Questions tagged [course-design]
For questions about creating a new course or altering the format of an existing course.
134
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Which books on geometry and topology are best for teaching an intro graduate course?
I'm teaching a graduate (Master's) introduction to geometry and topology (e.g. some basics on manifolds, vector bundles, algebraic topology). What textbooks have you found are best for teaching a ...
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AP Calculus BC Guidance
Hello wonderful educators. I am hoping to get some help on a tough situation I am in. So first, a little bit of background facts:
This is my first time teaching an AP class. I've adjuncted for Calc I ...
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Help me to prepare for my first job interview presentation
My First Job Interview presentation topic for a permanent assistant lecturer position in Mathematics and Data science is below:
''You have been asked by your Head of Department to design an elective ...
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Standards based grading design principles
I have taught some SBG courses in the past, and I am planning on converting all of my courses to SBG. I have enjoyed teaching these courses, I believe that students have learned more, and students ...
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Textbooks with solutions and catering to different circumstances
Questions: Are we really taking students into account FULLY when writing textbooks for various areas? Also, are we being unintentionally elitist or dismissive when neglecting to take a more humble ...
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Rings in parallel with groups in abstract algebra
In a previous question, I asked about the pros and cons of teaching rings before groups in abstract algebra. Recently, it has come to my attention that there is a third approach - a unified approach - ...
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Advice on teaching abstract algebra and logic to high-school students
NOTE:
This question will soon be duplicated, as I didn't make clear that I was a high school sophmore in the beginning. At first I thought it didn't matter, and somewhat arrogant to mention, but in ...
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Setting up a new Ximera course with randomized values in problems
I'm working on converting a course to make it free to the students, and I'm considering using Ximera. What I haven't found online is documentation for/information on tips and best practices for ...
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Number theory in an introductory course on discrete dynamical systems
Benjamin Hutz, in Chapter 10 of his An Experimental Introduction to Number Theory, allows for the optional inclusion of discrete dynamical systems with a number-theoretic flavor in an undergraduate ...
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How much literature research should one do when designing a course?
For each mathematical subject on the undergraduate level there are many textbooks, often with quite different approaches to the subject. Some are just concise and rigorous, some focus on examples, ...
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How to make maths explainer videos?
I am a maths teacher and I want to make maths explainer videos particularly like this guy is doing. In fact, in my research, I came to know that manim is the latest tool for creating maths animations ...
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How must the "ungrading" idea be adapted to work in a math class?
After seeing no direct responses to this question, I'll instead be more direct myself. Ungrading is a buzzword being tossed about for assessing students' progress without focusing on quantitative ...
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3
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What are some resources for "ungrading" in a math class?
Most of the stuff I'm finding online about ungrading are either general descriptions of its virtues, or personal accounts from instructors from subjects other than math. Does anyone know any resources ...
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Should LaTeX be taught in high school?
This semester, I was forced to learn LaTeX for my Real Analysis class. The professor wanted all homework assignments to be typed in LaTeX in order to produce "high-quality" work. At first I was ...
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Ideas and/or references for projects for a business calculus course
I have undertaken the teaching a business calculus course for this semester (spring II).
The various assesments for the students, include quizzes/hw/midterms/final exams, adjusted with suitable ...
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Teaching Calculus I to engineers
I am in a research project where one of our jobs is improving the first-year university experience for our students. One of the topics we are looking into is changing the way we teach our introductory ...
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Algorithmic thinking problems
In Norway we will have a new national mathematics curriculum for all ages including high school beginning august 2020. A fundamental change is the new focus on so called algorithmic thinking. In ...
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Prisoner's dilemma formulation for children
I am preparing an introductory course on Game Theory for children (between 10 and 17 years old). In the course description, I want to include a prisoner's dilemma in order to catch children's ...
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2
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What are the benefits of an expertly curated learning pathway?
What are the benefits of an expertly curated learning pathway?
Like that provided by a major publisher's textbook - CPM, a school district's mandated curriculum - IM's Open Up Resources or a ...
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Midterm in Mathematics Courses
Can someone point me to papers indicating whether or not a midterm is an important part of a course?
I suspect I can find many 'experiential anecdotes' that midterms are good/bad/moot but I would ...
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Why do standard geometry textbooks not start with trigonometry?
Throughout my geometry course, I was given many theorems and postulates, which I was were expected to memorize and apply. At the time, I sorta went along with it, but I couldn’t help but wonder where ...
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Would teaching nonstandard calculus in an introduction calculus course make it easier to learn?
Nonstandard calculus is a reformulation of calculus that is based on infinitesimals instead of epsilon-delta definitions. Of course, people had tried to use infinitesimals in calculus before; in fact, ...
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Is it feasible to expose undergraduates to a "map"-centric point of view early on?
Question: Would it be feasible to teach undergraduate math students a "map"-centric view early on? If so, how early on?
Now that I'm preparing for a phd program, I'm also reflecting on my ...
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Evaluation and feedback using Optical Mark Recognition systems in secondary school
OMR in exit tickets
I plan to use an
OMR, Optical Mark Recognition systems at the end of (some of) my classes.
I want to use the same OMR system for exit tickets scattered over the academic year (not ...
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2
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Supplemental text for undergraduate real analysis
Context: I am an assistant professor at a small college in the US.
Next semester I am teaching real analysis for the first time, and we are using Steven R. Lay's book. (It also happens to be the ...
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Teaching science and engineering students the field of inverse problems
There is a Mathematics Stack Exchange question on a good book on inverse problems for engineers. Here, I would like to ask for suggestions on how to approach teaching undergraduate upper-division ...
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Exposure to Algebra 2/Calculus Under Time Constraints
As part of a free summer enrichment program for highly-motivated high school students, I need to plan eight hour-long lessons for mini-courses titled as "Algebra 2" and "Calculus" separately. Despite ...
user8277
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3
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What tools are available for creating visual aids?
I would like to create some visual aids for illustrating principles in statistics, similar to the kind of graphic found here: https://en.wikipedia.org/wiki/Linear_regression#/media/File:Anscombe%...
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Using tensegrity structure to teach high school math?
I am exploring ideas to design a secondary-level-project-based-10-lessons-unit-learning-plan which can end with a creation from the students involving a tensegrity structure.
such as
or
My general ...
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Make a matrix algebra course (1st university year) more "project-based"
Among other courses, I'm teaching a (basic) matrix algebra course for 1st year university students (they are studying Economics, and the cursus leads them to management, finance, or econometrics in ...
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What can I teach a talented student who is enthusiastic about math?
I have a very clever student in Grade 7. Due to carelessness and English (which is not his native language), he failed the placement test and can't learn Grade 8 math (algebra 1) in school. School ...
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How to teach a student algebra who misses too much previous knowledge?
I am now tutoring a student in Grade 9, who falls behind in math study. He lacks the basic understanding of operations and inverse operations, and have trouble dealing with negative numbers and ...
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Is there a class curriculum that studies the work of a mathematician?
Are there classes dedicated to understanding the work of a particular mathematician?
I have seen courses dedicated to a theorem (I saw for example one that sought to prove and understand the Atiyah-...
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Is it a good idea to have one or two or three classes on basic logic before teaching $\varepsilon$-$\delta$ in Calculus?
I am teaching Calculus I and will be teaching it again. To me, the $\varepsilon$-$\delta$ definition of limit is one of the key ideas of Calculus; learning calculus without learning $\varepsilon$-$\...
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Using Substitution in place of the balance model
How does substitution work as an alternative to the balance model in introducing solving equations? My biggest worry is that, lacking a concrete representation, is too abstract for middle schoolers. ...
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How should I deal well-known versus the obvious rubric?
I happen to be a student in America taking AP Calculus BC, or Calculus II, and recently, I had the following problem:
Determine whether the following integral converges and evaluate it if it does:
$$\...
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Design of a math exam using multiple choice or computer
I'm teaching math in first years of university (matrix algebra, differential analysis, etc.) since maybe 5 years, and I usually give written (paper) exams to the students.
I'm looking for ideas to ...
user7559
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1
answer
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Pacing your teaching for a variety of learning speeds
I am often tasked with teaching large enrollment courses, and one thing that becomes obvious quickly is that students attempt to pick up new information and solve problems at much different rates. ...
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What reasons are there preventing me from using an old edition text?
Background: I'm a final-year math student applying for faculty jobs at small schools in the US.
I'm currently designing a few courses, and this questions has been bothering me for some time now: Why ...
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Topics for a general education course
I'm attempting to put together a list of topics for a general education course centered around "great ideas in mathematics," and I'm looking for input. Ultimately, I would like topics to be ...
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Is proof-based exercise-oriented math course without solution an effective way to teach pure math?
In recent years I have seen several courses in pure math in the undergrad level (year 2, 3, 4) such as real analysis and topology where the entire course consists of:
notes written during the lecture ...
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Course-based undergraduate research experiences in math
"Course-based undergraduate research experiences" (CUREs, or CBEs) are being explored
in various STEM fields, especially biology,
chemistry, geology.
Here is one geology link that gives a flavor: "...
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Split differential equations into two video courses; theory and calculation?
I'm creating a course on differential equations, and I'm painfully aware that there is a LOT to teach.
As of right now, I'm considering splitting the course into two, in the following manner:
theory ...
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Group theory for high schoolers, want the opinion of other educators
So I am going to be teaching the basics of group theory to high schoolers in a few weeks, and I want to hear what the Stack Exchange network has to say on the matter.
What are the applications and ...
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Ideas for teaching a bit of linear optimization to advanced undergraduates?
I am interested in ideas what to teach when the task is to teach a bit of (linear) optimization to third year undergraduate mathematics students.
More specifically:
Assume 'a bit' means I'd have ...
quid♦
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Cognitively Guided Instruction (CGI) for 5th Grade
Are there any schools out there successfully using CGI with a 5th grade curriculum? Our students have poor number sense, and we'd like to remediate using CGI. I'd love to compare sequences of lessons ...
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How important is the act of writing his own script for the learning outcome?
There are several styles of delivering a lecture:
The lecturer uses the blackboard and the students write their own lecture notes.
The lecturer uses the blackboard and also provide a script so that ...
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Rings before groups in abstract algebra?
The default approach to teaching abstract algebra seems to be groups first, then rings. However, occasionally a textbook pops up (e.g. Childs' A Concrete Introduction to Higher Algebra, Hodge et al's ...
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How important is it to show students an application of the topics seen in an undergraduate course?
I am currently designing a proof-based Math course for my University. I already designed and ordered all of the theoretical content in the course and included some ad hoc exercises for practicing each ...
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Looking for realistic applications of the average and instantaneous rate of change
I am looking for realistic applications of the average AND instantaneous rate of change, that can serve as an entry point to calculus for students.
The main-idea is to show them a (simplified) problem ...
