Hi there. In this math education post, I want to highlight the importance of mathematics homework. What I refer to as mathematics in this post is all the math topics past middle school and high school mathematics. It is pretty much the mathematics that involves algebra, problem solving, solving for x, writing math proofs and so on. Some of the contents in this post can also apply to the arithmetic aspect of mathematics (addition, subtraction, multiplication, division).
- Math Is Like A Language
- Cramming Doesn't Really Work
- Math Practice For Understanding, Building Skill, Speed & Retention
- Importance of Pushing Through
Math Is Like A Language
One of the pieces of advice that stood out for me when I entered first year university was the advice of "Math is like a language." or something like that from the Learning Services back then. It does take a lot of practice along with trial and error to be able to solve questions, understand abstract concepts and to build strong, precise and fast algebra skills.
Mathematics does contain a lot of symbols in the form of Greek letters, strange symbols, equal signs, and less than or greater than symbols. It is important to understand what those symbols mean, how they are used in the math context and how to communicate mathematical ideas with such symbols.
It seems that there is a large emphasis on numbers in mathematics and not so much on motivating real life math application and writing with mathematics. I think it would be a good idea to point out that writing skills and communication skills are very helpful in mathematics.
Cramming Doesn't Really Work
Cramming and studying the night before a test might work at the lower school grades or for knowledge based courses. With courses that require competency and skill at a high level such as mathematics, languages, science, programming and cooking cramming is not a good idea.
Math Practice For Understanding, Building Skill, Speed & Retention
Similar to how athletes, dancers and martial artists prepare for big events through practice, math students need practice too. The math practice is crucial for understanding, building skill, building speed and for math memory retention. It may be an easy scheduling decision to cram all the practice into the last few days before a test but there is so much material to digest in a short period of time.
Once the understanding of math concepts is grasped, the speed can be built from math homework. Many of the math tests out there are timed so it is beneficial to build speed in solving problems, algebra, reading and writing. For the writing part of mathematics during homework and tests, it is more time-efficient to write with short hand writing, math symbols instead of sentences. Any time savings is helpful for getting more done in less time and for fixing any (algebra) mistakes that you may catch yourself with. Speed definitely helps in the event of receiving math tests that are either long, difficult or even both. It is not good to lose marks due to a lack of speed regardless if you know the material.
Importance of Pushing Through
There are times when the math homework is either long, difficult or just confusing. It may even seem that some topics may never be understood in a short period of time before an assignment being due or for a test.
If you get stuck on a problem or math proof, it is a good idea to take a break from it. Let the mind not think about the problem and come back to it when the mind is fresh. Instead of looking at a problem for two hours, why not look at it for one hour in the morning then after several hours come back to the problem again for the second hour. As much as the body needs rest after physical exercise, the brain does need rest after usage. Sometimes you may even think of a solution when you are not actively thinking of the problem. The key point is to manage time well and avoid a brute force approach in thinking your way out of a problem. Over time with more exposure what seems difficult to understand gets easier to understand.