Let me describe a scenario that i came across, of gamification changing the way one tends to interact with something. I have been playing, as i suppose a lot of you have been, sudoku for some time. I have a version of sudoku which is a straightforward one. You select the level of the puzzle you want to play, and it generates the puzzle for you, and you go ahead. It tracks the best times for completing puzzles with different levels of difficulty.
Some time back i got another version of sudoku which has puzzles at different levels of difficulty. The difference is that in this one, the higher levels of difficulty need to be unlocked. Only once you have solved the puzzles at easy level, with a particular best time, and some other parameters, does the medium, difficult, and super levels get unlocked. You cant just jump to a higher level puzzle.
The same game, with simple functionality included creates a different level of motivation to solve the puzzle less time. Earlier, i wasnt too aware of the best timing for the different levels, but now, i was keeping track. And unlocking the level gave a sense of achievement. In short, i tended to look at two versions of the same game in different ways, and this was because of the small component of gamification introduced.
This is the impact of gamification, and this could be harnessed to create the motivation, engagement, and a sense of achievement, like in a game, in learning.
A recurring question which keeps coming up in discussions is how mathematics should be taught. There is a strong view that given the computing power which is available to us, we should relook the basic maths curriculum. So i went looking, and found this video which i feel looks at the problem in a logical way.
Conrad Wolfram is giving some compelling reasoning for why maths education should change, and gives a description of how it should change, too.
Hand-culcating the mundane way should not be the focus on the curriculum. Rather, the focus should be on building and enforcing the concepts, and leave the calculating to computers. In other words, as he says, students should be taught the procedures which define fundamental concepts, but the implementation of those should be left to computer programs. For example, students should know what a square root it, how it is calculated, but they shouldnt have to calculate, beyond illustrations. And here is the cool part he says … focus on teaching students how to write programs to calculate square roots, rather than having them mechanically execute the procedure for calculating. This will immensely help students clarify their concepts (how can one write a program without understanding the underlying principles to a very large extent?), while at the same time help them become more comfortable with the concept of application of these concepts. In other words, our mathematics curriculum should stress understanding and application (application to real world problems is a very good way of teaching these concepts) rather than stress on the mundane calculations which stress out students as well as parents alike. After all, why should a child lose marks in an exam (thats what happens) if he or she takes the square of 5 to be 10 when all the conceptual aspects of the solution are correct, and the only mistake is a calculation mistake?
Connect this with the post i had written earlier, and a rather innovative picture of mathematics teaching emerges.
When we talk about education, we are talking about giving the children the right answers. We teach the children to answer questions. That means, the focus of education is on answers, as Lawrence Krauss says in this video.
What is more important is to teach children to ask questions. Answers are the consequence of questions, so it is important for children to learn how to ask questions. If children know to ask the right questions, they can find the answers they need. Education needs to be to teach children to ask questions, and then, only then, try to find the answers. In the process of finding answers lies a high level of learning.
This isnt necessarily true of the sciences, but of any subject. I believe that this demarcation between science and the humanities is an artificial one, and that children need to be taught to ask questions and find their answers in all realms. For example, when teaching history, instead of telling them the facts, if children can be taught to ask questions like what circumstances led to the emergence of a civilization or a culture, or what was the social milieu in which an empire grew, the children would learn more about history just trying to find answers to these questions than today.
In this process, the teacher needs to, to begin with, guide students to the fundamental questions and their answers, about the subject being introduced, and from there on, help children formulate questions. Children should be encouraged to come up with new questions, and then, either the teachers could answer those questions, or enable collaboration in the classroom which lets children find out the answers to these questions.
As you can see from the Kalikuppam, Gateshead and Turin experiments, children’s natural curiosity, and their ability to collaborate easily can be harnessed to enhance education being provided. This curiosity can be channeled into asking the right questions, and this collaborative nature can be channeled into exploring the vast sources of information available to the children, and to find the right answers from there.
Thats a somewhat crazy question. I came across this video, and i would say its quite a nice watch.
This video makes a compelling case for the why and the how of teaching maths in a visual way. After all, maths is not about words or languages, is it? If so, why should mathematics education be so language heavy? It should be about the concepts of mathematics. And i have found that the visual impact of mathematics is quite powerful. I tried this trick with my then 10-year-old … I introduced him to the concepts of integers, and multiplication with negative numbers without bringing in negative numbers to begin with.
We started with directions. Left and right. So, theres 3 to the left and 2 to the right. Or, 4 to the right and 5 to the right. Now, adding the 4 to the right and the 5 to the right is easy, but how does one add 3 to the left and 2 to the right? This is where the concept of the negative sign came into the picture. And once this was done, then it was a simple extension of this to see how multiplication with negative numbers simply changed the direction and nothing else.
What this did is help him build a mental picture of these concepts. In my experience as a trainer, i have found that these mental pictures are far more enduring than theoretical concepts. To take an example, i used to teach the concept of min-max planning, or the sawtooth curve, using the analogy of mom planning to go out and buy rice. Now, a few days after the class, the students, even if they had forgotten the min-max planning theory, or the sawtooth curve, still remembered the rice story, and this helped them to relate to the concept. The rice story here helped build a mental picture which is more enduring than theoretical concepts. So this isnt just about children learning mathematics, but also about adults learning.
Now, knowing him, he would have built a picture of Ben10 doing something which saves the world from the wildest aliens imaginable while multiplying two negative numbers, but hey, thats a picture i can live with!
Oh by the way, where there are integers, can vectors be far behind?
Came across this really nice video on youtube … about Khan Academy Discovery Lab.
Today, the way children are taught in conventional schools is starting with theory. So, they are taught some theory, and then they get to see the application of this theory. And this is where children sometimes switch off. This is because children are natural at interacting with the world around them, and thats how they learn best. By seeing, by doing, and not by theory.
However, this approach could be a different way of teaching, far more effective. Start with the real world phenomena. Let the children do things which will help them to experience a phenomenon, and once they have had their fun, and are comfortable with the phenomenon, then lead them to the theory behind it, which describes why the phenomenon or experiment they did works in the particular way that it did.
After all, thats what science is all about, isnt it? And by science I mean all subjects which relate to facts, and here observation (whether this be an experiment or discerning patterns in natural phenomena) serves as the basis for theory, which is the tool to explain why things work the way they do. It is a decoding of these phenomena, not their definition. This method, being in synch with the fundamentals