# MathsClass

A blog about teaching and learning in a maths classroom.

Saturday, 25 August 2012 | 6 Comments

As I said in an earlier post...

2012 is looking like a year of quiet reflection (i.e. maybe not much on this blog), contemplation and trial and error.

Here is some recent thinking, please comment.

Lowering standards is not ok, but increasingly existing methods of assisting students to meet standards is not working. Therefore, the way I “teach” to help students reach the standard must adapt.

What is surprising for me is the timeframe in which the learning needs of students has changed. If I was teaching how I am today, 7 years ago when I started, I would have been brilliant. Today it is still not enough.

I think students are requiring:

• more and more structure to complete straightforward tasks.
• immediate feedback that is really not achievable without the use of technology.
• technology to aid and enhance, enabling them to learn in a different way to how we might have taught in the past.

Here’s something I did recently, and I’m still debating the validity of the approach.

The syllabus says, MS5.2.2:

using the formula V = ⅓Ah to find the volume of pyramids and cones where A is the base area and h is the perpendicular height

During class time my focus is on having the students apply this formula to solve basic problems, identifying the necessary dimensions to substitute into the formula. When it comes to a test, I would give the students the formula because they rarely are motivated to remember formulae.

We then went to Mathletics to review finding the volume of pyramids, cones, cylinders and spheres using the formulae we had previously applied. To me, Mathletics is taking an old style approach, i.e. here is a shape, what is it’s volume?

[Note: I’m not having a go at Mathletics, in fact, I think they know that the current method is not adequate. They recently had Dan Meyer out to talk to their developers.]

Anyway, leaving it at that would have been a pointless lesson. I made this available to the students.

It’s a calculator for finding the volume of these shapes where all the students have to do is input the variables. For a rectangular pyramid entering the length and breadth of the base, and the height of the pyramid is all that is required. Results were certainly better than could be expected without using the calculator.

Dan Meyer once said Be less helpful am I being too helpful? My current thought is that I’ve provided a suitable tool to help students move past the mechanics of the calculation potentially allowing them to solve more realistic problems.

Have I taken a step too far or does using a tool like this make solving problems more like the application of mathematics might look like in their future?

Volume Calculator XLS, 306 KB

Posted in • Lesson IdeaVolumeSoftwareExcelTools | Short URL: http://mths.co/2711

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Nordin Zuber on  25 August 12  at  10:32 PM #
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"
Nordin Zuber on  25 August 12  at  10:49 PM #
Lots more food for thought at [url=http://www.computerbasedmath.org/]http://www.computerbasedmath.org/[/url]
ronda on  25 August 12  at  11:25 PM #
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!
Nordin Zuber on  26 August 12  at  12:13 AM #
Great idea Ronda on students making their own calculator!! And I think this could (and should) be done for all students - not just the 'top' kids. It would help develop understanding of the formulae. Adjust the formulae used for the level of student readiness (some students would do cubes and triangular prisms, other might to spheres and cones).
Susan Leamon  on  26 August 12  at  06:25 AM #
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.

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Simon Job on  28 August 12  at  11:23 AM #
From Geoff Dix... You're the best judge of their entry point. For strugglers the scaffold you're setting up gives structure and method. Olden days would see this on the board ("working") and kids copy and fill in the gaps; gradually having to put in more of the working steps as the scaffold steps are gradually withdrawn in later questions. Simple but reasonably effective. The starting point always needs to be a challenge but achievable, for the group you've got; you wouldn't necessarily do this for a top class.

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Simon Job — eleventh year of teaching maths in a public high school in Western Sydney, Australia.
MathsClass is about teaching and learning in a maths classroom. more→

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