Reflection: Memory

In secondary school, math was my absolutely favourite subject. I had my teacher, Mr. B, to thank for that. He was that teacher that everyone had a healthy fear for, but was also the teacher that everyone wanted to impress. Through his thick exterior, he was generous to all his students, and always made sure everyone that needed extra attention got it. Though I never needed extra attention, he always made sure those of us doing better in the classroom were given the opportunity to be challenged. It was because of this teacher that I had such an amazing experience with secondary mathematics.

I never particularly had a terrible math teacher, but I did have a teacher who was very cut and dry about math. I was not challenged at all in the classroom, and did not feel my needs were met. I feel that it would have better if I was challenged and given more work to do, and I do not feel that I would been as bored if I had been given the opportunity to do more challenging activities in the classroom.

Reflection: TPI Survey

I felt the TPI survey matched my own personality very well. From the results above from the TPI survey, I am seen to be mostly nurturing, but still concerned with student development. My views on social reform are not particularly strong, which explains it being my lowest score.
I am opinionated on all of the sections the survey tested for, so I was surprised I did not have a higher score for all of the others as well. Overall, I understood I was mostly nurturing because I tend to care a lot for my students well-being in the classroom, all while making sure they know how to succeed academically.
In the future, I do want to work on being more even across the board when it comes to these topics. I feel they are all important aspects of teaching, so keeping them all in mind will allow for the success of the teacher. I don't think I'll ever lower my level of nurture, as I feel an extremely important part of teaching is being a caring - but still professional - individual that students can always look up to. I look forward to seeing how these aspects come through in my teaching.

Entrance Slip - How many squares in a chessboard ?

When thinking of how many squares are in a chessboard, I begin by thinking of a regular 8x8 chessboard.

In order to see all of the different types of squares that can be formed from this board, I must begin by thinking of the smallest squares that can be found, and work my way up to an 8x8 square.

To begin, I think of a 1x1 chessboard, seeing that it just has 1 square.

Moving to a 2x2 chessboard, one would see 5 squares.

* There is one large 2x2 square, and 4 1x1 squares.

In a 3x3 chessboard, one would see 14 squares

* There are 9 1x1 squares, 4 2x2 squares, and 1 3x3 square.

From these you can see that a pattern emerges:

For a 1x1 chessboard, 1^2 =1

For a 2x2 chessboard, 1^2 + 2^2 = 5

For a 3x3 chessboard, 1^2 + 2^2 + 3^2 = 14

etc.

When applying this pattern to an 8x8 chessboard, we see that 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 = 1+4+9+16+25+36+49+64=204.

From this we would see that there are 204 squares in a chessboard.

Initially, I entered this problem thinking of an obvious answer of 64 squares. I quickly realized there was more to this problem than I thought. I needed to find a way of calculating the number of squares in a quicker way than just counting. I began with the smallest size of squares and worked my way up to 3, before finding a pattern. I realized that through finding out the each number of squares, they were all "perfect squares", meaning they have a square root. Knowing perfect squares helps me, as well as deductive reasoning and seeing a pattern emerging. This problem could be extended by asking for the number of squares of a larger chessboard and checking understanding. 

Reflection

After discussing the differences and similarities of instrumental and relational learning, I still stand strong on my point of relational understanding. However, I do feel that instrumental learning has good points to it as well. Time is an important factor to making instrumental a strong point, while long term success allows relational understanding to come out on top.
My view is that both understandings should be combined in order to have a successful classroom. Students should be able to either learn the background before going into the step by step process of learning, but also be able to go the other way around. Teaching this way allows for a variety of different students to have their needs met.

Skemp Article Response

I had a very strong viewpoint in regards to the issue as I began this article, but as I read I began to question the views I was so certain of. The description of relational and instrumental understanding was raw and original, and I had never thought of teaching math as having two different paths. It became clear there was a divide between teachers who were only able to allow instrumental understanding, and teachers who only allowed relational understanding. I did not think there would be anything to attract me to allow students to understand instrumentally, until I came across reasons why it may be helpful, which pleasantly surprised me. Skemp's example of being in a new town also surprised me, as I had never seen a more thoughtful representation of relational and instrumental understanding.
My perspective on this issue is that teachers should always do their absolute best to relay relational understanding to their students, but it may not work for all students. Some students may take to learning theory very well, but some students may get confused and even pull away. A crucial part of being a good educator is being diverse with all students in the classroom; this can be achieved by attempting relational understanding with stronger students and instrumental understanding for students who may need more confidence with math. Once confidence has been built, attempts to change their understanding can be made.

Hello world! Welcome to my blog