Tests are supposed to measure the students’ abilities and potential. The student who performs well on a test is supposed to be good or talented in the subject and the student who does not do well in the test is supposed to be poor in the subject and needs extra training.
What is really happening today is that tests do not reflect the students’ abilities. This has disastrous consequences. When unqualified students go to do a mathematics degree and eventually become mathematics teachers or researchers they lead to the decline of future generations in mathematics.
What is happening in schools today is that administrators are applying pressure on teachers and the teachers pass this pressure on to the students. The teachers teach the students only to prepare them for the test. The point is not to make the students understand the concepts. After all this pressure exerted on the teacher he only cares that the students score high on the test. One of the main issues that face the teachers when they do that is that parts of the syllabus are skipped on the test and thus left out untaught by the teacher. However, though these parts that are skipped do not come in the exam they are important for understanding the other parts of the syllabus. This is enough to cripple the students’ understanding of the material. The teachers teach the students some tricks and mechanical drills that allow them to automatically solve exams without understanding.
Tests will be driving standards and curricula in the near future. This is why special attention should be given in how to design tests. In other words, there should be precise definitions of the concrete objectives of the subject and how to quantify the measure of success.
This problem has two sides. One side is the tests and this side is the dominant side due to pressures on schools to have good scores. The second side is the teachers. To drive the teachers to really get the students to understand rather than do mechanical work the exams should be designed to filter the students’ capabilities.
The test should be composed of several sections that cover all the different parts of the syllabus. Each section should contain questions that reflect the students’ abilities in using the different techniques taught. The student should know which technique suitable for which problem. The section should contain problems that examine the students’ abilities in using mathematics in solving real life problems. After all how good is mathematics if one does not know how to apply it to real life.
Part of the exam should be a project on an application of mathematics in real life. The student should use his earned mathematics skills to solve some real life problem in a project. The project should have two supervisors, one supervisor from the student’s school and one supervisor from another school. The students should be exposed to the many innovative software calculators that they can use to complete their projects.
When exams reflect the true abilities of students mathematics teachers would not concentrate on how to beat the system and would concentrate on developing the students’ abilities in the subject.
The school administration should help in this by giving teachers strong support by letting them attend training classes in mathematics and teaching psychology.
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* If you multiply a number with only 1s by itself, you end up with a palindrome of the numbers in ascending and then descending order. People have called this an example of the “beauty of mathematics.” If your number has N digits of 1, then its square will be the numbers 1 to N in ascending and then descending order. The pattern continues indefinitely, although it “breaks” after 9 because of carry over. I explain why the pattern happens using the method of multiplying by lines.
Multiply by lines: https://www.youtube.com/watch?v=0SZw8jpfAk0
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Here’s a listing of all my books
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“The Joy of Game Theory” shows how you can use math to out-think your competition. (rated 4/5 stars on 21 reviews) http://amzn.to/1uQvA20
“Math Puzzles Volume 1” features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.6/5 stars on 9 reviews. http://amzn.to/1GhUUSH
“Math Puzzles Volume 2” is a sequel book with more great problems. http://amzn.to/1NKbyCs
“Math Puzzles Volume 3” is the third in the series. http://amzn.to/1NKbGlp
“40 Paradoxes in Logic, Probability, and Game Theory” contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) http://amzn.to/1LOCI4U
“The Best Mental Math Tricks” teaches how you can look like a math genius by solving problems in your head http://amzn.to/18maAdo
“Multiply Numbers By Drawing Lines” This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. http://amzn.to/XRm7M4
111111111×111111111 – Beauty of Mathematics