Category: What is mathematics

Posted in What is mathematics

swimming, math, and life

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Phelps wins 200mJust like one learns to swim by swimming, one learns math best by doing math.





 

 

 

But unlike swimming where the swimming style one learns is NOT a function of the type of water one swims on, the style of mathematical thinking and communicating one learns is a function of the mathematical tasks one engages in.




Like learning mathematics, one learns about life by engaging with it. The quality of one’s life is a function of the relationships one engages in.


 

Posted in What is mathematics

Math is not easy to learn – that is a fact.

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I think it’s a waste of time trying to make math easy and fun to learn if your idea of fun does not involve challenge.

Mathematics is not an easy subject and it is not easy to learn it. That is a fact. The sooner the teacher accepts this, the better for her students. The challenge to us teachers is not in how we can make math easy to learn but in how we can make it makes sense and how we can make our students love the challenge that mathematics presents. Can math be challenging if students feel that what they are expected to do in the class is to follow the teacher’s method, the teacher’s way of thinking, and the teacher’s way of doing things? Where is the fun in that?

Mathematics is not fun to learn if the idea of fun is like playing bingo! However, if ‘fun’ is a function of the challenge a sport or a game presents, then indeed learning mathematics is fun. We love a sport because of the challenge it presents, the opportunities it gives us to make prediction, analyze, strategize, make our stand and defend it, etc and not because it is easy to play!

Everything in mathematics makes sense. Everything in mathematics is connected to everything else. I think this is where we teachers should be devoting our time to. And this is what this blog is about!

Posted in What is mathematics

The heart of mathematics

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Axioms, theorems, proofs, definitions, methods, are just some of the sacred words in mathematics. These words command respect and create awe  especially to mathematicians but deliver shock to many students. P.R. Halmos argued that not even one of these sacred words is the heart of mathematics. Then, what is? Problem solving. Solving problems is at the heart of mathematics.


Indeed, can you imagine mathematics without problem solving? It might as well be dead! But why is it that problem solving tasks are relegated as end of lesson activity? When it’s almost end of the term and the teacher’s in a hurry to finish their budget of work, the first to go are the problem solving activities. And when time allows the teacher to engage students in problems solving, the typical teaching sequence goes like this based on my observation in many math classes and from the teaching plans made by teachers.

  1. Teacher reviews the computational procedures needed to solve the problem.
  2. Teacher solves a sample problem first usually very neatly and algebraically (especially in high school)
  3. Teacher asks the class to solve a similar problem using the teacher’s solution
  4. Students practice solving problems using the teacher’s method.

Even textbooks are organized this way!In this strategy, students are given problem solving tasks only after having learned all the concepts and skills needed to solve the problem. Most often than not, they are also shown a sample method for solving the problem before they are given a set of similar problems to work on. I will not even call this a problem solving activity/lesson. How can a problem be a problem if you already know how to solve it? Of course, this particular strategy also gives the students the opportunity to deepen, consolidate and synthesize the new math concepts they just learned. But it also deprives them the opportunity to engage in real problem solving where they themselves figure out methods for solving the problem and using knowledge they already possess.

Another approach to increase students engagement with problem solving is to teach mathematics through problem solving.

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why study mathematics

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Mathematics is a language that can communicate visually and symbolically. It can express ideas that other languages cannot articulate with conciseness, clarity and precision. Mathematics is also a way of thinking that can empower an individual to be critical, creative, logical and methodical. Mathematics is a language and a way of thinking that everybody can and must learn.

 
Most mathematical concepts and principles developed from the need of humankind to understand, solve, and investigate problems in his day-to-day activities. In the present society, mathematics is one of the most powerful tool in understanding, and investigating problems in the real-world. This power of mathematics is due to the very nature of this discipline: it is both a language and a way of thinking.