Dear Hidam,

   It is a very large job and I don't think i can help. I would say, though, that looking at the curriculum at TEKOS and also the math curriculum at the Ross school (developed with Ralph Abraham) might help.

Thanks Bruce for a suggestion. 

Sounds like you need to apply the exemplarity principle! Pick out a few cases from different domains of maths, study them with the students, draw out similarities and differences. Start with simpler cases, where the maths was developed in relation to a specific problem, and then move onto more complex cases, where more "detours" happened, or new maths from other areas had to be drawn into the process.

Hi Hidam,

it might be worth looking at a History of Mathematics book and/or popular science books on Mathematical Ideas (e.g. 50 Mathematical Ideas) and build your course from there.

You do not say what level of mathematical understanding your students have to start with. "Enthusiasts of nature" may not have a background in elementary algebra or even a good grasp of ratios, much less understand the basic principles of calculus. You may want to think about writing the course so a 10-year-old child can understand it. Than you will not frustrate your learners (or yourself).

Designing a mathematics educational course curriculum.

Basically, a curriculum design should start with the simple, to complex; from known to unknown. Say, geometry first before topography; differential calculus before integral calculus.

Consider also spiraling in the course design--topics are repeating but increasing in complexity: plane geometry to solid geometry to differential geometry and even fractal geometry.

I would liken a course curriculum to a restaurant menu.

In most restaurant, you start with the hors-d'œuvre, then the main course, and finally the dessert.  (In Chinese restaurants they usually serve the soup last, while in others, soup is served ahead of the main course); so in a nice mathematics course there should also be variety in topics:  number theory, algebra, calculus, statistics, vectors, matrices, set theory, etc.

Include new ones like fractals, graph theory for social network analysis, combinatorics, and operations research. The curriculum should include a subscription to at least one mathematics journal listed in Thomson Reuters Master Journal List.

There shouldn't be too little number of topics, say just 6 or 7 (so as not to make the student bored or feel cheated) nor too many like 30 or more (so as not to cause mental indigestion). Benchmark with other schools and educational institutions like the University of Tokyo, Hong Kong Baptist University, and Boston College. 

The course curriculum include books and references, and they too should be from various authors, not just books by Jude Socrates of CalTech and the rest. Try to include authors from other leading Institutions--Cambridge, Harvard, Purdue, Michigan U, UCLA, UP, La Salle, and Ateneo.

Consider a backward design. Begin with what would you like the graduates of the course to be. Align it with your school's Mission-Vision. Thus, you will know whether you will include more applied math courses or more courses on math theories.

I also would like a course curriculum to a marriage contract. The course should show the students what to expect to learn, and the teachers what to teach. It should the grading system, the evaluation schemes, and the requirements for each of the courses.

At any rate, consider the use of technology in the curriculum. Well, these technologies need infrastructure. Consider the budget for the computer labs, or the mathematical simulation rooms. Prepare the "kitchen", prepare the "cooks". Who will be those teaching the courses listed?

Hi Hidam.

I think that to design any curriculum, learning outcomes have to be clearly stated first. You need to be clear with what you want your learners to achieve at the end of training and thereafter you will determine the relevant content, methods of instruction, materials required, and the organisation of the learning. You will be able to sequence learning material/content from known to unknown so that learners can use their prior knowledge to grasp new concepts. This is no different with Mathematics. I hope you will find this helpful.