Welcome to my blog, everyone!
This blog will consist of my thoughts and reflections on and responses to Education 3940 - Mathematics in the Primary and Elementary Grades. Each new posting will appear at the bottom of this page. I am interested in reading the views of the rest of the class and look forward to growing and learning together! Hope you find my blog to be insightful and interesting.
More posts to come...stay tuned!

Math Autobiography

     Math looked very different in the various classrooms I entered during my schooling. I can recall grade one consisting of many worksheets and grade two included traveling math and other math games. Grade three was very disorganized as far as I can remember. Some students completed a small portion of the math textbook, whereas one student finished the book in its entirety. Grade four was the year that I memorized my multiplication tables and specifically remember having many math tests. My grade five teacher was extremely organized and had worksheets divided into levels. Once you finished one sheet, you simply went to the front of the class to get the sheet that came next. This method allowed each student to be independent and move at their own pace. In grade six I remember working a lot with word problems. Most of these teachers seemed to see math as a very important part of the curriculum (besides my grade three teacher who seemed to allow the subject to go by the wayside). I remember learning math in many different ways throughout the years (lessons, memorization, games, tricks, etc) but in some ways I feel like my math teachers were merely getting us to memorize things and would then give out tests. The times I felt the most positively about math were when a lightbulb would turn on and I actually understood the process and - not when I just knew or had memorized the answers. When something actually clicked I felt the best and happiest about math.

     I have both good and bad memories surrounding math in elementary school. The best memory I can think of happened in grade four. We had a multiplication test with 108 questions and I had 107/108 right! I was really proud of that and still have the test in my room. Unfortunately, I wasn't very confident and used to get really nervous when a teacher would call on students to answer math questions in front of the class. I had a fear of giving the wrong answer and can still remember feeling completely embarrassed when that happened. I can see how these experiences have affected my current view of math - I still have conflicting emotions on the subject and am still scared I will give a wrong answer in class. 

     During elementary school I thought I was "good" at math for the most part. It just made sense to me. During junior high and high school I had mixed results in my math classes. From grade eight to ten I had a hard time with math. In addition to not doing very well in those classes, some of my family members used to randomly ask me to solve math equations. This didn't help my situation or feelings towards the subject at all - it just made me feel incompetent. It also didn't help that my older brother and sister were very "good" at math. I am more artsy and creative whereas they are very logical. This lead me to feel like I wasn't "as good" at math and that I was less intelligent because I saw math as being of a higher value than the arts. Then, strangely enough, for the last two years of high school I loved math, felt confident in my skills, and did really well in my classes. I also found the two math courses I have taken here at Memorial (Math 1050 and Math 1051) to be quite easy and enjoyable. I'm not sure if these varying results throughout my schooling were a consequence of the teachers or my own attitude/approach (or both), but either way I now feel fairly confident in my basic skills (however still hesitate to answer questions in front of others). In spite of some of my negative experiences and my occasional nervousness, I still like math and am really looking forward to gaining more knowledge and confidence this semester. 

Just in case you need some visuals...


Do Schools Kill Creativity?

     I found Sir Ken Robinson's talk to be extremely inspiring, motivating, and eye-opening. His perspective on the current school system (and the world) is something I had never even considered, but after listening believe it to be spot on. I had just been accepting the way the world worked and never thought to question it. Now I have an entirely new outlook on who I want to be as an educator (and as a member of society in general).

"Every child is an artist. The problem is how to remain an artist once you grow up." - Pablo Picasso

"We get educated out of creativity" - Sir Ken Robinson

     These quotes (along with many others in the video) really stuck with me. The entire section where Robinson spoke about how children are steered away from things they like because they won't find a job doing "that" is something that I have found to be true throughout my 21 years. It is the way of the school system to create "cookie-cutter" students...to simply look for and cultivate certain qualities and skills that society sees as the "norm" and as "good". It is completely true that wanting to be things like artists or musicians or other "far-fetched" occupations is seen as a somewhat impossible dream and is hardly ever taken seriously. I can only imagine the wasted talents and dreams of children that never had the chance to take shape...these people could have changed the world - or their world at least. The chance to explore their interests and do what makes them happy could make all the difference in peoples lives. 

     The way we go through life now is like going through a factory - or I feel like it is anyway. In my life it was grade school and then "of course" onto university because that is the next step - there was no other option. This worked out fine for me, but university isn't right for a lot of people. Sure, we can all be proud of ourselves for being here, but it shouldn't necessarily be seen as better than something else. It just so happens that this was our dream and going to university is the path you have to take if you want become a teacher. Taking a different path to do what you love shouldn't be frowned upon...many people just feel that school isn't right for them or might have been turned off by how their dreams or ideas were degraded. Additionally, people learn in different ways and have different strengths. This is frequently ignored in the school setting, where children are often taught using the same approach but are still expected to give the same results. It is no wonder so many people are left with negative feelings when it comes to school - they are told what they want to do when they grow up is impossible, that they have to be a certain way, and they have to learn like everyone else. Perhaps if we begin to change how schools are run and our views on what it is really for, school might be "right" and a positive experience for everyone. If we begin to not only allow children the freedom to discover and unlock what they are passionate about in their own way, but encourage them to do so, we will be promoting their creativity and enriching their lives. And if we can change the way we teach lessons and curriculum content to be more dynamic and inclusive of all types of learning, we will be changing the future of each student that passes through our classrooms and the future of our world. 

     I have always wanted to be a teacher, but there are many other things I have dreamed of doing with my life. Some of these things include: World traveler, dancer, choreographer, artist (drawing and painting), photographer, makeup artist, working for a magazine, interior designer, news anchor, actress, radio host, hair dresser, author/illustrator, song writer, flight attendant, psychologist, massage therapist...and many more. I would also like to travel. This video really inspired me and made me feel like maybe some of these dreams aren't as "silly" as I was lead to believe. I see my future as being wide-open...I'm not sure where I want to start, but what I do know is it's not too late. I definitely want to experience some of these things, whether in my free time as an educator or before I settle down. I hope to maintain this outlook of my future as being limitless for the rest of my life. If I can give any advice to the people reading this blog: dream big and do what inspires you and makes you happy - it's not too late! And pass that message on to your future (or current) students...you never know how it could change their lives!


     Why would we be shown this video in a class about teaching children mathematics? I thought of many possibilities. One of the more obvious reasons that came to mind was to get us to recognize the importance of creativity and dynamics as future math teachers. As we learned when considering and discussing our own experiences with math, many people have had negative experiences. Math needs to be taught in various ways to encompass the diverse needs of all students. We also need to create environments where children are not afraid to make mistakes. I imagine that Dr. Stordy also realizes the value of other subjects and believes that we should apply this view to all subjects in general. 
Some other reasons I thought might be possible are:
- Our responses to the video allow others to get to know us better and give us the opportunity to learn more about ourselves, both as students and future educators.
- This video is a good way to introduce a course which many students feel intimidated by and may be scared to be "wrong".
- Dr. Stordy knows that math isn't the be all end all - everyone has different strengths and interests.
- The video gave us the chance to reflect on our lives outside of math and even outside of being future teachers. 

Italy Painting - Sarah Kikuchi

So What?

     I started out in this faculty with the idea that I already had what it took to be a teacher. I felt that I knew all I needed to know, and that most of what I would learn would be either impractical or something I already knew. And, to be honest, for the first year and a half a lot of it was. I felt disconnected and it seemed everything we were "learning" (or as I like to call it, memorizing) was abstract. We memorized terms and definitions solely for the purpose of doing well on tests. Nothing was "real". Fast-forward to this semester. I now have a completely different outlook on teaching. I now see myself actually gaining knowledge and skills I will be able to apply through both the content and modeling of our professors. This has me highly motivated and inspired to be the best teacher I can possibly be. I have always wanted to be a teacher, but this semester has sparked an even higher level of passion. I can picture it all now. How I will guide the students, how they will learn and grow in the classroom...of course there will be ups and downs (this is to be expected)... but I am now seeing everything I have been learning and all the things our professors have been stressing. Everything is connecting and I'm finally getting the "big picture" of what being a teacher really means. And this math course is no exception to my newfound realization and energy. It is actually one if the bigger, if not the biggest, reason for this realization. I am beginning see all the framework coming together aka HOW we are supposed to teach. 

     In a sense, I was right. I believe I could have made a "good" teacher regarding the HOW but I completely underestimated the WHAT. This is where the principles and standards and knowledge about current influences and pressures come in to play. For, "your knowledge of mathematics and how students learn mathematics is the most important tool you can acquire to be an effective teacher of mathematics." (Elementary and Middle School Mathematics: Teaching Developmentally) So, in response to the question, "So what does this have to do with me?": Everything! Having the ability to be a great teacher means nothing if you do not have a strong understanding of the principles and standards to back it up. You must understand each principle and see how they all come together to guide educators in their teaching. A teacher must know the curriculum (content) inside and out and understand the ways (processes) through which students should acquire and use mathematical knowledge. Additionally, teachers must remain current and knowledgeable when it comes to shifts in the classroom environment (much has changed since I was in school), knowing what forces influence mathematics teaching, and knowing what resources are out there. It is only when all of these components come together that teachers will fully understand how to be an effective math teacher. If they practice what is outlined in chapter one, they will be providing students with an environment in which they (the students) will be able to acquire the proper mathematical skills and knowledge needed to survive as functioning members of society in an increasingly unpredictable future. 

     The past month and half has shown me that I have much more to learn than I previously thought. This means I must be more conscious of what we are doing and learning in class and more proactive outside of class. Although the task of wrapping my head around all of this seems daunting at times, I am looking forward to acquiring more knowledge and gaining a deeper understanding of mathematics, the principles and standards, the curriculum, and how these elements come together to affect us, the teachers. 

Observing Grade Five Math

     I haven't had much experience with math in my observation days but fortunately I was asked by a grade five teacher to help a student one-on-one. I was more than happy to help this student because not only was I gaining more experience and helping the student, but the teacher made it obvious they thought little of the student's (mathematical) abilities and had embarrassingly called them out in front of the class for missing a lot of school.

     The student had missed some of the work the class had done on multiplication and this day they were working on the "box method" of multiplication (which is actually really cool). I was determined to help the student and maybe give them a little bit of confidence in the process.
The student ended up doing really well and being able to do the problems on their own using the method.

     If it were my classroom, I would definitely not have just given the students a method and a sheet of problems to solve using that method, but as I was only "observing" I helped the student as much as I could based on what the teacher wanted. Additionally, if it were my classroom, I would obviously make it a comfortable environment where children are encouraged to discuss, take risks, and learn from their "mistakes" rather than lowering their confidence and embarrassing them.

     Many of my observation days were frustrating in that way and it seems I learned a lot more of what not to do than what I should actually be doing as a teacher.

(Box Method)


     I was very surprised and impressed by the available resources! Some things I took note of in the resources:

Really cute mathematical picture books containing concepts like money, numbers, sharing, more and less, and counting. It presented the concepts in a child-friendly and inviting manner. There was also a teacher guide for each unit. I thought this was really cute and the books would be a great addition to any classroom library.

Grade 1-3:
Textbooks including stories, journals, and worksheets. They included a description of the focus and home connections. I really liked that the children could connect what they were learning to "real life". The teacher guide included planning and assessment support for each unit. It also included teaching tips, cross curricular connections, activity banks, how to differentiate instruction, literacy links, and various teaching ideas and resources. I was surprised that all of this would be included in the teacher's guide and felt it was obviously well thought-out and constructed.

Grade 4-6:
Textbooks containing chapters on patterns, numeration, addition and subtraction, number relationships, date relationships, geometry, multiplication and division, ratio and percent, fractions and decimals, measurement, and probability. Textbook has an accompanying workbook (and answer book) that has worksheets to supplement the text. Also has a teacher's guide for each chapter and includes lesson ideas, questions to ask, assessment ideas, and ways to differentiate instruction.
I noticed that the text has a lot more questions than arithmetic, which is different from when I grew up. One problem I had with textbooks as a child was reading all the "extra" information that could help me make more connections to the "real world" or to gain a deeper understanding of the math. I remember ignoring everything except for the problems we had to solve on the page. I would speed through those as fast as I could, so in the end I really didn't understand what I was doing, I was merely repeating an abstract process that I couldn't actually relate to.

     I can only guess at how useful these resources (or the similar ones in other provinces) will be to me when I become a teacher. I feel we can't really judge how "good" they are until we really get to know the curriculum guides, and more importantly, the individuals in our class. I think however much these resources are used in the classroom, they should be tailored and adapted to fit the needs and interests of the unique set of students each year. I also think that many of the lessons and problems presented in these resources could be used successfully in the classroom, but teachers should make them their own. Rather than getting the students to open the textbook and solve problems, the teacher should take the problems that they like, personalize them, and bring them to life in the classroom. What the students learn and experience should be as "real life" as possible, not reading what the world is like from a textbook.


How hasn't my thinking shifted regarding teaching children mathematics?

     I have learned so much over the past 3 months about what it is to be a "teacher". And not learned in the traditional sense of what I read in a textbook and heard during lectures (and spit back out on a test), but through what I actually experienced. We weren't told what a good classroom would look like and how to teach mathematics, but were shown. And that's the key. It's not all about learning what it takes to become a "good teacher", but also understanding what it is to be a learner. As students, we felt comfortable to share our ideas, try new things, take risks, collaborate, and talk to each other. Being able to collaborate with others and the way problems were presented almost felt like we were "getting away with something", but it soon become obvious how affective this method was in learning mathematics. The work assigned in the course was also meaningful and as time went on we gained a continually deeper understanding of mathematics and teaching mathematics. At the same time, we were hearing that all of these things were what we should be doing in the future, but had we merely read or been told about it (like we have in most of our courses) they would have seemed abstract and I would probably still have the same traditional views of teaching and learning.

     It is all about giving children real world experiences and motivating them to be engaged and want to learn. It is also about balance. As a teacher, yes, you need to foster their skills and facilitate what's going on in the classroom, but you also need to allow your students to figure things out for themselves and actually learn, not just give them the answers. I also realized that students can often be the "teachers" and as a teacher, you are always going to be a learner. You will be constantly evolving, reflecting, changing, and improving.

     Throughout the semester, I have formed an idea of the kind of environment I hope to create for my future students. First and foremost, I hope it is a comfortable place where students feel at ease and want to explore, discover, share, and take risks. It will be a safe place of learning and growing, not a place to earn or lose grades. I find so often that as a student, you are so focused on your grades that you forget to actually learn anything, and consequently lose (or never develop) the drive to want to learn anything. And educators seem so focused on giving grades that they lose sight of what is important and forget to actually teach anything. The words "teacher" and "student" have certain connotations that need to be relinquished. I don't know who or what is to blame for this narrow and unfortunately common view of what school is supposed to be about and what it means to be a teacher or student, but I hope to change that in at least the lives of the children I have in my own classroom. I hope to be a facilitator providing the students with the skills to construct their own knowledge. It will also be a fun environment where the children enjoy spending time.

     The past three months in this course (and one other) have made more of a difference than the past three years. I see things in a new light, have a fresh take, am motivated, have a much deeper understanding, and feel hopeful (that I can make a difference). I know what I have learned it merely the foundation of what it means to be a teacher, but I feel that through this semester I have developed a good base to build upon once I become a teacher.

     I'm not sure if this post really encapsulates what I have learned and how passionate and hopeful I now feel, but I hope that it is somewhat representative of my new perspective and how life changing this experience has been. I can only hope to be able to inspire and motivate my future students half as much as I have been this semester. Thank you.

(I wanted to include an image for this post but nothing could quite capture how I feel. I hope words can do it justice!)