"What was your greatest 'learning' this semester with regard to teaching children mathematics? How has your thinking shifted?"

I have learned much throughout my math methods course; however, I have to say that my greatest 'learning' in regard to teaching mathematics has been centered around student "answers". Although there is typically a single "correct" answer to many problems in mathematics, teachers in today's schools need to be accepting of the numerous routes through which a student may travel to collect the "ideal" answer. With that being said, teachers must stop explicitly telling students how to go about solving problems, and instead allow them to meaningfully engage with the mathematics presented to them. After all, it is the student who plays the most significant role in their understanding of mathematics; teachers should facilitate this feat, but in no way shape or form preach the "only" way of doing something!

This notion has taken me by complete surprise; so much so, that when I reflect upon my grade school years they seem so confined it's troubling! Having now completed my observation days, I have been reminded to the diversity of learners that once sat beside me, and now can easily see where mathematics instruction had failed them. At that point in time, teachers were so caught up on the "right" way of doing math, that students who devised the "correct" answer but whose workings did not correspond to the answer key were wrong! Luckily, I was not one of those students, but now believe it was those students who were the ones with an enhanced understanding and appreciation for math, which sadly, was never fostered.

As I aspire toward my future career, I feel it necessary to make the connection between my new knowledge and previous experience.  To ensure the success of my students in the exciting field of mathematics, I hope to stimulate their interest in learning through creative instruction and relateable content; most importantly, I will allow my students to construct their own understanding of mathematics through which ever means is best suited to them!

NL Curriculum Resources

Last week, I was provided the opportunity to peruse the Newfoundland & Labrador mathematics curriculum resources; this experience was rather unique considering this had only been my second interaction with the the provided subject-specific curriculum supports as our program seems to have a particular focus on the curriculum guide itself. 

In my rotation through the seven tables displaying the kindergarten to grade six resources I was taken back by not only the amount but also quality of the materials which teachers in my province are provided with. All texts, at a glance, seemed to be quite comprehensive and provided ample student practice. Furthermore, there was a wonderful selection of mathematical children's literature provided for students in kindergarten through to grade two. 

After completing this session, I do however have a couple of questions that I forgot to ask my instructor. Firstly, stemming from my last point, I would really like to know why students in grades 3 to 6 were deprived of children's literature dealing with mathematics; I feel that students in these grades would benefit tremendously from their interactions with literature of this sort, as it would foster an appreciation for both mathematics and literacy. In addition, considering teacher's are provided with such great "paper" supports, are teacher's provided with the manipulatives that are being advertised in them? 

To extend this experience further, I think it would be eye opening to have the opportunity to review supports provided to teachers in other provinces or even states. As I do commend my own province now, I think an experience such as the one listed above may persuade me to believe otherwise!

Connecting this experience to the ideas presented in Chapter four of our text, I like to believe that these resources are useful to both students and teachers. Through my exploration of the grade three mathematics curriculum document in the class prior, I discovered that the document has been appropriately re-vamped to include more inquiry based practices. Under this assumption, I feel that the individuals who select these classroom supports have done a great job in choosing resources that will foster this particular type of learning, especially in the new resources available for students in kindergarten through grade two. Furthermore, another critical topic explored in chapter four was the notion of the distinction between drill and practice; as I explored these resources I was pleased to discover that even the old texts avoided "drill" and seemed to provide students with diverse problems to exercise their learning. 

YouCubed

YouCubed, the "revolutionary" math education project will hopefully live up to all it has advertised. At a glance, Jo Boaler, the leader of YouCubed, appears to be an expert in the field of math education and has developed this project as a means to "better teach math that will lead to math empowerment, rather than math failure", and to "allow students to see that math will help them in their lives and work". 

After hopping on to the "path to better understanding", I can see easily see how the four proposed components of the YouCubed project will be beneficial for both teachers and parents. Starting at "Big Ideas", Boaler plans to provide resources that will begin to get children excited about mathematics, which I believe to be a fantastic starting point for a project of this nature. Furthering their interest, in "Content and Tasks" she plans to clarify important mathematical concepts and provide "engaging" experiences for students in school and at home. "Math and Innovation" is meant to share interesting modern math problems that people are involved with in everyday life; these examples are intended to make math relateable to students and prove to them that mathematical knowledge is useful. The final component, and my personal favorite, is "Tools for PARENTS". Having worked with countless children and their parents, I am well aware of the stress endured by parents in attempting to help their children with homework. The resources that will be available on this site will hopefully alleviate most of these inconveniences, and allow parents to foster rather than hinder their child's learning. 

Aside from the framework, after perusing the papers on this site I highly admired Boaler's opinions on the importance of changing attitudes and disociating math with speed. In one particular article, her research has proven that all children are capable of exceptional performance, assuming they sport the right mentality; students need to know that they have potential, and understand that everyone learns from their mistakes! Equally important, there is no doubt that mathematical ability has historically been linked to speed. Boaler presents that speed "damages" math performance and thus should be highly discouraged. 

The methods of math education has changed dramatically in recent years. The inquiry based, YouCube project, when up and running, should prove a great resource for teachers and parents. I have "joined the revolution" and hopefully you will too!

Join here...

What is Mathematics?

There does not exist a "certified" definition for mathematics. In reality, Mathematics can be defined as any number of things, which are totally dependent upon the resource from which the definition was derived.

In the article "What is Mathematics?: An Elementary Approach to Ideas and Methods" by Richard Courant and Herbert Robbins, Mathematics is defined as "an expression of the human mind reflect(ing) the active will, the contemplative reason, and the desire for aesthetic perfection." This definition, though somewhat abstract, provides a fantastic starting point for my beliefs in mathematics. 

Further defining Mathematics in relation to human beings, Reuben Hursh in his book, "What is Mathematics, Really?" explains that Mathematics "must be understood as a human activity, a social phenomena, part of human culture, historically evolved, and intelligible only in a social context." This statement, being valid in every respect, communicates that Mathematics is simply a product of the human mind, not something that was handed down from above; it is an understanding and knowledge base that is attainable by everyone.

In contrast to those above, Google defines Mathematics as:

math·e·mat·ics

maTH(ə)ˈmatiks/

noun

1. 1.
2. the abstract science of number, quantity, and space. Mathematics may be studied in its own right ( pure mathematics ), or as it is applied to other disciplines such as physics and engineering ( applied mathematics ).

This definition is without a doubt "technical", and far less abstract than those above, but in my opinion is still correct. Google defines Mathematics as what we, as human beings, have constructed Mathematics to be, in addition to how use these constructs. I am especially drawn to this definition for I feel it is simple yet concise.

If we were to merge these definitions, I believe one would have a relatively good understanding of what exactly Mathematics is. Unbeknownst to me, I discovered that the Newfoundland and Labrador curriculum has adopted quite an eclectic view of Mathematics. In the curriculum framework, Mathematics is defined as being " one way of trying to understand, interpret and describe our world." It continues to state that, "there are a number of components that define the nature of mathematics ...[including] change, constancy, number sense, patterns, relationships, spatial sense and uncertainty." Most notably, the document concludes to state that, "students learn by attaching meaning to what they do, and they need to construct their own meaning of mathematics."

So what is Mathematics? As stated in the curriculum guide, Mathematics is defined by an individual as what they should have constructed it to be! I have an eclectic understanding of Mathematics, and believe that Mathematics is comprised of several distinct elements that have been constructed by the human mind. Similar to Hursh, I believe that Mathematics is very much a "social phenomena" that will continue to evolve and change in the future!

Are Schools Killing Creativity?

http://www.youtube.com/watch?v=iG9CE55wbtY

Sir Ken Robinson seems to think so! In this comedic TED talk, Robinson does a marvelous job putting into perspective the negative influence public schooling has on creativity. Without revealing too much about this lecture, I would like to comment on his closing statement about "our task" being "to educate their whole being".  This statement is valid in every respect. As a prospective educator, I believe it is important to be aware of the diversity of students that I will encounter within my classroom. Each of these students will have aptitudes for a number of different things, some of which may or may not be recognized as an academic "subject"; for that reason alone, I feel it is equally important that I cater to the learning needs of those individuals as well. Furthermore, I am a firm believer that an "education" is not merely a degree or diploma that qualifies someone to work in a particular field, rather a culmination of knowledge that relates to every aspect of that individuals life. Under this assumption,  I cannot stress the importance of the education of what Robinson has termed the "whole being". This video is definitely worth a watch, it is both funny and eye opening at the same time; I just hope you enjoy as much as I did!

Math Autobiography...

As a future math educator I feel it is extremely important to reflect critically upon my own early experiences with mathematics. From what I can remember, which is very little, I assume that mathematics did not cause me any stress, considering I am unable to conjure up any specific traumatizing or delightful memories!

Mathematics definitely did not have an "appearance" in my classroom throughout the primary and elementary grades. Math consisted of a text book, worksheets, and numbers, all of which were safely stored within my desk until needed. Taking this into consideration, I feel as though specific math memories easily evaded my long-term storage. The only memories that I do have, come from elementary, and don't quite fit into the "best" and "worst" memory categories. A memory that I would recall as being good, would be using tangible blocks to explore certain math problems; worst, would definitely be my hatred of waiting around for my classmates to finish assigned work as I seemed to always be the one to finish worksheets and tests first. These memories make me want to become the teacher who makes math a memorable subject for students. I hope to instill a "liking", at the very least, for math in children, which will hopefully flourish throughout their schooling. 

I think I was "good" at math. I recall doing very well on assignments and tests, which were reflected on my report cards. I do however, remember being not so "good" at particular kinds of problem solving which must have persisted into my university career, as I was have always been challenged when proving abstract theory. The teachers who assigned my marks, I believe generally lacked an interest in math. There is not a single person who comes to mind who had an aptitude for math or even teaching it. Their role was simply to work through the text, assign the exercises after each lesson, correct them upon completion, and to develop a formal test. Assessment always came in the form of a test, which consisted of a sampling of exercises from the text, in addition to the occasional bonus question to challenge students of greater ability. 

Math in high school was without a doubt my favorite subject. I had a fabulous teacher, who was genuinely excited to teach mathematics. I felt appropriately challenged in my courses, and admired how she incorporated math related "everything"  into our learning. My love of math was nurtured in university but eventually faded out. I had thought about completing a math degree and thus completed Math 1000, 1001, as well as Math 2050 (Linear Algebra) as an elective. I registered for Math 2000 a couple of times, and had dropped the course each time due to instructor complications. 

I still enjoy mathematics and love to engage children at my workplace as well as those of my friends and family with their homework. I take pride in sharing my mathematical knowledge and am still intrigued by it's complexity. Sadly, I do not engage with mathematics in my own life in major ways but hope to in my future. I actually look forward to manipulating the curriculum and discovering techniques which will engage my students!

Welcome!

Welcome,

The purpose of this blog is to allow me to share my opinions and experiences in mathematics with readers. Throughout my blogging I hope to explore my own relationship with this subject, in hopes of becoming a successful math educator.

Enjoy, Mitchell.