Math Galaxy Instructions

"The French mathematician Jacques S. Hadamard found, in a study of 100 leading mathematicians [including Einstein], that the majority of them were primarily visual in their approach."

Scientific American, Sept., 1984, p. 56.

Quick Start

You can do the exercises in either (1) Step-by-Step mode or (2) Final-Answer-Only mode by clicking the appropriate button at the bottom of each exercise. In Step-by-Step mode you are guided through a problem step by step. It is a good idea to do each exercise at least once in Step-by-Step mode, especially the explanations. In Final-Answer-Only mode you are asked only for the final answer. In Final-Answer-Only mode you will be given a score when you exit the exercise. To skip the graphics between exercises, just press the mouse or any key. Numbers are chosen randomly, so you have an unlimited supply of problems.

To maximize the effectiveness of the graphics in illustrating the concepts, the exercises need as much screen space as possible, so they are shown in a separate window using a program called an applet. At the bottom of the screen it will say "Warning: Applet window". This is to warn you that it is not a secure connection and you shouldn't give any personal information, which we won't ask for anyway. Some word problem exercises may ask for a first name as a way of personalizing the exercise, but you can give any name you like.

The exercises were designed for a screen resolution of 800 x 600 on PCs. They should appear full screen at other resolutions also. If you have trouble at other resolutions or on other computers let us know. This Quick Start should be enough to get you started. See below for more details.

Introduction

Math Galaxy is a comprehensive math tutorial that is like having an interactive textbook and your own private tutor, with explanations, practice and games that cover all of whole numbers, fractions, decimals, ratios, proportions, percents, word problems, length, area, volume, weight, time, money, angles, temperature, negative numbers, graphs and tables. Principles of geometry are spread throughout the exercises and algebra will eventually be added.

It's focus is on mastery of concepts and as such does not provide a day-by-day curriculum. Those more comfortable with a day-by-day planned curriculum can use it for enrichment. If, however, you are comfortable with the mastery style of learning, it provides a complete curriculum. Numbers are generated randomly, so you have an unlimited supply of problems. All exercises are supported by step-by-step graphical illustrations.

Operation

As noted above in Quick Start, you can do the exercises in two modes, selected by buttons at the bottom of each exercise.

Step-by-Step mode guides you through a problem step by step. All input is through the keyboard. A text box at the bottom of the screen provides instructions and highlights important concepts. This mode is best for review sections. Also, you should do each exercise at least once in this mode to see the detailed explanations. Since each exercise has its own pattern, children who are not able to read well should still be able to do the exercises if you go through a few examples with them. You can exit this mode at any time with the Esc key. Since each problem involves multiple steps, no score is given for the exercises.

In Final-Answer-Only mode, you use a calculator-like keypad to input the final answer. A textbox at the left of the screen provides comments. It may help to have scratch paper handy to do intermediate steps. You can use the Esc key or the onscreen Quit button to exit. When you exit an exercise, a score is given.

Our Philosophy

Math Galaxy's approach to learning math is based on the philosophy that:

New ideas must be connected to a child's current network of knowledge and experience.

Skills develop along a concrete-to-abstract continuum, with advanced skills developed by generalizing from more concrete experiences.

A child must see a wide range of instances of a concept in order to separate out extraneous material from what is essential.

A child needs to be actively engaged with new ideas and not passively entertained.

Mathematical concepts are tools that, like any other tools, involve actions that move you towards a goal. Mastery means that you know what the tool does and when to apply it. Students need to learn to analyse situations to see which tools are appropriate at each point, rather than memorizing a laundry list of steps for this week's problems that will fade from memory when they go on to next week's.

Teachers and computers have different strengths and weaknesses that, used together, can complement each other. A teacher can deal with a wide range of student responses and is much more flexible than a computer, which must be programmed for each possibility. However, teachers don't always have the time or energy to give students individual attention. If you can identify critical areas of instruction where a student needs help, a computer can review those skills tirelessly.

Math Galaxy starts from the beginning, with addition and multiplication tables and single-digit operations, but its main focus is on where children start having trouble with math: multi-step problem-solving. There are enough programs out there that teach number recognition and simple operations, with dancing bears and other frills, but stop short of where students start having trouble, making the leap from familiar and concrete experiences to abstract thinking.

Unlike most math textbooks, which throw a mass of material at the student, Math Galaxy focuses student attention on concepts sequentially and interactively, based upon the ideas behind math manipulatives (such as counting blocks): connect new concepts to something familiar. Unlike most math software, it goes beyond simple games, low-level operations or rule memorization to link familiar and concrete experiences to higher-level processes. It goes beyond physical math manipulatives by linking each physical operation to its mathematical counterpart at each step, and by allowing manipulations that are difficult to do with physical manipulatives. It stresses concepts that run through all of basic math to provide basic understanding rather than memorized rules. Our goal is to provide students a foundation for analytical thinking in the modern world and for higher-level math and science.

The key to learning math is consistency. It is best taken in small doses but done consistently. Even ten minutes or ten problems a day will improve your child's understanding of math if done consistently.

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