My Greatest "Learning..." :)

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

Upon reflection of this semester and Education 3940 as a course specifically, I have been granted with numerous great "learning" experiences, which I truly value and appreciate, with regards to teaching children mathematics. In preparation for my interview, I put a lot of thought into the final question, What was your greatest "learning" this semester with regard to teaching children mathematics? Has your thinking shifted?" When I first read this question, I was not sure how I could answer this question with one particular answer. I really have learned so much and, as previously stated, I have been granted with numerous great "learning" experiences throughout this course, all of which are beneficial and of value to me as a future teacher. The thought of choosing my one greatest "learning" was challenging as I can list and explain many. Then, it quickly dawned on me. As a result of this course and more than ever before, I recognize the importance of including open-ended mathematical questions and problems in my teachings to minimize the stereotype that math can only have one answer and reduce the general fear of mathematics for students. I also recognize the importance of letting go of my own fears and taking a positive approach to teaching mathematical concepts.

Taking a positive approach to teaching mathematics will shine through to students, providing students with a comfortable learning environment. This positive approach involves limiting feelings of being "wrong" in mathematics and broadening the view of mathematics to more than "textbook" problems with one determinable answer. Like I had experienced in our peer teaching episodes, students, too, must discover concepts of mathematics in authentic and hands-on ways. They must be exposed to mathematical problems which stir thoughts and require deep thinking and the testing of multiple strategies to to determine more than one possible answer. Math is much more than working out problems with one definitive answer, and students must recognize this.

I can say with honesty that my thinking has definitely shifted with regards to the teaching of mathematics, as a result of this course. Prior to this course, the thought of teaching a classroom of twenty five students, give or take, mathematics had always stirred feelings of fear, worry, and anxiousness. The thought had always brought upon butterflies and feelings of discomfort for me, more so than thoughts of teaching other core subject areas had. In my decision process of choosing education as my career and field of study, I often questioned myself, "Will I be able to teach children concepts of mathematics? Do I have what it takes to teach such concepts?" and "How will I best do this?" or even, at times, "What if I don't know the answer to a problem?"

My fears have been minimized substantially. Our class discussions, in-class activities and problem-solving examples, the presentation of the many mathematical resources available for teachers, and the open-ended type of problems in both our math fair and peer teaching episodes have all enlightened me and developed feelings of comfort rather than discomfort with regards to my future teachings of mathematics. This course has enlightened me and as the semester concludes, I feel a sense of relief with regards to my thoughts on teaching mathematical concepts. Like students and people of other professions, teachers, too, are humans. We all make mistakes and learn from them, it's part of life. So, will I be able to teach children concepts of mathematics? Yes. Do I have what it takes to teach mathematical concepts? Yes, you bet I do. How will I best do this? Through experience. What if I don't know the answer to a problem? I'll definitely figure it out!

Thank you, Mary, for the wonderful semester! I wish you the best of luck with your baby, and I hope to see you again throughout the remainder of my university years and career as a teacher! :)

My Thoughts on K-6 Curriculum Resources

Hi friends!

On Tuesday, February 25th our class was provided with a sample collection of the many educational resources that exist and are available for primary and elementary teachers. The K-6 resources were organized and assorted by grade level, allowing my classmates and I the opportunity to move about the tables, each assigned to a specific grade level and its sample educational resources.

I was especially impressed by the wide variety of primary resources available for both child and teacher usage. The resources which I viewed were evidently age-appropriate, including fun and engaging storybooks reflecting mathematical concepts. I could not help but notice the major difference in number with regards to how many resources could be explored at the younger grade levels in comparison to how many resources could be explored at the elementary grade levels. As I moved from table to table, it quickly became evident that as the grade level increased, less resources were provided for exploration and viewing purposes due to availability. In the primary grades especially, resources were abundant while resources were much more limited at the elementary tables. With this said, I recognize the importance and requirement of reaching out to other means of resources, aside from textbooks. Learning elementary mathematical concepts must be fun and engaging for students as such concepts are in primary grade levels. As an educator, it will be my role to find what is not provided in order to strengthen my teaching abilities and the learning of my students. The internet, for example, is a means of technology that can be used to explore various other educational resources to assist in teaching mathematics. Many fun and interactive websites and resources are available online for both child and teacher engagement with mathematics.

As a future primary and elementary mathematics teacher, I recognize the importance of providing students with a wide variety of educational resources to accommodate for the diversity of learning styles and speeds. I truly value and appreciate this opportunity and feel that I have gained insight with regards to the wide variety of resources available to assist in the teaching of mathematics. I take comfort in knowing that such resources as those presented exist and are accessible to classroom teachers. It is great to know that we as educators are not limited to the prescribed grade level textbook. I look forward to beginning my own collection of mathematics resources to assist me in my future teachings.

Natalie

My Thoughts on YouCubed

Hi there!

Here are my thoughts on the YouCubed project!

As a future educator of the 21st century, YouCubed is an exceptional resource to have at hand. Created and launched by math specialist Jo Boaler, the YouCubed project is the new movement to revolutionize math teaching and learning. In her 01:26 video introducing YouCubed, Boaler shares her intentions and main purpose for YouCubed - that being, to use her research and knowledge with regards to what excites children, what helps them learn, and what gets kids excited about mathematics to supply educators with exciting and innovative ways of teaching primary and elementary mathematics. As a current university student studying and learning how to be a teacher of mathematics, I was immediately intrigued after viewing this video and hearing Boaler's mission - to transform the beliefs that students form about math and their own potential with math.

On first glance and scroll-through, I was primarily impressed by the organization of the website. Boaler has organized the website into four main sections: 1) big ideas, 2) content and tasks, 3) math and innovation, and 4) tools for parents. After viewing each section independently, I feel in favor and supportive of the YouCubed project as I was able to better see and understand its high potential for students and parents as well as both current and future educators.

Under "big ideas," Boaler includes a link to her article titled "Unlocking Children's Math Potential: 5 Research Results to Transform Math Learning." I found this article particularly interesting. In this article, Boaler acknowledges what she refers to as "the huge elephant standing in most math classrooms" - the idea that only some students can do well in math. Her paper summarizes five recent and important areas of knowledge that have emerged from studies of the brain and learning that address this myth: 1) All students can achieve at high levels, 2) Students' ideas about their ability determine their learning pathways and math achievement, 3) Mistakes and struggle are extremely important for learning, 4) Mathematics should be disassociated from speed, and 5) Teachers messages are hugely powerful. This last point was intriguing and of most interest to me as a future educator who will someday deliver such powerful messages to my students. After reading this article, delivered and supplied by Boaler, I feel much more prepared for my future teachings and I now recognize, more than ever before, the importance of positive messages.

Under "content and tasks," math concepts are organized by elementary, middle school, and high school with links for each category.

Under "tools for parents," I was pleased to find another link to a new article written by Boaler, listing and explaining a number of highly interactive and motivating elementary math games. Although this document of games is found under "tools for parents," I found this article particularly interesting as it allowed me to gain knowledge of these games, all of which hold the potential to be included into my future teachings. Aside from providing me with some great and useful ideas, this document was also highly impressive to me as it is very well organized and includes all necessary information including how to play, what materials are required to play as well as any existing variations of the game. I feel that this document is a great resource to both educators and parents in motivating students to participate in and enjoy mathematics.

Also under "tools for parents," Boaler has again impressed me with her own document titled "Twelve Steps to Increase Your Child's Math Achievement and Make Math Fun," which can also be easily accessed through YouCubed. Although I recognize the importance of all twelve points, I was especially intrigued and surprised by numbers 1) Never praise children by telling them they are "smart," 6) Encourage drawing whenever you can, and 12) Play games. I appreciate the reminder of including the arts and playing games as other means of learning as such learning styles are not always accommodated in daily mathematics classes.

According to the website, "YouCubed will not only make math enjoyable for learners, it will allow students to see the way math will help them in their lives and work." I feel that this is extremely important as this way learning is authentic and meaningful. Although the site is not yet fully operational, Boaler ensures that the site will be filled with tasks, materials, and video ideas of engaging ways to teach multidimensional mathematics. Based on what I have seen thus far, I am a supporter of the YouCubed project. I look forward to the fully operational site and its yet-to-come customized professional development plans that include video, resources, and workshop options all designed to improve math teaching and learning. What a great resource!

Natalie

What is Mathematics Anyway?

Hi again!

When I first read the topic or guiding question for this week's blog, I was immediately intrigued as I had never before considered the complexity of this question nor had I put much thought into it. Considering the fact that mathematics is a core subject of the K-12 curriculum and the fact that I have been engaged in some form of mathematics on a daily basis since kindergarten, both in and outside of the school setting, I find it surprising to think that I had never before considered this question. So what is mathematics anyway?

Google search engine defines mathematics as "the abstract science of number, quantity, and space." According to Google's definition, 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)." When I asked Siri on my iPhone, "what is mathematics?," I was linked to Wikipedia's definition of mathematics: "mathematics is the abstract study of topics such as quantity, structure, space, and change." With two of these brief and specific definitions in mind, I was not satisfied so decided to continue researching and investigating this question.

What is Math About?

In Masao Morita's "What is Math About?" TEDx video, founded on YouTube, Morita describes math as not about numbers, not about calculations, but about logic. According to Morita, "it's the very act of looking inside your mind and encountering with your own self, encountering with your own rich inner universe, your jojo." So what does it mean to do mathematics? To do mathematics, as discussed in this video, one must encounter his or her own mind. It involves both patience and attention.

Throughout my research, I was faced with many deeper thoughts with regards to the subject of mathematics and its definition. I soon found myself, like many math fanatics, pondering the mind-boggling question: is mathematics invented or discovered? Can mathematics be discovered or is it simply invented by the minds of great mathematicians? Upon further research of this question, I came across several distinct theories, each expanding on the debate of mathematics as a human discovery or as a human invention. According to research, favors of the Platonic theory argue that math is a discoverable system that underlies the structure of the universe. In other words, the universe is made of math and the more we understand this vast interplay of numbers, the more we can understand nature itself. Greek philosopher Plato believed that mathematics exists independent of humans and will continue on long after we are extinct. Several other theories support the opposing argument - that math is a man-made tool and just so happens to correspond with the universe. For instance, the logistic theory holds that mathematics is an extension of human reasoning and logic. Similarly, the formalist theory argues that mathematics boils down to the manipulation of man-made symbols. According to research, mathematics has even been linked to fairy tales as in the fictionalist theory.

I feel that a person's defining or viewing of mathematics highly depends on that person's experiences with mathematics and recognition of its existence. I believe that mathematics is all around us. Its existence is unavoidable. It exists within our daily lives in many forms and ways. Like Morita, I believe that mathematics is much more than just numbers and calculations. Everyday there is a new theory, a new idea, a new concept is being created. A world without math is unimaginable.

Natalie

Sir Ken Robinson - Do Schools Kill Creativity?

Hi all!

Last class we were shown Sir Ken Robinson's 2006 TED Talk, a 20:04 minute video titled "Do Schools Kill Creativity?" Upon reflection of this video, there were many things that deeply resonated with me and struck me as both interesting and surprising. Robinson states that education "goes deep with people," similar to the ways of religion, money, and other things. This particular statement is interesting to me as it better depicts how educators are viewed and how important their many roles are to society. It makes me feel important and proud to say that I am studying to become an educator. Robinson also discusses how children starting school this year will be retiring in 2065 and that, despite all of the expertise, no one knows what the world will be like yet we, educators, are supposed to educate students about this world. This discussion is both interesting and troubling to me, resonating with me as a future educator. At 2:13, Robinson states: "It's education that's supposed to take us into this future that we can't grasp." After thinking about this statement, I was quick to realize how true these words really are in the rapidly advancing world in which we live.

With regards to why this video applies to our class about teaching children mathematics, the video demonstrates and explains the importance of recognizing how education must be kept up-to-date and match the world's rapid advancements. Technology, for example, must be incorporated into daily teachings and can be easily adapted to the subject of mathematics. As Robinson states at 18:24, "we have to rethink the fundamental principles on which we are educating our children." We, future educators, must prepare for the future world and for teaching our students who will be brought up in it. Especially in mathematics, creativity can be found and practiced in many new ways.

Natalie

Math Autobiography

Upon reflection of my own learning of mathematics in school, I recall always enjoying the subject of mathematics. I remember always looking forward to math class and enjoying practicing math problems as a young student.

With regards to what mathematics looked like in my K-6 classrooms, appearance varied depending on the grade level. In primary grades, I remember a number line display overhead above the chalk/white board as well as various posters and displays of number tables. I also remember the addition, subtraction, multiplication, and division signs that were placed on the classroom walls, almost as classroom decorations. In elementary grades, I remember poster displays of multiplication and division tables mounted on classroom walls, available for student viewing and learning. In both my primary and elementary classrooms, math was always evident in the classroom set-up. In a sense, math surrounded us primary and elementary students.

Throughout my primary and elementary school years, I always considered myself to be "good" at mathematics. I remember looking forward to getting my tests back and generally enjoying practicing math problems and working on my math homework especially. It wasn't until my last year of high school when I started feeling differently about mathematics as I was suddenly challenged by the material more so than in prior years. Although I still managed to do well, I remember having to dedicate much more of my time to studying math throughout my final year. It was no longer something that seemed to come natural to me and required little effort. As a fifth year student at Memorial University, I have completed the following mathematics courses: Math 1090 and Math 1051, which were two required courses upon entrance into the faculty of education.

The role of the teacher in my math classes often involved appearing enthusiastic and excited about the concepts of mathematics, demonstrating a positive and motivating attitude towards learning math. Upon reflection, the majority of my primary and elementary teachers introduced various concepts of math in an exciting way and always introduced math as a subject of great importance. In saying this, I think that my teachers recognized the importance of teaching math in a fun way wherever and whenever possible. I remember often using hands-on objects such as counting blocks in primary grades and money pieces in elementary grades, which I feel was very effective. 

As a university student, I recognize that math is everywhere and is a major component of my daily life. I utilize math on a daily basis whether it be through an actual mathematical problem, making a purchase and dealing with money, or filling out my monthly agenda assorted by numbered dates. My current feelings towards the subject of mathematics overall are positive. I feel as though math is an extremely important subject for students of all grade levels and people of all ages as it is in our lives daily in some form. I look forward to learning more about mathematics and how to effectively teach mathematics to primary and elementary students.

- Natalie

Welcome!

Welcome to my Education 3940 blog! Throughout the semester, I will compose and post various blogs detailing my experiences with mathematics as a subject as well as my experiences in learning about the teaching of primary and elementary mathematics.

I hope you all enjoy my shared experiences and thoughts!

- Natalie