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70 votes

What is the mathematical value of children learning and being tested on Roman numerals?

Learning about different numeral system develops the critical thinking and understanding. Arabic numerals are so ubiquitous that most of us take them for granted. Seeing other numeral systems and ...
Paul92's user avatar
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44 votes

What is the mathematical value of children learning and being tested on Roman numerals?

Common knowledge Roman numerals are part of the common knowledge in Western cultures for representing numbers. That's why it's valuable for children growing up in these societies to learn them. It's ...
Ben Kovitz's user avatar
37 votes

What is the mathematical value of children learning and being tested on Roman numerals?

As I said in the question this has attracted quite a bit of attention. And after a lot of nonsense, I did finally get an answer from a British maths teacher. Although measurements and conversions are ...
Bob Tway's user avatar
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34 votes
Accepted

How should I grade true-or-false questions if the student's writing is unclear?

I read them as TTTFT. But the fourth is very hard to tell, the first somewhat hard to tell, and all show poor writing, perhaps indicating a lack of engagement. You could tell him that such terrible ...
guest's user avatar
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28 votes

What is the mathematical value of children learning and being tested on Roman numerals?

One other little defense of roman numerals: a lot of students see the "place value" notation we have for numbers as inevitable, since they've used it from before they can remember. But of course it ...
hunter's user avatar
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25 votes

What is the mathematical value of children learning and being tested on Roman numerals?

You forget, that school is not only about knowledge, but also about thinking. Learning Roman numerals and how they work teaches child, that the same thing may be expressed in different ways. And ...
Spook's user avatar
  • 351
17 votes
Accepted

Does there exist a (statistical) topology induced by students on the space of algebraic formulas? :)

Has this "topology", i.e. the organization of student errors in algebra, been studied systematically? Is there any reference in literature that thoroughly deals with the issue of really ...
Justin Skycak's user avatar
16 votes

What is the mathematical value of children learning and being tested on Roman numerals?

Aside from your own answer, I also am a firm believer in providing our children with a good educational background. Knowledge in itself is value, even if you cannot always use it for any practical ...
AnoE's user avatar
  • 848
16 votes

How can I learn to write better questions to test for conceptual understanding?

Agreeing with comments and other posts: If you want more conceptual answers, give them less details in the set-up. Using your velocity problem, here are a couple of examples of making it more ...
Aeryk's user avatar
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15 votes
Accepted

What's it called when multiple concepts are combined into a single problem?

The answer I am about to give is a little tangential, but I think that it will help to answer the question "How do I communicate to students that the problem I am setting for them is going to ...
Xander Henderson's user avatar
  • 8,223
11 votes

Software for randomizing multiple choice tests

If you use LaTeX to prepare your documents, there are many packages that automatically randomize the order of choices in multiple-choice questions. One recently updated package is esami. (This ...
JRN's user avatar
  • 10.9k
11 votes
Accepted

Acceptability of creative questions in assessments

I think the given example is highly appropriate. You cannot cover every possible combination of ideas in class. Students display understanding of a concept (rather than "recipe following") by ...
Steven Gubkin's user avatar
10 votes

Acceptability of creative questions in assessments

I would frame this issue a little differently than you have. I think it's unreasonable, at least in the context of courses which aren't well into a math major, to ask students to do something they ...
Henry Towsner's user avatar
9 votes

Acceptability of creative questions in assessments

My advice is to minimize the amount of such synthesis required. Don't make it a large fraction of your tests, if at all. Teach the students the methods you expect them to display on the exam. Not ...
guest's user avatar
  • 129
8 votes

How can I learn to write better questions to test for conceptual understanding?

Asking students to explain why something happens can be useful for assessing understanding, although it is often harder to grade and works best with many demonstrations before the exam. (Students ...
semmelchicken's user avatar
7 votes

Software for randomizing multiple choice tests

Pearson's TestGen is a crucial tool for my teaching for this reason and others. If you have an instructor account with Pearson, then the software download is free, and so are testbanks for almost all ...
Daniel R. Collins's user avatar
7 votes

Take-Home Examination on Ordinary Differential Equations?

Comment-answer, but too long for a comment: I think you are thinking about this wrong. Tests are some of the MOST valuable hours in a course. They are high stakes performances (like in music or ...
guest's user avatar
  • 139
7 votes
Accepted

Write calculus multiple choice questions with only numerical answer choices?

I think it is good to pose both numerical and non-numerical problems. While the numerical problems are generally the focus in a Calculus class, a strong conceptual understanding helps make everything ...
Isaiah's user avatar
  • 259
7 votes

How should I grade true-or-false questions if the student's writing is unclear?

There seem to be two questions here. I am going to answer them separately: How should I mark ambiguous answers? Students often write things which are ambiguous or hard to understand. For example, ...
Xander Henderson's user avatar
  • 8,223
6 votes

What is your workflow for producing high school mathematics test papers?

Disclaimer: I do not teach high school, and this isn't the easiest startup option. But if you don't mind a bit of a learning curve, I would suggest using LaTeX, which is very customizable and (key) ...
kcrisman's user avatar
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6 votes

Placing incoming college freshmen: basic algebra, pre-calc, calc

In recent literature, this issue would be referenced as multiple measures placements. There's been quite a bit of work in this area in recent years, and a number of places cite positive results (in ...
Daniel R. Collins's user avatar
6 votes

What is the mathematical value of children learning and being tested on Roman numerals?

Maybe it's not purely a maths thing, but maths comes into other subjects, and the crossover is both ways. As a former teacher in U.K. I can't believe that the national curriculum contains only 'M' and ...
Tim's user avatar
  • 161
6 votes

How can I learn to write better questions to test for conceptual understanding?

I agree with @BrendanW.Sullivan's comment. That is, when teaching an undergraduate course, like calculus, students need more than procedural knowledge. For a deeper understanding, and efforts to ...
amWhy's user avatar
  • 2,095
6 votes

What to do with "wild goose chase" or "quantum leap"-types of incorrect solutions when you ask students to prove/show something?

It's quite likely to be a consequence of the belief that they have to answer the question. When they can't work it out, when they've gone around in circles and got lost, but still they have to give an ...
Nullius in Verba's user avatar
5 votes

What is the mathematical value of children learning and being tested on Roman numerals?

In my country, many buildings (city halls and other official buildings) have their construction date, sculpted upon the building, in Roman numerals. Imagine my standing next to a 12-year old child, ...
Dominique's user avatar
  • 2,165
5 votes

How can I learn to write better questions to test for conceptual understanding?

As stated in other comments, try not to "invite" your students to merely apply rules they do know. In the specific example you mention, I would prefer a multiple choice question of the form: A ...
Vassilis Markos's user avatar
4 votes

What is your workflow for producing high school mathematics test papers?

As a community-college math lecturer, my primary course-preparation tool is the Pearson TestGen program. Pearson provides pre-made testbanks to accompany all of their textbooks; so you can begin by ...
Daniel R. Collins's user avatar
4 votes

Suggested idea: Course exams written by someone else other than the instructors/coordinators. Good or Bad?

Your point about less weighting of the final exam is made as both a con and a pro (not logically consistent). The issue of less flexibility to alter the curriculum is not purely a con, can be a pro. ...
guest's user avatar
  • 41

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