A Broadened Perspective of Mathematics

As my primary/elementary mathematics course comes to an end, and I am only months away from my internship, I am left to think about what I have learned about teaching math. One thing is for certain- when I started this course, I was pretty nervous. If you've read my first blog post, that was probably pretty obvious! It wasn't long into the course though, that my anxiety started to melt away. The kind of experience and learning environment that we were give was a very relaxed, pressure-free, and co-operative one. I quickly realized the benefit in providing this kind of environment for students. Without the pressure of time constraints, being called upon in front of everyone, or being singled out, I started to gain the confidence that I needed to really engage with the mathematics problems placed in front of me. If I, as an adult, was able to benefit from such an environment, than I am sure that children would also benefit from it.

 I also began to see that it is not always about getting the "right" answer. Often times in math, I spend so much time worrying about whether or not I am getting the right answer, that I won't let myself try new strategies, and my anxiety over getting the right answer kills the confidence that I need to give it my best shot. I have to admit, that when I first heard of the idea of not telling children whether they are wrong or right, I was a little confused. I mean it's math after all, isn't there always one right answer?? This course quickly allowed me to see that in fact, this kind of thinking can destroy a child's chances at succeeding in math. Even within our classroom of adults, it was amazing to see how when the first volunteered answer was not acknowledged as being right or wrong, how many more people went on to volunteer their responses and ways of thinking. I began to think of all the children whose ways of thinking and personal strategies will never be attended to, because when one "quicker-thinking" child volunteers the correct answer, the search for answers ends.

Above all else, this course has taught me something that is extremely profound to me. I do not need to be an expert in math in order to effectively teach math. Coming into this course, I thought that I had to have all the answers, all the time, in order to teach my students math. In fact, this way of thinking was completely wrong. First of all, even if I did know the answers to everything myself, my way of arriving at those answers is likely going to be vastly different from that of my students. It is more important for me as a teacher to familiarize myself with the various strategies, ways of representing, and ways of engaging with math problems, than it is to consume all of my time with "arriving at correct answers." In my classroom, I want to reach as many students as possible, and to open the avenues to success for as many as I can. The key to doing this lies not in my ability to give students the right answer, but in the diverse ways in which I can guide my students to come to their own conclusions.

My Thoughts on the K-6 Mathematics Resources

      

K-6 Mathematics Resources

     During yesterday's Mathematics class, we were given the opportunity to explore the K-6 Mathematics resources. I had only see bits and parts of these resources before this class. During my observations days, I was able to see some being implemented in the classroom on occasion. Nonetheless, my experience with these resources has been far from extensive, so it was nice to have some time to get all seven levels in my own hands, and check them out for myself.

  

      I was really impressed by the primary resources. I found it neat that they used so many colours, patterns, photos, and illustrations that children could really identify with, and would be interested in. The building of number sense in the primary grades is extremely important. Without adequate number sense, students will be lacking the necessary foundation that they need in order to acquire further mathematics skills. I think that the emphasis on visuals in the primary resources would really help with this. If children visually see "two ears", "two feathers", and so on, as in some of the books that used animal references, they will be continually adding to that picture in their minds of numbers and the various contexts in which they can be used. I also think that presenting mathematics in a real-world context will aid tremendously in fostering problem-solving skills. If a child can solve a problem in one context, but cannot take that same knowledge and apply it a novel situation within the real world, then what is the value in knowing how to solve that initial problem? A huge part of ensuring that children can apply Mathematics in a real-world situation, is it present it this way in the first place. After seeing the language, pictures, and format of the primary resources, I do feel that this has been taken into account.

      As we worked our way up in grade level, the main thing that stuck out to me was the dramatic change in the sophistication of the language used in the resources. After grade two, the language seemed to take a dramatic leap. I do believe that the synthesis of Language Arts and Mathematics is important in fostering a holistic and translatable understanding of numerical concepts. However, I couldn't help but feel a sense of worry and panic for the children whose language skills might be a little behind others. It hardly seems fair that a child could be set up to fall behind in Mathematics as a result of any language deficiencies. I feel that there could be a greater effort to include multiple presentations of the concepts. I'm not suggesting that the use of language be completely halted or diminished, but I am suggesting that the use of visuals be maintained, regardless of the increasing grade level. 

      We would never walk into a classroom with twenty pairs of shoes, all in size 5, expecting all the children to fit into them because they are all the same age. So why then, do we walk into classrooms with resources and outcomes, assuming they will "fit" all children, because they are all the same age? It would be near impossible to create individualized resources for every single student. I am completely aware of this. However, I do feel that the resources that are out there should try and present the concepts in as many ways possible, so as to include more and more types of learners and interests, giving all children the best possible chance at learning. With that being said, the best resource we have as teachers is ourselves. We need to be constantly connected to, and in tune with our students' needs. Regardless of what these resources have to offer, we should not feel limited in our abilities to reach every single child in our class. We are not limited by resources- we are limited by our creativity. So, if Jimmy doesn't seem to be responding to one particular method- toss it! I apologize for the cliche, but "the world is our oyster". Today's technology allows us more information and resources at our fingertips than ever before. It is our responsibility as teachers to get out there, get to know our students, and find a way to make it work. The success of our students depends upon it!

My Thoughts on YouCubed

       During our last Mathematic's class, we were given the opportunity to go to http://www.youcubed.org/ and explore this website and its potential benefits in the classroom.

        As a future teacher, I am always excited to add new resources to my bank of knowledge, in hopes of making the task a little easier in the future. With that being said, not every resource is a good resource. There are some bad ones out there- I know. I've seen my share. So how does YouCubed compare?

        The first thing I discovered about YouCubed is that it is a nonprofit organization, offering free and affordable math resources for both parents and educators. Right away, I see this as being commendable. I think it is so important that Mathematics resources be made accessible for everyone, and that the lines of communication be kept open between educators and parents, so that the children are getting the most of their experiences- at school and at home. As an educator using this resource, all you would need to do in order to share this resource with parents is simply give them the link.

       As I continued to explore the site, I was continually impressed. This entire website functions on the assumption that all children have the potential to be exceptional at Math. Their goal is to make students, educators, and parents realize this. This is a phenomenal and innovative approach towards Mathematics since, I believe, students will only ever achieve what they truly believe they are capable of achieving. We've all been there- Mathematics has been given the rep of a terrifyingly scary subject, that only the "top students" in the class can do well in. The rest of us, well...we just give it a mediocre shot and wait until those others are finished and can help us through. But, what would happen if this myth was completely dispelled, and students began their Mathematics career hopeful and excited for what they could achieve? YouCubed believes the results would be a revolutionized view of Mathematics, with growing numbers of children succeeding. 

     It is clear that YouCubed is on to something. As I watched the video of a group of children working with their techniques, I head them say things like "math is fun", "math is like a game", "math can be like a story"...how often have you ever heard children refer to math in these ways? Throughout the entire video, the children were interacting, smiling, and, believe it or not, laughing. 

     One aspect of the site that I found very intriguing is when they use modern, well-known companies like Google, which I would assume most children are  quite familiar with today, and show how these companies use Mathematics to solve problems everyday. How often does a child think about the Mathematics that is happening behind their everyday searches? What better way to motivate students in math than to give them relevant, modern-day problems that they can relate to? Technology has become such a huge part of children's everyday lives today, that Mathematics being put into this context could certainly be a revolutionary motivator.

     Throughout the remainder of my exploration, I found more and more potential in this site. The are so many games found here that teach everything from fact trees, multiplication, prime numbers, and so much more. Using these games, I feel that my students could begin to see that Math is not scary. Math can be "fun", "like a game", "like a story", and, most importantly- achievable. 

     At the end of the website, YouCubed states that they will be fully operational in a few months. I, for one, cannot wait to see what else YouCubed will have to offer. I will most certainly be implementing this resource in my own classroom someday, and at home with my daughter. So, do yourself, your students, and your own children a gigantic favour, and check YouCubed out!!

Andrea 

       

What IS Mathematics Anyway?

What IS Mathematics Anyway?

            What is Mathematics? For this particular blog, we were asked to think about and research this very question. I thought about my answer for a very long time, and came to realize that the answer is actually quite complex.

            Before doing any research, I wanted to think first about what Mathematics means to me. If I were asked to write my own 'definition', I decided that it would probably go like this: Mathematics is a logical system of numbers, patterns, formulas, rules, and equations, that help us to communicate and problem solve. I am completely aware that this is a fairly lacking definition, and it is quite possible that this does not even come close to the true definition of Mathematics and what it entails- as I mentioned in my first blog post, Math is kind of a 'scary' matter for me. My relationship with Math could be described as a person about to ride a terrifying roller coaster: you are frightened to try it, but deep down, you know that you will enjoy it. So, after some coaxing, you give it a shot. 

        The first thing that I found when I googled "what is mathematics?", was a book written by Robert Courant and Herbert Robbins, titled "What Is Mathematics?" Well...that book would certainly come in handy right now wouldn't it. Unfortunately, I do not own a copy. So, on to the next search result!

        Of all the sites that I found which tried to neatly define Mathematics (there are a lot- evidently, this is not an easy task), the 'definition' that I found to be the most precise came from www.thefreedictionary.com . This site defines math as "the study of measurement, properties, and relationships of quantities and sets, using numbers and symbols." Okay, so I wasn't that far off in my attempt to define math! According to this site anyway. I like this site. 

      More important though than a definition of Mathematics, is what it actually means to do Math, or to think mathematically. I think that for a lot of people, including myself, when we think of someone doing math, we think of a person sitting to a desk with a pen and paper, head bowed down, scribbling and erasing frantically, trying to solve a given problem. I believe that much of this comes from the pressure that teachers often put on students in this subject area. We have talked a lot about "Mad Minutes" in our Math classes lately, and I have to admit, I nearly panic just thinking about being placed under this kind of pressure. Imagine then, what this can do a seven or eight year old child. It is largely believed, and by me as well, that Math takes an enormous and pressure-laden amount of thought and effort to do any kind of math. If I manage to take a step outside of this mind frame though, I can quickly see that this is not always the case. I have been exposing my daughter to math from the first time that I counted her tiny toes. I am doing math right now as I glance at the clock on my computer screen, and calculate many hours of sleep I think I will manage to get tonight. I know deep down that to think Mathematically does not always mean using long and complex equations, following an exact and precise set of steps, just like a person knows deep down that the roller coaster will be fun. However, for me, Math comes with a sort of stigma. That stigma is that if you do not follow the exact steps, to get the exact answer, in exactly the 'appropriate' time frame, you are not good at math. 

      I hope to, and am confident that I will, learn a lot more about what Mathematics is, and what it is to think mathematically, throughout this semester. However, in closing, I would like to add these thoughts: in order to teach children not to fear Mathematics, but to embrace it in their everyday lives, we must change the way that we teach and assess Mathematics. I believe that children only truly learn when they are able to retain a concept, gain and store the accompanying knowledge, and then, most importantly, be able to apply this knowledge to a completely novel situation. We cannot expect children to use a concept in the real world, if they are never taught in a real way. 

     Lets let children see how these concepts work in an authentic and hands-on way, rather than drilling into their heads a formula that looks about as simple as yX2=500b+3KX-40XYZ=500.

Andrea

       

 Do Schools Kills Creativity? :

A Response to Ken Robinson's TED Talk

           When our math prof first showed us the video of Ken Robinson's TED Talk, I felt a sigh of relief. I thought "ok, this math prof isn't going to be a one size fits all type of prof. She isn't going to put that kind of pressure on us. She thinks differently". I mean, how many math profs do you think would show a video that actually questions the highly-valued hierarchy of our public education system, in which math has been sitting pretty for all these years. How many math profs would plant this seed of doubt in their students' minds? By the end of the class though, I began to think a little differently. Maybe she isn't asking us to question how important math actually is. Maybe, she is asking us to look at math in a new light- in a way that, dare I say it, actually links math to the arts.

         Robinson makes  a lot of brilliantly bold statements in this video that call for, what I believe to be, a much-needed second look at the skills and talents that we value in our education system, and those that we debunk as "silly hobbies that will never get you anywhere in life". It sounds harsh when you put it that way- but often, that is the sad reality. Robinson really hammers this idea home when he states that in most public schools, the amazingly talented and successful Gillian Lynne, would have been "put on medication and told to calm down." Maybe a little crude, but the truth often is. 

       As the mother of a five-year old, I like to think that I have been pretty 'up' on a lot of the literature out there, that "guides" parents in nurturing a child's mind. It has been my experience that much of this literature focuses on imagination, fostering creativity, ample opportunities for exploration and discovery, and, first and foremost, play. This is all fine and wonderful, and I would consider myself to be an advocate of all of the above. However, I can't help but wonder if all of this nurturing of the imagination might be in vein. Will she wind up being reprimanded and told that she is not "focused" or "compliant" enough if she puts to use this same imagination that I have spent so much time encouraging? Or, to paraphrase Robinson: will she be told that she is wrong if she "takes a stab at it", like the little boy in the Christmas play who gives it his best shot and, in a delightfully oblivious manner, says "frank sent this?" 

      Another of Robinson's superbly-articulated ideas comes from his statement that our society is still engulfed in an industrial-based revolution in which the most highly-valued subjects, are those that get you the highest-valued jobs. However, it does not take a genius to figure out that times have changed since the 19th century. So why then, as Robinson seems to be asking, has the hierarchy not changed? I am not in any way saying that mathematics and science should not be highly valued. But, they are most certainly not the only avenues to success. Why slander a child's hope of becoming successful, on the grounds that they aren't cut out to be engineers or doctors? Why not, instead, help them to flourish and thrive in an avenue to success that is plausible to them. Behind door number one, sits an adult who has not found personal success in his life, and on top of that, feels so discouraged by teachers who told him he couldn't, that he does not even recognize his own worth. Behind door number two, sits an adult who has gone on to lead a happy and successful life- just as successful as any scientist or engineer out there.

     To sum up my thoughts on this video, I will refer to another of Robinson's ideas: "creativity is as important in education as is literacy, and we should treat it with the same status". I could not agree more with this statement. What good are facts, formulas, dates, and definitions, if students do not have the creativity to actually put this knowledge to use, and to apply it in the real world? We might as well be giving them broken pencils with which to write.

Andrea

My Math Autobiography

         I have never written an autobiography. So, I don't think it is any surprise that I have never written a math autobiography. In fact, even after all of the reflecting that I have done as an education student, I have never thought about it in that way before. Now that I think about it, it is kind of a neat way of looking at it, since all of my subject experiences have helped shape who I am today. Regardless, I am about to write my first autobiography, and more specifically, my first math autobiography!

       I guess Kindergarten is a good place to start. My first experience with math in a school setting was probably playing with the large, brightly coloured blocks during play time on that first day. Although, at the time, I did not realize that. Throughout the Primary grades, my teachers took great care in surrounding us with numbers, and making them become very familiar to us. I remember seeing plenty of large, brightly coloured posters that displayed concepts such as groups of ten, counting by twos, and so on. I also remember having a math centre in each of my Primary grades, and in this centre there was an abundance of counters, blocks, buttons, plastic figurines, worksheets, ten frames, sticks, "jacks", games and so much more! I remember having so much fun in these centres that I don't think I ever viewed it as learning. To me, going to a centre was the playtime that I looked forward to after completing seat-work. Into the elementary grades however, there was a significant decrease in the amount of informal exposure we were given to mathematical concepts. This became more and more true with each increasing grade. After grade three, and maybe even grade two, almost everything that I can remember being displayed on the walls represented science, and reading and writing concepts. Much of my memory surrounding math in the Elementary grades surrounds the daunting task of memorizing my times tables and having my parents quiz me on them nightly. There were no more math games or math centres, and math suddenly became something that most of us were frightened of. Perhaps the intimidation came with the seriousness with which most math concepts were now delivered to us. It seemed as though we were no longer allowed to "enjoy" math, and so, it became much more of a requirement than an intrigue, as it had been in the primary grades, at least for myself.   

         There is one experience in particular that stands out for me when I think about Math. It occurred in Elementary school, and is probably one of the worst school experiences that I have had in those years. I was in grade 6 and we were doing a chapter on graphing. First of all, let me tell you-I hated graphing, and to be completely honest, I am still not all that tore up about it. Looking back, I guess this little fact added to the trauma of this experience. I was called up to graph a problem in front of the class on the large graph paper. I did not have the problem completed yet, but I did not want to admit this because it seemed as though the rest of the class had already moved on. So, I went up to the front, and gave it my best shot. While there, I completely blanked out. I panicked. I could not, for the life of me, even begin the graph because I could not decide on a scale that would fit the problem. After several minutes, I could hear some of my classmates snickering, and with each giggle, my face burned hotter. My teacher would not allow me to sit down until I could figure out a scale that worked. Looking back, I am not really sure on the time frame. I may have only been up there for five minutes. But, what I can tell you is this-it felt like, and still does feel like, I was there for an eternity. As an adult looking back on this experience, I have come to the realization that much of my fear of Mathematics stems from this one experience. It may have seemed relatively insignificant to my teacher at the time, and I am sure if you were to ask any one of my classmates about it, they would not even as much as remember the incident. However, I believe it was enough to instil a fear of Math within me.

        When I stop to think about whether I was "good" or "not good" at math, it is hard to come to a conclusion that is not clouded by my perception of math as being a scary subject. I know that I have always secretly really enjoyed math. The secretive part came from my wanting an excuse to back up any poor grades in the subject, which, I was certain I would get. It did not matter how many 90's and even 100's I received in math, I still did not, and could not, believe that I was strong in math. I would like to say that as an adult looking back, I can see now that I really am good at math. However, if I am being totally honest, I  have had these exact feelings in the most recent math courses that I have done, even at the university level. I guess some scars never heal!

       During my Primary years, I feel that the best way to describe my teachers' role in math would be as facilitators. It feels to me as though they kind of stepped back and let us do the discovering, after they had given us the tools and beginning knowledge we needed to do so. As I mentioned previously, in the Primary grades, we were made to feel as though math was fun and we were encouraged to learn through play. This probably contributes to my view that their feelings towards math were positive. In the Elementary grades, I feel as though the role of my teachers changed from facilitator to dictator. Most of what I remember being taught to us was done so in a fairly rigid fashion, with not much opportunity for exploration or self-discovery, outside of "you may start working from #1, or you can jump ahead if you like, and go back to the rest later." As a whole, I cannot really seem to pin-point how I think my Elementary teachers felt about math. I think that they were fairly neutral from what I can remember, and did not really favour it over any other subject, nor did they ignore its importance. I just remember feeling as though if I did not do each problem in the exact, precise way that they just showed me on the board...I was doomed.

      Assessment has alway been a source of anxiety for me in any subject, even those in which I am confident in my abilities. So, you can imagine my delight in having a math test put in front of me! What I remember about assessment is that it was usually very formal, and in the form of a written test. I cannot remember much in the way of informal assessment, but I like to think that it was really just so informal that I didn't even know it was happening!

      During high school my fear of math both continued, and dramatically increased. By high school, I was almost consistently a straight A student, and math was no exception. However, within the walls of my mind, I was just not good with math. I remember my math teacher in grade 10, pleading with both me and my parents that I take the advanced math program, because he believed that was where I should be. Needless to say, I ignored his pleading and continued on the regular stream because I did not believe I was capable of advanced math. I still regret that decision to this day.

      Since beginning post-secondary education, I have to admit that I have not given much thought to math outside of the courses that were required to apply to the Faculty of Education. I have taken Math 1090, and Math 1051. I did very well in both courses, and even got a 92 in Math 1051. However, the entire course caused me a major amount of stress and worry, and a constant feeling of "I'm going to fail". Whenever possible, I have steered clear of dealing with math in major ways in my life. However, I am about to engage with math in the most significant and tremendously important way that a person ever could- I am going to teach it. Because of this, I am ready and willing to look at math in a new light, and I am dedicated to doing everything in my power to ensure that my students will not fear math, but will embrace it!

This, is my unfinished math autobiography.

       

Welcome, readers!

     If you haven't already read this in my intro, my name is Andrea Boone, and this is my very first blog ever! I am twenty-four years old. I was born on April 23rd, 1989, and grew up in the small town of Bonavista, NL. I am currently studying at Memorial University of Newfoundland to become a Primary/Elementary teacher, which has been a dream of mine for as long as I can remember. As well as being a full-time student,  I am also a full-time Mommy! My daughter's name is Eve. She is five years old, in Kindergarten, and is absolutely the light of my life. 

        I have always enjoyed writing ever since I was old enough to know how, and have considered starting a blog several times before, but never did actually do it. I guess maybe this is the push I needed! This blog is for an Education course- Mathematics In Primary and Elementary grades, so I think it's safe to say that each blog post will make some connection to this subject area. I hope that anyone who reads it can take something positive and beneficial away from it!

Enjoy :)

Andrea