A Parent's Experience
Murali Sharma, Trustee, SKET
I still remember vividly, one chilly night on a family camping trip in Maine over ten years ago, sitting next to a campfire trying to explain to my eight year old son what a math problem was asking, and giving up after a few attempts because it seemed too hard for him to understand. Waking up earlier than the others the next morning, I was puttering outside enjoying the crisp morning air, when he suddenly came running out of the tent crying "I got it! I got it!". He indeed had, and the thrill I felt on seeing his excitement at having solved a problem all by himself, is emblazoned in my memory.
I had discovered the Abacus website by quite by luck, when, disappointed in the school curriculum, I was looking for alternatives. (In 2015, the Abacus program was renamed in honor of Paul Erdős). I was surprised to find such a large variety of delightful problems (this particular one was attributed to Euler!) designed for such an early age, and eagerly printed out several old problem sets to think about on our long drive. Once past the initial step, a snowball effect set in, and over the subsequent years, many of the most enjoyable moments for my two sons (naturally, the younger son also wanted to do whatever his older brother did) came from problem solving, especially the Abacus program.
Subsequently, I twice volunteered to teach a year long math olympiad program at my local elementary school. Again, I found how enchanted many of the kids were by these problems. I cannot forget the innocence of the cute little girl who raised her hand to ask where my friend, the one with the ostriches and zebras, lived. (The notes I handed out can be downloaded here).
Based on these experiences, my opinion on the strengths and limitations of such a program follow. These should be taken as one interested layman’s opinions; and no undue authority should be attached to them. I welcome feedback from those with more experience in mathematical pedagogy.
Any program has limitations. In my experience, the benefits far outweigh the limitations. Still, it is fair to list ones that I know of.
Need for Parental Involvement, dependence on honor system. Since the program is targeted to students in elementary and middle schools, the quality of parental involvement is a significant factor in whether kids will invest the time needed to participate. Realistically, especially in the initial stages, some parental assistance will be needed in understanding the problems. But, how many parents will know how to tread the fine line between giving hints and moral support, and simply giving the solution? It is also tempting for parents to help the kids more than required, simply for the pride of seeing their children's position on the leaderboard.
Not a replacement for traditional techniques. It would be interesting to find out how much the program directly correlates with success in learning the traditional curriculum. While some problems lend themselves to standard techniques taught in schools, most don't. Thus, participation will not by itself make up for any drawbacks in the teaching of the traditional curriculum.
Quality of feedback, especially in the absence of solutions. The benefit of the program is strongly limited by the quality of the feedback provided to the student, since no solutions are provided. If the grader does not fully understand the thinking behind the submission, the feedback provided will not be helpful, and the students will only be frustrated.
Initial barrier to entry. A student without access to an adult, such as a relative or parent, familiar with the problem solving culture is likely to find it very difficult initially to get started.
Strengths of the Program
An early exposure to the pleasures of thinking and independent discovery. Mathematics is perhaps the most accessible subject to learn to think at an early age. Perhaps the most significant benefit is that even kids in elementary school get exposed to the pleasures of creative problem solving, and by continuing in the program over several years, gradually become much stronger at it. While there are several similar venues at the high school level, this program is unique in its ability to target elementary and middle school children.
Mathematics as fun. Equally important is that the kids start finding mathematics to be fun. Solving problems like 'Are the great grandfathers of your grandfathers the same as the grandfathers of your great grandfathers', or finding the number of ostriches and zebras given the number of legs and heads, lure kids into the joy of mathematical thinking.
But also requiring hard thinking. Several problems, while intriguing, also turn out to require hard thinking. I have observed that when gradually introduced, kids start to find it pleasurable to think hard (at least when they reach a solution at the end). The program inculcates persistence.
Feedback as intellectual correspondence. There is a certain delight a kid feels to knowing that an adult he hasn't met has read his solution carefully and is corresponding with him. Having such an 'intellectual exchange' is very satisfying for kids. The intent is to reward an honest attempt with sufficient feedback to guide the student towards a solution.
Absence of time constraints. An unusual aspect of the program is that solutions are accepted throughout the season, without any artificial time constraints. This encourages the student to try long and hard, and multiple times if necessary, to achieve a solution. This again is very different from the usual approach at school.
The satisfaction of receiving broader recognition. The program publishes its standings on the internet. This is often the first exposure a child has to a set of peers outside of his immediate circle, with similar interests. I observed my children forming 'virtual connections' with other participants across the world.
Exposure to 'out-of-the-box' thinking. The program also provides an early exposure to 'out-of-the-box' thinking.
Early exposure to fundamental principles. Many of the problems, even at the elementary school level, lead the child to intuitively discover and understand deep principles such as 'invariance', 'symmetry', 'linearity', etc., in a natural way.
'Natural' pathways on a blank slate. I often observed that children found some ways of thinking very natural, despite adults needing to strain to think that way, or needing to use standard methods. Perhaps, like music and language, some things are most effectively learnt in an early window.
Open ended nature. The program does not provide solutions to the student. While frustrating at times, it also introduces the student to a different aspect of intellectual endeavor - that sometimes the understanding might only come much later, that others might have better methods, and that a few problems might forever be frustrating. I believe this provides an early exposure to real life research.
Multiple solutions. An especially noteworthy aspect of the problems are that they lend themselves to multiple ways of solving them, and credit is given for identifying these. By looking at the published scores, students realize that others have found alternative solutions, and therefore are induced to actively look for them. This is in contrast to the typical curriculum in school, with its standards methods for solving a problem of a given type. I have found this to be especially enjoyable for students.
Generalization. A special aspect of the credit for multiple solutions is that given for generalizations, an important aspect of mathematical thinking.
Problem Posing. The program sometimes receives problems posed by the participants themselves, presumably triggered by thinking about the problems in the program. In my own experience, I have seen this happen - the student enjoys coming up with an original problem. Again, this is an early experience akin to research.
Potential to identify extraordinary talent. Of course, in any such program, one regularly finds what can only be ascribed to in-born talent. Whether such students go on to achieve great things is worth following up.
Transferable skills. I believe that the skills cultivated by participation in the program are transferable to other endeavors. These skills include the importance of persistence, the pleasures of hard thinking, clear communication of ideas to others, the acceptance of areas of difficulty, etc. Mathematics is an especially suitable arena to cultivate these skills at an early age.
Continual Stretching of Abilities. Through the years, the program seems to offer problems that always seem just on the border of solvability. This continual stretching of abilities provides an smooth transition to the more competitive high school math olympiads.
Encouragement of parental involvement. An unexpected benefit is the strengthening of family relationships, especially in deepening the involvement of parents in their children's education.
Purity of purpose. It is my observation that in later years, students inevitably end up worrying about the destination rather than the journey - entrance examinations and competitions rather than the acquisition of knowledge. While these have their place, I believe that cultivating a love of thinking for its own sake, has tremendous value, and is an especially valuable foundation best cultivated at a young age.