Assembling the heterogeneous elements for (digital) learning

Category: mathematics

"Clickers", success, and why do I feel dirty?

Apart from starting the hassle map exercise my last lesson in 10 Mathematics also included my first use of the Active Expression “student learner learner response system”. While a bit disorganised, I can see some benefits. But I still feel a bit dirty.

What are they?

The following photo gives you an idea of what the he ActivExpression “clickers” look like. Basically an oversized calculator with a mobile phone-like keyboard, some extra buttons, and a small LCD screen. It goes with a little dongle that plugs into the back of a (usually teacher) computer to receive the student responses and that works with the Promethean Interactive WhiteBoard (IWB) software.



Mainly because they are there. The classroom I teach in has an IWB and a computer and there are 30-odd of these devices laying around not being used. But also because they might provide some additional insight into how the students are progressing. Then there is the observation that being on my internship with a mentor teacher hanging around is probably the best chance I have to do some experimentation, at least experimentation that sticks within the “grammar of school”.

The final reason was that this was the last lesson on a Friday afternoon for these students. A lesson that typically doesn’t find them focusing much on the mathematics. Playing with some toys might generate some interest.


The plan was to spent 15/20 minutes getting the students using the devices to answer a couple of stand alone questions (quick polls) and then do a self-paced test.

There was probably a good 10 minutes spent getting the devices set up and ready. And about the same spent doing the questions.

Most of the students seemed to handle the devices okay. Their use generated some engagement/interest out of some students who are generally more disengaged. No real learning about mathematics happened, but they became familiar with the devices so the next time might be a bit easier.


I’m a bit conflicted about the experience.

On the positive side it engaged the students and could provide some useful insights into just how well the students are “getting” the mathematics I’m trying to teach them.

Of course, the very words I’m using in that paragraph reveal some of the drawbacks. The use on Friday was very traditional. It assumes it’s my job to teach, there’s to learn and the clickers are there to check how well the transaction occurred. I’m using tech to improve the existing processes. Evolution, not revolution.

That’s the bit I feel dirty about.

I like the quote from Martin Davis used by Lasry (2008) when comparing clickers and flash cards

As men get older, the toys get more expensive.

But given that the expense has already been spent, I may as well use it. And this is but a stepping stone.

What’s next?

I’ve been aware of Mazur’s work on peer instruction for awhile as one approach to effectively using clickers, without really knowing the details. A possible way forward would be to modify the class approach to use peer instruction.

Only now do I realise that one of the assumptions about peer instruction is that it is associated with the “flipped” classroom. i.e. students are expected to do some pre-reading. I can probably modify this a bit, though I should read some more about peer instruction.

I am interested by the possibility of whether or not peer instruction would address some of the issues students have with the boring nature of the class (as revealed in the hassle map results). I wonder if regularly pausing to talk with a peer would be counted as a “fun activity”.

Associated with this, I also wonder how engaging the clickers would be for the students if all we did for them was answer the standard mathematics questions. Might the novelty wear off?

In the shorter-term, I need to analyse some of the results from Friday’s experience. The Promethean software records student responses. Some of the value of the clickers is the ability to become aware of student progress.


Lasry, N. (2008). Clickers or Flashcards: Is There Really a Difference? The Physics Teacher, 46(4), 242. doi:10.1119/1.2895678

Looking for "learning objects" measurement, perimeter etc.

So next week sees me actively engage in a bit of teaching through leading small episodes that form part of my mentor teachers’ existing plans. In another week or two that will expand into complete lessons. One of the interesting parts of this activity has been the necessity to fit within the existing plans and approaches used by my mentor teachers. Approaches that I wouldn’t necessarily have thought of and which place some constraints on what I can do.

On the plus side, the topics I’ve been allocated both initially and for the complete lessons have some connection. All focused around measurement, perimeter, area, volume…., though at two different grade levels (Year 8 and Year 10). For the year 8s I’ve been asked to find some computer-based activities that engage the students around these topics. I’m also hoping to find some similar work for the Year 10s. So, the aim of this post is to document my exploration for computer-based activities/learning objects for this content area.

To some extent, it’s turned into a battle between cathedral (formal learning object repositories) and the bazaar (the open Internet), and the bazaar seems to be winning.

The Learning Federation

The standard place to look for these resources for Australian educators seems to be The Learning Federation and its many guises. For example, the folk at my first school talk about using Scootle which seems to be the “interface” used by non-Government schools. As a student teacher at an Australian university my fellow students and I get access. Yes, access is restricted in someway. My access is via this site.

As expected there is a browse by subject area and ability to search. The advanced search feature is, at first glance, quite useful with the ability to limit to years of schooling (which says something about the school system, but still remains useful within that system).

What am I looking for?

The initial class will cover units of length (measuring and converting) and perimeter. The plan when introducing this topic is to rotate the students through three separate activity groupings. I’ll be taking the one using the computers, hence the search for LOs.

Okay, so I’ve found an object. A flash application that uses a “space” context to get students doing conversions. It has its limitations, but is a start. The question I have now, is how do I get access to this object in class? Can I download it or do I have to point to the external URL in class?.

Ahh, downloading can be done with a bit of playing around. And going by the terms and conditions this seems allowed, as long as the resulting file is only used within an educational institution that has a connection with The Learning Federation. Though this doesn’t work with all apps.

I’m also unsure that I can actually give the readers of this post a link so you can take a look. I have added it to my “learning paths”, even though I’m not sure what that actually means yet. Am assuming it makes it easier to find it again.

It is interesting to note that while there is a “rate & suggest” feature in this repository, all of the resources I’ve looked at so far don’t have any ratings or suggestions. The detail on the learning object does point to there being a script writer, a subject matter expert, an external validator and a technical implementer (external company) and a publisher (Education Services Australia) involved in the production of this. This is striking me as a heavy weight approach to producing learning objects.

Okay, there’s another one with area and perimeter. Another flash app, basically to compare and contrast area and perimeter of the same rectangle. This one has a PDF with some lesson ideas.

That’s it, I’m a little disappointed with that. The addition of flash apps offers some advantages, but not a lot and the pseudo-context of it all is something I find a touch sad. Especially given the amount of money that would have been spent on producing these objects.

A quick google on the same topic brings up this page which has a collection of “sheets” with ideas for teaching measurement. While not exactly the grade level, there’s a bit of creativity in these with much simpler technology and more of them..

Incorporating research

That same google search revealed this journal article, while not directly related, it does raise the question of how many of the above objects and teachers using those objects have been informed by, or even aware of, research into the teaching area. There seems a gulf there.

Google earth

Whilst in the midst of browsing the Learning Federation Alice Leung tweeted!/aliceleung/status/67033842342567937

When thinking about this topic area, Google earth was what sprang to mind first. I think a comparison between the closed world of the Learning Federation versus the open net and Google Earth might be interesting. Some criteria for comparison might be

  • Ease of finding resources.
  • Quality of resources.

A simple Google search “perimeter google earth” gets quite a few resources back. Including a blog post from a teacher that explains exactly the sort of thing I had in mind. Then there is the Google Earth Lessons site and I imagine there are many similar sites.

And of course a site I found previously.

Some misc “mind dump” ideas

  • Before starting Google earth, have the students estimate the following distances (as in all cases, encourage them to specify the appropriate unit of measurement and then convert it to some silly unit)
    • Distance from their locker to the classroom (reminding them that a typical human walks about 4.3km/h)
    • Where they will sleep tonight (some of the students are boarders).
    • The diameter of Lords Cricket Ground in London.
      The point here is to get the creative juices flowing for the next one.
    • Think of someplace you’ve always wanted to visit, think of a measurement associated with it (e.g. diameter of Lords Cricket Ground, the distance between your place and Rockhampton, how long is one of the sides of the Pentagon in Washington DC etc).
  • Have them find the school on Google Earth.
  • Get them to check their answers to the above measurements using Google earth.

Questions about using Google earth

  1. Is it installed on the school laptops?
  2. Is the school bandwidth sufficient to support ~18 Google earth connections + other data?
  3. How many of the students have used Google Earth before?
  4. How long will it take to get the students comfortable with using Google earth?
    I’m guessing minimal.
  5. What are the gotchas about Google Earth which my ad hoc usage hasn’t revealed, but which having a collection of students playing will almost certainly reveal?

Real life, mathematics, partial proportion and race horses

The following post brings together two recent events in my life into an attempt at a WCYDWT question for mathematics. It’s not a perfect fit for WCWYDT, but close.

What can you do with this?

The following is a photo of “Credit Muncher” just one of the race horses that has arisen out of my wife’s latest hobby, breeding race horses.

Portrait #1

She’s called “Credit Muncher” because I am somewhat worried about the potential for this hobby to consume vast amounts of money. I was, however, a little happy that we were breeding race horses, not racing them.

Racing a horse involves a continual outlay of money. First, there’s the expense of purchasing a yearling and then breaking it. At which stage you pause for a while before the horse is sent off to a trainer. This is when the real money starts being spent. Paying for someone to train the horse can cost upwards of $3,000 a month and the chances of winning are pretty slim. This has always seemed like a mug’s game to me. A good way to burn money. Thankfully, we were only breeding horses to sell to others.

That changed last night. My wife and mother-in-law went to the local thoroughbred sales. “Only to look”, said the wife. “I left my wallet at home by mistake”, was the cry on the day of the sales. So, I felt safe. Then last night, to my great surprise and chagrin, I find that both my wife and mother-in-law have purchased a yearling each. With the grand plan of breaking them, training them, and entering them in the Capricornia Sales race this time next year. The race has a total price purse of around $150,000 and all horses sold through a specific brand of sales is qualified (59 from this sale alone).

What questions spring to mind?


As of yet, I haven’t seen the new horse. We’ve already spent some money for it to go to a professional for breaking. A video or photo of the specific horse would be an improvement. Perhaps a bit more context of horse racing as well.

The story could do with some work. I do, however, think that the pain in my voice as I explain the story is likely to be the secret ingredient to motivate the students.

Working in some more detail about the prize money (1st, 2nd, 3rd etc) and other potential races might help.

Of course, the big potential problem is that the topic is horse racing and I hear gambling can be a bit of a no go topic in schools.

There’s also the problem that this problem doesn’t leave a lot of room for exploration, or at least I don’t see it.

My questions

The proper WCYDWT is to leave it to the students to come up with the questions from the story/prompt.

This idea comes about from the fact that I have a driving question. How much is this going to cost us? And an extension, how much is this going to cost me as the months roll on?

The idea for this post came from the fact that one of the first mathematics classes I was in during EPL (embedded professional learning i.e. prac teaching) covered partial proportion. And the students just didn’t see the application. This class was one of those that contributed to an earlier post about the relevance of mathematics.

Partial proportion

The basic formula for partial proportion is

y = kx + c

In this case, y is the total cost of the horse. The total cost is partially proportional to the monthly cost of training plus the initial cost of purchasing and breaking the horse. Using some round about figures, that gives

y = $3000*x + $5000

Given there is about 6 months of training to occur before the sales race

y = $3000*6 + $5000
y = $23,000


If we race the horse for 12 months

y = $3000 * 12 + $5000
y = $41,000

2 years

y = $3000 * 24 + $5000
y = $77,000

Sir, when are we going to use this?

My first two days of prac teaching last week included three mathematics classes. In two of the classes I heard students ask the teacher, “Sir, when are we going to use this? Why are we studying it?”. The other mathematics class was grade 12, obviously they benefited from their longer experience and were more pragmatic when they asked, “Will this be on the test?”. Since that time I’ve been wondering how I might answer this question when it is asked of me.

What follows are some initial ideas for how I might respond. Somewhat phrased as how I might use it with students. Thoughts? Suggestions?

The “icing on top”/”math as a badge of honour” response

Do you find mathematics difficult? How many other people do you know that find mathematics difficult? What is a potential employer going to think when they see a *insert top grade here* (VHA/A/7 etc) for mathematics on your report card? Showing an ability to engage with a subject that people find challenging will say something about your nature, something an employer may like.

The “it’s important to industry” response

Especially given recent noises made by the Australian Skills Council about the limited numeracy skills of potential employees for trades and professional jobs. Which includes statistics like “53% of working age Australians have difficulty with numeracy skills”. And looks at reports on the maths skills of starting bricklaying apprentices

  • 75% couldn’t do addition with decimals or subtraction requiring “borrowings”.
  • 80% couldn’t calculate the area of a rectangle.

The “turnaround” response: tell me what you will be doing

It’s a bit hard to explain what you might use this mathematics for when I don’t know what you might do in the future. What do you want to do when you leave school?

At this stage I’m thinking of an exercise where the students write their future career plans on a post-it and stick it to their forehead. And then for me to do it with what I was thinking at 15 and what has happened since. i.e. 3 changes before I left high school, a completely different outcome after Uni, and two more career changes since then.

Then show a bit of the Did You Know video that mentions various trends like numerous common jobs didn’t exist 6 years ago, and that a new worker today will have on average 14 different jobs.

Now, are you sure that is the only thing you’ll be doing?

So, while we may not know all that much about what you’re going to do, we do know that mathematics underpins and is needed by many new jobs. (e.g. the XKCD cartoon on purity).

The “how I have used it” response.

In the end, I can show you how I’ve used mathematics in my life. Which is what I’ll aim to do in most of my lessons. Failing that, I’ll aim to use interesting examples, exercises and activities around mathematics concepts that other people have used.

A feeble first attempt at moving towards WCYDWT

Late last week I was thinking about how I could develop something approaching a WCYDWT lesson for mathematics. It is something I am going to have to do very soon now. As it happens, in looking for the WCYDWT link, I came across this Diigo group that I am going to have to return to.

The following is a first attempt. Actually, it’s the first example of me seeing something in my everyday life that I can connect to the curriculum and see some ideas for developing a lesson. Given that I am going to have to be developing lessons soon, I’m hoping to get into this practice more.

This type of thing may not connect directly with the strictures (if such exist) of WCYDWT. I guess I am using that as a useful label to encourage me to structure lessons that ask the students to generate the questions (which I am hopefully strongly guiding towards the curriculum) in the hope that it is more meaningful and interesting to them and consequently leads to better outcomes. The ultimate aim being to encourage them to see the relevance of mathematics.

A comparison of Household finances – The McGuffin

The Weekend Australian Magazine from last weekend had a “Trend Tracker” column on infographics (can’t find it online) which led with some infographics comparing Australian household finances from 1971 to those for 2011. The following table summarises the figures. In a lesson, I’d probably go with the graphics or some form of multimedia.

Figure 1971 2011
Average price of a home $21,000 $557,000
Average grocery bill $23 $250
Average household size 3.3 2.6
Average # of cars per dwelling 0.75 1.5
Average # of household appliances and gadgets 9 27
Average wage $84 $1250

This is one of the difficulties that I see with WCYWDT type problems, while I can see a number of questions that arise from this prompt, what will the students see? Of course, that is also one of the interesting aspects of this type of problem.

Within the Queensland syllabus, this seems to fit with “Chance and Data” and discussions of averages/means, but also with decimals, money and a few other places. Making these connections is one of the skills I need to develop further.

Some of the questions I can see (feel free to suggest more)

  • What does it mean to have 2.6 people in a household?
    The notion of averages etc.
  • Given the costs of houses, groceries etc and the average wage, are people better off or worse?
    Apart from the calculations, there are a range of further questions – not necessarily mathematical questions – about what “better off” means. i.e. do 27 gadgets make you better off than 9 etc.
  • What were the maximum and minimum values for these averages?
    Leading into more questions about what “average” actually means

An extension of this, somewhat fraught with peril, would be to get the students to provide data to do an in-class calculation of equivalent figures. Some possibilities might include

  • Real figures from home.
    i.e. bring in the grocery bill, Mum and Dad’s group certificate….obviously there are some major privacy issues arising from this approach.
  • Actually start with the students providing their figures.
    i.e. start the lesson with students in groups talking about how much they would like to earn, how much they think the would need to spend on groceries etc. Or perhaps ask them to provide the minimum, just right and maximum wages they’d like to earn (a Goldilocks approach). Get the class playing with those figures and then reveal the national figures.

An obvious extension to this would be to get access to the ABS raw data and see what other interesting data can be pulled from there, but also see if there are ways to get the students mining and manipulating that data.

Another option might be to get some average salary figures for different occupations (perhaps from the ABS) to give the students some idea of the range of salaries and then also to use those as data points to illustrate the concept of average. i.e. some occupations are above and some are below.

Which obviously leads into some of those survey results where everyone thinks they are average.

Mathematics and the net generation – not in textbook exercises

So, in a few weeks time I’ll be teaching mathematics to high school kids. Almost certainly grades 8 & 9 (find out next week). I’ve been doing a bit of reading and have joined various online groups. Last week I purchased a couple of textbooks used in local schools to refresh my knowledge and see what’s being covered.

As it happens I started looking in the textbook for ideas for a video. In this post I was playing with What can you do with this (WCYDWT) idea from Dan Meyer. That’s when I came across this problem

Ying has five 90-minute cassettes that have been partly filled with recordings

I’ll stop there, I’m trying to imagine explaining to a 13 year old kid that doesn’t see the relevance of mathematics what a cassette is. I was a late adopter of CDs, and I don’t think I was buying cassettes after 1995. a 13yo will have been born in 1997/1998.

The “net generation” and “they think differently due to technology” has been getting a run in the some of the courses we’re taking. It seems that message hasn’t gotten through to the textbook folk.

Though, I do have to admit, that coming up with a textbook’s worth of authentic exercises and examples that can be fit within the constraints of a commercial textbook, is not a challenge I want to take on anytime soon.

Two questions down, there is a similar question, but this time it’s a 3-hour videotape.

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