Guest Post: Twenty First Century Mathematics
What will 21st century mathematics look like?
There is a lot of talk about the need for students to develop "21st century skills". Singapore's Ministry of Education developed a framework 21st Century Competencies and Desired Student Outcomes which outlines what students need to learn to "thrive in a fast-changing and highly-connected world".
Among the desired outcomes are that students should be confident, self-directed learners who are concerned citizens and active contributors to society.
The 21st century skills that students need, according to MOE, are:
• Civic literacy, global awareness and cross-cultural skills
• Critical and inventive thinking
• Information and communication skills
So how does all this relate to mathematics?
My observation is that the math teaching profession is one of the most conservative of them all. There is normally great resistance to adopting any technology tools and it seems to me, most math teachers would like to stay in a comfortable time warp.
A good example was in the 1970s when the pocket calculator became more affordable and thus widespread. Math teachers were generally horrified that the use of such tools would reduce students' mental arithmetic skills. It took a long time before calculators were allowed in classrooms, and even longer for them to be allowed in examinations. Meanwhile, industry had well and truly embraced the use of calculators. Why use cumbersome log tables (as they were still doing in schools) when you could use the electronic tool to come up with the answer in a fraction of the time?
We have a similar situation currently. We've had computer algebra systems for some 30 years now, but mathematics is still taught in the same way it has been for the last 50 years. The emphasis is still on paper-based calculation steps, whereas we should be using such computer tools to perform the calculations instantly, and we should spend more time on how math concepts can be used to solve real world problems.
I'll address the 21st century skills most relevant to math teaching.
Global Awareness & Cross-cultural Skills
Every country has math students, and every country has real problems that desperately need a solution.
It is now so easy and inexpensive to communicate with people in other countries via Web conferencing (Skype or Google+). What we should be getting students to do is to collaborate with their peers in other countries and help them solve some of the problems they have in their local area.
A good place to start for ideas is High Noon: Twenty Global Problems and Twenty Years to Solve Them by Jean-Francois Rischard.
In the process, students learn about other countries, their people, and their issues - not from a text-book, but from helping them to identify and solve pressing issues.
Critical and Inventive Thinking
A lot of people have become "Google gullible". That is, they do a search, click on the very first link at the top of the search results page, and assume it is an unbiased, accurate answer to their question. A key 21st century skill is to be able to determine the reliability of such information.
Similarly, when using computer math software, it is very easy to get an answer which is very wrong! This is the "garbage in - garbage out" principle. This means students need to develop skills in estimating the answer (before even starting the software), and being able to spot any issues with their answer.
"Computers are incredibly fast, accurate and stupid; humans are incredibly slow, inaccurate and brilliant; together they are powerful beyond imagination." [Leo Chern, often wrongly attributed to Einstein]
Mathematics and creativity are 2 concepts that rarely exist in the same sentence. In most schools, there is one right answer and one way to get that right answer. If you do it another way, you get penalized. But this is very far from what mathematicians actually do! All mathematics was "created" (or discovered) at some point by some one, somewhere, usually to help solve a problem.
So we need more creativity in math classrooms. Solving real problems is a good way to encourage this (since there is no answer in the back of the book already). Another way to encourage this is to get students to develop their own media about mathematics. They can create videos, or images explaining concepts. Recognition should be given to the most creative efforts and the ones that communicate the concept best.
Information and Communication Skills
Many educators say the students are "tech-savvy", but I don't always agree. Sure, some are very "computer game-savvy", while others are "YouTube-savvy". But very few are competent when it comes to spreadsheet skills, or computer algebra skills. I've seen enough terrible Powerpoint presentations to know many student still have a way to go there!
The suggestions I've given above would help to enhance information and communication skills.
Math class is an opportunity to develop many of the desired 21st century skills. We need to spend less time on inefficient paper-based calculations, and more time developing the actual skills our students need in the 21st century.
Of course, for this to happen we would need to reduce the emphasis on high stakes paper-based tests - but I can't see that happening any time soon.
ABOUT THE AUTHOR
Murray Bourne has devoted his life to education and has taught a wide range of things, including math, music, aeroplanes, technology and English as a foreign language. He has developed 2 popular math resources: IntMath.com, a series of math tutorials covering topics from basic algebra to Laplace Transform; squareCircleZ, a math education blog