Qama Calculators

The calculator that only thinks if you do!

So we have just invested in a few of these Qama calculators to play with. I think I just needed to see one for myself and see how it worked. The basic logic is really quite simple. You enter a calculation and press 'equals'. Then the cursor moves to a new line where it expects you to make an 'estimation' for the answer. If the calculator is happy with your estimation,then it will give you the actual answer. If it is not, then you must try again. What a beautiful idea! It has clearly been a terrific effort from conception and design to manufacture and distribution and these are now really easy to get hold of a relatively inexpensive. The question is to think really carefully about how we might choose to use them in mathematics education. There are a few questions that people might think about...

On investment

1. Would we consider a wholesale swap and ask all our students to get one of these?
2. Would we like a situation where students had one of these alongside anoher traditional calculator?
3. Would we go for something like a class set that can be brought out for particular activities?
4. Is it just something we might recommend for some students?

Well, my usual take on something like this would be option 2, because this leaves all options for use open. You would need to be pretty certain that they were going to get used before you asked parents or schools to make an investment.

On activity

If this was the default calculator, then we imagine that there would be long term improvement in estimating ability and the asociated number sense, but it is worth thinking about the implications. Calculators are often a bridge that allow an activity to focus on particular skills without letting calculating skills hinder progress.

1. Would permanent use of these calculators slow down activity? Does that matter?
2. How would we adjust our teaching style to accomodate for the extra stage of involvement?
3. What would be the implications fo increasing the emphasis on estimation from an early stage?
4. Is there potential for thinking about specific activities that might make the best use of this calculator?

I think there is a need for experimentation here and possibly picking a class to trial them with one way or another. The first question here helps me answer the first one above, in that I dont think I would want it to be a permanent replacement. I do think that it would interupt some teaching and learning activity. I also think there will be a significant implication for teaching style.
Really importantly and potentially one of the most exciting implications of using these calculators is likely to be the increased emphasis on estimation as a skill. There are so many reasons to encourage this, but my favourite is because of the potential impact on understanding.

Specific activities

I think that these calculators could introduce a whole new level to activity design. Here are a few ideas that have popped in to mind in the first few days I have had this calculator....
Percentage error - I am really curious about the margin of error that the calculator is accepting in different contexts. My colleague tried log120 and was denied with an estimation of 2.1 Quite demanding I think, but there is a lot of potential to investgiate different types of operation and the percentage error allowed.
Least guesses - I like the idea of some activity where students have to try and estimate difficult operations in as few guesses as possible.
Trigonometry - I had fun estimating some trig ratios. I found myself thinking about the ratio between different sides of a traingle and how it would change as the angle increased. What a great way to encourage students to think about what trig ratios actually mean.
Again - this is just a start of lots of ideas that are bound to come from playing with these calculators.
Thanks Qama for these - a really exciting development.

More Popular Math

More Popular Maths

I have just watched my first episode of 'School of Hard Sums' and really enjoyed it. I dont live in the UK and so am playing catch up. It is another great example of what I put under the heading of Popular Maths and I am delighted that so many people are making an effort to get more people watching, thinking and talking about maths. Terrific. I want to watch more for sure and certainly before I make any general comments about the show. As ever though, my first thought is about how this sort of stuff can be used in schools. As I have said before, I always think the challenge is how to take this sort of media and focus on the maths involved and making this in to some sort of activity. Here is the you youtube clip I watched.

My focus is on the dancing problem. In short, if you are stood still in a dance hall and everyone kisses the person they are closest to, how can you position people so that you get the most number of kisses and what is the most number of kisses you can get? I liked this problem because I thought the context was fun - I can see playing musical statues with a class a few times. Secondly, I was interested in the three aproaches used to solve the problem, all of which were apparently different to mine. This is always the sign of a rich problem for me. As ever, it makes it more difficult to control which 'learning objective' can be taught in a given lesson, but I think that is a sacrifice worth making for the potential to get students using mathematical reasoning, testing, evidence gathering and so on. Perhaps also, there could be an activity that offers the different explanations as a starting point and asks students to discern between them. Either way there is a lot of potential and now I have more things I want to watch, do and plan! It is frustrating (lack of time) but exciting that there seems to be a never ending stream of possibilities in this profession! Thanks to the School of Hard Sums team - I am looking forward to more.