How we learn problem-solving skills? Let us consider a typical math task, such as “solve an equation”. A formal indicator that a task is solved is a set of consecutive calculations proving the solution. To produce this set we should be capable to set an objective for each solution step and convert these objectives into math transformations, be aware of suitable solution methods and be able to apply them, know all necessary definitions, formulas and rules and be able to apply them. In pedagogics, this capability is referred to as a level of knowledge, abilities and skills. If this complex lacks just one element basic for decision-making, we will be not able to make the following solution step and cope with a task.
To reach a decent level of knowledge, abilities and skills we need help of someone who would provide us with the needed information. If the help is unprofessional, then this someone will simply show us what the next step must be. A professional, on the other hand, will go into the whys and wherefores of the problem and will help us to fill a vacancy in our basic knowledge, abilities and skills. An experienced teacher is usually familiar with typical student’s errors and their roots. Below, I specify a few typical flaws in math knowledge and skills that limit student’s ability to perform math transformations:
- Lack of knowledge of solution methods for a given type of task
- Lack of understanding of objectives of the transformation steps
- Lack of knowledge of definitions and other math concepts related with solution
- Lack of knowledge of related formulas and theorems
- Lack of skill to apply definitions
- Lack of skill to apply formulas or theorems
- Lack of ability to relate math categories with each other
Any of the flaws from the list above can, and most likely will, result in “braking” the process of solution. In a similar situation this “braking” will almost inevitably appear again. It is worthy to treat the root of the disease instead of treating consequences. This means that we should build knowledge, abilities and skills that are lacking.
Ideally, every teacher should do this work with every student. In the real life, however, classroom teacher lacks time and strength to do this job. As a result, some students fall behind. You probably know what happens next? The teacher begins talking about kid’s “inability” and recommends parents to find some “easier” school, with a “lowered” level of mathematical requirements. (By the way, about abilities: do you know that Einstein and Hilbert were classified at school as “incapable”? As a teacher, I personally prefer the word “neglected”. “Incapable” sounds as a God’s burn while the “neglected” child can be helped if proper efforts are applied).
What to do if your child takes dust? There are two ways. The best, but rather expensive way is to employ a personal math tutor. If you cannot affors this option, then help your child yourself! This is your own child – you should fight for him.
How The EMTeachline Mathematics Software can help you?
Let us explain you how to work with the EMTeachline software. Firstly, you open the list of contents with themes, chapters and sections, and select an example. Secondly, you select a methodical scheme to work with the chosen example. If you have no slightest idea where to begin, the best choice would be the simplest learning technique “To view”. Go through the course of solution step by step. For each step observe related definitions, rules and formulas. Learn these categories with one of the schemes “To learn”. What is next? Try to go through the same example with another learning technique, e.g. “To insert”. The program will provide you with questions and hints at each solution step. After you finish, press button “Results” and call an option of performance analysis. The program will show you your errors and recommend a set of tasks to develop missing skills. Try to solve recommended exercises with recommended techniques. Well, and so on.
What is really difficult that is to get used to the software, learn working with it. However, there is no way out; you have to learn how to work with any tool, even with a hammer. Do you need to go through each example with all available techniques? Certainly not. If you “went through” an example with one technique without any problem, then you can set this learning technique aside. In some time, you will get familiar with all methodical schemes.
Training problem solving skills is a long procedure. You cannot do this in a couple of hours. None of the training programs can learn mathematics instead of you. You have to work hard, but you will be rewarded! You can try a number of training techniques online right now. Alternatively, you can download a trial software version and try all training techniques off-line.