Last night I attended at dinner with Lärarförbundet in connection with the SETT conference. It was a lovely evening with equally interesting and brilliant people within education. One of the people I had the privilege was Laura Allen – founder and CEO of Vemny and RoboFun. She told me about a method of testing new ideas that decreases development time and cost by prioritizing early user feedback. As a primary school teacher I quickly got interested in trying to apply it within my classroom. As I understand it the method seems to be a way to as a group evaluate a number of possible solutions in order to find the best/better ones. This comes in handy as the curriculum in math is based upon a set of skills, one of them being choosing and applying relevant mathematical methods. How do you teach kids that skill? One way could be to tell them ”This is the best way to do things” and hope that they follow. But is that really a learning experience? Probably not. So I made a mental note of some day trying Rapid Prototyping in class.
Early next morning I got on a train back to Göteborg and my school. As I arrived at work, directly from the train and with all my luggage in hand, it struck me: I have more or less forgot to plan todays classes! All caught up in the SETT conference and my double presentations I quite simply forgot about life after SETT. After a quick chat with my closest co-worker we had a plan. This would be the first, and probably only time when I showed up at work with 10 000 Swedish kronors in cash (the prize from the Trevor Dolan award). So for todays math class we just had to give the kids the following problem: What does 10 000 kronor weigh? The only piece of information I provided was the weight of one coin. From the start that was it. A fun way to create learning out of the insane amount of money that I brought to class. The kids were amazed. And in the back of my mind I could see a connection to the past 6 months worth of developing my students mathematical problem solving skills. After a while it hit me: This would be a perfect opportunity to try that method that Laura told me about. During recess I brushed up on the principles and then we went at it.
1. Everyone gets a bunch of post-its.
Being a public school I had the students scribble down possible solutions on an ordinary piece of paper instead. Probably that was just as good. I asked them to spend a few minutes reflecting on the problems individually. Normally I would encourage co-operation but here I made an exception in order to get all my students involved.
2. Post them randomly on a wall
I used our whiteboard.When Laura presented to model I remember thinking ”Ah! This is probably usefull when working with rich problems with a variety of possible solutions.” As it turns out this problem maybe wasn’t rich enough, as the kids only came up with six or seven possible solutions. I had expected maybe ten or fifteen. So for the future I will try to select richer problems. But for this, our first try, it turned out just fine with a limited variety of solutions.
3. One person divides by properties.
I presented this part of the method to the students and half way through had an idea: ”Maybe it will be too hard for one of them to do this as it is the first time?” So I had my two brilliant co-workers who I co-teach with to be in charge of this part. But I asked my students to carefully pay attention as they will be offered to do this the next time around. We ended up in five possible approaches.
4. Testing in pairs/groups
As I understand it this is a method primarily for smaller teams. (At least smaller than an average Swedish school class.) So instead of having one or two or three kids try out each method I had them pick one of their choice and simply try it out. I encouraged them to work alone, in paris or in threes. As I have 32 kids in my room it turned out that all approaches where tested by multiple groups, which really isn’t a problem at all. To keep their findings un-interrupted I asked them to only try one of the approaches, even if several of them seemed feasible. When done I asked them to quite simply wait for the rest to finish their work. In order to prevent too much ”dead” time I limited the students testing to 10 minutes, which proved to be just enough for everyone to finish.
5. Evaluating different approaches
One by one we evaluated the approaches. First I had each group asses their success simply by a show of fingers, between 0 and 5 where 0 is ”failure” and 5 ”complete success”. I made it clear that this would not be a sign of each students mathematical ability but rather the usefulness of the selected approach. Right from the start we could see that one group reported a lower level of success than the others. ”But that really isn’t evidence enough to rule it out as a valuable approach”, I said. And the students agreed.
So I had one group per approach present their work and results. I simultaneously made notes on the whiteboard paying careful attention to writing down their exact words. Especially regarding their results.
Division – 151,51
weighing the money – 6,6 kg
Multiplication using a calculator – 6 600
Mental arithmetic – 66 000
Written arithmetic – 6 600 = 6,6 kg
Soon after that we could see that the group with lower self-reported success also had an answer that stood out from the rest. As the kids had the unique opportunity of actually feeling the weight of 10 000 kronors we could rule out their answer as unreasonable. Division quite simply isn’t a useful approach here. After that I had the students compare the remaining results. Some of them could see the difference but most of them described the results as equal, but with different units. So I showed them the connection between 6,6 kilograms and 6 600 grams. That opened their eyes to 66 000 grams being an incorrect answer. They all agreed that the approach of mental arithmetic itself probably works but that it is easy to make simply mistakes like adding a zero too much. One of my students noted that most kids had forgot to report what unit their result was in, but that the group who chose to weigh the moeny hadn’t forgotten. Those students on the other hand shared that it was quite tricky to get the weighing right. Especially as the scale they used only went up to 5 kilgrams. So they weighed half of the moeny and multiplied the result by two.
All in all we ruled out division as a suitable approach to solving the problem at hand and made a collective mental note to be careful when using mental arithmetic to solve problems like this. Using a calculator or written arithmetic seems equally feasible.
It’s easy for me to get excited about new ways of teaching. And that was exactly what I felt when I left the classroom today. But with that in mind I’m quite sure that Rapid prototyping will prove to be a method that I will return to in the future. Especially as the math curriculum in Sweden largely is based upon the students developing the skill to evaluate and use suitable approaches in solving mathematical problems.
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