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Learning tips

I get extra income tutoring science and math so these tips relate mostly to science and math learning.

Paper is cheap.
Write down everything neatly and in plenty of detail. If you make a mistake it will be easy to find and correct. You may get partial credit even if you make a calculation error. If you need to study later you can see how you did the work. You can scribble the solution to a problem on scratch paper then transcribe a neat version onto your final paper. Draw diagrams and sketches freely, you will get better with practice. A simple diagram or table can make complicated problems easy to understand.

Vocabulary is a big part of many subjects. Think about how much knowledge of medicine or chemistry is in the vocabulary. If you don't know the words you will miss questions that you know how to solve because you don't understand them. Organized vocabulary study helps bring complex subjects under control. Text books have glossaries and indexes to make finding word definitions easy.

Here is an organized way to study vocabulary.

Solving equations
The golden rule for solving equations; you can do whatever you want to one side of an equation as long as you do the same thing to the other side (except never divide by zero). You can add, subtract, and raise to a power any way you choose; this is the basic step. Problem solving consists of choosing transformations that get you from problem to solution without making errors.

Equations are solved by steps. The given problem is where you start. The given solution form is your destination. Each time you transform the equation (by doing the same thing to both sides) you move one step closer to the solution form. Many different paths can lead to the same solution. Finding the best path is much less important than getting to the solution. Sometimes you follow a path for several steps then realize it isn't working; you have to go back and try a different path. Completely different ways of solving an equation can lead to the same correct answer. They are like different paths that all go from point A to point B.

Complicated problems are just simple problems with more steps. When you see a complicated problem you may want to hurry because it will take longer. Resist this temptation because your error rate per step is constant and you are already more likely to miss complicated problems because they have more steps; hurrying makes this worse. You should do each step more carefully in complicated problems to compensate for the larger number of steps.

Solve word problems in two stages. First translate the word problem into a math problem; pay special attention to what solution is asked for. Diagrams and tables can be especially helpful. After translation is finished, solve the math problem. It is easy to get confused if you try to translate and solve at the same time.