Since then, people have been trying to figure out how to make a math test easier and more convenient for students. One of the proposed solutions has been to use knowledge based tests like the SAT.
Although the mathematics college entrance exams are not as challenging as the mathematics test that gets college credit in high school, they still offer many students great potential for high marks. However, the SAT is difficult because it demands a lot of logical thinking. It is designed to test and emphasize a student’s ability to think logically and solve problems in an analytical manner.
There are many types of tests that are often used to measure and evaluate a student’s academic skills. Some people argue that taking multiple choice and true/false questions is the best way to measure students’ knowledge. Other people argue that having to write an essay about a certain topic is the best way to assess a student’s mathematical abilities.
What is clear is that one of the ways that the SAT will be harder than the normal math test is because it requires more problem solving and more basic mathematical knowledge. There are also several ways that this test can be made more complex.
There are two types of systems for teaching mathematics that are sometimes combined in the classroom and are sometimes used independently: Riemannian geometry and elementary number theory. Because of the similarities between these two systems, some teachers give students both kinds of geometry. In reality, the two systems work very differently from each other.
Each system has many different ways of describing sets and numbers. While Riemannian geometry often uses graphs, these are usually not true, solid objects. There are also some sets that are real but not necessarily measurable in terms of dimension. Students also do not know what the real numbers are because these are not the standard units in mathematics.
Elementary number theory uses the real numbers as its basis. Although the real numbers are the basis of algebra, they are not a basis of number theory in elementary number theory. Therefore, both systems require students to know a great deal of algebra.
Algebra can actually be a challenge for students. Some students struggle with the concepts and some students are simply not able to learn algebra. For this reason, some teachers make up an algebra lesson on the spot. Teachers can use Riemannian geometry as a test case for developing algebra skills.
If the real numbers are no longer the standard units in algebra, what can be done? Teachers can tell students that the units of algebra are higher powers of ten instead of the standard integers. The difficulty will decrease somewhat and a teacher can show a student the range of fractional powers of ten.
There are two types of problems that students can use in their algebraic number theory class. The first type is the Pythagorean Theorem. The second type is counting on the right hand side of a right triangle.
When the real numbers are used in place of the standard integers, the students are going to have to use the ratios. The question will be how to convert the Riemannian geometry to the standard math.
