Multidimensional Mathematics

Mathematics is a beautiful, open, creative, and multi-dimensional subject. But school mathematics is often uninspiring, procedural and one-dimensional – it is all about memorizing methods and procedures.  The narrowness of the mathematics taught in schools is one of the reasons so many students disengage from math. One-dimensional math is not the mathematics of the world and it is not the mathematics of our 21st century workplace.

So what is multidimensional mathematics?  It is real mathematics. Let’s consider the work of a mathematician:  She first has to pose an important problem, then map out a mathematical approach, she will probably collaborate with others on ideas, and engage in what Lakatos describes as a zig-zagging process of conjecturing, refining counter examples and proving. She has to form a mathematical model, apply methods, draw diagrams, connect ideas, reason about connections and communicate in different forms. The work is multidimensional. When math is taught as a multidimensional subject in classrooms students engage more, enjoy math more and achieve at higher levels.  Put simply:

Many more students are successful because there are many more ways to be successful.

In addition students are learning real math – the math they will need, for their lives, for work and for engaging as powerful citizens in the world.

Our Complex Instruction post gives examples of teachers who taught multidimensional math.

Instead of teaching math as a multidimensional subject and a growth, learning subject it is often taught as a performance subject.  What do I mean by that? If you ask most students in math classrooms what their role is in math class they will tell you it is to answer questions correctly. They do not talk about the beauty of the subject, or its creativity and applications. Students of other subjects do not talk in these ways. A colleague of mine, Rachel Lambert, told me that her 6-year old son had come home one day saying he didn’t like math, when she asked him why he said:

“Math is too much answer time and not enough learning time.”

Students know math is different from other subjects, from kindergarten up, they believe they are in math classrooms to answer questions – to perform. Read more on moving from a performance to a learning orientation here

When we open up math classrooms and teach multidimensional mathematics amazing things happen. Our tasks here on youcubed invite students into the world of multidimensional mathematics. IMP is one of the high school curriculum that teaches multidimensional math, here is an interview from a student from one of my research studies who learned through this applied curriculum:

“Math is really beautiful and has these patterns in it that are amazing.  Most art is just made up of patterns anyway.  And so I’ve written a lot of poems about it, and a lot of songs involving it. Polyrhythms was one thing that kind of interspersed music and math for me—because it’s like patterns that take multiple measures to repeat because they don’t fit evenly over four bars, and it’s exactly like a fraction because if you take a fraction high enough there’s going to be common denominators.  And so seeing how patterns can be interesting and, artistic.  And math intersperses a lot for me that way”.  (Toby, IMP student, age 16)

Multidimensional mathematics is beautiful, creative, inspiring and engaging. It is also the mathematics people need for the world.  When teachers move to teaching multidimensional mathematics amazing things happen.  Now is the time to change the face of mathematics in classrooms, to teach creative, open and multidimensional math, for our students’ futures and for the future of our ever more quantitative society.


Watch one of the leaders of Wolfram-Alpha talk about the need to broaden the math taught in schools



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