One of these things is not like the other...

The biggest obstacle for me in regards to teaching math is adopting a new relational understanding of mathematical concepts so that I can in turn teach students how to have a greater understanding as well. This means I am constantly cycling through a process of unlearning and then relearning old concepts that I thought I understood! I really did appreciate Skemp's article for this reason. There was a passage in his article on the circumference of a circle that I need to share, "The circumference of a circle (that is its perimeter or the length of its boundary) is found by measurement to be a little more than three times the length of its diameter. In any circle the circumference is approximately 3·1416 times the diameter which is roughly 3 times the diameter. Neither of these figures is exact, as the exact number cannot be expressed either as a fraction or a decimal. The number is represented by the Greek letter π." This is the first time in my life that I have EVER understood why on earth we used the formula we did to determine circumference! Well if teachers had explained it like that in the first place, I wouldn't have struggled so much to retain the formula.

I appreciated Skemp's defense of instrumental instruction though, and how both are important when teaching and learning mathematics. I agree that it is difficult to shed the instrumental instruction we were originally taught because understanding things relationally is not easy... at all! And we may encounter dissonance and push back from students when they are comfortable with memorizing a formula like we often used when dividing fractions! I was reluctant to abandon this "old tradition" as I didn't have to think about it much.

In all honesty, I have not enjoyed reading a lot of our text book material prior to our classes as I feel discouraged from the onset and I am left all on my own to understand it! When we come to class and get to use hands on materials and work together, that is when I am making the biggest strides and breakthroughs. I can then return to the text with a fresh perspective and deeper understanding. Then I see its value as a future resource for instruction because I have adopted a more relational lens on these once challenging concepts.

Skemp layed out the advantages of relational math as being:

1 It is more adaptable to new tasks.

2 It is easier to remember.

There is a seeming paradox here, in that it is certainly harder to learn.

3 Relational knowledge can be effective as a goal in itself

4 Relational schemas are organic in quality.

I strongly agree with the second point, I am remembering concepts better now because they have become deeply embedded through hands on practice and by adopting the skills and methods my colleagues have taught me as we collaborate together. This weeks class was a great example of that, we got to use hands on manipulatives! Instead of looking at pictures of geometric shapes, we created them. This certainly warrants a big thumbs up!

I had no idea that there were so many children's book on math! I love books and they are such a fun way of getting students engaged! This week in class we read about the Greedy Triangle. 

This was my favourite part... 

I will definitely be looking online or through the library in the future if I am teaching a new concept to students as it is a great minds on to start a lesson.