Week 3 reflection

          In todays class we opened with some presentations on addition and subtraction of whole numbers. Danielle, Sneha, and Daniel led the presentations, which were the first of the semester. Sneha led an activity that was called the broken calculator experiment in which we, playing students, were presented with a problem where we had to find the answer without using the number 8 on our calculators. Daniel led an adlib activity in which we were invited to create a fun adlib that was used to explain a simple division problem. He added some difficulty to the problem by making our final answer have to contain a two in some place value mandatory. Lastly Danielle led an exercise on addition and subtraction of whole numbers based around horse racing. I found her activity to be the most engaging and was able to keep everyone in the class interested for the whole presentation. Her activity involved a horse that had to run 2400 meters. We were given a number of cards with different values and we had to subtract these values from the 2400 to see how far our horse would run. After the presentations we looked at algorithms for the four main operations, addition, subtraction, multiplication and division. As a class we were presented some basic questions and were challenged to use our known algorithms to solve the problems. I found it very interesting that so many different people in the class had so many different ways of solving the question. Even for a simple subtraction question there were multiple ways that people suggested that we solve the problem.
I thought that, for the most part, we were all taught the same way to subtract, but then Patricia showed us a completely foreign way to subtract in which she borrows from the bottom number rather than the top. This is interesting, and is beneficial to my pursuit to become a teacher because it enforces the fact that there are multiple different ways to do and make sense of mathematical problems and algorithms; there is no definite right or wrong way, and every person has their own perspective on how to reach this answer. This thought process was reinforced by our readings, the handout we were given and the video we had to watch by Jo Boaler. Specifically, in our handout, “How Students Should Be Taught Mathematics: Reflections from Research and Practice”, Jo says that the math classroom should be a place where can talk about differing ideas and should be encouraged to solve problems in different ways and with different solutions.
           Having a valid and reliable resource is integral in the process of building knowledge as it may force you to look at things from a different perspective, or it may reinforce your and strengthen your current beliefs. Also, these reliable resources are extremely useful in furthering your professional learning. The website www.Edugains.ca is extremely useful and their professional learning facilitator has a plethora of resources that can be used to help build knowledge. I can see myself accessing these resources later in my career to get lesson plan ideas and to help navigate through specific problems in the classroom and with the curriculum. There was also an interesting section in the textbook readings, (M. Small, Making Math Meaningful, 36) in which the different types of assessment were discussed, assessment FOR learning, assessment AS learning, and assessment OF learning. These different types of assessment relate to differentiated instruction and the different levels of learning that each student may be at; rather than comparing the students to each other each student is evaluated in their own way.

A. Teacher. (2007) Different solutions. [Online Image] http://bit.ly/1gSFWMh

Week 2 Reflection

         In this weeks readings we looked at the Ontario Math curriculum for grades 1-8, as well as an article by Ball and Bass titled “Toward a Practice-based Theory of Mathematical Knowledge for Teaching”. As brought up in the lecture slides, there is undoubtedly a generally negative public opinion of math. Generally speaking, math is usually depicted as a chore and everyone’s least favourite subject, except for what the media depicts as nerds. When ideologies like this are depicted on children television shows it fosters a negative opinion of math from an early age. I can definitely say that this was the case for me when I was a child. When I was growing up math was my least favourite subject, and as soon as math wasn’t a mandatory course I stopped taking it. Due to the fact that I never took any post-secondary math courses I used to think that I would not be as good at teaching math, as I would be at teaching English, my undergrad major. However, in the article by Ball and Bass an interesting point was made. 
             There was a study that was based on math teachers and their student’s grades. The general thought was that those teachers who took math classes beyond the mandatory courses would have higher student grades in math. The results, however, were much different. In fact, the teachers who took more advanced math classes “produced positive main effects on students’ achievements in only 10% of the cases, and perhaps more unsettling, negative main effects in 8%.” (Ball and Bass, 3, http://bit.ly/1iHjN5o) The teachers who took very advanced math courses could have a very advanced thought process about math and therefore might be conditioned to think about and explain mathematical concepts in a very advanced way. This conditioning does not necessarily convert into high student grades, as the advanced way of thinking and explaining may confuse some children. Ball and Bass suggest certain teachers might be very advanced at memorizing formulas rather than knowing the pedagogy of math or how to explain the concepts. Another example; if you ask your Dad who is an engineer how to solve an equation, he may just quickly tell you the answer without explaining you through every step along the way of the problem solving. The advanced knowledge can hinder your teaching. Therefore, an excellent math teacher is someone who can relate every mathematical concept to every student individually, and explain in depth how to reach the answer. An excellent teacher must also understand that there are many different ways to reach the same answer. He or she should encourage students to find the answer and understand math any way that they can rather than just teach that there is a right and wrong way to do math, as most of us were taught. That is why the mathematical process of problem solving will be my focus over the next few weeks. Knowing how to explain a child through a concept is incredibly important in effectively helping them understand and excel at math. It is also, “the primary focus and goal of mathematics in the real world.”(Ontario Math Curr., 12, http://bit.ly/1dVS6Ck) This is important because basic mathematical problem solving principals and functions are used everyday in life and it’s crucial to learn how to effectively solve problems. 
The process of problem solving can also include every single mathematical process stated in the Curriculum. Equipping a child with the ability and the confidence to use math in the real world may help motivate them to learn and work through problems becoming better students, and ultimately better equipped adults.

Coleman, Mary. (2009). Chess. [Online Image]. http://bit.ly/1PhtNML

MATH BLOG INTRODUCTION

Hey, what's up everyone. My name is Tyler Bridgemohan Singh, I am 24 and did my undergrad at UofT majoring in English and minoring in philosophy and history of religions. This purpose of this blog is to record what I learn and and my thoughts and experiences gained from this course. It is also to synthesize ideas from the readings and lectures with my own thoughts. In addition, this blog is the beginning of a new professional digital identity that I am creating for myself that future employers can look back on to gain an idea of what I am about. I currently cook for a living at a restaurant called Turtle Jacks Muskoka Grill, which specializes in homestyle cottage style dishes. I enjoy reading, especially books that focus on race relations and colonial/post-colonial issues as well listening to music. Music is a passion of mine and I enjoy basically all types. Another one of my passions in life is sports. I love watching and playing football and basketball, and in the time between my undergrad and now I coached a basketball team for youths and ran a development league for the Oakville Basketball Club. I am excited to be back in school after 3 years off and look forward to working with all of you. I hope to learn some new teaching techniques in this class as well as refreshing my knowledge of math, which has never been my strong suit.