Module Two was designed to get you to reflect on some important aspects to classroom teaching, including:

- The role of awareness in developing as a teacher.
- Student Agency.
- The role of poor student behaviour on our teaching.
- Control: 'Being controlling' vs having 'Authentic control'.

Deb Morton - The problem with tricksI once had a student that was convinced that there was a special maths "trick" needed for every question she did and it made her very anxious because she never knew which one to use or if she even knew the trick at all! That alone made me stop using the word "trick", like it was some secret knowledge or magic act whic was potentially mysterious and unable to be understood easily. I do work hard at memory strategies for shortcuts so that students remember when and how to apply them, but I like the idea of going back to first principles instead when students aren't sure which procedure to use.RichardYes, 'Trick' is a shocking term to be used in mathematics. Well done for shifting away from that. |
Angus VossI am currently teaching Trigonometry to my 5.1 students and a lot of them have a strong dislike for mathematics. When teaching them about what we do when the pronumeral is on the bottom of the fraction, I did one example then told them the trick and just left it there for them to repeat every time. I loved the idea of 'Teach the long way first. Ask students to find a shortcut, then start using the shortcut.' At the same time it also brings that understand to the concept. RichardExactly! Avoid showing tricks at all costs! It does way more harm than good. So well done Angus. |

Michelle Millar - Time to think about how I teach shortcuts!I know I explain the long way to help with the students' understanding but I'm also aware there are many students who don't absorb this and cut straight to 'tell me what I need to do'. They just want to be spoon fed.RichardAgain, Michelle, I see this as pointing to a needed change re the culture of learning within the classroom. Kids who have been spoonfed for 8 years will demand spoon-feeding. I would 1) decide to make the change 2) address the idea with them and explain the reason for the changed approach 3) suggest they may not like the changes for a while (handle the objections before they arise) 4) state the complaints office is closed for 6 weeks 5) proceed with the changes! It's best to expect that students will resist, and be prepared for that resistance. With smiles on our faces, of course! My two-bob's worth. Indar DeoI have used the switchroo in the trig when running short of time. I will try not to use this. Some times i teach the concepts with out saying it as a trick RichardShortcuts are fine as long as they know how it works. |
Heath Barlin - Fraction DivisionI have used the division of fractions trick to solve these but realised I haven't explained what is happening originally, which has meant I haven't been consistent in teaching concepts. I found this interesting as a lot of these trick maths ideas have been popping up on my feed. I'm thinking of one in particular which has a repeated tagline of 'why don't they teach this in schools?"RichardYou mean you've seen a trick demonstrated on social with the tagline 'why don't they teach this in schools?' I've seen a few as well. Most educators have no idea how damaging it is for students to teach shortcuts as tricks. Great to see you reflecting deeply Heath. Jasmyn Du PlessisI am definitely guilty of teaching the "switcharoo" in trig. I had to teach Trig via zoom and out of frustration just taught the kids that as we were so far behind and needed to get through the topic. I do agree, it is not the best way. I agree with the use of acronyms. They really help. I usually get the student to try and come up with their own rhymes or songs for it. The hotmaths work sheets are great as they often start with deriving the formulas. I usually introduce a new formula with them when possible. RichardAwesome Jasmyn and we are all guilty as charged at some point haha. All good! |

I think that a lot of 'tricks' that people teach I would usually just avoid. The trig one, for example, doesn't really save any time so I would just say that we're dividing by something and multiplying by something else. Sometimes, however, going back to fundamentals every time can be quite time consuming, especially when dealing with lower ability students that forget the explanations and the tricks completely. A good example is with fraction divisions. When they've forgotten anything and they need something to be able to access the questions, giving them the trick can help them to remember whatever understanding they had before, for better or worse. I think the main thing is to use understanding-focused language when dealing with misconceptions. For example, when students are swapping numerators and denominators left and right with no thought, we can talk about the fact that we are doing the first number divided by the second, so the second value should change. Just like when we are using negative numbers and we are subtracting negatives, the first value stays the same but the second value might look a little different as we calculate it.

Thomas, you hit the nail on the head when you say ' I think the main thing is to use understanding-focused language when dealing with misconceptions'! As long as the understanding is presented first - and present enough to be jolted in them - then we are OK. My take!

I also forgot to mention one of my favourite things to do in these situations is to just put in simple values and show students an easy way to convince themselves that any trick they half-remember is correct or not. Just an hour ago when talking through the results from a small test with a student, he was solving equations with lines of working that looked like: 3x+2 = 19 -> 19 + 2 = 3x, no doubt misremembering some trick of switching terms he learned previously. As soon as he saw 3 + 2 = 5 -> 5 + 2 = 3, he could see how this trick didn't work. I think reinforcing this idea of checking these kinds of tricks to just verify them when you're feeling like you've only half-remembered them is a really good habit to give students.

Sensational! Again, coming from understanding!

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