Author Archives: nik_d_maths

Remove the map and the territory takes a hit.

Original Post on MY BLOG

Sometimes we are reminded just how different classes can be.

Earlier this year I did this project with my Use of Maths class. It went well, they worked hard and were proud of the networks they had drawn; and they really understood the link ebtween that and the matrix. We had a bunch of good discussions about real life things; like logistics, mistakes we can make when getting information off the internet (Ashford International versus Ashford, Surrey – you don’t wanna get the wrong one to start your holiday!)

So I whipped the same project out for one of my AS Decision groups who had just learned about netowrks and matrix representation.

Didn’t work.

All the good stuff we got before was lost in a cacophony of hatred of worded things, the frustration of having to redraw networks when they get too confusing just because of where you have placed your locations. The size of the matrix was too intimidating. The searching online for train times was pointless to them because the lack of a definite answer was unsatisfying.

We got there in the end, but rather than being a productive struggle experience, it was a frustrating battle that used up a lot of my currency as a teacher. So now I gotta reflect on that.

What was different:

  1. The class is generally higher ability.
  2. They have spent the last few months working on mostly algebra and trig, with one acceptable answer to questions, as opposed to use fo maths, who are more used to ‘nasty’ answers
  3. I feel like context is not really important to a lot of the AS students – their intellectual need is to pass the exma with the best score possible
  4. I didn’t give them the Map of England to locate the towns on

That last point is the big one for me; everything else is something I can’t directly control but I think that map was actually a big abstraction step I took away.

That’s bad. I forgot the point of the task. To go from information to a graph based in reality to a network that abstracts that, to the higher abstraction level of a matrix, completely removed from the actual location of the towns.

By removing a rung from the ladder of abstraction and forcing them to enter at a higher stage I gutted a task.

So it’s time to damn well put that map back in, and to go back and reassess tasks with this in mind. Those lower abstraction levels are so important.

I’ll let you know how it goes.

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#FailFriday – Normal Distribution

Original post here.

This is actually a couple of weeks ago, where a topic seemed to take aaages for the students to grok a few important things about Normal Distribution. I’m going to try and highlight the different ways I tried to explain, and get some feedback on how I might approach it differently.

What I wanted them to grok early on:

20130129 - Normal Dist probabilities_3a

We did some sketching and some examples of different normal dists after calculating mean and standard dev for some data sets (why does it feel like they ALL need to relearn the graphic calc everytime?) then introduced the standard curve with the areas labelled.

What I feel like they took away from that first lesson:

20130129 - Normal Dist probabilities_4

However, I did not realise this (as they produced for me some nice distributions drawn with appropriate scales) until we tried to do this the next day (excuse the sketch, the sheet is at school and I am not):

DSCF0671

So we had to go back over what the area was and what it meant in terms of a probability and how all possible outcomes were under the curve and I felt like I couldn’t explain and they were frustrated by the symmetry and we ran out of time.

So next lesson we went back to the mean and standard deviation and drew some more distributions for things like height sets and weight sets on mini whiteboards so I could see them drawing it. Then We plotted the line for a particular height or weight.

Then we shaded areas and talked about what they represented.

Then we drew some symmetry on the curves and talked about which were the same and how we could work it out (using word-sentence-equations like:

‘Probability of more than 1.55m is the probability of less than 1.55m taken away from 1 (because 1 is everything that could happen’

With symbols becoming more frequent as they went through.

So after that, and a bit of practice reading the normal tables, we could try some standardisation problems; and suddenly it seemed to work. I thought. So I exitslipped them and it seemed alright, and the next day, we built it up again in the first activity: Draw a curve for given mean and SD, shade the area you want, standardise, read the table, find the result and interpret it as a percentage.

WE WERE FREAKING THERE. Time for some problems. YES YES YES.

The two real questions are:

  • Why the hell didn’t I think to do it that way right away?
  • Will they remember in 2 weeks time

The second will be answered next week…

So my failure here was pretty much a bunch of time where me and the students were frustrated by what we were doing, before I got myself together and figured out a way to redo what I did. So what do people think?

p.s. this wasn’t all fail, one student made me feel much better at the end of the final lesson, having done a TON of exam questions and said ‘I got it on Monday, but I didn’t want to make the others feel bad, so I just helped my table and got on with the work’ THANKS KIDDO!

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The Monopoly Project

Original Post here

I stole this idea from Yummy Maths, but unfortunatley theirs was all American, so I had to adapt it for the UK version of the game. I made up this handout for the students to work though:

My plan was 2-3 lessons and then the weeks homework to finish off whatever else needing doing. I rooted round my mum and dad’s place and found a few copies of the game to use in class (less dice, pieces, cash and houses) and basically let them run with it. Man I learned a lot:

  • Students are insanely resourceful when they think they can play a game; bottle caps became playing pieces, phones had dice apps, written accounts of what money people have appeared. I really wih I could channel that resourcefulness into productive research regularly
  • There was just too much to fill in. About 30ish properties, all with 9 pieces of data. Thats a hell of a table to fill in and it took some students AAAAGEEESS. I shied away from giving them the data already in a table because I wanted them to encounter the board and properties. Future versions of this will have some to most of the data filled in, with gaps to complete
  • Some students have never played Monopoly. I was a little shocked, I mean I despise the game, it’s an awful example of a board game that is made and played even worse by house rules and a win-more attitude. But seriously, never played?! wow. Maybe college needs a board games club?
  • Theres a hella lot of scatter graphs in there.
  • I wonder if the project would have gone better using a computer spreadsheet package. It would elimate a lot of the dead time from data entry to the graphic calculators but would lose the practise of plotting graphs and drawing lines of linear regression.
  • I don’t think the students LEARNED any new material. They just applied a bunch of techniques to a (somewhat) new situation. I am unconvinced that this task was more that a glorified practise exercise.

So it was not overall a resounding success. So taking in to account the above I have updated the handout to this:

And hopefully next time I do this it will be better. I would love some feedback on this; can this be more than skills practise? Should I throw this at them at the start of the unit with less ‘calculate this’ and more ‘compare these, oh wait, you can’t?’. I also think the document might benefit from a bit if a graphical spruce up. But I suck at cutesy, so…. sorry! Laters

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