The simple solutions to the first point of my last post are to modify college instruction to ensure real understanding of the subject, to learn appropriate and creative methodologies to transmit this knowledge effectively to the student, and to provide incentives to aspiring teachers entering these fields. All of these are done in some college-level settings, yet it hasn’t become widespread. Even if it were widespread, we would have to wait years to see real results.
Now, let’s suppose that your one of the few to get such training in college or that you acquired it on your own through initiative and hard work. Would you actually employ these skills in the classroom? With so many cookie-cutter lesson plans available on the internet and resources offered by textbook manufacturers, the demanding work load that our current teachers face makes it so tempting to sacrifice the time needed to employ the skills learned in college in favor of these time-saving crutches. This leads to my second point, modifying instruction to actually connect with students lives.
In regard to mathematics, the typical and most simplistic form of instruction is rote memorization. While I do agree with this at the elementary level, since this is the foundation of all advanced mathematical subjects, like algebra and so on, I disagree with this method of instruction during math education in grades 7-12, yet this method still persists.
The connection of elementary mathematics education is easy to connect to students lives (they see examples everyday), but advanced subjects are more of a challenge to convey. It requires a large sacrifice of time on the part of the teacher to develop such lessons, since the resources readily available don’t usually have the necessary focus—check the research studies done on mathematics textbooks and their associated resources and you will find that they are rated poorly in most instances. Furthermore, real-life scenarios/problems for math subjects offered in grades 7-12 require more critical and creative thinking on the part of the student…something they are not used to and is a skill in and of itself. Research shows that, in general, students value the learning of a subject if it appears useful or important to them, so we must not neglect this fact and target it in our instruction.
Here’s a simple example to show why knowledge of trigonometry is important to the student. In the future, the student will likely buy a house. They may eventually decide that they want to cut down a tree that resides on their property, and that they want to do this task themselves to save money, yet the layout of their property and the general appearance of the height of the tree makes this appear like a risky endeavor. If the tree has only one cut at its base, will it fall on the house, or will two cuts and the extra work be necessary? Using their critical thinking skills and knowledge of trigonometry, the former student realizes that they can accurately measure the baseline from some position to the tree and the angle from this position to the top of the tree and compute the height of the tree to good accuracy. Thus, the question is answered and learning trigonometry has proved useful to the student. There are many more examples that can convey the value of advanced mathematics, but it requires competency on the part of the teacher to show this to students, and unfortunately, this does not generally happen in our classrooms.
The last point, modifying the K-12 curriculum (mostly 7-12), is connected to the discussion of the second point. What mathematical knowledge is really necessary for students who choose vocational studies vs. college prep studies in the sciences or liberal arts? Usually, students in the vocational studies don’t take calculus, while students in college prep do and for many of them it will never be of any use except for a well-rounded educational background. Instead of requiring calculus for these particular students, it should be offered as an elective vs. another class that explores familiar mathematical subjects and their connections to real-life scenarios in order to build problem solving skills. This aspect of mathematics education should be specifically tailored to the student's chosen path of study and should provide the student with freedom of choice rather than required restraint. So, if a student is planning to pursue the sciences then calculus should definitely be taught in high school.
