The Value of Math Projects

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The Value of Math Projects

 

Math projects are usually assigned or demonstrated with one or more of several purposes in mind.

 

–  They are given to show that mathematics can be fun.

–  They are given to show where mathematics can be useful.

–  They are given to show that mathematics can be easier to grasp if given in a context that enables a person to use his or her natural cognitive powers to solve a problem.

–  They can show there is often more than one way to solve a problem.

–  They can show ways to deal with seemingly complex problems.

 

There may well be more reasons. Math is often taught by writing equations on the blackboard and giving the students instructions on how to go about solving them. All goes well one begins to encounter those problems in higher mathematics where there are multiple ways to arrive at a solution. Some problems have no solution, and some solutions that can be arrived at are at best approximate.

 

The five reasons given above for assigning math projects might be summed up as follows: Encourage students to learn how to think outside the box.

 

There Are Often Different Ways to Solve a Problem – Subtracting by Addition for Example

 

One example for a math project would be a simple example of how a computer makes calculations. First of all, what a computer does best, in fact the only thing the machine can do without help is to count. A computer can count very fast of course. It can also be programmed to add two numbers. It can also be programmed to subtract, multiply, and divide, which it actually accomplishes by a counting and adding. In other words, even though it is programmed by a person, a computer solves math problems differently than a person does.

 

Most math teachers, at least the good ones, are aware of the fact that many problems can be solved by more than one method, yet they never pass this fact along to their students, who basically learn one and only one way, and from rote. A simple example of subtracting by addition would be to subtract 890 from 1051. The larger number is 51 more than 1000. Set 51 aside. Add 110 to the smaller number, 890 to get 1,000. The answer is 110. Set that number aside. Adding the two numbers, 110 and 51, gives you 161, which is your answer.

 

Writing Down an Infinite Number of Numbers – Simplified

 

Another example would be to find all the numbers which when added to any other number would add up to 15. If you take fractions and decimals into account the answer is that there are an infinite number of solutions to this problem, since an infinite number of numbers is involved. A simple math expression illustrates the power of algebra; x + y = 15, where x or y could be any two numbers, as long as their sum was 15. Too many beginning algebra students are still trying to get a handle on the significance of x when y is suddenly introduced, and all of a sudden there is more than one solution to an equation.

 

Figure It Out for Yourself

 

Many math projects present a problem but don’t show what the answer is or how to arrive at it. The observer is left to scratch his or her head, wondering how to proceed. In many if not most schools in the United States, students are shown the rules for solving a problem, and then given some problems to solve, which they can do if they follow the rules. Math isn’t taught this way everywhere. Some schools teach math by what is generally known as the Socratic Approach. Socrates was a very good teacher. His method of teaching was to ask questions and let his students figure out how to go about finding an answer. That’s how they learned. An example might be to find the answer to a problem that involves throwing a pair of dice. The only clue would be that probability is somehow involved, but that might be enough of a clue. These kinds of problems are what we call puzzles. In math classes, students are usually given problems to solve. Unfortunately they are not often given puzzles to solve, which can sometimes lead to more meaningful learning experiences.

 

From Counting Beans in a Paper Cup to  the Fundamental Theorem of Calculus

 

There are countless books, workbooks, and kits filled with math projects and math project ideas on the market. Some are free and others are not. They are for all levels although the majority tend to focus on students in preschool, kindergarten, or the lower grades. That is somewhat of a shame as high schools students and even some college students could profit from looking at math from different angles. So for that matter could some adults who were taught mathematics in the traditional manner. For many adults, math wasn’t all that much fun and there were many concepts presented that were harder to grasp than they really needed to be. Even the fundamental theorem of calculus, which sounds scary, can be presented in a manner that is easy to grasp. Given the power of computerized graphics and animation, the power of calculus can be presented by visual examples which can be fascinating to follow.