Final Reflection

Education 3940: Mathematics in the Primary/Elementary Grades was the course I dreaded completing the most. Through primary school right up through the elementary grades, I struggled with understanding mathematics. During high school, I completed an advanced math course by efficiently remembering formula upon formula. By the time I completed two math courses in my first year of university, I still had not gained a conceptual understanding of the mathematics involved. Therefore, my own personal struggle with mathematics left me feeling incompetent. I dreaded taking the Mathematics 3940 course.

And now, as I write my final reflection for Education 3940, I feel as though I have grown as an individual and am one step closer to becoming an effective teacher. First and foremost, I have alleviated my own fear of mathematics. When on the first day of class, we placed ourselves accordingly to how we felt about math, I stood nearer the middle of the classroom. I knew at that moment that I wanted to be able to stand at the front of the classroom where I could proudly say that I loved math. Even as I write these words, I cringe a little. I cannot yet say that I love math but I am very proud with the progress I have made over alleviating my own personal fear of math. The key to alleviating my fear of math was to jump into the course with no hesitation and most importantly, to keep an open mind. I believe the math fair really opened my eyes to what I could accomplish in the area of my own mathematical learning. As I completed each new problem-solving question presented by my peers with enthusiasm and determination, I felt such a great sense of accomplishment. For one of my observation days, I had the opportunity to participate in a mathematics professional development day. I was given the opportunity to view firsthand how students respond to mathematical content by way of reasoning and communication. That experience showed me the significance of understanding the mathematics behind a given formula. Both experiences allowed me to overcome my own fear of math to truly learn how to make math more meaningful to and engaging for students.

Over the course of this semester, the most important thing I learned was knowing how to create a safe and comfortable environment in which students could effectively learn mathematics. All throughout school, I was expected to complete a mathematical problem or formula the exact same way the teacher had shown us. I never could understand why students could not use their own strategy to complete a problem. Needless to say, I recognize the significance of enabling students to apply a number of strategies to a problem. When a student is encouraged to develop and/or apply a particular strategy to a problem, he/she can more effectively determine if the solution is justifiable. This in turn, allows the student a more comprehensive understanding of the mathematics at hand. I learned that mathematics need not be completed in isolation but rather should be encouraged through group work. Students effectively grow into learning when interacting with peers.

Another important thing I learned this semester was that problem-solving should be an integral part of the mathematics program. Instead of setting one day aside for problem-solving, open-ended questions should be offered to students consistently. Problem-solving questions should reflect the mathemmatics which is to be learned, be encouraged as group or whole class initiatives and be meaningful in relation to the real world, again allowing for a more comprehensive understanding of the math involved.

The most important thing I have taken away from this course is that as effective mathematics teachers, it is our responsibility to ensure that students not only efficiently complete a mathematics problem but to also provide a justifiable response as to how the mathematics makes sense.

"Go down deep enough into anything and you will find mathematics"
                                                                         Dean Schlicter

Team Teaching Reflection

For our team teaching assignment, Vicky, Jen and I presented an open-ended problem designed for a grade six class. Initially, we believed that the problem focused on the mathematical concept of area. But, upon further reflection, we decided that the problem enabled students a deeper understanding of spatial reasoning. The title of the open-ended problem was "Arranging Your Bedroom." Students were given a bedroom template, whereby they were asked to fill the space with at least six different pieces of bedroom furniture such as a bed, dresser and toybox. Students were given the dimensions of each piece of furniture so that they could determine how much space was being taken up. Students were also provided with some basic points to keep in mind when arranging their bedroom such as that tall furniture could not be placed in front of windows and furniture could not be placed in front of heaters. Vicky, Jen and I believed "Arranging Your Bedroom" was an effective open-ended, problem-solving question for a number of reasons. First, the question did not have one set solution. As long as the students took into account the points to remember and included at least six pieces of furniture, the bedroom plan could be arranged in any way, shape or form. Because there were limited restrictions as to how the problem could be solved, diverse learners could potentially find success in solving the problem. Therefore, the "Arranging Your Bedroom" problem would effectively challenge all students alike. Secondly, students were able to apply a number of strategies to solve the problem. For example, students could strategically map out the dimensions on the grid first and then draw in the furniture, students could fit in the furniture as best as possible without mapping out the dimensions first or students could use one or more of the same type of furniture such as three dressers and one bed. During the teaching presentation, a student had brought it to our attention that the bedroom could be arranged differently according to the way that the actual template was looked at, either horizontally or vertically. The problem could therefore be solved effectively in a number of ways depending on how the student saw it. The problem allowed for students to work independently but to also share their strategies with their fellow classmates. Thus, students learned from one another to gain a better understanding of spatial reasoning. In the context of the practical classroom, the problem could be presented as a whole class initiative. The students could potentially map out an entire section of the classroom and use life size manipulatives to fill the dimensions of a particular area. Lastly, the problem was effective because extended questions were provided to further expand the student's knowledge of spatial reasoning. The questions were deemed as optional because in the context of the practical classroom, some students may or may not have the opportunity to move beyond the initial problem. The extended questions were intended to challenge the learner. That being said, upon further reflection Vicky, Jen and I realized that the initial problem would not have adequately challenged the grade six learner. In order to challenge the learner, Vicky, Jen and I could have provided a second bedroom template with given restrictions, such as a smaller bedroom with more pieces of furniture required. As well, manipulatives could have been made accessible for students who benefit from a more hands-on approach.

In regards to the actual presentation, I felt that Vicky, Jen and I were confident in presenting the "Arranging Your Bedroom" problem. Vicky, Jen and I briefly discussed the problem at hand and then allowed for adequate time for the problem to be solved. I believe the most effective part of our presentation was when we asked fellow classmates to show how they individually designed their bedroom plan. In doing so, students could see how fellow classmates made use of multiple strategies to solve the problem. As well, difficulties encountered when solving the problem were discussed which allowed for a deeper understanding of the mathematics at hand. Vicky, Jen and I demonstrated effective time management and use of technology. The one thing I would change about our presentation was our interaction with the students while they worked to solve the problem. Vicky, Jen and I had initially planned to tell our classmates to focus on solving the main problem and to simply look over the extended questions. Looking back, I realize that the whole class discussion could have been enriched if some of the students had completed the extended questions.

Overall, I believe the team teaching assignment provided me with a positive learning experience. Through my own presentation, I learned that there are multiple ways to engage a classroom of learners in a problem-solving question that allows for multiple entry points. The team teaching experience taught me that as students work and struggle together to find a justifiable solution to a problem, growth in learning occurs and knowledge of mathematical concepts are extended.

Math Fair Reflection

For the math fair, my partner Vicky and I created a "Touching Circles" problem-solving activity. The activity was designed for a primary grade level but could be modified in such a way to challenge the elementary learner as well. The main objective of the "Touching Circles" activity was to fill a large size triangle with red, yellow and blue circles without having a same color circle touch vertically, horizontally or diagonally. The triangle was divided into three different levels so that problem-solvers could be challenged accordingly. Vicky and I had also provided problem-solvers with four different extensions to the "Touching Circles" activity. The extensions included filling a hexagon with the same three color circles (again, without having them touch), finding the shape (either a circle or a pentagon) that could not be filled without having a same color circle touch, and filling another triangle plus a rectangle in the same way but with an extra color of green added. The extensions allowed problem-solvers to think outside of the initial problem but to maintain a focus on patterns and relationships. As problem-solvers explored patterns and relationships in how  the different color circles could be arranged accordingly, an increased understanding of predictability occurred. A positive response was received by my fellow classmates as individuals appeared quite eager to complete the problem. The "Touching Circles" problem-solving activity was presented in a visually appealing and interactive style and so drew problem-solvers in.

Initially, I remained with the "Touching Circles" problem-solving activity while Vicky set off to tackle the other activities presented in the classroom. By remaining at the activity, I learned three important lessons regarding the context of the primary/elementary classroom. First, as individuals began to circulate the classroom to have a go at the problem-solving activities, I thought about how people would be attracted to activities that were visually appealing, perhaps activities that were presented by close friends or simply activities that seemed to catch a curious eye. In the context of the primary/elementary classroom, it was reinforced for me that math has to be made engaging and meaningful to students to garner success. Just as my fellow classmates and I had chosen to participate in activities that appealed to us, students will engage more so with the task at hand if it is presented in a motivating and engaging way. Also, I discovered just how tempting it is to simply give the answer to somebody when they have not quite understood the concept yet. However, as hard as it may have been, I refrained from giving anyone (okay, maybe just one! ) the answer. Nonetheless, I realize in the context of the primary/elementary classroom, that it is more beneficial to allow students to struggle through a problem to make sense of the task at hand. Students need to be given the tools to know how to use their knowledge in application of other problems and situations. I also learned the value of limiting my use of "praise phrases." As individuals discovered a solution to my problem, I would eagerly say "yay!" or "you found a pattern!" In doing so, I allowed for problem-solvers to ask of themselves the question "I found a pattern...could there be another one?" The same idea can be applied to young students. When told specifically what was considered to be a "good job" students are enabled to then think more critically of their positve behaviours and themselves.

When it was my turn to circulate the classroom, I left all my fears and hesitations about math aside and confidently approached each problem. The first problem I approached, I amazed myself with my own determination to find a solution. And I did. Each new problem I then attempted, I had even more confidence to do so, and most importantly, I had fun! At one particular problem-solving activity, I was told that I had found a new strategy that was not thought of previously. My self-confidence in my ability to do math soared and I realized in that moment that I would never approach math in the same grudging way again. I want my future students to feel that way about math, and to feel confident, even when in doubt.

All in all, I feel the math fair experience was a great success! If I were to facilitate this particular problem-solving activity again, I would use a combination of colors and numbers. As the extensions followed the same sequence as the original problem, problem-solvers were not adequately given the opportunity to extend their newfound knowledge to advanced patterns and relationships.

The ideas and approaches explored in class and the math fair experience itself has really opened my eyes to my ability to teach math in the primary/elementary classroom. I no longer think "fear" when I think of math; I now  think "possibility." The math fair experience allowed me to open myself up to new  ideas and personally take on the positive attitude about math that I wish to instill in my future students.

I believe a math fair would be most applicable in the context of the primary/elementary classroom as well. I believe a math fair experience would give students the excitement and motivation to engage in mathematics problems with little fear or hesitation.

The Shifting View of Mathematics

What a relief it is to know that the view of mathematics is changing and that we as future teachers will continue and embrace that change!

Mathematics for me as a child was downright frightening! I can distinctly remember that sickening feeling in the pit of my stomach when the teacher began to call upon students for answers. Nine chances out of ten, I didn't have the correct answer and if I just so happened to have it, then it came from a nearby friend. I also remember when doing seatwork, how  the teacher would circulate the rows of desks, peering over the student's shoulder to check their work. When the teacher stopped by my desk, I always pretended to be deep in thought but...I didn't really have a clue! I remember how when tests and quizzes were passed back, questions that I had wrong (and there were many!) were never explained to me. I was never shown where I had gone wrong in my attempt to calculate the right answer and so I felt as though I wasn't intelligent enough to understand math.

Calling upon a child in front of their peers for an answer to a problem often embarrasses and instills fear in a child. Peering over a student's shoulder without recognizing that he/she needs guidance does not build confidence within. Not helping a child understand where he/she went wrong in a problem does not enable further understanding. Simply telling a child if they are right or wrong when it comes to a mathematics problem is to enable the child dependent on the teacher for justification of solutions. For me personally, I relied on memorizing formulas to complete a math problem. Now, students are expected to justify a solution which allows for a deeper understanding of the mathematics at hand. I believe the shifting view of mathematics is steering both the teacher and the student alike, away from negative practices and moving towards effective problem-solving skills. Even though my own experiences with mathematics were mostly negative, I believe that I can use my personal experiences to create positive learning experiences for my future students. I feel as though my own fear of math is subsiding when I realize I can create a safe and comfortable atmosphere in which children grow and thrive in learning together.

I believe the key concept is found in the word "together" when it comes to the shifting view of mathematics. I believe as with every other discipline, active learning and participation with one another should be encouraged and enforced. I believe that when students can be made to feel safe in exploring different ways to do math, the overall rate of success will be great. What I like the most about the shifting view  of mathematics is the encouragement of using multiple strategies to solve a problem. When I was in school, if I did not use the teacher's method of solving a problem, then the problem was marked incorrect. Encouraging students to apply a number of strategies to a problem enables active learning and construction of one's own knowledge. Applying a number of strategies to a problem also enables a deeper understanding of how  and why a solution is deemed correct. Students therefore, strengthen their reasoning and communication skills, allowing for a more comprehensive understanding of mathematics.

I can now  begin to view mathematics as a humanity. Mathematics for me was always completed in isolation. With the shifting change, mathematics can be explored in a positive group setting. Mathematics for me was always a question of is this right or wrong? With the shifting change, mathematics can make sense in the justification of the math itself. Mathematics for me was a subject always put on the back burner and willingly ignored. With the new shifting view of mathematics, I can explore new problems and situations with confidence and know  that mathematics is a positive aspect of my life and not a negative one.

With the new shifting change of mathematics, I know that I can put aside my fears, even tackle the problems in the text with little hesitation and use my newfound attitude and knowledge to create a positive learning experience for my future students.

Mathematics is a humanity; it is a relationship between people and involves the exploration and discovery of patterns and solutions. Math can bring together a group of active learners who ultimately construct their own knowledge and meaning.

Do Schools Kill Creativity?

"A teacher's purpose is not to create students in their own image, but to develop students who can create their own image."

Author Unknown

In the video "Do Schools Kill Creativity", Ken Robinson makes a vital point about the unpredictability of the future. Teachers are given the immense responsibility of preparing students for a future we simply cannot grasp. If the education system continues to insist on a hierarchy of teaching language, mathematics, science and so on, the whole being is not being educated and therefore, teachers have failed to truly teach students.

I agree with Ken Robinson when he says that the education system is predicated on university exam entrances. Absolutely! Growing up, that was the main message in school-"this will prepare you for university!" I remember how I would feel absolutely nauseated as I heard those words over and over as a child. For one, I grew up in a single-parent home...do you think there was money set aside for me to attend university? Not on your life. I always knew at a young age that attending university would be a struggle for me in the way of financial matters. I wish someone had said to me "Tiffany, the world is yours to behold. You can be a musician, you can be an artist, you can be a teacher." Yet, my "world to behold" was already set for me and everyone else, regardless-university. What pressure!

Ken Robinson is right. Degrees aren't worth anything. All too often you hear, "Oh, I'm just working here until I can find a job", "There are no jobs in my field." Sure, I realize that that happens but how many of those people do you think should have done something different, something meaningful with their lives? I bet a whole lot.

Teachers are killing student's creativity when we force each and every student to learn in the same way; when students are subjected to pen and paper assessment and when we place too much importance on one subject and not enough importance on the other. Teachers are creating students in their own image. Students should be given the tools to become critical thinkers; to question what it is they are being taught so that they can dictate their own lives. Why can't the child who loves to dance tell a story through motion, why can't the child who loves to act improvise a historical play, why can't the child who loves to draw, draw a picture of a thousand words? Why must the child who loves to play the piano be encouraged to do so only as a past time? Why must the child in science write a response to everything when she can perform all kinds of experiments? Why must a child show his workings in math when you as a teacher can see that he has extraordinary mental math skills?

Mary Stordy's words have truly made me reflect on what it means to be a teacher. "Every child has a strength and it is our responsibility as teachers to draw from and make prominent that strength in every child, not squander it." If intelligence is diverse, dynamic and distinct, the education system needs to be changed so that teachers can enable students to grow into creativity and not out of it.

My Math Autobiography

If you asked me today what I thought about mathematics, I would offer three different opinions on the subject: math is challenging, math is intimidating and an extreme fear of math can be overcome.

From kindergarten to grade six, I have vague memories of what mathematics looked like in my classroom. I do however, remember that most of my math lessons took place in a highly teacher oriented way. At all grade levels (of which I can remember) the teacher would stand at the front of the classroom, writing examples on the board from which the students would copy down. I remember oftentimes, how students would be called upon to give an answer or would be asked to record the answer on the chalkboard in front of the entire class. For me, the thought of having to show my answer to a math problem in front of the whole class was absolutely terrifying. Needless to say, I always felt much stress and anxiety during math class. After the teaching sequence, my fellow classmates and I would be given individual seatwork and the remainder would be assigned for homework. I remember how using hands-on materials such as blocks or cubes would rarely be used and almost treated as a positive reinforcer rather than as a learning resource. Although, I do remember how the majority of the students would be much more engaged with the task at hand during these particular lessons. Nevertheless, I feel as though the way mathematics was taught reflected upon my teacher's attitudes towards the subject itself. I believe most of my teachers might have had some concerns and/or dislikes with mathematics and so my fellow classmates and I were not engaged or encouraged in a positive way in this subject area.


My absolute worst memory surrounding mathematics occurred when I was in grade three. My class had just returned from music and the teacher quickly ushered us back to our seats. The teacher then stood at the front of the classroom and not too subtlety told me in front of the entire class that I did not understand how to add or subtract properly. She then proceeded to tell me in front of the class that my math book was being sent home for further practice. I was devastated and embarrassed to say the least. I clearly struggled with mathematics at a young age and so my teacher's grand announcement did little to improve my self-esteem.


As I got older, I would consider myself to have been "okay" at math. I did not fail at math by any means but when compared to my other subjects, there was a significant decrease in my grades. Assessment consisted of just that-grades. Assessment was comprised of giving a test and assigning a particular letter or number grade. The worst form of assessment I can remember was the test of mental math. The teacher would stand at the front of the classroom and call out a math problem which had to be completed in so many minutes or perhaps even less than. I failed almost every single one of those mental math assessments. Knowing that I had to complete the problem in a set amount of time caused me great anxiety. I could never actually complete the problem efficiently because I was too worried about having to produce an answer, just like that!


My very first math quiz in high school I failed miserably. Something inside of me ticked and I vowed to put my all into mathematics from there on in. I found myself a tutor in the classroom with whom I would work with the entire class instead of sitting with my friends. After that, math came quite easily to me- much to my surprise. In grade eleven, I took advanced math and did very well. I chose to return to academic math in grade twelve and again did very well. One of my greatest accomplishments with mathematics occured when I was in grade eleven. As part of a mentoring program at school, I replaced one of my courses with mentoring a high school math course. In that class, I was responsible for answering student questions and working one-on-one with struggling learners. That experience helped alleviate some of my own personal fears of mathematics and instilled in me a sense of great pride.


The math courses I took in University were Math 1050 and Math 1051 and I did not take any math electives. I did fairly well with those courses but by that time the stress of university had gotten to me and I did not put as much effort into math as I did in high school.


As for today, my daily life relies heavily on the use of mathematics. I have rent to pay, bills to uphold and a budget to follow. After high school, I worked at the YMCA for a period of time. There, I was responsible for completing invoices for birthday party and membership sales transactions. At the end of each night shift, I was responsible for cashing off my transactions made throughout the day. More recently, I work at Extreme Pita where I am responsible for cash, debit and credit transactions. Time, money, space and relationships make up my daily life- mathematics.


I feel as though I have had a long journey with mathematics. I have gone from being intimidated by math in primary/elementary, to not caring and barely scraping by in junior high and to overcoming my challenges in high school. Right now, I see math as a subject which I want to learn to like. I want to learn how to see math as engaging so that I can instill that same kind of positive attitude in my future students.

Welcome to my Blog! :)

"Mathematics should be fun"-Peter J. Hilton

Hi! :) My name is Tiffany Fifield. I am currently in my fourth year at Memorial University studying to become a primary/elementary teacher. I have created this blog as part of a course requirement for Education 3940: Mathematics in the Primary and Elementary Grades. I believe as future teachers, it is important to find within ourselves our own personal expression of creativity to foster creativity and knowledge within our students. By reflecting on my experiences with mathematics and posting my thoughts and opinions on the subject, I am given the opportunity to do just so. Throughout this course, I hope to learn how to make mathematics less intimidating and more engaging for students.

I look forward to this new experience!