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21

Sonnert and Sadler (2014) investigated what factors influence success in college calculus courses, including putting students into a pre-calculus course, which they described as "often a review of material students learned (or were supposed to learn) in high school." This may correspond to what you are calling "remedial." In their results, they found ...


16

When a student writes incorrect notation, ask them to read it out loud. I would say something like: Something here doesn't look right, but we can fix it. Could you read this work out loud? I think probably you are not super familiar with this topic, and that's okay, but this can help us fix it. I had success with this when dealing with a student who ...


15

I don't know about the research you ask for - supporting remediation. I am learning a lot lately about how problematic remediation is. There are two sorts of problems - placement and the remediation coursework. Placement tests can be harder than the tests students encounter at the end of their courses. I took the ACT/Compass placement test that our college ...


9

Personally in my own math courses, I have found that the gold-standard is to have an advance cycle of short-answer responses, document the most common student responses, and then turn those into the multiple-choice options in the future. Disclaimer: In general I frown upon multiple-choice testing, since the math discipline is inherently about explaining/...


9

This is an opinion, but perhaps worth sharing: When I assign that I expect students (particularly lower division students, such as those in calculus or precalculus classes) to do on their own time, I assume that they are going to collaborate, ask the Google, and otherwise use all of the resources that are available to them. Demanding that they do the work ...


8

Remediation is more about the politics of mathematics education than about learning mathematics. When students don't use their mathematics they often lose it quickly. My own experience was that it was much better for students to take the courses that their high school record said they had taken the prerequisite courses for than to have them take "remedial" ...


8

Use them for what they're best at testing, like conceptual understanding questions. One way to do this is by having students evaluate statements they would never be expected to come up with on their own, but should be able to understand the truth or falsehood of. This can also be useful for questions that have many different way of getting to an answer ...


6

Accelerated developmental education includes a variety of mechanisms to shorten time students spend in remediation. It can include: Batching together multiple courses of remediation in one semester (say: 6 or 9 credits in one semester), likely with "supports" such as tutors and learning communities; batching together remediation in simultaneous credit-...


6

In general, I'd think that anything that helps students to break out of a tendency to passivity is good. Initiative should be rewarded, looking ahead is good, and so on. Sure, if there is a pervasive assumption that everything is "curved" in an invidious way, there are even larger problems... but the possibility of "curving" unfairly (don't do it) is not a ...


6

After writing an email, I received a response from Ernie Danforth, the NE regional vice president of AMATYC which answer my question. Keep in mind these are GUIDELINES, they are not hard and fast rules. No mathematics education courses do not count as mathematics preparation, although they are still considered valuable. You are correct that ...


6

The question is broad, so my answer will be as well. Students who have been in school for a sufficient length of time have probably learned highly effective strategies for accomplishing their scholastic goals -- whatever those may be. You (it sounds to me) have identified that the learning strategies many of your students have adopted (and likely adopted ...


6

I've had a remarkable (remarkable to me) success in a different environment on a different topic, so I am not sure this will translate. But I'll mention in anyway. With one change, the same quiet "labs" turned into such lively conversations that I now have to raise my voice above the din to interrupt them with instructions. The change was from allowing ...


6

Start calling on students individually without waiting for any one to raise their hand. For a long time I never did this since I am conflict avoidant and since I didn’t want to put students on the spot, but then I witnessed another instructor masterfully call on every student throughout the course of one class period. The key point to add is that when a ...


6

I teach in the Universidad Politécnica de Madrid, which is a fairly large public engineering school with research objectives. The students are comparable to those I have taught in engineering degrees at places like Georgia Tech or the University of Washington, although they enter the univesity with better preparation. The teaching of calculus in the UPM ...


5

If I understand you, I do often think this way when solving a problem. For example, see this answer of mine at Mathematics Stack Exchange. However, limits involving infinity (as the independent or dependent variable) seem to be losing importance in textbooks. For example, I teach from Calculus: Graphical, Numerical, Algebraic by Ross L. Finney et al., and ...


5

Generalizing from your personal experience with a small, local group of students to trends in "mathematics education in the US" is a tremendous leap. The evidence you have for this "trend" could just as well be evidence that over the last 10 years you have become better at identifying students' weaknesses in arithmetic.


4

A graduate degree does not necessarily correlate closely with knowledge of the subject. It's common for people with a master's in math education to be hired at a community college despite simply not knowing calculus. Something like half of people interviewing for a tenure-track position will flub a question that probes their knowledge of first-semester ...


4

This grew a bit long for a comment. (My first note is similar to Alexander Woo's remark about factoring polynomials; perhaps he intended "polynomials" to subsume the case here, in which we add constant functions...) Given $413 + 91$, it may not be clear that this can be re-written as $7 \times 59 + 7 \times 13 = 7(59+13)$. (Plenty of people seem to ...


4

I'd recommend not being intimidated by textbook trends! "In real life" (as opposed to textbook-life, for sure, and often opposed to required-curriculum "school-math"), _of_course_ the two things you mention, "the limit", and "how it is approached", matter a great deal. Do not be intimidated by silly books (written by non-mathematicians, almost entirely) to ...


4

I've recently switched to using OpenStax open education resources in my college algebra courses. That is, they are: Free of cost, free to redistribute, free to edit if desired. For many years I thought the quality of OER materials was unacceptably low, but in the last year or two they've crossed the threshold of usability for me. They're digital in format (...


4

I teach a highly selective Liberal Arts College. If you don't assign a component of the final grade to the homework, the majority students in a typical introductory class just won't do it or, if they do it, they'll do it carelessly. They'll rely on their previous knowledge for the quizzes and it won't go well for them. In my classes I assign and collect ...


4

Here are some ideas: Try using shared vertical surfaces for doing problems. For example use whiteboards/windows. According to Peter Liljedahl http://www.peterliljedahl.com/publications/building-thinking-classrooms, having to share the writing space can encourage discussion. He suggests vertical non-permanent surfaces, but any shared space is better than ...


4

At the University of Michigan, all instruction at the level of Precalculus, Calculus 1, and Calculus 2 is conducted in small "Recitation" sections -- no lectures!. Traditionally (since the mid-1990s), these sections were capped at a maximum enrollment of 30 students; since 2016, the University has invested in lowering the class sizes to a ceiling of 20 ...


4

I'm studying physics at Eötvös Loránd University, Hungary, so my answer will not be complete, but I will try my best. In the first semester, we can choose between "advanced" and "normal" level calculus (there aren't many proofs on calculus for us). Both of them last for a $2/3$ semester, with $3$hr lecture + $3$hr practice/week. "In my times", there were $1$...


3

Consider how a student can solve the problems you present. Identify the potential errors they may commit - forgetting to carry the tens or acting on addition before multiplication, for example. For each error, work out the result from making this error. It is helpful to make a list of answers and the "cause" of that answer - remember to put the correct one ...


3

You might be able to find a "math appreciation" or "math for elementary education majors" type of text that works for you. Around 1993-1996 I taught perhaps 12 to 15 semester courses from an earlier edition of Mathematical Ideas by Miller/Heeren/Hornsby for a 2-semester course sequence for students (in nursing, education, and some other related majors) that ...


3

No good can come of this. The students who are already at the top of the class will easily grab the points, and those who actually wait for you to lecture on the topic to learn it from you, will resent the steepening of the curve. What do you really hope to gain from this? Edit - part of my knee-jerk reaction is from my own experience. A freshman class ...


3

You might try getting the students to understand Braess's Paradox, which can be phrased as a paradox about traffic flow, modeled by a weighted graph. The paradox is that the addition of a "short cut" road leads, under individual rational behavior by each driver, to everyone taking longer to reach their destination.           The ...


3

Here's how I would have attempted the lesson. First I would have given the students various cards such as: $\sin(A+B)=\sin A+\sin B$ $\sin(A+B)=\sin A \cos B + \sin B \cos A$ $\sin(A+B)=\sin(B+A)$ As a rule of thumb 8 cards is usually good. Never do more than 12 It just gets messy. Ask the students to sort them in to piles of true and false. No ...


3

There is probably not a single answer to this, but there are fads and fashions in the practice of elementary education. Some of the participants here have seen some of them come and go, and the value of practice and drill at basic skills has been questioned by many teachers as well as students. Without slighting the competence or dedication of teachers, ...


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