Dr. STeve fawthrop

Department of Mathematics & Statistics, Radford University, Virginia

     My Teaching Philosophy

You cannot teach a person anything; you can only help him find it within himself." ~Galileo Gallilei
"Tell me and I'll forget. Show me and I may remember. Involve me and I'll understand." ~Chinese Proverb
“If you never make a mistake you never learn anything, you just memorize what is correct.

OVERVIEW

Learning is an active process. Unless one is trying to study a topic by oneself it is a symbiotic relationship between a teacher and a pupil: the teacher cannot successfully impart understanding unless the pupil is receptive to learning; the pupil cannot successfully understand the material unless given the maximum opportunity to do so by the teacher. The word “student” is derived from an old French word meaning “one who studies”. The Latin word for “to teach” is docere, from which we get the modern word “doctor”, a teacher. As a doctor of mathematics it is my responsibility to teach those who wish to study. However, it is a simple fact of life that everyone, teacher and student alike, is unique, with individual strengths and weaknesses, abilities, desires and motivations. This creates an interesting challenge for both student and teacher.

I try to base my teaching and classroom activities on the above paragraph. In particular, I try to give every student many ways to gain understanding and to get the desired grade, although I do not consider success in grade to be the primary objective. Nor I do consider it my responsibility to force unwilling students to make an effort, although I will do everything I can to encourage that. I also try to help students individually based on their abilities and learning styles. Every student learns differently and what works in the classroom for one student my not necessarily work for everyone. If two people have different learning styles and habits then it is unlikely that they will benefit equally from any individual class session. As a result, one of them (at least) is not being given the maximum opportunity to understand the subject. This creates a dilemma for the instructor. In order to get round this issue additional opportunities must be given.

I therefore try to provide a mixture of approaches in the classroom and also a number of ways to earn credit towards the final grade. Each of these is discussed later in this page. I also strongly encourage students to talk to me outside the classroom so that they do not get left behind. I believe in this so strongly that I incorporate it into the grading scheme, although I still make it very possible for a student to achieve the desired grade without doing so.

Most people are not aware that there are different learning styles and that most people learn in different ways. The most common division is into Visual, Auditory, and Kinesthetic. There is also a separation into Dependent and Independent learners. Another option is to classify people according to certain opposites. This last one is the approach I take and I ask all students to determine their learning style during the first week of classes. The short quiz I use allows students to determine their relative position in four different categories. You can find information about each of these at this link. It is unfortunate that the style of any instructor tends to be directed more towards certain combinations of these styles to the detriment of the others. It is possible to modify the instruction style from class to class, but this does nothing more than dilute the issue -- for any single class there is a conflict for many students.

 

“YOU CAN LEAD A HORSE TO WATER BUT YOU CANNOT MAKE IT DRINK”

Everyone has heard this proverb. Translated into the current context it would be “You can give students every opportunity to learn but you cannot force them to learn.” I strongly believe in encouraging students to do as much as is necessary to get the desired grade. On the assumption that nobody joins a class to fail, I assume the desired grade is at least a C. As a result, I do not have an attendance policy per se but do have what I call a "participation policy". This is based on the principle that the worse a student is doing, the more participation is required to give that student the maximum opportunity to understand. I therefore expect less participation from a student who is currently getting an "A", but significantly more from a student who is currently getting an "F", with varying degrees of participation in between. Full details of this are set out in the participation section below.

The simple fact is, that unless the student is a naturally talented mathematician then it is going to be impossible to gain complete understanding without work, and even then the more work done the greater will be the understanding. Think of a two dimensional grid.

 

 

 

 

 

 

 

 

 

 

 

 

In this table the letter is the expected grade and the number is the average number of hours per week of study out of class. I must stress that these are only average over a large number of students and may not be accurate for any individual. It is based on the principle of 2-for-1, that is 2 hours of study out of class for every hour in class. According to this, even a student with minimal abilities can get a C in a class with the right combination of study and effort. On the other hand, the best of students is going to have trouble getting better than a C without making an effort. The truth is, the average student is going to be somewhere in the middle and an average amount of work is just not going to make a high grade. I work on the assumption that the average student is going to fall somewhere in the middle of the table. In other words, you either have to have a little above average ability or be willing to make a little above average effort to get a B. An average amount of effort will get the best students an A and an average student can get an A by making a large effort, but these will not be the norm. It is therefore my goal to help the student increase both ability and effort.

It should be noted that the average GPA for all undergraduate students at Radford is approximately 2.8 and that the average grade given in all 100-level math classes is slightly less: for 200-level math classes it is only about 2.5. Therefore a student who wants to get a grade B (3.0) or better must perform above average. This is the idea behind the above diagram. You can be above average by increasing your effort or by making better use of the ability you have.

I cannot force people to make a greater effort, but I can give encouragement. I do this by a series of alternatives. These are described in the following sections. As for ability, it is hard for a student to improve intrinsic ability but it is possible to increase the effective use of what ability the student has. Again, I try to encourage this using the methods described here.

PARTICIPATION

As can be seen from the above grid, the greater the effort the better the grade. This is not just based on common sense. I have gathered statistics from my classes and there appears to be a cutoff at 70% participation. Few students who participate less than this will pass. At the other extreme rarely does a student get below a C with a participation rate of 90% or more. I have rarely seen a student with less than 50% get anything but an F but at the other extreme the vast majority of students with 100% participation get an A or a B.

So what do I mean by participation? I define it in a very specific way. During the semester I give students several different ways to accumulate credit towards the final grade. Everyone one of these ways involves participation to some extent, although I give different weights to each. Briefly, they are as follows. Details are given later.

1. Attendance at class.
2. Completion of all assignments
3. Participating in all group activities
4. Making office visits as and when needed

I give “participation credit” for each of these and this is added to the grade obtained on assigned work. This may sound like free points just for showing up and doing all work, but in reality it is not. I expect students to fully participate and I factor this into my grading scale. You should think of failure to participate as a penalty rather than participation as a bonus. However, the scale is such that a student can still get a grade A with minimal participation if so desired, but in this case a higher grade on assigned work will be required,

Another consideration is that many students, especially in general education classes, are struggling with the transition from high school to university. Many have not yet discovered the discipline required to attain success in a different environment. Although it is not my responsibility to teach people how to make this transition per se, it is my responsibility to help all students achieve the highest level of understanding possible given these limitations. Several of the participation elements are geared specifically towards this goal.

 

THE ELEMENTS OF MY GRADING SYSTEM

Each element of my participation credit is there for a reason. In this section of the document I outline the rationale for inclusion of each of them. Several of them also count as credit towards the final grade over and above the participation element.

Assignments

The primary purpose of assignments is to give the student problems by which they can gauge their progress. This can be done by attempting problems from books but frequently there are too many to attempt all and it is hard to know exactly which ones to do. There will be weekly homework assignments and these will generally include ones of several levels of difficulty, all the way up to ones which will challenge the best of students. It is not expected that the average student will be able to complete all of these on the first effort but for those who sign the Second Chance Contract (see below) there will be multiple opportunities to attempt similar problems. The secondary purpose of assignments is to give me some idea of your progress so that I can help you when it is needed and also give credit towards your grade. All questions on assignments should generally be doable by a ‘B’ student, but only an 'A' student can expect to get them all right on the first effort.

In addition I recognize that the learning style of some students is not conducive to having to complete assignments within a few days of covering the material on class. For this type of student it takes a while to mull over the ideas before they are fully digested and understood. Such a student may not initially do well on assignments but may still be a good student. I therefore give the option, as an elective as the beginning of the semester, to sign a Second Chance Contract which allows makeup assignments.

There will be three different types of assignments: concept questions, usually multiple choice; calculation questions, usually requiring only calculator work; application questions requiring thought about the material learned. Each type will be assigned separately and you will have the opportunity to redo each one separately. There will normally be some of each every week. In addition, practice assignments with answers are given each time so that students may practice the material before handing in anything for credit.

Group Work

When you leave university and start working in the outside world you will find that working with your peers in a cooperative environment is crucial for success in most occupations. Working together has been shown to be productive use of time for most people. Doing group work in class serves several purposes: it breaks up the monotony of the normal lecture mode; the weaker student gains by active participation in group discussions; the stronger student gains by having to help the weaker student; all gain experience in working on problems together. Group work is part of the grade and occurs throughout the semester. This requires student to work outside of class together. I require students to evaluate their fellow group members at the end of the semester to ensure that all are pulling their weight equally.

Office Visits

Although only counting towards the participation part of the grade, these are a key element for success, especially for those people who are trying to increase the effectiveness of their study habits. I require office visits in certain situations, with the goal of helping students plan a way to improve their poor grades. I also offer a special “Second Chance” contract to all students: the opportunity to make office visits to improve poor scores on assignments but, if the contract is accepted and the visits are not made, points are lost. I hold more office hours than required, some by appointment and some walk-in and will always find extra time for a student who cannot make my scheduled hours because of class conflicts. Also, office visit are an essential step to success for those students whose learning style does not match the teaching style I use in class.

Attendance

This only counts for participation but I consider it essential to be present at every class to attain complete understanding. Some students are good enough to pass a course without attending class, but they are a small minority. My grading system is such that they can pass without attending if they so wish. It is inevitable that students will occasionally miss a class for reasons beyond their control. In most classes there is no recourse for the student but, for students who have accepted the “Second Chance” contract, I offer to give credit for the missed class provided that the student first looks over the class notes published online and then makes an office visit to discuss them with me.

 

OFFICE HOURS & HELPING THE STRUGGLING STUDENT

I try to modify my teaching style to accommodate the majority of students but place a heavy emphasis on the use of office hours for those students who find that the class instruction does not fit their own learning style. This is especially true for the student who is not doing as well as he or she was hoping. Because of this mismatch the student is not being given the maximum opportunity to learn in class alone but, it is hoped, if classes are augmented by use of office hours then the student can be exposed to different instruction methods. It is not expected that these office visits will be extra work. The main benefit of this is that a student who is struggling will not be left without help. There are requirements for office hour visits on a regular basis for students whose grade is below a C, with the expectation that this will help both student and instructor identify problems before they get out of control. Problems can be identified and the student will then have feedback which gives the maximum opportunity to understand. It is then the responsibility of the student to act on that feedback. Another benefit, almost as important, is that the student who is not doing well in class will get an opportunity to work one-on-one with the instructor and be given an alternative way of looking at a problem: one which may make it easier to understand.

Note the stress placed on opportunity. This refers back to the comments above regarding the amount of effort required depending on ability. No one can make a person learn if they do not put in an effort themselves. I consider it my responsibility to give a student every chance to understand, not necessarily to make a grade. It is the student's responsibility to turn that understanding into an acceptable grade. Students who shows a willingness to help themselves will receive as much help as possible from me, but I consider time spent helping those who will not help themselves as being time wasted.

Work Sessions

As time permits we will have classes which are just work sessions. They are not for credit but are to give students a chance to work on new concepts or practice old ones while I circulate to help whoever needs it. Ideally we will have them at all critical points in the course, but time constraints may preclude that.

 

FEEDBACK

Finally, in order to keep a line of communication open between students and instructor I encourage the use of Feedback Notes. These are used by the student to let the instructor know how things are going. You will be given the opportunity to give them with each assignment but they are not required. They can be about anything but the three main types are:

Students can name something which was difficult to understand during the previous week's class. If a large enough number indicate a problem with a topic we will go back over it. This includes specific homework assignments which you had trouble with, although the first resort after problems with assignments should be to go over the solutions when they are published.

Comments about the class itself or the presentation of it which you found particularly useful. This is useful so that I can determine if a particular presentation was easier for people to follow and should therefore be used in the future.

General comments about anything related to the course. These will be used to help adapt to the needs of the class so that we may all work together to make life easier for everyone.

If you have nothing specific to say in any given week then you are you are not required to do so. Some students do not use this at all, other provide feedback every week. Students should be willing to make negative comments in the notes if appropriate. Under no circumstances will feedback notes be used to affect a grade, either positively or negatively.

 

 

 

This page is written primarily for the benefit of those students who are currently enrolled in my courses and for those who might be considering taking one in the future.   Here I try to give some idea of what to expect in my classes, what you can expect of me, and what I will be expecting of you.

 

This page is required reading during the first week of all my classes.  Throughout the semester all students should keep the contents of this page in mind.  The most successful students will be those who try to direct their study along the lines set out here.