Like the vast majority of my classmates, I was not looking forward to starting EDBE 8P29 at Brock University. I had previously believed that the last math class I would ever have to take in school was Grade 12 Data Management & Probability, and I was less than ecstatic to discover that this was not the case. Math had never been my strong suit, and although I was never "bad" at it, I certainly did not feel as though I would ever be able to teach it confidently. I quickly decided that my Mathematics class would be my least favourite and most difficult of the semester.

As you may have guessed, I couldn't have been more wrong. And for that, I am very glad. As it turns out, learning to teach math is actually one of the best ways to increase your own confidence in your mathematical abilities! Over the past few months, I have come to view myself as relatively well-informed individual on the subject of Whole Number Operations, Fractions, Integers, Proportional Thinking, Patterning and Algebra, Geometry and Spatial Sense, Measurement, Data Management and Probability.

The most enlightening and comforting concept illustrated in EDBE 8P29 is that everyone approaches math in their own unique way. Just as we are all unique individuals, we all bring our own unique perspectives to mathematical problems. When we solve problems, we often do so in ways that are reflective of our personal creativity. We learn differently, and as a result we discover ways to solve math problems that are different from the ways others may approach the same problem. Teachers must be aware of this when instructing students. Differentiated Instruction is crucial when teaching mathematics. Teachers who focus more on questions rather than correct answers enable their students to learn in an environment that supports their creativity and natural sense of inquiry.

As a teacher, I want to fill my math lessons with open-ended questions that allow for students to establish a sense of engagement and wonder in the realm of mathematics. I do not want my students to feel anxious about right answers or following strict formulas. Instead, I will teach them to look for alternative methods and original solutions to subjects of inquiry. I will provide my students with as many real-world examples of how mathematics can function in the world around them. I will also give students opportunity to participate in the Gamification of math, so that they can experience the fun side of mathematical challenges.

I want my students to feel excited about the possibilities for inquiry that math class provides. When they think of math, adjectives like "boring" or "difficult" will be far from their mind. Instead, they will think of math as an expression of conquest and positivity, much like Finn, lead character of Adventure Time.  Just as I mentioned in my very first post, Adventure Time does a great job of equating mathematics with fun and success. I can only hope that one day I'll hear students using mathematical terms in the same positive way that Finn does. Who know? Maybe one day when I tell my students that I'll be taking them on a field trip to Tim Hortons I'll be lucky enough to hear one of them shout "that's so rhombus!" or "totally mathematical!" or "algebraic!" amongst the usually "yippies!" and "yays!".

Cartoon Network. (2012, January) Algebraic! T-Shirt [photograph]. Retrieved from www.cartoonnetwork.com

• Assessment FOR Learning is the process of seeking and interpreting evidence that can be used to decide where the learners are in their learning, where they need to go and how best to get there. The most common example of this is Formative Assessments that teachers use to determine what students already know.
• Assessment AS Learning is the use of a task/activity to allow students the opportunity to use assessment to further their learning. This kind of assessment usually manifests through self or peer evaluation. 
• Assessment OF Learning describes assessment that becomes public and results in statements or symbols about how well students are learning. It is usually represented in the form of reports, judgements about the quality of learning, and assigned grades.

As a student, my only concerns with assessment centred on Assessment Of Learning. I hardly took notice of formative assessment or peer evaluation. My interest was divided only between scores on test and assignments, and grades on report cards.  This meant that whenever Report Card season crept up, an undeniable increase in anxiety seem to arise. As a high achiever and a confirmed perfectionist, Report Cards represented the totality of my need to be successful. Although I performed very well academically, I always managed to feel nervous about my grades. What if I got a B instead of an A? Did it mean I was losing my intelligence, slipping from my high standards in the previous grade?

When students realize assessment is criterion-referenced and properly spread between Assessment For, As and Of Learning, the pressures surrounding assessment can be reduced, and students can avoid some of the anxiety that it entails.

In terms of Mathematics, teachers sometimes need a reminder that there is more than one way to solve a problem mathematical equation, and therefore more than one way to assess students. Students and teachers can sometimes find themselves focusing too much on the “right way” or traditional way to solve a problem, when in reality, there are almost always multiple ways to arrive at an answer. Teachers should especially keep this in mind when assessing students’ work. If a student’s method for solving a problem differs from their own, it is not necessarily wrong. It is important to study the entire work involved in a student’s solution, rather than just marking the answer as “right” or “wrong”. Often, small errors are made that effect the student’s final answer, even though the student understood the processes and concepts necessary to solving the problem. In cases like these, students still demonstrate an understanding and/or application of Specific Curriculum Expectations, and thus it is important that they assessed with more than just respect to Assessment of Learning.

This motivates me to actively avoid ever giving a student a "zero" when they solve problems in math class. As long as the student shows their work, I believe there is opportunity to discover what is right about the student's wrongs.

One of the highlights of this topic was the in-class mini lesson provided by two of my peers this week. May and Kaytlyn created a very helpful interactive lesson about Data Management using an app called Nearpod. I loved this app, because it allows teachers to use tech in the classroom, in a way that creates a collaborative learning environment for students. Not only did May and Kaytlyn teach us about the Measures of Central Tendency, such as mean, median, mode and range, but they also taught us how to teach it. Nearpod is not necessary for teaching these concepts, but as my two peers demonstrated, it can be very helpful when doing so. I would love to create my own Nearpod lesson, similar to theirs, when I teach Data Management to my own students.

Our discussion of Probability also provided me with inspiration for my own teaching. My instructor, Sue, shared the brilliant idea of having students directly interact with theoretical and experimental probability at Tim Hortons! During Roll Up The Rim season, teachers can take students on a field trip to a local Tim Hortons where they can compare the results of the theoretical and experimental probability of winning a prize in Roll Up The Rim. As a teacher, I would buy every student in my class a hot chocolate, and then have them roll up their rim. The actual number of students with winning cups could be compared to an estimated number of winning cups determined by the class, based on the contest statistics provided by Tim Hortons. After comparing the class' winning number of cups to what Tim Hortons asserted would be the average number of winning cups, students would be able to recognize that theoretical probability represents what we think will happen based on statistics and that experimental probably represents what actually happens when we carry out the event. If my previous experiences with Roll Up The Rim serve as any indication, chances are we will have two very different results!

Nystrand, Shawn. (2011, March, 26). Canada's New Motto [photograph]. Retrieved from http://bit.ly/2gQsUmb

Despite the fact that some students may be left disappointed when they don't win a Napoleon Gourmet Grill (oh wait, that's me), I think they will still really enjoy the outing to Tim Hortons and the chance (ha ha, probability is a great unit because there's probably going to be many opportunities to sneak in a pun or two) to test out experimental probability. And the added bonus of a tasty hot chocolate doesn't hurt either!

How many tools can you think of that help us measure?

To reinforce this concept, we played the "Mini-Metric Olympics". This involved the enjoyable experience of playing "sports" such as Paper Plate Discus, Paper Straw Javelin, Cotton Ball Shot Put and The Big Foot Contest. These "sports" made measuring distance and size into a fun and competitive activity. Yet again, the Gamification of mathematics proves to make simple concepts, like measurement, not only engaging to students, but it also makes these concepts applicable to real-life situations.  I can't wait to host my own Mini-Metric Olympics with my own students, as I love the interactive and collaborative learning environment in creates.

AIMS Education Foundation. (1987,  January). Mini-Metric Olympics [worksheet]. Retrieved from http://www.nclark.net/mini-metrics.pdf

Measurement can be made fun through more than just the Mini-Metric Olympics, however. As a class, we also learned about more measurement-themed games such as Area Dice and Measurement Jeopardy. We also discussed the different ways in which measurement can be interpreted. Remember when I asked you to picture tools that help us measure? We discussed many tools - everything from the humble 30 cm ruler to a high-tech galvanometer. But what if we move beyond these tools and think outside the box?




As Drew Brees and Elmo point out in the video above, you can use anything to measure ... even a potato! When young students are first introduced to measurement, this concept of open-ended measurement can be extremely helpful. Students can learn to use everyday objects to estimate the length, width or height of any object, including themselves! Measurement should never be introduced as a restrictive concept with limiting rules. Instead, using open-ended and relative measurement, as well as gamification can help students to view measurement as a site of wonder and inquiry.

I absolutely lost it in class this week when this video was played during our lesson: I believe James Blunt's Your Beautiful was released when I was 15 years old. At the time, I believed it was the sole most romantic song ever. Never did I guess that I would rediscover my love for the sappy ballad nearly 10 years later, in math class, no less. And yet there I was, on Monday night, learning about Geometry and Spatial Sense and absolutely cracking up over "My Triangle", Sesame Street's brilliant parody of my former favourite song. Sesame Street has a wonderful method of pairing pop culture with educational concepts. Occasionally the show will feature a guest star, usually a popular actor or musician, to help explain principles of language, social studies and mathematics to very young children. In James Blunt's feature, a very simple geometric concept, that of a triangle, is sung in detail to children. Triangles may not seem like the most interesting concept in the world, but when they, and other geometric concepts, are addressed in a fun way, such as through song, kids become enthusiastic about learning. In class, we applied this principle to other topics related to Geometry & Spatial Sense. Using marshmallows and toothpicks, we created geometric shapes like rectangular prisms, cubes and pyramids. This kind of activity gives kids hands-on experience with geometry while engaging them through the novelty of creating 3D objects and solids using fun materials.

Inrig, E. (2016, November 7). Building Shapes with Marshmallows [photograph]. Retrieved from my iPhone.

When students are able to put together the elements of a solid object, such as the sides (toothpicks) and vertices (marshmallows), they gain a more thorough understanding of geometry.

We continued to explore other ways of making geometry fun and exciting. Gamification of geometry can be achieved through games like Tangrams and Shape Battleship. I personally enjoyed guessing shapes using Tangrams and sinking rectangular prisms on a grid while playing Shape Battleship, and I'm sure young students would love to do so as well.

I hate to admit it, but prior to this class, I very seldom thought of patterning and algebra as related. Patterning, to me, was about repeating images and numbers. It was a visual arrangement; a part of mathematics that was tangible and easier to understand than algebra. Algebra was mystery. It was about solving unknowns, and it was usually a challenge. Algebra looked like x's and y's. It looked like an extra complicated equation, and it was not visually friendly the way patterning was.

I'm beginning to develop a new-found appreciation for math-based storybooks. Initially, The Hershey's Milk Chocolate Fraction Book left a bad taste in my mouth, pun very much intended. I found the book to be rather vapid, thanks to its general lack of a plot. This week, however, we read another mathematically-themed book, If You Hoped Like a Frog by David M. Schwartz. This picture book revealed the sweeter side to math stories. Imaginative pictures made the book engaging, even though it did not contain any tangible plot. Schwartz's creative analogies made the concept of proportional thinking relatable for children. Kids can wrap their heads around ratios when they are likened to scenarios that occur in their daily lives.

Once kids have a basic understanding of number sense and numeration, and particularly of ratios and proportioning, they can begin to take on open ended mathematical puzzles. In class we took on the question of a Giant's Height. Armed with only a gigantic hand print belonging to a "giant", we were tasked with solving the mystery of how tall such a giant would stand. The best part of this inquiry is that there is no official "right answer". Nor was there any one way to go about solving it.
In my table group, I discovered that we all had different methods of trying to determine how tall the giant could be. I was most interested in using statistics to determine the height. I believed that if we compared the height of the giant's hand to the statistical average of a human male's hand, we could use the ratio to determine the overall height. My tablemates chose to solve the question differently, by actually measuring their own heights and comparing it to the hand of the giant. Once again, I am reminded that there are many ways of determining the answer to a problem. Even when it comes to proportions, your method of choice is only proportional to others'!

Integers was the topic of study in this week's math class. Although dealing with negative numbers can sometimes be stressful to some students, we discovered several ways to make adding and subtraction with positive and negative numbers fun. 

Fractions don't seem to be the most popular topic with students, and I can certainly relate. It's not that I find fractions to be extremely challenging, but rather that I do not find them to be particularly engaging.  For whatever reason, fractions often felt abstract to me, and I did not enjoy comparing them. As many young students will affirm, it is sometimes tricky to envision the difference between fractions with uncommon denominators, such as 4/5 and 5/9.

Amos, Evan. (2010, August 28). Regular Hershey's Bar [photograph]. Retrieved from http://bit.ly/2eL8pEF

In class we discovered some ways that can help students visualize fractions more readily. In order to introduce the concept of fractions in a practical and relatable way, it was suggested to read a book about fractions. We listened to a YouTube reading of The Hershey's Milk Chocolate Fractions Book which illustrated the use of fractions using the ever-popular chocolate treat.

There were two themes to our learning this week in math class. The more obvious theme was Whole Number Operations. We (re)learned how to add, subtract, cross multiply and complete long division. While these operations probably should have been easy to complete, I'd be lying if I said I didn't quickly Google how to properly do long division. It's been a very long time since such an equation had been presented to me....without the aid of calculator. Reviewing these whole number operations was rather beneficial in my case, as I certainly needed the refresher!

BH, Richard. (2011, October 2). Timbits [photograph]. Retrieved from https://www.flickr.com/photos/rbh/6624232893

Here's hoping you read the title of my blog, "Mathematical!" in the voice of Finn, from the cartoon Adventure Time. One of my favourite things about the quirky kids show was its use of math related terms as synonyms for "awesome" or "cool". Too often kids are led to believe that math is stuffy and boring, and something of a chore. I personally felt this way throughout my high school career. Although I was by no means a poor math student, it was the one subject that I felt did not come naturally to me. Math seemed like an intangible burden, one that I would never be able to truly divine. I felt into the popular mode of thinking, believing math was for mathematicians, but certainly not for me. It wasn't fun and it certainly wasn't worth getting excited about.
When I first caught wind of Adventure Time's 12 year old hero shouting phrases like "mathematical!" or "that's so rhombus!" as he defeated villains, I couldn't help but love the quiet suggestion the cartoon was making. By associating mathematics with Finn's heroics or cool discoveries, Adventure Time was subtly hinting that maybe math wasn't so drab after all. Perhaps it could be fun, and even useful.

Glarbinator. (2013, December 4). Mathematical Finn! [digital drawing]. Retrieved from http://fav.me/d6wq85n

By the time I left my first 8P29 class, I was determined to adopt Adventure Time's attitude toward the subject that I had once snubbed. Mathematics didn't have to be intimidating or difficult. It also didn't have to be about right or wrong answers. Sometime the questions asked were the most important aspect of math themselves.
I'm sure you all saw my little doodle of the stereotypical mathematician verses ourselves when our instructor held it up for the class. But what you didn't see were the changes I made to the drawing as the class progressed. Initially I had drawn the image of myself frowning; my thought bubble filled with unorganized numbers and symbols. As open minded as I wanted to be about mathematics, I certainly didn't think I'd ever be happy about solving a math problem. But by the time my paper had been held up for you to see, I'd already made some changes:

Inrig, E. (2016, September 12). Mathematician vs Me [poorly drawn scribble on paper]. Retrieved from my binder.