What do you think would be the best way to structure a math course?

[member2357]

What do you think is the best way to structure a maths course in general? Be it algebra, calculus, analysis, probability, geometry, etc.

What I mean by structure is number of exams, their percentages, type of exams, and timing of exams. I am looking for a structure that best helps students manage the material by motivating them to study for exams.

My university does the following:

• 10 assignments due by the end of each week, each assignment has 4 difficult questions that cover the material of the week before, each assignment worth 2% of final mark, therefore the assignment are worth 20%..
• An exam in the last week of the semester that covers everything studied throughout the semester, worth 10%.
• Final exam is a 3 hours exam done in examination period 1 week after the end of semester, worth 70%

I find this structure very helpful as it motivated me to be always up to date with the material being covered in lectures and the exam in the final week (worth 10%) is very helpful in preparing for the final exam.

What do you think of this structure? Would it be better to have a quiz each week rather than assignments? I know many students who do the assignments together despite not being allowed to do so so a quiz would test what students know rather than who they know.

I did a chemistry subject in first semester and I really hated the structure, it is 25% practical experiments, 10% tutorial attendance and participation, 15% mid-semester test and 50% final.

 

[Ackbach]

I think it matters greatly what age group you're teaching. If you're doing high school math or science, I would highly recommend Weekly Cumulative Quizzes counting for the vast majority (70-80%) of the final grade. Homework should never count for a large percentage in these courses, because of all the shortcuts possible. I like the quizzes better than tests, because you can give more frequent feedback to the students (which is really what grades are all about, anyway). And, as we know in control theory, more frequent data can help make a system more stable...

Why cumulative? Because ideally, you'd like the students to remember what they have learned well beyond your class. Nothing does that like cumulative quizzes.

However, one caveat: most students have never had such a course, and they don't know how to study for it. So I would give them study guides to ease the total amount of time they have to spend studying for your course.

Incidentally: the idea of weekly cumulative quizzes is VERY not original with me. I got it from John Mays's book Teaching Science so that Students Learn Science.

If you're doing more advanced work, this structure is not so easy to do. In graduate-level courses, e.g., homework often counts for 50% of the grade or more. There are very few, if any, shortcuts to the homework, because graduate-level texts never publish answers to any problems whatsoever. (Ok, that's a slight exaggeration, but only slight.)

In-between, in the undergraduate years, I'd recommend some sort of gradual transition from the high-school idea to the graduate-level idea, as appropriate.

I would never make a final exam worth more than 20% of the final grade. That amount of feedback for the students is downright unhelpful.

 

[Patolord]

I think if the passing grade is like 60% for example them the final exam have to be at max 50%
having a 70% final exam will make the students slack of the whole course study the very last week all the material to get a passing grade, that would be 8.6/10 in a worst case scenario for them.

• An exam in the last week of the semester that covers everything studied throughout the semester, worth 10%.

• Final exam is a 3 hours exam done in examination period 1 week after the end of semester, worth 70%

an exam worth 10% with ALL the material studied throughout the semester? does`nt seem it is worth the effort.

I know i`m basing on worst students scenario which could be not needed if you are teaching for really interested and smart students.

 

[snatchingthepi]

My mathematical methods professor (a physics course) had the following mark break-down which I thought was very fair.

5 assignments (one for each major section of the course) - 50%
midterm - 25%
final - 25%