My best and worst Math teacher

From what I could remember, my Grade 8 math school teacher, Mrs. Sandy was by far the toughest and scariest. We were banned from using correction fluid in class but the thing we hated the most was how she would go around the room and check for mistakes. The students who got the question wrong, would be forced to go and solve it in front of the entire class. This was humiliating and if you could not solve the problem, you would be punished in front of the class. Her terrible attitude and lack of teaching made me hate her class.

              Well, the best teacher I had was Mr. Ceaser. He always made learning fun for us and the most important thing I loved about him is the way he valued each student. He always used to say that “Mistakes are the proof that you are trying” and he used to encourage us to ask questions. His dedication and commitment in our class made math easier. Mr. Ceaser would often stay back after class to clarify and explain difficult questions to students needing help. His passion for teaching has inspired me to follow in his footstep.

Reflection on my TPI results

According to my TPI result, I was very pleased to see that my highest score was in apprenticeship. When I was studying in Delhi, India, I taught math for one year to the underprivileged kids. These kids could not afford to go to school and since I was volunteering in a Non- Governmental Organisation, I had the pleasure to help those students. During my time, I had kids with different level of education and so I tried to incorporate different ways of teaching with real life examples, loads of activities and flash cards. Making the class fun was one of the main objectives as these kids were not used to the classroom environment. I wanted them to interact and participate in the classroom.

From the graph, my scores were consistent in transmission, apprenticeship, developmental and nurturing with a score ranging from 30-34 but I feel I should put more to enhance my social reform as I scored only 26.  Being a teacher, I should try and teach the values of the society but it is quite difficult to do that in a math class.

However, I was surprised to see that my developmental skills were quite low, only 30. As an educator, I try to use different resources and activities to make my class lively and creative. As I am still learning, I will try and incorporate new methods during my practicum and hope to improve my technical aspects of my teaching.

How many square are there in a chessboard?

If you ask this question in any class, the first thing which can come to our mind is " ohh if it is 8 by 8 chessboard, then we just need to do 8*8= 64 ",which is obviously wrong

Thinking of the number of squares is not an easy task for everybody and it can be easier for students who visualize it. 

            I found that it is easier to cut the squares and place it on the board and since on a chess board the squares are of two colors (in my example it is black and white) so I would recommend to use only one color. (My case I am using only white)

            While looking at an 8 by 8 board, we get only 1 square.

We can observe that from a 7*7 board, we obtained 4 squares

For a 6*6 board, we get 9 squares. ( as shown below)

Now we can observed that there is a pattern of square numbers

8*8 board = 1 square

7*7 board = 4 squares 

6*6 board =9 squares    

So obviously 5*5 board will be = 16 squares

4*4 board= 25 squares

3*3 board = 36 squares

2*2 board= 49 squares

1*1 board = 64

and since we need to calculate the total, we add them and we get 204 squares.

By visually looking at the chessboard, it was easier to calculate the number of squares. It is difficult to just say that there is a pattern/sequence behind this problem.

I will extend the problem by asking the student about the number of squares in a 10*10 chessboard and see if they understood the pattern.
I could even extend it to a 100*100 chessboard since now the students will know the pattern and I also thought we could even ask the students how many triangles we can get from that triangular chessboard shown below

Reflection on Integrating Instrumental & Relational Learning

I like the idea of relational understanding because the student learns both the "what" and "why" of Mathematics but for students who naturally find maths difficult, teachers might feel that relational learning is not the appropriate method.

Thus after Wednesday’s debate on instrumental and relational learning, I see that we should integrate both together. Visual representation is a good way to incorporate relational understanding and afterwards we can come up with any formula or theory.

I would like to take the example of how to calculate the sum of interior angles of a regular polygon. Here we would take pentagon as example.

Instrumental method:

Sum of Interior angle of a regular polygon = 180^◦ (n-2), where n is the number of sides.

Therefore, Sum of Interior angle of a pentagon = 180^◦ (5-2)

                                                                            =540^◦ 

Relational method:

Let us draw a regular pentagon. 

Start from any corner and draw a triangle.Continue drawing triangles but always start from the same starting point.

Here we can observed that the pentagon is made up of 3 triangles and since we know that in a triangle, the sum of angle of the interior angles is 180^◦.

Therefore, we can easily calculate the sum of interior angles of a regular pentagon

= 3 X 180^◦ 

=540^◦ 

Note that a pentagon has 5 sides and 3 triangles. So, we can see that the number of triangles will be 2 less than the number of sides.

            This pattern can be used for all regular polygons.

Our system of teaching Mathematics tends to favor instrumental understanding but still we should incorporate both as there is always a proof behind a formula. It is very easy to forget a formula but if we understand the concept, we can slowly derive the formula.

Richard Skemp on instrumental vs. relational ways of knowing in mathematics

Write about

·         three things that made you “stop” as you read this piece, and why

·         where you stand on the issue Skemp raises, and why.

When I started reading the article “Relational Understanding and Instrumental Understanding” by Richard Skemp, the first point which came to my attention was what the word “Faux amis” have to do with mathematics and why he was  translating some French words into English. This was a very good scenario to introduce the topic rather than just giving the definition of relational and instrumental understanding. Also, when I read about the two terms and without reading the article completely, I started thinking about the activity we did yesterday in our Math class. Our first lesson was relational understanding where we had visual understanding of geometry. Moreover, it was surprising to see the important point Skemp made about teachers, “At present most teachers have to learn from their own mistakes”. The teacher is not the only one who will deliver knowledge to the classroom. We all learn from our own mistake and we also learn from students as they may have different thoughts and ideas.

Both methods have advantages and disadvantages but I don’t think that you can avoid one of them. As a future teacher, I will use both methods and it will all depend on the topic I will teach. Mathematics is not only about formulas and problem-solving but the logic behind it and how you can explore your ideas.

Welcome to my math world