Your 'Demystifying The Algebraic Method' Comment ...
Share your 'Demystifying' takeaways below.
Some past comments ...
It is not often we get the opportunity to watch a peer teach and so this was really helpful.
I liked that you didn’t use a pro-numeral, I also liked your scaffolding.
I have always taught the students to write down their thinking eg -5 -5 On both sides so that they can keep track of what they are doing and so that I can quickly help them when they get stuck. I noticed that you told your students that they didn’t have to write down their thinking, does this generally work for students. I really don’t want them to be writing out Woking that is not worthwhile?
Hi Natalia, I think I was making it optional in that situation. (I'm not exactly sure the exact thing you are referring to!)
I tended to do:
X + 5 = 12
X = 7
But in that case above I wouldn't demand they do the -5 -5 as it is rather obvious.
I really like students were prompted to give their own answers using their own method. They each came up with their reason how they formed their solution.
That is key, Doha! Makes a huge difference!
Conceptual understanding is key
From my experiences as a student and conversations I've had with my colleagues as a tutor and a teacher, I know that many people choose to simply teach the rules, since they're fast to teach and don't require students to do the hard work of understanding what they're doing. Unfortunately, using these "shortcuts" without understanding is problematic once questions get more complex. Hence, the importance of using the balance model.
One thing I'm wondering about is the scaffolding shown in the video. We teach students an order for inverse operations; the whole backtracking method is to teach this order. But doesn't this create misconceptions? Should we show students that there is no order for inverse operations? That for 2x+1=3 you could just as easily divide both sides by 2 first (you'll end up with some fractions though), or would that add to the cognitive load? Teaching is too hard.
Spot on James. This applies across all maths. I call the teaching you describe (simply teach the rules, since they're fast to teach and don't require students to do the hard work of understanding what they're doing) as trick teaching. Becasue that is exactly what it is. What many maths teachers do not understand is that trying to learn multiple procedures WITHOUT understanding the concepts that underpin those procedures is an impossible task for the majority of students. (Those students with a natural flair for memorising maths cope OK) The reason maths teachers don't realise this is because e never struggled with maths at school. So we teach the way we were taught. For now ... hone the Need-Levels-Choice approach for equations! (And remember ... no calculators!)