"But what does this have to do with anything?"

Demme, Ethan (28 August, 2014). Math Road Sign [photograph]. Retrieved from https://demmelearning.com/learning-blog/welcome-to-the-real-world-math-in-action/

As bane of every Math teacher, and favourite fall-back phrase of every bored student, the above question is no stranger to modern classrooms.

But fear not, fellow educators! No cheeky students will leave you speechless or dumbfounded! Mathematics is a subject that can easily be applied to everyday situations and real life settings. When your students question what good fractions is, or why they have to learn to subtract, you will have plenty of examples to offer - some of which your students may one day secretly be thanking you for!

The best way to help students appreciate the all-encompassing nature of Mathematics is to build these real-life examples right into your lessons. 

Asking a student to solve find 13% of 80 isn't going to excite your students. However, if the same question is modified to "how much in taxes will you spend on the new copy of Super Mario Odyssey ($79.99)?" you'll find students are much more curious to determine  13% of 80.

In other words, engaging students involves providing them with Mathematics problems that are more than likely to occur in their own lives. Any time those real-life scenarios apply to their interests, you've got a class that's twice as motivated than usual. 

So let's take a look at some real life examples of Mathematics that students will find particularly helpful and relevant:

1. Around the holidays, ask students to create a Christmas wish-list with 5 items from Canadian retailers. Students must find out the price of each item, plus tax, and then add the price of these items up to find the total price of their "receipt". Students will be much more interested in calculating percentages when these percentages are of items that they are specifically interested in buying. Instead of listing things that students might like (ie., generic laptop, random video game, etc), allow students to determine those items on their own. It does not matter if the costs of their items vary from that of another students' - they are still learning to work with percentages whether the cost of their item is $20 or $499.99.  Students will be learning how to be savvy shoppers one day, and they might even gain a little extra appreciation for all the shopping their parents will be doing over the holiday season as they see all the taxes add up!

2. Group students into tables of 4-5. Bring in small snacks for your students and act as a waiter or waitress for each table. Students can pay for the snacks using Monopoly money (or another faux currency), but when they receive the bill for their table, all the snacks purchased will be on one receipt. Inform students that they must use fractions or division to split up their bill evenly between all parties at the table, and they also must calculate the change that they will be given based on the monetary notes they use to pay with. Additionally, remind students that they must include a tip of 15% for their teacher (unfortunately also in Monopoly money). This will be great practice for when students get a little older and begin to go out to restaurants with their friends.

3. Ask students to design their dream home. They must create a floor plan of the first floor of the house, and every rooms' perimetre and area must be calculated for their architect's consideration. Inform students that the land they are building their house on is of a certain perimetre and they must ensure that their home fits within its area. Students can be permitted to design any kind of rooms they want (movie theatre, video arcade room, walk-in closet, secret laboratory, etc) as long as it fits in their yard.


Students will be able to recognize that these kind of Math activities are actually "real life" activities. One day students be responsible for their own shopping. They will have part-time jobs (more than likely in retail or dining) that require them to calculate totals for receipts, change given to customers or percentages saved during discount sales. They will visit restaurants, use taxis, receive haircuts, have their nails painted - all of which require them to calculate tips. One day they may be homeowners, deciding whether they can fit a swimming pool or flower garden into a specific area of their backyard. 

And students know this. They will be able to see that these scenarios have practical use, and in their not-so-distant future, these Math lessons will save them from hurriedly searching for a "How To Tip Your Server" video on YouTube as their waitress approaches their table, receipt in hand, during their first dinner date.

When students are able to clearly see how Math encompasses so much of their daily lives, they are far more engaged and willing to learn. So remember to show your students how valuable and useable Mathematics can be. If you're lucky, you might never have to answer "but what does this have to do with anything?" ever again.

The Magic School Bus (1994, September). Make Mistakes [film]. Retrieved from http://www.scholastic.com/magicschoolbus/index.htm

When I was in elementary school, my favourite television show was The Magic School Bus. The show featured a class of 8 young students, a sentient bus with transformative powers, an anthropomorphic lizard and a theme song by Little Richard. Little Richard.

Surprisingly, the best part about this show wasn't any of the aforementioned features, nor was it that awesome Halloween special when the class got trapped in a haunted mansion (a close second, to be sure). The real magic of The Magic School Bus lay in the hands of Ms. Frizzle, the class' fearless teacher and bus driver. Every kid who grew up watching The Magic School Bus wished Ms. Frizzle could be their teacher. Ms. Frizzle made an entire half hour of scientific education the most fun and exciting thing on TV; quite often I found myself "ahead of the game" in my actual science classes at school, because "Ms. Frizzle already taught me that".

The Friz (voiced by none other than Lily Tomlin) certainly did teach myself, and many other "90's kids" about everything from biological symbiosis to the inner workings of the human immune system. But one of the less obvious lessons provided by Ms. Frizzle was that of the value of a Growth Mindset. Ms. Frizzle never explicitly preached to her audience class about fostering a Growth Mindset - in fact, The Magic School Bus aired over 10 years before Carol Dweck would go on to publish Mindset: The New Psychology of Success. However, Ms. Frizzle could often be heard reciting one of her trademark catchphrases, telling students not to be afraid to "take chances, make mistakes and get messy!".

I've long since graduated from wanting to be in Ms. Frizzle's class to wanting to be Ms. Frizzle herself. I've always liked her thematic outfits, outlandish earrings, and absolute gusto for learning. I want my students to be just as engaged as Ms. Frizzle's class (and audience). I want my enthusiasm for education to be just as infectious as The Friz's was to her students. And most of all, I want to be just as encouraging to my students as Ms. Frizzle was to thousands of young children across the world.

I think Ms. Frizzle's challenge to "take chances" and "make mistakes" in education should be applied to the ways in which modern educators approach teaching Mathematics in the classroom. We know that many students are intimidated by Mathematics. Too often they feel pressured to only produce speedy and correct answers. The work that is put into finding an answer is often dismissed; only the final product, and only when produced with accuracy, is believed to be of value. Students may shy away from exploring Mathematics because they feel they are "too stupid" or "too slow" to truly apply themselves.

Take Laurent-Moïse Schwartz for example. Schwartz won the Fields Medal* in 1950, but as a student he was not considered strong in Mathematics because his approach to Math was more slowly paced than that of his classmates. Schwartz believed himself to be "stupid" because he could not solve Math problems as quickly as his peers.  It was not until much later in his educational career that Schwartz realized that rapidity had no correlation to intelligence.

As teachers, we have to remind our students that it is far more useful to think deeply and to fully understand how things relate to one another than it is to simply speed through Mathematical problems. Although producing a quick and accurate answer can be gratifying, there is nothing to be ashamed of when taking one's time to solve a problem. And if that problem cannot be solved correctly, it is no matter of disgrace. Making mistakes and taking educational risks is one of the best ways to learn - as a teacher, I would much rather see my students attempting to find the right answer, and making mistakes while trying, than to see them not try at all.

Students who feel that they cannot do well in Math class because they are "not math people" must be reminded to slow down, and to embrace the fact that things may "get messy" at first. Developing a skill of any sort - artistry, musicianship, or even Mathematics - involves putting in time and practice. Making mistakes shows students where to focus deliberate practice and where they need to take the time to slow down. Teachers ought to encourage students not to shy away from mistakes, but rather to feel comfortable enough to embrace the potential for mistakes and to view them as a natural part of learning.

There's a phrase in Latin that can be applied to this Ms. Frizzle / Carol Dweck way of viewing mistakes. Known as the "felix culpa", the phrase can be roughly translated to a that of a "lucky fall" or "happy fault".  In literature, it is used to describe how a series of mistakes or unfavourable events can eventually lead to a happier outcome. In my future math classes, it will be used to describe the wonderful opportunity to improve that only derives from making happy little mistakes.



*In our Math Class modules for this week, I was amused to hear the Fields Medal likened to that of "winning an Oscar in Math". The Fields Medal actually originates from my hometown; its namesake, John Charles Fields is a Hamiltonian :)

I Love Hamilton Ontario (2017, September 22). An Absolutely Real Photo of John Charles Fields [not photoshop]. Retrieved from John Charles' Fields' diary, I think.

Have you ever watched a movie that employed the use of the "Worthless Treasure" trope? Usually, it goes something like this:

1. Hero fixates on achieving some goal or finding some highly valuable treasure
2. Hero goes on adventure to find treasure
3. Hero finds treasure
4. Treasure is not what is expected; it ends up being some kind of MacGuffin or worthless item 5. Hero comes to realization they didn't really need the treasure to begin with; the "real" treasure was in the adventure of finding such an item
6. Wise Old Man stock character confirms this by saying some variation of "you didn't need the magic treasure to prove you're a hero, the real magic was inside you all along!"



While most film critics would argue that we need to get away from the Worthless Treasure trope, I'd say as educators, we could use a lot more of this particular experience, especially when it comes to Mathematics.

A lot of students unwittingly view themselves as "academic heroes". They've got a treasure to find, and if they don't find it, no one will ever see their academic value.The treasure, of course, is the "right answer". Too often, the value of Mathematic experience is placed on finding that right answer and solving the Math problem correctly. If the right answer can't be found, students believe that all is lost - they've failed their academic quest.

As teachers, we have to remind students that it is the journey, the effort and process of solving the Math problem, that is truly rewarding and valuable. Finding right answers can certainly be gratifying, but if everything is viewed as either right or wrong, much of the value of Mathematics is lost. The hard work that goes into solving an equation, even if the final answer is not quite right, is still valuable. It is this effort, that allows students to find the most valuable treasure of all - that of a Growth Mindset.

Teachers must be careful to avoid praising students who produce correct answers as "smart". When students are told they are "smart", they believe that they have been perceived as clever, and wish to maintain this image. In order to ensure that they continue to produce correct answers, and thus cultivate their image as a clever student, they will shy away from academic challenges. These students are left with the impression that they have a fixed intelligence, and thus feel the pressure to continue to be seen as "smart". They learn to value only the final product, rather than the process of hard work, because they do not see effort as a means to expand one's intelligence.

However, when teachers praise students for their effort and diligence, rather than for some innate acuity, students can see that their hard work is valued. They understand that even if there is a chance they do not find the correct answer, the effort put into finding it is rewarding in itself; practice will allow them to build upon their skills and eventually they will be able to tackle harder problems with greater proficiency. A Growth Mindset is fostered by valuing the endeavour itself and the persistence necessary to expand one's abilities in Mathematics.


Teachers have the ability to play into the "Wise Old Man" trope in this situation. When students are discouraged because they are working hard, but not achieving the results they had hoped to see, we can remind them, "you didn't need the right answer, the math was inside of you all along!". Or something like that.

Welcome back, teacher candidates. Year Two Mathematics is officially underway!
Last year, I related the theme of my blog, the cartoon television show Adventure Time, to my goal of wanting to promote Math as a positive experience for my students. I love how the show puts a positive spin on Mathematics, using it as an expression of awesomeness and a favourite past time of Finn, the young hero of the series. 

I think it is critical for students to become familiarized with the fun and enjoyable side of Math, as Math is often stereotyped quite negatively.

As we have learned in Week One, the general Math Mindset that pervades academic experiences is a negative one. Poor attitudes toward Math, Math Myths, problematic brain growth, and harmful stereotypes have adversely impacted the general public's experience in the field of Mathematics.


The image is actually from a Spanish telenovela, Senhora do Destino. Across the internet, very few people will describe it as an image of Nazaré Tedesco. Instead, it is colloquially referred to as "Confused Math Lady". 

Confused Math Lady literally embodies the two most prominent mindsets that deter students from enjoying Mathematics. It illustrates the belief that Math is confusing and difficult; something that many people are supposedly just "not good at". It also brings to focus the popular, albeit erroneous, myth that "girls can't do math". 

As a young student, I was often exposed to the unfortunate belief that girls cannot participate in domains such as athletics, science or mathematics with the same competence of their male counterparts. In my youth, I assumed that one day the boys in my class would outgrow this mindset and stop teasing girls about what we could and could not do. 

Unfortunately, some myths manage to pervade all ages and genders. In my adult life, I have still witnessed examples of women being discouraged or questioned when operating in the field of mathematics. And both male and female students avoid math as much as possible, because they find it confusing and cannot understand how it will be useful in the "real world". 

So how do we avoid promoting the Confused Math Lady stereotype?

In the video Stanford Math Myths and The Brain 2, Montse says that people have been turned off from Math primarily because of how it is taught. She states that people often describe Math classes as "monotonous, too abstract and not linked to life". To combat this, Montse suggests creating classrooms that treat Math as a "living, breathing subject with lots of ways to access it". Providing students with fun exposure to Mathematics can help to encourage students to practice their Math skills. Many people who find Math "confusing" feel like they are "not Math people" and therefore will never be good at it. These people buy into the myth that Math is only for certain people, when in reality, anyone with a Growth Mindset can become a good Mathematician! When we avoid Mathematics, we do not give the prefrontal cortex in our brains the change to flex its muscles and become stronger when solving Mathematical problems. Just as athletes and musicians must practice to develop their skills, Mathematicians must practice as well! 

Teachers must be sure to provide students with a positive, Growth Mindset-inspired view of Mathematics. They must provide welcoming exposure to Math in the classroom, and seek to illustrate how Math pervades many aspects of daily life. It is also important for teachers to be especially welcoming to female students, who may still be impacted by societal norms and stereotypes that assert that they are better suited to subjects that are more "left-brain" oriented. It is important that young girls see themselves as capable Mathematicians and feel just as welcomed in academics domains as their male counterparts.

When a young woman asks her teachers what limitations girls face in terms of Mathematics, there should only be one answer:

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