In mathematics education it is necessary to include development of principal-philosophical concepts of mathematical thinks in the Curriculum, by my opinion.

Daniel A. Romano

I am not sure about the utility of a science history as a full three credit hour course but it can be offered as an elective especially for those who wish to stay in the academia (for broadening the mind to alternate ideas). Teaching science without an element of history is a bunch of facts and information which any robot can easily remember and regurgitate later in the exam. History teaches the human side of science; it shows how complex ideas evolve in science- and how incorrect but popular ideas were dispelled. It does not mean that concepts be taught in a chronological order with full history but mentioning tit-bits of historical notes bring life to the class. Knowing some history removes that common bookish story of how scientific research is done i.e. someone proposes a hypothesis out of nowhere then tests it by experiments and formulates a theory. 

In mathematics education it is necessary to include development of principal-philosophical concepts of mathematical thinks in the Curriculum, by my opinion.

Daniel A. Romano

It is suitable as pre-requsite coverage before learning further.

Example -

History and Philosophy of Physics - Same as PHIL 4450 and PHYS 5450. Prerequisites: Restricted to Philosophy graduate students only.

http://www.colorado.edu/catalog/2012-13/courses/arsc/b-phil/5450-history-and-philosophy-physics

Dear Sudev.

Thank you for an interesting subject on debate.

I know I would !

I would add historical introduction to any of my scientific endeavours.

As an Anatomist, I certainly always recur to historical notes and facts, to build knowledge that I transmit. (Otherwise, I run the risk of making a fool of myself, or gain total discredit, pretending to have discovered the human body. !)

To answer your question in a broader wider sense, I have the conviction that any scientific course should prepare the students' minds to learn scientific method. The large acumulation of knowledge to be transmitted can easily be found on any knowledge source, such as libraries and the internet...

The scientific method of reasoning will easierly be taught, through historical notes, and philosophy of Sciences. Thus, it is the most difficult subject to teach, and also to learn. (Maybe this is why many highly technological courses prefer to forget or underestimate the subject...)

Hope this was useful.

I believe it is absolutely necessary. However, my personal experience is that a separate course, or courses, on the subject matter (history of science, history of physics, history of mathematics, etc.) may not be attractive to young students (I am here focussing on students of physics and mathematics, and not those of history); one's interest in history grows with age, when one naturally arrives at a stage where one yearns to delve into the origins of ideas. It is therefore important that the relevant history be presented as part of the major courses on physics and mathematics. Naturally, one can have an advanced course for post-graduate students, wholly devoted to the relevant histories.

History and philosophy of science are necessary in almost all curricula for both graduate and undergraduate! Dear @Sudev, You have not precisely defined what field of study we are discussing. In engineering fields of study, it is good to have it. 

We did have have a thread about subjects from humanities to be included in Medicine and Engineering. Many good responses were made to this thread posted by dear @Maria. It is good, since they have something in common with your question.

https://www.researchgate.net/post/Would_you_consider_the_interest_of_adding_disciplines_from_the_Humanities_to_the_more_technical_Courses_such_as_Medicine_or_Engineering

I believe that including the history and philosophy of science and mathematics  would help the students better appreciate and understand the subjects. Although I believe that putting the history of mathematics and the like in the curriculum is a little much. What can be done is to include the vignette in the syllabi instead.

Not only in Science (and Technology), but in every field, it is essential to include the history and philosophy of subjcets concerned in the curriculum. It will connect the students with the historical perspective of the subject to the present status of the contents. Rather, it will help the students to think reflectively.

Why STEM is not enough (and we still need the humanities) is fine article about the issue. "...Actor John Lithgow recently protested that no STEM can reproduce and sustain itself without a bloom. He made his remarks at the celebration of this year’s recipients of the National Medal of Arts and the National Humanities Medal. Without beauty, creativity, and the deep, sustaining truths of history, philosophy, and literature, he insisted, STEM learning is joyless.

Science and technology are meaningful when interwoven with all of the other modes of learning. A STEM, without its bloom, quickly withers in the forest of everday life..."

http://www.washingtonpost.com/blogs/answer-sheet/post/why-stem-is-not-enough-and-we-still-need-the-humanities/2012/03/04/gIQAniScrR_blog.html

To enable students understand that some properties intrinsic to entities are not relations between entities, no matter how it is cut. Instance of theory reduction are entirely historical and philosophical, where framework of concepts, identity statements and laws play no role,

http://philosophyfaculty.ucsd.edu/faculty/pschurchland/papers/neuroscience82mindbrainreductionphilsci.pdf

The history and philosophy of subjcets concerned be included in the curriculum, as a backdrop it gives better understanding of the subjects.

I do agree with @Subhash. Better understanding and development of a subject, history timeline is necessary for our student. I have put history of automation in my books of control engineering.