in our lives. They can represent ratios, measurements, area, volume and mass. With so many uses and applications, introducing students to fractions should be considered as one of the core operations that elementary students need in order to further their math learning later in life.

                Our textbook, Making Math Meaningful to Canadian Students , K-8 written by Marian Small,  does an unbelievable job at illustrating the various meanings fractions can present to students. It brings up the fact that eventually students must pull together the various “meanings of fractions” that a fractions are not just a number with a numerator and denominator, that they can represent part of a whole set, compare things ad be part of a continuous set.

                Students often start with learning very simple fractions, very often known as “unit fractions” that have a 1 as the denominator and any other number as the denominator. An example of a unit fracture can be seen in the image below. Unit fractions are always less than one. Fractions, like many aspects of math, have specific divisions and traits that stay constant no matter how complicated they may seem. These traits or definitions also include Proper fractions, characterized by still equaling less than 1, but have a number more than one at the numerator, e.g. 4/9 . There are also Improper Fractions, where the numerator I more than the denominator e.g.  8/6  or have a whole number and a proper fraction, e.g.  2 4/9 . Getting a grasp on the simple definitions and trait about fractions is the first step or students. It is the educator’s responsibility to build upon this, highlighting that fractions have many uses and exists everywhere. Like most math operations, more understanding about fractions is obtained with the use of manipulatives. 

JudeGRolfe., (February 13, 2013). A Unique, Unit Fraction. Retrieved from http://bit.ly/2cWKwHm

                  One of the most common manipulatives used when teaching how fractions can work is egg cartons. Not only are students already prone to saying “half a dozen”, students can also be shown how often fractions are used during activities like baking and cooking. Manipulatives such as egg cartons, and Pattern Blocks (depicted in the picture below), can be used by students in order to visualize how fractions and change and are able to b compared and altered. Physically touching the objects allows students of all ages to develop deeper understanding.

Jimmie., (August 1, 2009). Pattern Block Math Manipulatives. Retrieved from http://bit.ly/2dvvGye

Fractions can be simple, but they also can be very hard for students to grasp. Most of the errors that occur when dealing with fractions is when students start to add, subtract and multiply fractions. The use of manipulatives should not be limited to the younger grades as they are still useful when it comes to the more advanced operations of fraction operations. The list of what fractions can represent is almost endless, which is why teachers of math should see their lesson plans involving fractions as crucial classes because it can have a profound effect on their students ability to learn the topics that follows. 

One way, or Another, We're Gonna Get It

                Many people have several things they excel at, some more than others. Canadians use the four main math operations every single day, but most people don’t do it the same. Maybe they were taught different, maybe they figured out different ways to do their subtraction, addition, division and multiplication in their own way. In the past, our math curriculum as based on several different rules, the same can be said about teaching and using the four math operations. But if everyone is different, wouldn’t it make sense to provide students with alternative ways to learn and do math?

                Students often struggle with the real world practicality of the math they learn; the common notion is “why am I learning all of this stuff? I’m never going to use it again.” In recent years, educators have focused on creating real-world exercises and problems for students to do, in order to show them that math is everywhere, and they will use it every day. The phenomenon of incorporating open questions into math is crucial to sparking students imagination, and can be used a great teaching tool at any grade level. But what about the basics, the foundations to all math taught early on in students education, isn’t that all the same? If everyone is different, would showing them one way suffice all students? Should we as educators just aim to “suffice” or should we show them many ways and let them develop their own tactics?

Mihallov, D. (2010, May 12). Concrete Math. Retrieved from http://bit.ly/2dLekvP

                What educators ought to do is allow students to build their own foundations early on, believing in the idea that students will be able to develop their own algorithms for the four operations after they have identified the “facts” of math. Educators must first start with having students realize the crucial facts within math operations, specifically the multiplication and addition time tables. Within these facts, educators can highlight key facts, useful facts that will allow students to build a base for their procedures and algorithms. Students must start with the facts, then begin to build their knowledge about the various relationships within the operations, supported by the educators guidance.

                An example of learning the facts, then building onto them would be realization of the commonalities within the multiplication table. If students know that 2 x 3 = 6, then it is possible for them to estimate what 20 x 30 would be. Knowing the simple facts is crucial for a student’s future to build onto their understanding within the four operations. It is important to acknowledge that the age where we as educators rewarded the speed at which students learn and complete the facts is gone. Educators must now focus on being flexible when it comes to students learning the facts, and teaching them about the inter-relations. Too often in the past, students memorized sets of number combinations without really understanding them.

                The future of math is based on educators commitment to showing students all the tools and letting them pick which ones they want to use. Student’s don’t have to use every tactic their teacher shows them, as well as they do not need to use the same procedure forever. Students will often leave behind things they have learned because they do not need them anymore or because they have realized or been shown another way to do it. The image below shows a procedure that helps students add large numbers without the use of a device. The tactic is often called “skip counting”, and is based on the students knowing that a number like 332 can also be shown as 300 + 30 + 2.

                The purpose of this post was to shed light on the fact that math is not the only subject that has rigid rules to follow, it too should be fluid and allow for all students to be able to learn their way and with a better pace. Educators must allow students to do what they feel most comfortable with when it comes to the development of various algorithms and procedures. Educators must take this in stride, so they can show all students that math is sensible, useful and do-able. 

Welcoming a New Math

Unpleasant.

 That is the word I would chose to describe not only how I would view my math experience in primary and secondary school, but it was also how I would describe how I felt when I learned I would be taking a math course in teachers college. “I'm going to be teaching geography, why do I have to learn how to teach math?” is what I was thinking. After two weeks in my math course, I quickly learned that this course is not what I thought it was, and teaching math is not going to be what I thought it was.

                There is a shift happening with how we are teaching students in Ontario and across Canada about math, changes for the good. In general, there seems to be profound focus on how educators are teaching their students math in regards to how their students learn best. I often felt behind the curve while in math class. In secondary school I recall on the struggles I had, most of which I can now relate to how I was being taught math, not the math itself. I am ecstatic to learn that math in Ontario is being shifted towards a more co-operative learning experience between teachers and students. I am even more excited that I will be learning and involved in this shift.

                When it comes down to it, teaching math is being shifted from a primarily “fixed mindset” to what is known as a “growth mind set”. What this means is that math teachers are being asked to think outside the box, or the text book, in order to get their students to learn math in a more tangible, real-world way. A main way educators can do this is focus on more problem solving based activities, questions and exercises that make math more sense, increase mathematical dialogue between students, while promoting more challenging questions and the development and use of a student’s own judgement.

Anderson, M. (2010, March 31). Math Manipulatives. Retrieved from http://bit.ly/2df2GpB

                A key idea that was outlined in the second week of the math class was the use of manipulatives in math. Before, manipulatives in math were mostly associated with struggling students, but that is no longer the case. A Growth Mind Set empowers the use of manipulatives for all levels of student learning as they can create more understanding and student engagement in the classroom.

                Another key idea is that some students and people are inherently bad at math, while some are great at it. This belief is often supported by many and can be routinely seen throughout the media. I was one of those students; I placed the blame on my math class struggles on the thought that I did not get the math “gene”. However, most people’s negative view on math can be broken down to the way they were taught math, a way that did not spark imagination and engagement, a way that would often leave students behind.

                As educators, we must leave behind the way we were taught math in order to develop a better understanding of how our students want to learn, and what the best way for them to learn. Math can be fun and engaging, but only if the teacher makes it that way. 

             The main goal of this blog is to educate the readers about how teaching math is changing, highlighting new ideas that facilitate a Growth Mind Set towards math instruction and learning by ways of useful tips and educational write ups centered around numerous math processes  for students K-8.