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32 votes
Accepted

Whether to tell students how difficult (you think) a problem is

In a setting where students aren't working from a book with these labels on questions, is it worthwhile for the instructor to indicate to students where the work they are asking them to do falls on a ...
Justin Skycak's user avatar
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 ...
Benoît Kloeckner's user avatar
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, ...
Aeryk's user avatar
  • 8,019
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 ...
guest's user avatar
  • 169
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 ...
Thinkeye's user avatar
  • 741
12 votes
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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 ...
Benoît Kloeckner's user avatar
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 ...
JRN's user avatar
  • 10.9k
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 ...
idmercer's user avatar
  • 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's user avatar
  • 7,722
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, ...
Jessica B's user avatar
  • 5,840
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". ...
Jon Bannon's user avatar
  • 6,173
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 ...
David Benjamin's user avatar
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. ...
Xander Henderson's user avatar
  • 8,288
8 votes

Whether to tell students how difficult (you think) a problem is

A Frame Challenge I think that the premise of the question is slightly flawed: I do not think that the distinction between "exercises" and "problems" is one of difficulty—an ...
Xander Henderson's user avatar
  • 8,288
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 ...
Nick C's user avatar
  • 9,729
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 ...
Ben I.'s user avatar
  • 361
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 ...
guest's user avatar
  • 71
7 votes

Whether to tell students how difficult (you think) a problem is

Donald Knuth certainly thought so: he graded the exercises in his monumental work The Art Of Computer Programming from 00 ‘An extremely easy exercise that can be answered immediately if the material ...
gidds's user avatar
  • 405
6 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 ...
Joseph O'Rourke's user avatar
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 ...
JTP - Apologise to Monica's user avatar
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 ...
Rusty Core's user avatar
  • 1,317
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 ...
anomaly's user avatar
  • 535
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 ...
Daniel R. Collins's user avatar
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 ...
Gerald Edgar's user avatar
  • 7,607
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 ...
TAR86's user avatar
  • 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:...
Benjamin Dickman's user avatar
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 $G$-...
Adam's user avatar
  • 5,883

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