MathsClass

Lots to think about here (this is my second iteration at this comment). I think the essential question is : How does this sheet change the current process? The three main things I notice about the sheet: (i) It helps students locate the correct formula, (ii) Allows students to avoid problems with order of operations and entering fractions, squares and cubes into their calculator, (iii) Lets students focus on the input parameters - without dealing with intermediate calculation steps (such as calculating an Area first, then using this to get the volume). The process becomes: locate the required input parameter, get an answer out. For (i) : Most of us provide the formula for 5.1 students. Either because we know the consequences will be terrible results, or because more fundamentally we don't believe memorising formula is essential. Interesting to note the syllabus says 'use' the formula, not 'know' the formula! For (ii) : Being able to work with numbers and operations in a calculator (which really means : being able to understand and manipulate algebraic expressions and order of operations) is a huge problem I see across many classes. So I worry the automation in this sheet reduces the chance a teacher or student will spend time on this. Volume calculations could be a good time to revise what it means to multiply by 1/3 - that it's equivalent to dividing by 3, etc, etc. So for me, the act of working with calculator operations is not so much that they help us find the answer, but that they reinforce algorithmic procedures which use number properties. I'm probably most concerned about (iii) - that the sheet turns volume into a black-box operation: parameters in, result out. For me understanding the method behind the formula, and the reasons for the method - are the key to content and the Working Mathematically process. What is Volume? How do we get it from a base Area? Why does this work? Why is there a 1/3 when we do a pyramid - what does this mean about pyramids fitting into cubes? But in practice, how often do we follow this path in class? I try hard to but it's a struggle - and you fall behind in the program. So at the core of your question is: Should we be teaching students to use mathematical tools or should be we teaching them the mathematical process behind the tools? I don't think this is an either/or situation - I would say both, and we adjust the mix according to the context. I would hope (and I haven't worked this out in my own practice!) that time saved on the mechanics of doing mathematics for those who need support, is replaced with more quality time in exploration so that at least the tools support Working Mathematically in other ways - and the endpoint is not just 'getting the answer to V"

I'm not a maths teacher, but I'm someone who struggled in high school maths (despite doing 3u!) and I think this is a fantastic scaffold to help students on their way to developing independence and automaticity in this area. It reduces the cognitive load and allows you interact and see how the formula works (rather than just being a passive recipient of a YouTube clip). I wonder if you can create a Phase 1, Phase 2, Phase 3 calculator, that gradually reduces the scaffolding, requiring the students to do more of their own working out? Then you could always challenge the top kids to create their own Excel calculators to demonstrate a deep understanding 😊 Wish this had been around when I was doing HS maths! 😊 Well done, Simon!

I don't know if the question should be "Am I being too helpful?", but "Do I continue to be too helpful after the help is no longer needed?". There is definitely a place for explicit scaffolding, but I know I am guilty of spoon feeding students a little too much. And I suffer because of it as I then need to somehow get my students to be independent and resilient thinkers again. I am currently trying with one of my less able classes to begin by overscaffolding and then slowly take the scaffolding away so that the last lot of working out in an exercise is all their own. It's lots of work making the worksheets but I think it is paying off.