Standardised Normal Distribution [Hinge Questions]

This post is to check understanding of normal distributions when students are required to standardise. Note that the answers given are from using the normal table to look up P(Z < z), not a calculator method.

Normal Distribution hinge q 1_1

a) The student mixed their units and so ended up with an incorrect z value
b) Correct answer
c) Student used the standardised value as the probability
d) Student made an error in the standardising formula (rather than X – μ, student did μ – X)
e) Student looked up the value given (1.45) rather than standardising

In case you wondered; this is for a different class ;-)

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Resolving using F = ma [Hinge Questions]

This question is for checking students understanding of resolving forces using Newton’s Second Law F = ma

MEch hingw forces slope_1

a) Student has misunderstood how to use the parity of the force components.
b) Correct solution
c) Student has used the incorrect component of the weight force
d) The student has assumed equilibrium rather than acceleration.
e) The student has not split the weight force into components; does not understand that only parallel components are considered
f) The student has not understood that perpendicular forces have no effect on the resolution.

More to follow soon I hope!

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Force Diagrams [Hinge Questions]

This question comes fresh from teaching Mechanics 1; for assessing whether students can draw force diagrams involving motion.


a) Student has selected the diagram where R is not perpendicular to the surface on which the object sits.
b) Student has selected the diagram with an additional force (friction) onto the diagram, where the question states a smooth slope
c) Student has selected the diagram with an additional force in the direction of motion; showing they believe that resultant forces should be drawn on the diagram.
d) Student forgot that acceleration should be represented on the diagram
e) Correct diagram
f) Student has selected a diagram that shows the correct forces, but has forgotten that the weight of the object should include the acceleration due to gravity. (note this could also show the student believes g to be a unit)

More mechanics themed questions to follow.

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Kruskal’s Algorithm [Hinge Questions]

I wrote another Hinge Question:

20131115 - AS UoM Kruskal_4


a) Student performed Prim not Kruskal starting at A,B,C,G or H
b) Student performed prim starting at D, E, F or I
c) Student allowed a loop to be created
d) Student did Kruskal correctly
e) Student did not order edges before performing algorithm
f) Student allowed a loop to be created

I used this in my recent observation lesson, and my HoD was keen on the use, though he seemed somewhat surprised by the time sink it is trying to make the question as informative for the teacher and as focused as possible.

If I was to use this one again, I would possibly get students to work on the question first; then give the selection of answers, as the question is fairly long – I think this is mostly to do with the topic; it is difficult to gauge someone’s understanding of an the steps of an algorithm without working through the whole thing.

More to follow as I write them.


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Do Farmers use Desmos?

Last year I wrote about min and max tasks with real life examples.

This year I used the same ‘tray’ task again:
20131016 - AS Mech Max Min 1_1

But this time I used Desmos to collect their results:

And then to check our function seemed valid:

And then to see if our calculated maxima matched up with Desmos:
20131016 - AS Mech Max Min 1_3
Which it did, and that was awesome.

Sorcery just keeps making my lessons a little bit slicker and a little bit easier and a little bit more visual.

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#ExploreMTBoS Task 4 – More listening, more learning.

This feels like a bit of a cop out for Mission 4; but I *did* host the #GlobalMath Autumn special. I figured I would write a post thanking all those who presented rather than talk about what went on – if you want details the go listen!Screen Shot 2013-09-14 at 7.39.21 PM

So thanks go to:
David Wees – his interactive presentation was the highlight of many people’s session and gave us all a lot of food for thought about questioning – If you wanted more details you could look up the original GMD session he gave on the topic or go read his blog

Chris Smith – his first time at a #GlobalMath and not only did he present but survived an alien attack! Thanks to him for a reminder that there are many ways to share and collaborate and not all of them involve super high tech solutions.

Julie Reulbach – I’m hoping that the people who signed up for Explore the MTBoS following her presentation are in equal numbers to the new faces I saw at GMD thanks to her, Sam, Tina and Justin. And I can’t help it; I hear her voice and it makes me want to chair dance – INFECTIOUS ENTHUSIASM.

Kev Lister – when we decided to do seasonal specials at a more convenient time for the UK Kev was one of the first people on my list to ask. If you haven’t read his blog on developing a department and working as a HoD then you really should. I’m hoping the GMD sends his spreadsheet downloads through the roof…

Hedge- She won’t believe me when I tell her that people loved her ideas; but it’s true. Hedge has so much to share about teaching Stats, and her love for the subject pours out when she presents. If you EVER get the chance to talk to her about teaching stats then DO IT. You won’t regret it. Unless she makes you do press ups.

Justin Lanier – Justin calmed us all down after the pace of Hedge with a lovely introduction to Math Munch. While it’s great to hear about what people do in the classroom; it’s also fantastic to remember that there is so much mathematics that students can experience recreationally. I love the niche Math Munch is working to fill and you should all check it out.

Thanks again to all the presenters, to all the people who came along and to all those who have contributed to making #GlobalMath special over the last year. I hope to see you all again at another session.


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Hinge Questions

What is a hinge question?

A check for understanding at a ‘hinge-point’ in a lesson, so-called because of two inter-linked meanings:
1) It is the point where you move from one key idea/activity/point on to another.
2) Understanding the content before the hinge is a prerequisite for the next chunk of learning.1

Dylan Wiliam writes that this helps teachers make a hugely important decision in the classroom; whether to move on or whether to recap and who is ready for this.

Sounds awesome right?

The thing is, writing these questions is hard. It’s hard because they need to be:

  1. Answerable in a short space of time (Dylan Wiliam suggests 2mins or less)
  2. Possible to interpret in a short space of time (around 15 seconds)
  3. You have to know why students have answered in a certain way

That last part is about the answers being semi-dense2 I won’t go into the details of that, that’s for another post but basically:

  • Any answer a student selects should suggest one, and only one, thought pattern or misconception
  • It should be impossible for incorrect though processes to reach a correct answer

So here is what I tried today:


And here is my rationale:


It’s not perfect; I’m happy enough that the question tells me what students do or do ot understand, but not what their thinking is. It’s a first step. The writing of the questions is easy, it’s making the responses useful that I find hard.

I’m going to finish this post off with a few thoughts:

  1. I am going to keep trying with this, and I’ll post anything I create here, with the idea that I will post the interpretation as well – because that’s the important bit.
  2. I would love to share ideas with anyone who wants to try creating these, or who has some great examples I can use to get myself into a better mindset for this
  3. This site is very cool, but lacks the interpretation element that makes these so crucial. I find myself looking at site and saying “lovely questions – what do they tell me?”
  4. That’s right, they’re multiple choice.

That’s all for now.

1: From Harry Fletcher Wood: Do they understand this well enough to move on
2Dylan Wiliam wrote a paper about this

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#ExploreMTBoS Task 3 – Global Collaboration

Screen Shot 2013-09-14 at 7.39.21 PM

Two parts to this post:

Part 1 – #TMSoton

I actually gave a talk about global collaboration opportunities, many of which were included in this post as things to do or look at. This is the presentation:

Part 2 – Some things I’ve done with this stuff:

I cannot stress enough how awesome these projects are for your classroom – so go look, share and collaborate!


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#GlobalMath Autumn Special

That’s right folks; you’ve heard about it on twitter; you’ve heard about it on the blogs; you’ve heard about it IN THE STAFFROOM (maybe). It’s finally here – the event of the quarter! It’s the:

GMD Autumn Special Poster

Come and join us on the 2nd November for the first of the Global Mathematics Department seasonal specials. This TWO HOUR basket of presentations, ideas sharing and collaboration is the first foray into making #GlobalMath happen at a time that is more convenient for folks across the globe, on a different Day.

The presenters we have on this time are a really special mix of teachers, curriculum specialists and department leaders; there should be something there for everyone from questioning, to lesson ideas, to ways to use software in new ways, to opportunities for recreational mathematics.

I’ll be hosting the event and it would be amazing to see as many folks as possible there to join us – the chat window is something you just have to experience and don’t ever feel worried about chipping in; we have two only rules at #GlobalMath:

  • We share freely
  • We’re nice to each other

So please join in!

You can sign up for the community here and the conference itself here

And don’t worry if you can’t make it, like everything else we run on Big Marker the conference will be recorded for your viewing pleasure – though that’s not as good as BEING THERE.

See you on the 2nd!

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One year on

I’ve been blogging a whole year. I can scarcely believe it was only a year ago I was dipping my toes into this amazing world and worrying about introducing myself on twitter. In this last year I’ve written 56 posts, a rate of a little over one a week (holy crap that’s a lot!) with my most used categories being Classroom (34), Lessons (29) and Conferences (20). It’s been a mental journey.

Goals for the next year:

  • Write about more lessons
    I’m glad that writing about lessons is one of my biggest categories because that’s one of the reasons I set out to blog. I just feel like it has been a long time since I wrote about one, so I guess I need to rectify that over the next few weeks. I will aim for one post about a lesson per month at a minimum.
  • comment more on other people’s blogs
    Explore the MTBoS has helped with this. I always try to reply to people who comment on my blog, well I would like to go a step further and follow back to their blog and find something to comment on if I can. We will see if this is manageable.
  • Continue to post with a similar level of regularity
    I like blogging, but sometimes I feel like I have nothing to write about, and sometimes I feel like I have too much. This next two weeks feels like it will be one of those “too much” times. Hopefully that means lots of blog posts.
  • Go to TMC14
    It was an amazing experience this year and it totally something I want to repeat :-)

Onward to many more years…

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