There is a little doubt that most of the students feel anxious in the sound of the words math and physics. Most of us have heard the phrase "math anxiety" used very often from educators to describe this phenomenon where pupils struggle to overcome the difficulties they have dealing with math. We know in fact that many students will choose some other subject as an elective when given the opportunity. But what is really about these subjects that makes many of us to have a negative attitude toward them? From my own experience for more than three decades as a student, tutor, teacher and educator I can very positively and without any hesitation assure you that is not the nature of math or physics who is to blame about those negative feelings and relatively poor performance of millions of youngsters around the world. And in case you don't believe me I invite you to ask anyone close to you (a family member, a friend) who is, or were good in these subjects, about this fact. I am very certain that will agree with me and if you go further asking that person how he/she managed to perform that well he/she would most likely answer you that had a great school teacher, or a fabulous tutor at home or that even a friend suggested him/her to study from a particular textbooks who was really excellent.
The point that I am trying to make here, is that there is really nothing difficult in math or physics and that students should try to ignore any bad past experience when trying to study them and face their future studies with optimism and without any negativity. I can guarantee you that the overwhelming majority of the student population can excel in these subjects. The cause of the poor performance should be pursued in some other domain of study, which in my opinion is not other than the pedagogy associated with the teaching and learning of mathematics and physics. The real problem is the failure in the learning process which is directly associated with an insufficient instructional procedure.
My teaching approach is a very simple one and it is based on the nature of these two disciplines. The learning process can't be disconnected from the subject matter itself. Induction and deduction the main features of sciences have to be the most important elements of the learning process. What does this mean? Let's say that a student today has to learn a concept X. First I have to make sure that he/she is familiar with all the prerequisite knowledge that this concept involves. The student have to master 100% that prerequisite knowledge. Answers of the form I understand "pretty much" or "more or less" are an indication that I have to go over with the student, because there is where the problem starts. Leaving even the smallest gap in the learners notion of the concept it can be very harmful especially if this is repeated very often, because the further advances to the course the accumulation of those uncertainties can lead to a chaotic situation and things will then be more difficult. Once I make sure that the student completely masters the necessary knowledge I try to make the connections with the concept that has to learn. These connections have to be very strong so they can last in time. Once I have finished with the theory I go on with problems.Here I would like to make a distinction between the two subjects;
a) Math: In mathematics mainly you have two types of problems; the pure math problems and the applied math problems. In the first one which is somehow less complicated you just have to use the mathematical formulas directly. Here I do a few examples of the types of questions that the particular topic involves and I also ask students to try to do some. I try to categorize the problems as much as possible so the student knows how to tackle the majority of exercises. Of course there are always some problems that don't belong to any of the general categories, that examiners add in tests in order to distinguish the very good from the excellent student. My advice for this type of exercises is one you are familiar with the mainstream type of questions try to practice as much as possible with challenging ones. Once you have the problem in front of you use your creativity and write down your thoughts. In general a well prepared student will solve this kind of problem 90% of the times.
Now I would like to come on the applied math problems. In this case before you proceed with the step in pure math problem solution that I described above, you have to do some work which sometimes can be challenging ; You have to "translate" the words in the problem, to mathematical formulas. Here students may have to deal with a rigorous applied course (physics, economics, etc) where the formulas are given and the student has just to use them. The most common obstacle in this case is that pupils have difficulty selecting a formula. What I recommend here is check the data of the question and what you are looking to find, and then pick the formula that involve all the above. Some times specifically in secondary math courses have to use common sense to do this translation. Again here the phrase "practice makes perfection" is the most appropriate recommendation.
b) Physics: Physics essentially is one of the applied math areas. Hence one has to do whatever I suggested just above for the applied math problems where the mathematical formulas chosen interpret the laws of physics.