In a recent post Occupy Math tried to provide some good advice for taking your first university math class. In this post, Occupy Math turns to tactics for exam survival. One of the most effective techniques, when it is available, is to discuss the exam format with the instructor. Occupy Math gives some ideas for different ways an exam can be conducted — and some of these make the instructor’s life easier. Immediately below the fold we will begin with the more generic good advice and then move on to the innovative ideas.
This post looks at how students just starting university can think math is hell while the professor looks at the papers he is grading in stunned disbelief because the students appear to have learned nothing in their previous twelve years in school. Occupy Math usually teaches a first year university class, either calculus or calculus mixed with physics. The material is not too hard in an absolute sense, but for many of the students it is quite hard. This post is about the reasons for the different perspective: the math professor thinks the material is pretty basic, but students — who finished a complete high school course of study in mathematics! — think it’s hard-to-awful. It turns out there are several reasons for this disjunction of experience. They include many factors including really bad design of the high school classes, active parental sabotage, administrative handicapping of teachers, and a failure to teach effective study techniques.
There is a crisis in the price of textbooks. Occupy Math paid eighteen dollars for the calculus book he used for his first two courses in calculus. The calculus book used for the first-year for-majors calculus course at Occupy Math’s institution costs more than ten times that, though the price varies from year to year. Worse, after you buy many textbooks, you have to cough up a hundred dollars for access codes to let you get to the on-line material that comes with the book. The professor may well assign parts of the on-line material, from exercises to pre-generated homework problems, so access to the on-line material is not optional. With a book, roommates or study-buddies might buy one copy and share. The on-line materials track one person’s progress and grades, so sharing is impractical. This post is about the mechanisms behind insane pricing and some resistance strategies.
If you want to be a doctor you need to earn a university degree with good grades in hard classes and then go to medical school after which you do an apprenticeship (residency). In addition to the four years of university, medical school and the residency take about eight years –making it about twelve years of post-secondary education. Given this remarkable level of preparation, why are a large number of the diagnostic protocols used by medical doctors way too simple, ineffective, and generally something a high-school drop-out could probably run? In this week’s post we look at the problems with threshold-based medical protocols.
The Illusion of Control is the natural tendency of people to overestimate how much control they have over a situation. When you are in control, it increases your confidence and decreases your fear, so people like to feel in control. In this post Occupy Math will discuss an instance of the illusion of control that decreases students’ grades on a math test. This post raises and discusses a point about how to teach effectively and Occupy Math’s position on the issue is debatable and disliked by many of his students. Interested? Read on!
Occupy Math is in the process of fine-tuning his syllabus for his first-year calculus class, getting the class web site up and polished, picking papers for his research group’s journal club, and in general preparing for the onslaught of students young and old. This post is about surviving your math classes in your first year of university, though some of the advice is good for both upper-level high school courses and second- and even third-year university courses. The advice includes how to interact with your instructor: a much neglected topic in Occupy Math’s opinion. Occupy Math is teaching first year calculus in a blended calculus and physics course so the issue of “transition to University” is much on his mind.
Please don’t be intimidated by the calculations below! Occupy Math needs them to make a point — part of which is that lines two through six are completely not needed. This post was written directly after grading a midterm in a first-year university calculus class. What that grading taught Occupy Math is that the students have been deceived about the very nature of math!
One of the questions on the midterm was “Find a sixth degree polynomial with exactly two roots”. Occupy Math thought that this would be a freebie question. There are many correct answers, one of which is the first line of the calculations above. About 20 of the 100+ students at the exam took this correct answer and drove it right off a cliff by trying to multiply it out. Occupy Math has multiplied it out to show how much work that is! Here’s the punch line: not one of the students got the arithmetic correct. As far as Occupy Math can tell, they have been indoctrinated to believe they have not answered a question until they have done a good deal of calculation? They feel that math is not math without the busywork!
There is an inaccurate stereotype of millennials as lazy, entitled, self-absorbed lumps who live with their parents. When Occupy Math’s editor graduated from Bard College, it took her a couple of internships and several years to find a good position. Her grandmother could not understand why finding a job took so long and was concerned that lack of zeal might be the problem. What’s actually going on is that good jobs are far rarer than they used to be and affordable housing is also really hard to find, hence living with their parents. This inaccurate stereotype is an example of a smooshing error. This is an error where you combine a whole bunch of diverse factors (job availability, housing prices, the impact of automation and the internet) into one thing in your head and then map it onto your own experience, drawing a wildly incorrect conclusion. In the late 1940s (when the above-mentioned grandmother was hunting for a job), inability to find a position probably would have required laziness. It was a different world then.
This week’s Occupy Math is on a familiar topic, the effective teaching of math, but it was sparked by a number of recent media reports on why students in Occupy Math’s part of Canada are doing worse into the teeth of increased spending and emphasis on math. The problem has two parts. The first is the elementary teachers are not required to learn math themselves and are often afraid of it. The second is they are being handed a teaching strategy that cannot work and then getting no help trying to make it work. This is a big multi-part problem and Occupy Math hopes we can all dive in and help.
For the past three years Occupy Math has been working on a calculus text for the integrated first-year math and physics course he co-designed. The regular books did not have the right topics in the correct order. This post announces that the book is ready. It is the second edition (now with far fewer errors!) We used the book last year and found a need to revise and extend. The book is not a standard calculus book and the rest of the post is about that. The big points are: we got the cost down to less than half that of the book it replaces. It covers all the topics of a standard first year calculus course for science majors. The presentation is different based on decades of experience with what does and does not work.