One step back and Two steps forward

As this semester comes to an end and we (finally) reach the end of the course, I feel that my thoughts on teaching mathematics hasn't shifted a whole lot. That's not necessarily a bad thing, I just feel that I have already been exposed to many of the ideas brought forth in this course, therefore most of the enlightenment comes from a second glance at mathematics and a different set of glasses (as Dorothy would say). 

One idea I had that was challenged through this course was the fact that the teacher is not some all-knowing being for students to run up to and ask "is this right?" The onus really is on the student to determine if their response to an answer is "right" or not... or even if there is a "right" answer to the question. At least, it should be on the student. 

Also, through this course, we had the opportunity to participate in a math fair. If you had a chance to see me do all those activities (not to mention "practising" aka playing my game at menchies the night before) you would know how absolutely ecstatic that made me. I love games: all the games. By having this math fair we made math fun. I will definitely consider doing activities like this in my future classrooms. You just wait for the day when my students are the weirdos in high school being all like "math is fun!" and having everyone else think they're crazy for thinking that. 

Another idea I took from this course is the importance of making real life connections; making math practical. I think this is crucial if we want to create successful citizens of the world. Seeing my number sense (well, lack thereof) makes me feel like I have a duty to prepare my students better than I was prepared and to teach them practicality with math. Similarly, it is also important to have critical discussions about math. Not only will this be beneficial to their futures, it will also strengthen their connection to the topics and therefore deepen their learning experience. 

At the end of the day I think it is important to remember that math is all about problem solving and teaching math is all about creating a balance. Although all these "new" ideas are truly wonderful, we can't just throw out the idea of formalized testing and using worksheets altogether. We need to create authentic learning experiences that nurture our students' strengths and abilities, plays off of our strengths and passions as teachers and creates the best possible future leaders of the world. 

With this course in my pocket and a whole bunch of resources by my side, I not only feel very prepared to teach math, but more importantly, I feel very excited to get out there and start teaching math. So thank you Ms. (Dr.) Mary Mathematics and good luck with your future baby Einstein; you have been so positive, passionate and enlightening, it has truly been a pleasure. 

Not everything that can be counted counts, 

and not everything that counts can be counted. 

- Albert Einstein

Reviewing Resources

Although I have previously looked through various math curriculum guides along with some resources (specifically math makes sense) this past Tuesday was my first opportunity to compare and closely examine some of the mathematics resources from K-6 and it gave me a lot to consider. 

First of all, I loved the big books for kindergarten and grade one. They are cute and captivating and a great way to introduce math at an early stage. I was a little sad to see that there weren't any big books for grade two or three. 

The math resources that we looked at seemed to reflect the idea that students mature grade by grade. There is an evident jump in language found in books; this is especially evident when going from grade one to grade two. Then, in grade three, students start using text books and by grade five all the fun seems to be gone. There does also seem to be a reoccurring theme of pizza and candy when talking about math... So much for that new healthy lifestyle ideal that schools are supposed to be adopting.

Speaking about the text books... Although these can be a good tool when used properly and not too often, I found that the majority of the questions were close-ended. This type of question is good when ideas need to be practised and reinforced but I don't see it as a useful way to introduce new concepts. Students need to get thinking and relate ideas to real concrete situations, especially ones that can be found in the real-world. 

Also, from experience, I found that a few of the questions to be sort of "trick" questions. For example, today during my observation day, one question asked students to represent a number two different ways but both ways had to use decimals. Turns out they wanted one number to one decimal place (like 1.0) and the second number to two decimal places (as in 1.00). Even I had to ask the teacher about that one. 

Furthermore, I find that some concepts are laid out to be way more complicated than they need to. Like the idea of teaching four strategies to solve a problem and reinforcing the use of each strategy all the time when only one is needed and the others may make things harder for the child. That's may not be the best example, but I still stand by my point. 

I think the main point to take from all of this is to understand and know that there are plenty of resources out there for us future teachers to use but that we are not limited to just these resources. It is important that we use the curriculum simply as a guide and introduce other resources and materials as needed to suit our individual students' interests and learning needs.

The essence of mathematics is not to make simple things complicated,

but to make complicated things simple. 

- S. Gudder

math·e·mat·ics

According to the Merriam-Webster online dictionary, mathematics is defined as "the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations." So it's basically anything and everything to do with numbers, right? But is that all mathematics really is?

When I asked my dad (who, by the way, is a high school math teacher) about what mathematics is, he quite simply told me that it is problem solving. When you do math, you solve problems. And when you think mathematically, it means you think logically; you plan and execute steps that will take you from point A to point B in a logical manner. 

Being my father's daughter, I would have to agree with him. Math isn't just about numbers, it's about problems and solutions. It's more of a way of life than a science or a school subject. Math is more than a text book of equations. 

In 2011, Get Real Math blogged about what it means to 'do mathematics.' They had some really great points which included a quote from Paul Lockhart, author of A Mathematician's Lament which states: 

“mathematics is about problems, and problems must be made the focus of a student’s mathematical life. Painfully and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process of doing mathematics — having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other’s work.”

In a more recent blog post (published in 2013), mathematician and programmer, Jeremy Kun, talked about the myth that math is solving for x. Here, he explains that "the primary skill [in regards to algebra] is in reasoning about complex problems in a principled way." Education.com also talks about what it means to do mathematics, showing how mathematics utilizes science verbs that indicate the process of "making sense" and "figuring out." 

So it seems to me that my dad is onto something... Mathematics is more than its textbook definition. Math is more than numbers. Math is problem solving. Math is life. Don't you agree? 

Go down deep enough into anything and you will find mathematics.

- Dean Schlicter