16
votes
Accepted
Why are proofs written in flowery language incomprehensible?
To answer the question in the title, I would say that one problem with no-symbols reasonings is that one need to use a lot of pronouns. Problem is, pronouns usually leave too much ambiguity. At some ...
- 9,079
16
votes
Taxonomy of bad proofs
Perhaps related to "The Tangle" is what I call "Wishful Thinking". This most often happens when the student has a correct algebraic expression/equality and knows the correct final expression/equality, ...
- 7,500
16
votes
The Future of Worksheets - will they still be used or abandoned?
It's hard to tell what will be the changes in 10 years. Maybe we will all have jacks in our heads. Then again, some things change slower. (Where's my flying car?)
Most of the reasons for getting ...
- 169
13
votes
Accepted
Tips to improve blackboard writing
There are probably many tips on this; I remember some discussions of font choice happening here. Let me give only one: take your time.
One easily feels that writing on the board is too slow, and is ...
- 9,079
13
votes
How to Write Steps of Solving Equations?
I wouldn't do that. The parenthesis in use are also used for legal expressions within equations. So you can end with one line containing the same parenthesis meaning different things, what looks like ...
- 741
10
votes
How to Write Steps of Solving Equations?
The problem with
$(4x+7=6x+2)-6x$
is that there is no subtraction operation that involves subtracting a term from an equation. Subtraction involves subtracting a term from a term. So the correct ...
- 10.8k
10
votes
How to Write Steps of Solving Equations?
Speaking as someone who has taught college precalculus several times, I have an intense dislike for the way that Geogebra writes this step.
In my opinion, it is very important to emphasize to ...
- 345
10
votes
Electronic devices to replace pencil and paper
Taking a break from a convoluted computation...
To me the key limiting factor is space. I can spread out several sheets over the table and have various bits and pieces directly visible. I cannot do ...
quid♦
- 7,652
10
votes
Tips to improve blackboard writing
Blackboard writing 101: always break the chalk (to reduce the likelihood of squeaking)
Other points will depend on how much space you have available. Working consistently from left to right helps, ...
- 5,762
8
votes
How to write like a mathematician?
My favorite little tidbit on this topic is due to Jean Pierre Serre: One should aim to be "precise, yet informal". Here, "informal" means not using symbols and notation, i.e. not using "formalism".
...
- 6,095
8
votes
Tips to improve blackboard writing
Let students see what you're writing as you're writing. Otherwise, they're bored while you write and must hurry to read when you finish. Instead of facing the board, stand with your side to the ...
8
votes
How to layout a solution to a trig equation?
In most mathematics classes, we don't actually care about the solution to an exercise. The point is to get students to practice with the concepts, and figure out how to communicate their thinking. ...
- 7,520
7
votes
How to Write Steps of Solving Equations?
I'm going to use GeoGebra to teach equations. Is it OK to let the students write the steps just like GeoGebra (I mean, with parenthesis)?
I would not allow this in my class, but it would depend what ...
- 9,184
7
votes
What are some strategies to remedy and accommodate dysgraphia?
(Quick note: I am not a math teacher. I am a CS teacher with a bit of dysgraphia myself. However, my insights here actually came from when I used to be a high school music teacher, where I was ...
- 351
7
votes
Solving math problems and learning
Write stuff down. If you only do it in your head, you'll fake yourself into thinking you know more than you do. When you force yourself to write things down, you show the steps and ensure you really ...
- 71
6
votes
Accepted
Electronic devices to replace pencil and paper
Here's a sample of the iPad's resolution. The original is a page wide (8in) but clipped a bit short. The writing tends to be a bit bigger than I'd have with pencil and paper. The graph was just a ...
6
votes
The Future of Worksheets - will they still be used or abandoned?
Worksheets are useful as a fill-in-the blanks forms to sign up for a credit card or for a car registration, but are detrimental in education. They instill the thinking that all information needed to ...
- 1,309
5
votes
How to write like a mathematician?
Mathematical writing is very different from other kinds of writing, including other kinds of technical writing. Aside from low-level textbooks, the audience is generally assumed to be other competent ...
- 535
5
votes
Calculation versus writing in mathematics
Another thought occurred to me regarding this, after having read Reuben Hersh's collection of essays. There is a quote of Bill Thurston, which I paraphrase as "thinking is the same as seeing". In a ...
- 6,095
5
votes
Native language, writing, and mathematical problem solving
Based on a quick Google Scholar search, it seems like there was a flurry of activity in this area ("education literature on writing to learn mathematics") circa 1990, with at least 3 book-sized ...
- 24.4k
5
votes
How to write variables on the board, which are supposed to be italicised?
I choose (1). On the board, write an x normally. There is no distinction between roman and italic in this setting.
Back in the Olden Days (before personal computers) I would accosionally need to ...
- 7,369
5
votes
How to teach students the value of concrete counterexamples?
Perhaps "thinking in counterexamples is hard" because that requires thorough understanding, a grasp of the boundaries where a claim holds, and where it does not. For example, is matrix multiplication ...
- 29.5k
5
votes
How to Write Steps of Solving Equations?
Thinkeye's answer is good in that it easily extends to dividing two related equations and similar, more advanced operations. On the other hand, for the sake of brevity, I would suggest the way I have ...
- 151
5
votes
How to Write Steps of Solving Equations?
Since I recently had a math teacher from another institution observe me during an Algebra 2 lesson and comment positively on my notation ("I'm going to steal that!") here is a worked example:...
- 18.4k
5
votes
Why are proofs written in flowery language incomprehensible?
Honestly, both seem pretty bad and don't prove the statement in an obvious way. For example, there is confusion betwen irreps and the representations of individual elements. You can make the $G$-...
- 5,192
5
votes
Taxonomy of bad proofs
My friend, who is currently teaching an abstract algebra course, recently provided me with an example of an incorrect proof that I think showcases a few types of faulty reasoning that are common among ...
- 521
5
votes
How to layout a solution to a trig equation?
This was written after the OP's Edit update, which in turn was made after Xander Henderson's answer.
Using $\;a \cos x + b \sin x \; = \;R \sin (x + \alpha)$
Assuming the student is allowed to use ...
- 5,768
Only top scored, non community-wiki answers of a minimum length are eligible