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Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

What is Math?

Somehow it's okay for people to chuckle about not being good at math. Yet if I said "I never learned to read," they'd say I was an illiterate dolt.

Neil Degrasse Tyson

Math is more than just solving variables or calculating numbers. It promotes skills you can apply to many contexts in every day living. Here are some skills inherent in learning mathematics.

You Sniff out Patterns while working on Mathematics

The analysis of current and historical events, all require one to be on the lookout for patterns.

When you make decisions, you are behaving through a pattern, understanding those patterns develop your awareness.

In mathematics, patterns exist in every calculation. For example, understanding that multiplying a whole number sequentially starting from 1 (e.g., \(7\times 1=7\), \(7\times 2=14\), \(7\times 3=21\), \(7\times 4=28\)) is the same as adding by 7 every time. Understanding these patterns help you connect multiplication with addition. There are hidden pattern such as square of integers between 1 and 100 (e.g., \(1^2\),\(2^2\),\(3^2\),...\(100^2\)). Students should always be on the lookout for patterns. The search for regularity extend to daily lives. 

You Learn to Experiment

When faced with a mathematical problem, a good habit is to immediately start playing with it. Simple ideas include recording results, keeping all but one variable fixed, and trying very small or large numbers. There are mental experiments, such as trying to perform operations without writing anything down. 

One should also develop skepticism for experimental results, realizing the inaccuracies as one experiments.

You Learn to Describe

Describing precisely what you do is an important step in understanding. Mathematical sophistication comes from the ability to say what you mean. One way to see the utility and elegance of mathematical formulations is to struggle with problems which ordinary language descriptions are too cumbersome, forcing one to precisely describe in a way for someone else to understand. Making convincing arguments to your peers develops your reasoning abilities by articulating evidence of your convictions. Writing down thoughts, conjectures, arguments, questions, and opinions are useful in developing your skills to describe mathematics. Through description, you learn to collaborate with others. 

You Learn to Tinker

Taking ideas apart and putting them back together allows one to see possibilities of how things can be put back in different ways.

After experimenting with a rotation followed by a translation, you can wonder if the same applies to a translation followed by a rotation. 

You Learn to Invent

Tinkering with ideas, apps, or machines leads to expertise in building new ones. Inventions range from rules for a game, steps to doing things, explanations of how things work, or mathematical theorems. Good inventions give the impression of being innovative. For example, good rules for a game make it intriguing for everyone and have internal consistencies that make sense. For example, if chess players had to do five jumping jacks before each move, the rule does not fit with the rest of the game and not many people would stand for it. Although it may seem that mathematics is full of rules and formulas, they emerge from the experiences of the inventors and arise from their attempts to bring clarity to situations. Experiencing the situations that gave rise to the rules and formulas allows one to develop meaning for algorithms.

You Learn to Visualize

Mathematics can be visualized. Algebra is a representation of what is inherently visual. Multiplication of two values can be visualized as an application of area. One purpose is to aid understanding of the process. Visual reasoning is applied, every time you drive, estimate how far an object is, and when you play games. It also helps you perform mental calculations.

You Learn to Conjecture and Guess

Making plausible conjectures takes time to develop. It is central not only in mathematics. Conjectures are driven by the experiences and evidence you gather from inventing, experimenting, and tinkering, and need to be tested out.

What you are learning in math? by Matthew Cheung. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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