I am going to state these proven skills mentioned above and then I will give some tips that fall in line with these universal learning skills. These skills resume to three:
- Reality of concepts. The more concrete a concept is the more it can be learned. Concepts can be clarified and made easy to understand by using pictures or the real object that is being learned. Math use symbols and shapes. So this visual imagery can help in the study of math. In some situations some concrete tools can be used to facilitate the understanding of concepts. For example one can divide a pizza in several slices to make it easy to understand fractions. For example if you divide a pizza into eight equal slices each slice represents a fraction of the actual pizza or 1/8 of the pizza unit.
- Respecting the order of sequences. We know how the structure of the 4 basic operations is interrelated. It is impossible to just start to learn addition and to move to the learning of division since doing a division involve multiplying and subtracting. Subtracting itself implies knowing how to add. The learning of the 4 basic operations have to be sequential: first addition, then subtraction, multiplication and division.
- Understanding words Knowing the vocabulary used in every discipline is important in the learning of that discipline. Knowing the definitions of math words is important in being successful in math. Math is built on fundamental words, propositions, axioms, theorems. It is essential to know this structure in order to be successful in math.
These tips involve some learning tools, the skills mentioned above and an approriate behavior
1. Math can't be learned by listening only to lectures or videos. Learning involves using some tools like seeing, listening, reading, writing and doing. It has been said in regular educatiion that too much lecturing is not good for learning. While open education that includes online education tries to be innovative and to remedy the traditional closed system of education it is regrettable to see the same practices repudiated are being promoted in online or open education. For example most of online course providers promote exclusively watching videos as the only tool for learning. While short videos can be useful to learn something but the content can be forgotten quickly and there is no way of getting back to some concepts explained in the video without re-watching it entirely. Taking notes that one can review later while watching the video is important. Some videos have transcripts that may help. Reading and practicing are the most important skills in learning math. Reading allows to review and master the concepts. You can't expect to know math without knowing the concepts. Reading and studying are ways that allow to master the concepts. Concepts can't be mastered by just listening to lectures. Concepts need to be reviewed in order to master them completely. That is the reason why they have to be written in order to be read, studied and reviewed. Lectures can be an easy introduction and a motivating factor in learning a concept. Math has also to be practiced constantly in order to master it.
2. Math is a sequential subject. Concepts learned in a given day are based on concepts learned previously. It's important to learn the concepts of each lesson successfully and do the related assignments. Craming before a test or an exam isn't productive. If there are concepts that you don't master or if your performance is poor it is recommended to get some help as soon as possible.
3. Math is a complex subject. Math require to spend more time time studying than what is required in other subjects. The reason is math involve a lot of time practicing in order to master it.
4. Memorization alone doesn't work in math. Concepts have to be understood before being memorized. It is important to learn the procedures to solve problems. After learning the concepts, definitions, rules and theorems it is important to know how these are applied to solve problems. Solving a problem involves a step by step procedure. This procedure is applied in the examples and problems solved in the book or during a lesson. Once you know the concepts and procedures you can apply them to the solution of other problems.
5. Learn the math vocabulary. Math words have a different meaning than in other contexts. That is the reason why it is important to learn the vocabulary. For example the word volume in math refers to the amount of space within a solid figure while in another context it has a different meaning.
6. Math can make students anxious. Students can feel anxious as a result of having to learn math. It is essential that students develop confidence in themselves in order to overcome the feeling of anxiety. One way to develop this confidence is to master the theoretical and practical aspect of math. One can say instead that this confidence arises by practicing math a lot and very often.
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