Maths not = calculating

I came across computerbasedmath.org (maths ≠ calculating) via @JeffUtecht’s post My 25%PD. Both these links are worth visiting but let me focus on the first.

computerbasedmath.org founded by Conrad Wolfram – yup, the Wolfram behind the site anyone who’s ever googled a maths problem/question would have visited at some stage. Conrad Wolfram’s TED talk \”Stop teaching calculating – start teaching math\” is an engaging insight into how maths education can be…and it’s a big challenge in many ways, e.g.

  1. Shift the focus on calculations/computations to real application of maths by using computers/technology to do the calculations.
  2. Change current scope-and-sequence driven by the difficulty in calculations rather than concepts. For instance, with interactive visuals  even primary/elementary students can access concepts such as calculus.
  3. The best way to teach procedural aspects of maths is to involve programming (I agree as the process of defining an algorithm deepens understanding).
  4. Make maths an elective; the rationale is that maths is embedded in other subjects and in a contextualised manner
  5. The big hurdle is exams – education is “test”ed so changing the curriculum is a challenge

This is what I have been trying to do – in a rather crude form – in the past few years. And #5 is a real dilemma. Also, any change must be systemic because I find that students, whether they like it or not, come to expect a “format” for maths lessons. While I enjoy veering away from the standard format, I know that the expectation is there to “teach calculation”.

But, where to now?

I’ve signed up to support computerbasedmath.org to be in the loop and help spread the word.  I wonder if I’ll see any changes along these lines in my lifetime. I think the Australian national curriculum changes for maths embeds calculation more than ever.

Btw, I should add that the website links to plenty of interactive resources allowing teachers to follow these principles. It also seems that programming contributions are also welcome. These people are serious. Do check them out.

Percentage Composition

I wanted to make this lesson a bit more interesting as well as incorporate opportunities for connections with other maths topics.

I knew my year 8 class students loved music so I devised a very simple poll on Rob Thomas (one of the students was going to his concert): like him, don’t like him, don’t know him. This was a good opportunity to revise Frequency Distribution.

Just by fluke, our 3 fractions turned out percentages of recurring decimals (another connection). In that sense, it’s really not a very good first example! Anyway, someone asked if the percentages will total a hundred (I love it when they think!). So, we added and of course it didn’t. We got a result of 99.8%.  This opened up a discussion on the consequences of rounding/truncating decimals.

I made a statement that the most accurate way to represent not whole (fractional) values is via fractions. Nods all around until I asked, “‘Do you believe me?” The consensus was yes because I was the teacher. I was quick to point out that they should not always believe everything teachers say – they have to think if it’s reasonable; teachers are humans, after all, and can make mistakes. Besides, I really wanted to challenge my students to develop their thinking and reasoning.

So, I went back to the Frequency Distribution Table and 3 fractions. Adding the fractions naturally gave a total of 1 and nearly everyone said that’s 100%, as expected. Joy!

Were it a more able class (we stream our Maths classes), I could have pursued more connectionist opportunities but I did sense I’ve pushed enough today. I know I’ll refer back to this lesson when we actually do Data later in the school year. The class was engaged because they knew the meaning behind the numbers.

By the way, the statement is a fact I had truly learned in my previous career in IT. Particularly when I worked for a bank calculating interests, calculations in programs (software rather than curricular) were designed to stick to fractions as much as possible to minimise rounding errors.

In summary (more for my future reference),

Learning strategies: connectionism, motivation and engagement via meaningful and relevant examples, question/reason validity, compare/contrast

Fractions, Decimals and Percentages – provide different ways to represent fractional values, of which fractions are the most accurate

Directed Numbers

Analogies and Directed Numbers

Directed Numbers – positive and negative numbers – is abstract, particularly the negative thing.  Bank statements aside, it is rare for us to see negative numbers. We don’t even have sub-zero temperatures here in Sydney; not in our waking moments anyway.

While I’ve taught my year 7 class about ‘two negatives make a positive”, this remains an elusive concept to understand.  At least they remembered what I said.

Being an ESL-speaker myself, I spend a fair amount of time with literacy within the context of maths. Revising Directed Numbers today, we went through words that were associated with Positive and Negative. One of the most useful ones was ‘not’ for negative.

not down – up

not left – right

not negative – positive; i.e. minus negative is a plus (positive)

On the last period on a warm Friday afternoon, cheerful “I get it” from students is like a cooling G&T or glass of iced water (non-alcoholic option).

I guess this post is more about my teaching than learning.

I’d like to say the ‘not’ thing was completely random. The truth is, I used ‘not’ a lot in my computer programming days. If you think of computers as a collection of switches (which is a very simple but apt analogy), all you’ve got is on and not on (off). I still use ‘not’ in my SQLs. Sometimes it’s a lot easier to say NOT (A or B), particularly when you want the rest of the 24 letters, or something like that. Example is interpreted as Not A AND Not B; the not applies to the OR as well. But this is going into Boolean Algebra…oops, algebra again.