Instructor Notes on MATH MS165
aka Technical Math 1
The purpose of this course is to equalize the mathematics knowledge of all incoming students. Some modules may be new for some students while old and review for others. By the end of the course all students will be at the same level, able to tackle more difficult concepts and succeed in their program. For this reason, it is important to remind students that although they may find some parts boring and review, later ones will be more challenging, and components of every module should provide new insight to all students.
The course is a blended learning model, with self-study content students complete on their own before class, and lecture material students and faculty work through and practice together in class.
The self-study content is generally concepts students should have learnt previously and are foundational to the module. It is completed by obtaining at least one mastery point through the study plan, then completing a weekly quiz on the material before the weekly lectures. Students should choose the mastery point they will gain the most value, and/or complete all points if they are new concepts.
Homework material is designed to be only investigated before class, then learnt and practiced in class, and finally completed after class. Class time should mostly be spent in actual practice of the concepts through live formative assessments, with any lecturing focusing on why and understanding the mathematics, and only little time spent on procedure and mechanics.
The bulk of grading is thus focused on the formative assessment quizzes and homework, with less weight and emphasis on summative assessments at the end of each pair of modules, or so.
As the course builds in difficulty, constant review of old concepts is done in subsequent tests, and should be modified based on where students struggled on previous tests. Course success should ultimately be based on complete course understanding across all modules and not perfection of a select few.
The course consists of 6 modules. Each of these modules is based on simpler concepts students should have seen, to some degree, previously, but covers more depth and breadth than most have seen before. Once each concept is introduced it is then woven into and augmented in each of the following modules. In some cases it is critically essential that students at least grasp the core fundamentals of the first, say Algebraic Expressions, before moving on to the second, Solving Equations.
- Calculators – How to use technology to solve problems
Features like equation solvers, prime factorization, long division, engineering notation (μ, M, G etc), advanced usage of memory storage and writing full equations on the calculator should be covered.
- Algebraic Expressions – Simplification and expanding of equations involving variables, especially with exponents
Here it is important to explain exactly what an exponent is, especially negative, and reinforce that variables are placeholders for actual numbers. This may elicit questions like “if these were numbers we wouldn’t do all this” which is correct, and shows understanding. Radicals and rationalizing the denominator, and expanding pairs and squares of polynomials need special attention. Test 1 generally falls after this module.
- Solving Equations – Manipulating equations to solve for a variable, especially with variables in the denominator
These are mostly applications of properties from Algebraic Expressions. Special care is needed on implicit (variable mostly/only) equations and complex equations with variables in the denominator, and of course word problems.
- Trigonometry – Solving for sides and angles of 2 dimensional triangles, with some applications to vectors
Preparation for vectors is key here, and learning to work in radians by using π=180º and simple algebra to convert (not formulae). Deriving how the cos and sin laws work is helpful, if there is time.
- Linear Equations – Solving 2 and 3 simultaneous equations using graphing, calculator/computers, algebraic and Cramer’s rule methods
Understanding the usage and mechanics of solving multiple simultaneous equations is important, but calculation errors can make them difficult to complete by hand. Testing for the ability to setup, and interpret results are the main learning goals here, and not the ability to carry out long complex computations.
- Quadratics – Solving and graphing of 2nd order equations
Applications of quadratics to previous modules if the main goal. Solving and working with larger equations of a quadratic form i.e. (2x-3)^2 +3(2x-3)-3, and graphing are important for a deeper understanding of quadratics.
Points of note to enhance teaching
If you have made it this far, you are interested in learning about how to best teach this course.
- The best support for students in this course is fast and reliable feedback.
- Regular lectures and office hours are essential for this course, but adding a Teams classroom/direct ability to chat with the prof further augments this.
- Help students set up their notification and profile settings. This is a first year, first semester course, so general learning orientation can go a long way.
- Set up any auto sync features so grades are posted to MyCanvas as quickly as possible, and students always know what their overall grade is. Also be sure to quickly zero out any missed grades for the same reason.
- Try to focus as many reminders as possible to only those students that need it by using the “message students who” feature in the Canvas grade book.
- For digital assessments DO NOT review the answers/grades. Instead encourage students to review the correct answers themselves and schedule time with the instructor (use the Appointment Group feature in Canvas) to discuss their rough work and possible part marks (or via email if the issue is simple).
- For Pearson assessments a 20% blanket late penalty ensures students can still practice after the due date, and can catch up where needed.
- Talk about Rough work. What are you expecting? What is the purpose? Why is it important? These are new college students, and “you must include rough work” means nothing to many of them.
- Create a culture of “bug bounties”, especially if using Pearson. Feedback can be limited, harsh and often just clearly wrong, so create an atmosphere where students can ask questions, question their results and seek help when they’re unsure.
As mentioned earlier the goal of the course should be understanding and insight into all modules with no module lacking. The final exam focuses on Quadratics but should also include any/all content from previous modules especially where students previously struggled. In this way the final exam can also act as a guide for any borderline student in determining if they have sufficient skill to advance. Any student advancing beyond this course without a competent understanding of all modules will struggle or fail later, with no recourse to move back or succeed.
Lastly, these students naturally form small communities and work groups. Use these to your advantage to promote group learning and strengths and magnify the effort you put in.