It is impossible to learn every single thing about math.
Students can never know exactly what questions will will be asked ask but they can develop the skills and knowledge that will allow them to answer questions they have never seen before.
Here’s how: By building up math skills in the following eight ways.
1. Develop speed
It isn’t about being fast, but being efficient in answering questions that have been seen before and moving effectively through questions that students have never been seen. It is about learning methods that will help students to not waste time. This also shows that the student logically understands the relationships between the parts of the problem.
For example, if I divide 3 by 4 instead of 4 by 3 on my calculator, I don’t need to retype everything. I can just use the inverse function on my calculator so that it gives me the answer I need.
Another was to develop speed is in improving mental math. Sometimes, students will write every little detail down even when they don’t have to because they can just calculate the steps in their minds.
2. Developing precision
This mastery is about understanding the question being given. Precision includes knowing what is being asked, what unit the answer should be in, and what formula to use.
It helps if students write down their work so that they can spot any errors in your calculation.
Not doing so may cause students to lose points, which can also be a source of frustration.
3. Developing understanding
Some tests will present the same type of question but in a different form. Students should have the ability to see that these are still the same questions. They should be able to approach the different forms of the question, even if they have never seen it before, and feel confident about answering it.
4. Developing the ability to persevere
When working on problems, it is natural to get stuck. But when students persevere, they are able to power through this hurdle by applying past knowledge. They also grow in confidence because they are able to know how to deal with
5. Developing the ability to create
This is the ability to apply math to new situations, especially in real life.
Say you are going on a trip you need to calculate how long it will take you to reach your destination. Students should be able to recall how to do this based on what you were taught in school and apply it to what you need in real life.
When my family was building our aquaponics system, we used our mathematical thinking to make a cone for the system. We had to use our understanding of math to create a cone with the correct dimensions.
6. Developing the ability to analyze
Students who can analyze what they are doing can improve upon what they have done before. They can understand relationships and concepts and come up with conclusions based on data and patterns
7. Develop the ability to justify.
Along with the ability to analyze, it is important to be able to explain your thinking. If a student is unable to explain their solution or how they got their answer, other people also cannot understand what is being done. They need to be able to write clearly and in organized manner, using both mathematical notation and in words.
8. Memorization of fundamental facts and developing a depth of knowledge
While students may be able to look most answers up on the internet, there is still something to be said about memorization. Memorization of key facts, figures, and formulas allows for instantaneous recall. Students can also make strong connections between the information that they have memorized. I encourage students to understand and know the most essential formulas and vocabulary so that they don’t have to pause, look it up, and possibly get confused.
Student should also learn more about math than is just taught in school. Mathematics is in art. Math is in science. There are great math stories and biographies that students should read. There is both theoretical and applied mathematics. There are interesting math problems and puzzles that have may take more time to solve and have important consequences, but are not typically in the regular math curriculum.
How do these work together?
I am always curious to see how students approach a new topic that they have never seen before. If they have a strong foundation and knowledge base they can solve problems without having been taught how to solve the problem directly.
When giving a pre-test, I see that my top students often score at least 50% based on past understanding even before being taught the material. It’s because of their level of understanding and depth of knowledge as well as a multitude of other skills for which they are developing mastery.
How does your student fare in these eight areas? Think about where they can get more practice or experience so that they can develop math mastery.
