Influential math teachers

My fifth grade teacher in California was the most memorable first teacher who made math an interesting and fun subject for me. I came out of that school year telling everyone that I loved math. At the beginning of each class day, we worked on the exercise called "Star Voyager" which consists of small math problems and one challenge question. Each student accumulated points based on the number of problems solved. I don't remember exactly but it somehow added to our imaginary adventure into outer space. I hope to bring fun and challenging problems that would further interest students in the subject.

I think a not very exciting math teacher would be my junior high math teacher. She excelled at solving problems and answering our questions. I learned a lot from following her examples but the format of every lecture was the same. In my teaching, I will plan to have a diverse range of activities to approach different concepts in problem solving. 

In my Pre-Calculus class in high school, the teacher was enthusiastic about the subject. This really made me desire the same love for math and teaching math as I had a role model there. I found that helping my peers with the concepts and assignments in math was very enjoyable and rewarding. The teacher provided a space for student pair/group discussions which I think is crucial in learning math.

Reflection on Teaching Perspectives Inventory(TPI) results

This graph depicts my results from taking the TPI test. My scores were pretty consistent in the first four perspectives, transmission, apprenticeship, developmental, and nurturing, around 34-36 with the highest score in apprenticeship. Due to the similar scores and the fact that none is exactly above the top line, I would not say that a specific perspective is dominant. However, I scored the lowest in social reform, 25, which is 9 points less from the nearest neighbor so social reform is a recessive perspective. On average, I received a score of 32.6 with a standard deviation of 3.88. 

From the definition of the apprenticeship teaching perspective, this test shows that I strongly value good teachers being skilled practitioners of what they teach. As a teacher, I am there to demonstrate to students the knowledge through performing examples and to guide them in different levels of learning. For the other three in which I scored equally high, I think what the test reveals is true. Of course, the transmission of content is important but so are understanding each learner's way of thinking and nurturing the students to have confidence in themselves. I really echo that part in the definition about caring for the students by way of encouraging their efforts and challenging them while supporting their goals.

What surprised me was that my score for the social reform teaching perspective appeared so low on the scale. After much thought, yes, mathematics is not a social studies class and we may not think much about incorporating messages about societal change into the math classroom but there are ways to direct the students to think critically. For example, students can work on projects on a social issue of their interest and apply the appropriate mathematical skills in their presentation and analysis of data. Other lessons could incorporate optimization and decision-making for instance, in education funding or low-income housing options. I would try to be more creative in this area of lesson planning. Regardless of the various activities, the goal is for students to associate their learning with the environment we live in and how their actions would impact the future world.

Provincial Pro-D Day

On October 23rd and 24th, I will be attending the IB-DP Mathematics workshop.

Number of squares in a chessboard

How many squares are in an 8-by-8 chessboard?

The first thought that pops into the mind is that 8*8 yields 64 squares. However, these only account for the 1-by-1 size squares. We quickly realize that squares can be seen in different sizes on a chessboard.

Let us consider how many 2-by-2 squares are possible.
I'd like to think that there are 7 horizontal positions for a 2-by-2 square since a square cannot move outside the board. Likewise, there are 7 vertical positions for squares of this size. 7 times 7 gives 49 squares here.

Similarly, for 3-by-3 squares, there are 6 horizontal positions and 6 vertical positions. =>36 squares.
Also, for 4-by-4 squares, there are 5 horizontal positions and 5 vertical positions. =>25 squares.

We see a pattern!
Taking it all the way, we get 1 square for 8-by-8 size.

The total number of squares is the sum of the squares: 64+49+36+25+16+9+4+1= 204 squares.

Ways we can extend this puzzle:
Q: How many 3-by-2 rectangles are in a chessboard? (The student must think about positioning these rectangles on the board.)

Q: How many triangles are there below?

Reflection on integrating instrumental and relational learning

After reading Skemp's article, I fully stood on the side of relational understanding of mathematics and hence was surprised to discover a good number of the class in support of the instrumental approach. Throughout the discussion, some stressed teaching students instrumentally first so that they would gain confidence in learning math; however, others contended that it is more important to present students with the relational understanding before showing them the shortcuts/formulas. 

For example, on teaching angles in polygons, one could easily give out the formulas for computing the sum of the interior angles (180 degrees*(n-2)) and calculating each interior angle of a regular polygon (180 degrees*(n-2)/n). Nevertheless, it is much more helpful to have students start by looking at the sum of interior angles in a triangle, which is 180 degrees. Then, we see that a square/rectangle is composed of two triangles and that a pentagon can be divided into three triangles, etc. From this point, the students can come up with the formula themselves about the sum of the interior angles in a polygon. Furthermore, they can also figure out each interior angle in a regular polygon. 

I now feel that both instrumental and relational learning are crucial to mastering mathematics and that it is the teacher's responsibility to discern how to integrate both approaches with regards to specific lessons. 

Response - Richard Skemp's article

I stopped to think about the course of my education in mathematics, how I was taught, and my attitude toward the learning of the subject. Were they instrumental or relational ways of understanding? One of the things that struck me in the article were the clear analogies differentiating instrumental mathematics and relational mathematics. If we see mathematics in this light, the approaches to teaching and learning the subject would be revolutionized. I was also surprised by the fact that once concepts were learned relationally, these carry on a long-term, even organic(!) effect in the student's future learning. In conclusion, I believe that relational mathematics is far more beneficial to teachers and students alike than instrumental mathematics. We would love to grade a 100% exam but we would be doing learners more justice by instructing the ways to navigate and construct their mathematical knowledge.

Welcome to my blog on teaching secondary mathematics

Hello, it's wonderful to see you on my first blog ever!