Rambling Teacher's Blog

Image by Bkrmadtya Karki from Pixabay Question: “Why learn maths when AI can solve all the problems?”  In this post, I will be writing my thoughts on the topic and giving my answer, as it currently stands. Spoiler: My answer is “It is still worth our while learning maths, not because we can find the answer to any particular problem, but because of the person it helps you become.” Note that I am writing from the point of view of a secondary school teacher who works with students in Grades 7 to 12. Whether you are in my shoes, those of a learner or of a parent, I invite you to come up with your own answer and share it in the comments. Humans are curious As human beings, we are innately curious about the world in which we live. We want to observe the repeating patterns of fern leaves and we want to know whether this phenomenon is unique to them or if it exists elsewhere. Humans have always wanted to study the locations of stars relative to the earth. They have calculated the trajec...

Anyone who’s had anything to do with kids up to the age of 14, has heard the meme “6-7”. As a teacher whose homeroom convened in classroom 67, you can just imagine how many times I heard it! Well, for this blog post, we will pretend that the number is actually 67 (sixty seven). By the power invested in me by my blog readers, all 67 of them, I hereby declare 67 “Number of the year”. Now, let’s explore the number’s properties. 67 candy canes will rot a kid’s teeth! 67 is a prime number. This means that, if a grandpa has 67 candy canes to give out to grandchildren this Christmas, there are two scenarios in which he can do this sharing fairly: If he has one grandchild; or If he has 67 grandchildren. You see, there is no way to split 67 candy canes equally among any other number of grandchildren. 67 as a sum 67 can be written as the sum of five prime numbers: 7+11+13+17+19 = 67 These specific 5 prime numbers are consecutive primes . This means that we wrote this sum with all of the prime nu...

In part 1 , we saw how Gauss, at the age of 8, found a quick way to add all the counting numbers from 1 to 100. The question that was left hanging was, what if the teacher had asked him to stop at 99? After all, his trick of pairing the numbers (100 + 1, 99 + 2, ...,  51+50) could not work for an odd number of values. Or could it? Well, the intuition here is simple: Adding zero does not change a sum . Using this fact, we can change our question to: What is the sum of the whole numbers from 0 to 99? This reduces the sum to a simple calculation: 50 groups of 99 or  A visual representation of the problem Let's start small and answer the question, "What is the sum of the counting numbers from 1 to 9?" We can go back to where it all started: Representing our numbers with dots in a triangular formation. This time, we will arrange the dots in a right-angled triangle: Please don't add up the dots!  Let's just notice that the blue dots, which we want to total, are half of ...

This post will show some beautiful and simple arithmetic. We will represent a seemingly complex question using triangles and and see how, at 8 years of age, famous 19th century mathematician Gauss added all the whole numbers from 1 to 100 in seconds.  How many dots in the triangle? Here are a few triangles, drawn with dots only:                          A triangle with 2 levels and 3 dots                   A triangle with   3 levels  and  6 dots      A triangle with  4 levels  and  10 dots Notice that each triangle answers the question, what is the sum of the whole numbers from 1 to the last level of the triangle?  The triangle with  2 levels  has 1 + 2 = 3 dots The triangle with  3 levels has  1 + 2 + 3 = 6 dots The triangle with  4 levels  has  1 + 2 + 3 + 4 = 10 dots Th...

Today, we had a professional learning day where we concentrated on 5 principles of curriculum implementation. The final principle was: Is it beautiful? Immediately, I thought of some 3D animations that some students were creating. My second thought was: Cryptography! Bear with me, I will explain it! If you cannot "bear with me", feel free to skip to the section: How I know it is beautiful !

In this blog, I want to discuss one of the issues in Maths education: The focus on one method to solve problems of a particular type. The example I will use throughout is the unitary method : When you work out the cost per unit of an item. The unitary method The following illustration of the unitary method comes from a very good textbook (Lipson et. al., 2022):  Students can apply this method to compare "cost per unit" when deciding which of the following to buy: Hopefully, students realise that 100g would be a good unit here, rather than feel compelled to use 1g. Using one method: The good and the bad It is a good thing to practise a method that applies in as many contexts as the unitary method does. It gives the student a strategy and enables them to master it. It also gives the teacher direction on how to teach. I am all for explicit teaching and it is difficult to teach explicitly in the absence of a repeatable method. The bad thing about emphasising one method is that i...