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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 ...

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 ...

13

The AC-method is often presented as an unmotivated rule-based algorithm, e.g. here. If that is the way that you learned it, then I can understand why you hate it. Below I explain the (little-known) algebraic ideas that lie at the heart of the algorithm, e.g. I emphasize how the non-monic factorization algorithm can be viewed as a conjugation of the monic ...

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" ...

7

This is specifically in response to the question: Are there any other "methods" I'm overlooking? Here's how I do it. After I teach factoring $x^2 + bx + c$, but before I teach factoring $ax^2 + bx + c$ for $a ≠ 1$, I like to teach factoring by grouping of four-term cubic polynomials such as $2x^3 + 12x^2 + 5x + 30$. I teach students to start by factoring ...

7

I made a handout with 10 true false questions, titled Algebra Temptations. I've put it on google drive here. I have students work in groups to decide which are true. I think it makes a good activity, though there is the risk mentioned in another answer of reinforcing the wrong idea.

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-...

5

First, it certainly shouldn't be called or considered "remedial". I think a course on mathematical modeling would be best. You could include a little bit of statistics, a little bit of rudimentary calculus and a little bit of scientific computing/programming. That should be enough to get some people hooked, it should be different from what they've seen ...

4

A common example is that students think that $\sqrt{ab}=\sqrt a \sqrt b$ for all $a,b$; try tricking them by saying that $1=\sqrt{1}=\sqrt{-1\cdot -1} = \sqrt{-1}\sqrt{-1} = i\cdot i = -1$. Similarly students will not often realize that $f(x) = \sqrt{x^2}$ is NOT $x$, but rather $|x|$. Extraneous solutions (i.e. solutions that pop out when solving but are ...

4

My answer was just a little too long for a comment. I'd start with "X puzzles" (which I put in quotes because I'm not sure they have a name). These are just big X's where you have 1 number on the top and 1 on the bottom. Then they write 1 number on the left and 1 on the right that will add to the bottom and multiply to the top (or vice versa if you want). ...

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 ...

2

Manipulatives work well for exploring quadratic forms. Algetiles are the standard, but you could use base 10 blocks if algetiles aren't available. You can easily make a set of algetiles if don't have one available. One of the issues with manipulatives is that students sadly don't encounter them enough, so you will probably have to run over the basics with ...

1

I wouldn't necessarily call them "trap" questions, but I wouldn't be surprised if a vocabulary quiz on middle/high school math could be difficult or low scoring. Ask students to define or to give examples for "degenerate triangle", "extraneous solution", "rational number", "principle square root", "inverse function", "quotient", "numerator", etc. Even ...

1

Hatred is not equal to phobia (fear). Not meant to nit, but being precise helps in the issue analysis. I suspect that those who are better at math, like it more (hate it less) and fear it less. [OK, point one has some sub correlation! ;-)] Different jobs require different amounts of math, regardless of whether the people fear/hate math. An engineer needs ...

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