There is no specific or specific method. I think it would be interesting to do a psycho-educational assessment of pupils or students to see what would be for them the most appropriate method for better understanding. It is the transmitter (teacher) to get in phase with the receiver (or other students)

Research based teaching.

Hi Vidya,

Any active learning method may suit you fine. Say Problem-based learning; task-based learning, brain-based learning.

Ke, F. (2014). An implementation of design-based learning through creating educational computer games: A case study on mathematics learning during design and computing. Computers & Education, 73, 26-39.

ISO 690

My view this is that, there's no preferred method or approach. You can resort to the traditional didactic approach or you can either resort to a more modern approach by applying technology based learning. The answer is to make sure you differentiate your lesson / teaching on the basis of ability and ensuring sufficient support is provided to make sure all students in your lesson make good progress. 

You ou may even resort to asking your students about their most preferred approach to learning  respinses from then will help you decide on the best methods you may need to you in all your lessons . Even with this, you may have to consider varying it as every individual is different. 

There is no specific or specific method. I think it would be interesting to do a psycho-educational assessment of pupils or students to see what would be for them the most appropriate method for better understanding. It is the transmitter (teacher) to get in phase with the receiver (or other students)

The secret is how to manage both technical rigor and structural intuitive explanation in a kind of inspired (and seminal) mix up. One has to repeat every time fundamental things (what is a real number, a line, a convergent sequence, a prime and so on). In order not to be boring, one must often repeat explanations of this kind using other words. In the same time, students must continue to develop their computation skills, and rigor must be kept in writing down proofs, lemmas, arguments. In fact it is hard to find the good mix up which keeps the students attentive and curious untill the lesson is closed. The best method is to be empathetic and feel what the students would like more in the sequel. Very few people are born with the gift of being good teachers, but differently from other people, I believe that one can learn it from the own experience, (of course only working very hardly...)

There is no specific best method to teach mathematics at college level --- it depends on teacher's way teaching and students level.

Mathematics comes at the roots every discipline in general and science discipline in particular. The efficacy of mathematics is not uni-polar rather multi-polar which include, the teacher, taught, environment. Here also the level of students and the interest and intellect of the teacher matters much. The success of mathematics teaching and its outcome depends upon the parity attitude of the teacher and the taught. To have long lasing outcome, the teacher will have reach to level of taught for its further elevation which require multiplicity of methods instead of single method.    

I am not aware of the existence of specific methods that are available out there to teach mathematics in colleges, but to make teaching at that level appealing to students, one thing we can do is to make visible the ubiquity of mathematics in everyday activity of their lives, by making connections between mathematics and what they have done to wake and come to class and perform their daily activities on time which all are required decisions that are purely mathematical but intuitive.

So what they are there is to actually describe formally or in mathematical expressions what they do, what things are in nature and what all mathematical truths contain. 

Dear Mario,

You are correct that not every mathematics expresses reality at the moment ( as long as we know very little portion of the universe or nature)  but almost all activities are expressible in mathematics and it is also true that as long as mathematical truths are logically consistent structures established from fundamental axioms established from our basic understanding of reality, they will eventually be found to describe a reality of natural phenomena.

Consider the case of general relativity theory, Einstein had his idea of that concept but could not describe it mathematically,  but after he has been informed the existence of a non-Euclidean hyperbolic geometry that perfectly fits what he wanted, he put his imagination in mathematical formulations which was found to be a perfect result of a human mind and mathematics.

But a priori to that find,  it was not known  such a geometry represents reality but because it was a logically consistent mathematical structure from basic axioms, it later finds a natural reality that it describes.  

Here, our methods are reasonably good.  We have lectures to communicate the info and knowledge to a large lecture class (about 180), followed up with tutorials for small groups (about 20 students).  During tutorials, we practice collaborative learning techniques including 'learning together' and 'games/ tournaments'.  Attendance is always taken.

Dear Miranda, the information you shared is very useful.

Teaching mathematics at any levels is a challenging task. Even among studious students, there is a mixed feelings to Mathematics. So we need to modify our teaching style in such a way that the beauty and elegance of mathematics are properly transferred to student minds. Basically, a teacher should create a rapport with students. 

Some articles on innovative mathematics teaching methods are attached herewith.

http://iirpublications.com/papers/october/ijcoa/paper%2029.pdf

http://waymadedu.org/StudentSupport/Rachnamadam.pdf

http://www.ams.org/programs/edu-support/Innovations-College-Level

http://conference.pixel-online.net/foe2013/common/download/Paper_pdf/179-ITL31-FP-Kremzarova-FOE2013.pdf

http://www.hkame.org.hk/html/modules/tinyd2/content/Edumath/v5/v5_59to66.pdf

http://opinionator.blogs.nytimes.com/2011/04/18/a-better-way-to-teach-math/?_r=0

An Introduction to Teaching Mathematics at the College Level is very good resource for different approaches to College math teaching. Experienced!

Applications GeoGebra into Teaching Some Topics of Mathematics at the College Level is contribution to teaching e-mathematics. " This paper presents new trends in technology and learning through Geogebra, which could be especially important for the future development of e-learning for College mathematics. Also, contribution of this paper is presentation of methodological frames on several specifics

examples for teaching mathematics at the college level on interactive and creative way..."

http://www.ams.org/profession/career-info/grad-school/Kelton-TEACH.pdf

http://www.doiserbia.nb.rs/img/doi/1820-0214/2009/1820-02140902191D.pdf

I really do not have a specific technique for teaching mathematics in college. I usually "feel" my students' maturity and attitude. Since most of my students are mathematics majors, engineering or computer science majors, I do not really have any difficulty dealing with them.

In teaching math logic, graph theory or sets, I use real life situations. As you probably know, Manny Paquiao is from my country. But his mother is equally famous as he is. So I use the name of his mother in constructing statements to make the students relate easily to the topic. Sometimes I introduce unfamiliar concepts like the platypus or the butanding. Not only they learn mathematics but they also learn other things in life.

In teaching calculus, there are a lot of things you can use when introducing area and volume, like the container of dishwashing paste, how one can minimize materials while maximizing volume.

One time, we used an online game, Farmville, to show maximization of profit while minimizing cost. Since Farmville was a very popular game at the time, it was a hit to students.

B ut when students really get bored or tired at times, I sing to them, even dance and my most effective weapon - I crack jokes. In fact, I think my jokes are more of a hit than my lectures!

Cracking jokes are usual in case of many teachers. It sometimes helps students to create interest, not all time.

That is true Prof. Kundu, that is why, even jokes, as much as possible, must be related to the topic.

The initial teaching of math is by rote. We learn to count, add, subtract, multiply, and divide. While rote, we attempt to explain and build intuition by example: 1 apple + 2 apples = 3 apples, You have 10 apples that you are to give to 5 people 10/5 = 2 each. Sometimes we explain that not only do we count by 10s, we add, subtract, multiply, and divide by 10s. Effort is made to define the process by 1s column, 10s column, ... Nevertheless, the stress is rote. Is a child ready to appreciate why we are doing this. Yes. A child is ready. Do we take the time? A little, but in a class of 20 or more students we have to have them proficient in the times tables.

We advance to algebra and geometry. Geometry has applications we can all see, but why memorize all those rules. Do people understand more geometry than they know? It seems that way when we test for knowledge, yet, many know how to apply. Algebra is a chore that we are promised will be useful. Most learning algebra will not see it again in their lives even though they will be exposed to it every day and use the concepts. Is it not more important to learn the concepts and mental organization? Teach algebra for what it is, not as a task to complete.

Trigonometry follows as yet another task when the beauty of mathematics surely should be dawning on our young minds. Here is something else to master, like an ancient language, to qualify as an educated person. There are wonders to behold, e.g., cos2 + sin2 =1 (or one more rule to memorize).

The height seems to be reached with calculus, but little did we know that the end is math for maths sake. Here is a world of proofs, lemmas and axioms. We have developed a marvelous system of calculation of physical laws and concepts and developed equations and transforms that provide descriptions of effects. Of course, they are ideal descriptions, but what powerful descriptions and applications. Why simply accept these because they work? No. We need proofs, lemmas, and axioms. Here we need consistency and completeness and to step beyond Euclidian methods to sets and paradoxes of our own making in an effort to make mathematics the most perfect philosophy. The seeking of perfection engenders more imperfection so math withdraws from being a tool to being MATHEMATICS.

Spare us scientist from your seeking. Let those who need math learn it as a tool. Let us learn it as a useful device and scientific language. Teach math as something useful and use useful examples. Make it live through science and engineering. The current method of teaching math is extended rote not mastering methods. The current method teaching math is initiation into the club and earning passage to the next level.

Put joy into learning math. The joy of seeing what it can do, not just how it is done.

Thanks for fine and honest answer dear @Joseph. Yes, "Put joy into learning math. The joy of seeing what it can do, not just how it is done."