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Tips How to Create and Teach a Pre Calculus Course
It is essential to have a pre-calculus course that combines all the topics covered in pre-calculus into a single topic. This subject is overwhelming for many students. This is because they must have thorough knowledge of many other subjects. Students should have a solid foundation in algebra, geometry and trigonometry. Special attention should be paid to binomial theorem, conic section, complex numbers and real numbers.
Calculus is the branch of science that deals with rates of change. In algebra students are taught about functions that represent physical quantities, for example the volume of water in a tank relative to time. However; Interest in the calculation is the rate of change of water in the tank relative to time. It can be clearly seen how calculus completes the picture after algebra. Algebra answers one question and calculus answers a different question and together they give the whole picture.
Calculus requires students to have a good knowledge of algebra. A good strategy for teaching algebra in a pre-calculus course is to point out points that most students have trouble with. Students studying algebra have particular problems with exponents and logarithms.
It is best to use calculators to perform laboratory experiments for students to understand exponents. For example, a teacher might ask students to use their calculators to find the exponents of 0, 2, 4, 100, and 200. Students will see how changes in output can be very rapid with small changes in input. The teacher should then ask the students to use their calculators to plot the graph of the exponential function. Students should examine the curve and see how a small change in the input causes a dramatic change in the output. The same experiments should be done with logarithms. The teacher should choose the base and choose the values to take the logarithm. The teacher should let the students try forbidden values such as negative values and see how the calculator responds. Also the teacher should let the students plot the logarithmic function and find the forbidden values on the graph.
Geometry is very important for calculus. The most important concept in geometry related to calculus is area. The student should see how he can find the area of the shape by cutting it into simple shapes and then adding the individual areas of these shapes. The student should see that we can simplify the calculation of the perimeter by simplifying the circle by treating it as a polygon. This simplification leads to some margin of error. However; The error decreases as we increase the number of sides of the polygon. The error is zero when the number of sides is infinite.
Even if trigonometry is not required at the beginning of a calculus class, students should know the basic trigonometric functions and their relationships. Students should understand that a cosine is a shifted sine and that a sine is a shifted cosine. They should view their graphs simultaneously on the calculator.
After knowing what is taught in the pre-calculus course, one should choose the appropriate textbook to assign to the class. Choosing a textbook is not an easy task. Some students do not do well in the course simply because the textbook is not suitable or easy to understand. The textbook should be easy to understand with lots of examples and start from the beginning. The teacher’s explanation for the concepts should be consistent with the textbook so that students do not get confused.
For each new concept or idea the teacher must solve several demonstration problems. This allows the student to really follow the ideas discussed in class.
The teacher should allow students to ask as many questions as necessary for understanding. Students should know that their questions are welcome and that it is important to the teacher that they understand the concepts.
Throughout the course students must perform laboratory experiments using calculators to break down concepts. They need algebraic calculators, basic scientific calculators and graphing calculators. There are many new innovative software calculators such as kinematics calculators and many more. These calculators allow the teacher to be creative in the way they create math lab experiments.
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