Philosophy of Mathematics
- June 12, 2022
There are a variety of demands for Mathematics in the modern world. Math courses are now more relevant than ever before to the 21st century learner and they prepare students for their futures. Many jobs now call for competence in statistics, computing, numerical analysis and in applied mathematics. The development of science and technology makes new demands on mathematics for assistance. Critical thinking and problem solving are not just the features of mathematics but have become the catchwords and responsibility therefore of all the academic disciplines. One might be a physicist, engineer, a computer scientist, an economist, a geographer, a statistician or a psychologist and be operating at the highest level of mathematics.
There has to be values and practical goals attached to every activity so that there are real life contexts and applications to math. While many students will enjoy mathematics best when seen in a practical context, there should also be rigorous pathways to gain that practical knowledge. Mathematics will be useful only when it teaches how to think and reason with precision. A major factor in the teaching of math would be the true understanding of mathematical principles and problem solving skills. We as educators are committed to inquiry based learning; however, real life applications and modeling uses some rigorous math techniques. Students must be exposed to skills of scrutiny and judgment through the proofs of theorems. Mathematics students should practice to be fluent in the construction of mathematical arguments and develop strong skills in mathematical thinking. There should also be a greater emphasis on how to attack problems and new situations so that students can build their problem solving skills, appreciate the notion that there are many correct pathways towards a solution and that some of these pathways are more elegant and insightful than others.
Students should be able to appreciate Mathematics and participate in a conversation about it. They should individually and collaboratively be able to enhance their knowledge of math. This is also one of the new aims added by the new IB Diploma Math Programme. Gone also are the days when it was enough to simply do some calculations and get an answer – students will be expected to interpret what they are doing. Especially in our data-driven world, it is vitally important to be able to analyze data and interpret the data so that informed decisions are made. Perhaps “Data Science” will emerge as a new subject in the coming years, there would be a need to have teacher experts who understand Math and Computing together to develop algorithmic and computational thinking.
The lack of fear of mathematics is also so important! Mathematics teaching should aim to cater for the various needs, aspirations, interests and abilities of different students. Math also needs time for direct drill and practice for skills to gain strategic competence to be applied in new situations. Students should be fascinated by exploring real and abstract applications of these ideas, with and without the use of technology. The use of technology, visualization, use of drawings, manipulatives, drawing meaningful connections etc., should be encouraged as an approach to equip all students to be confident mathematicians to solve complex problems. Ultimately, it will all come down to implementing A SHIFT IN CURRICULUM PERSPECTIVE towards “what opportunities can I provide that will ensure deep and rich understanding to make our future mathematical leaders on a pathway towards success in this global world?”
(Written by Yogesh Dhingra – ideas gathered over years of discussions with many math colleagues and educators and readings particularly inspired by ‘The Mathematical Experience’ by Hersh and Davis)