In a Maths Club session at Lewa Maths Camp held in April 2017, one of the students approached me with a problem about speed and velocity that he was unable to solve. Anytime a student came up to me with a problem I would ask them, have you discussed this with your group members? We had divided a total of 52 students into groups of 3-4 and they were required to solve problems together. These groups comprised of 27 female and 24 male students who are in their third year in high school. This particular student told me that he had not yet consulted with the members of his group and so my response was to ask him to discuss with his group members and seek for help again should the problem be a hard nut to crack. He didn't come up and upon follow up, they were able to solve the problem. A discussion about the need to work together in teams and consulting among peers came up during the follow up I made with the students.
More than often, teachers give out worked out problems to students. Is this really helpful? Isn't this akin to robbing the student a typical thought process that should happen with any Maths problem.
What if I had chosen to work out the problem with this particular student? One of the key things that we usually to try to inculcate to students during our Maths camps is the spirit of collaboration. And hence, when the students have a worked out problem in front of them there will be no need to collaborate. And yet we know that collaboration is a vital key in 21st century workplaces and hence there is a need to start encouraging this from young level.
Worked out problems also kill creativity and in turn promotes memorization. If you do not give the student a chance to be creative by giving them answers to problems, they won't be able to develop their creativity. They won't give a deep thought on the process of arriving at different solutions.
Worked out problems also encourage navigating problems through shortcuts. The idea of worked out answer keys is so that students will work out the problem on their own, and then check with the worked out answer key to see if they are correct.What ends up happening is the students will have the problem and the answer side by side. So when the student gets even the least bit anxious about not knowing what to do, they look at the worked out answer key. What sort of learning is this? A student will obviously need to figure out different ways of getting the answer if the solution wasn't provided and that is what learning is all about.
Another group of students approached me with a Maths problem on quadratic equations that they were struggling with. They had discussed various ways of approaching the problem but they were stuck. What if there were available solutions, say on a separate paper made available to them? Why would they ask questions when they can refer to the worked out problems? Apart from collaborating together in finding solutions, there is also a need among educators to inculcate the urge to ask questions to students after they have explored other ways of solving problems .
When teachers and educators present students with worked out problems it reduces the struggle to find solutions. To what extent is this of benefit to students? One of the most important skills in the current world is problem-solving, it's a skill that is vital across all spheres, be it in entrepreneurship, public affairs, health, innovation etc. Problem-solving is a product of constant struggle, creative thinking, collaboration and teamwork work e.t.c. Why should we expect the students to be problem-solvers if the problem is already solved for them?
So the next time you are presenting problems to students, you could be an educator, app developer or even an author of a Maths book, you must ask yourself, what skills do I want to leave these students with? Do I want to offer quick fixes or do I want to encourage the growth and development a group of collaborators, creative thinkers and problem-solvers?