71
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 ...
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45
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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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19
votes
Accepted
Source of conceptual, multiple choice calculus questions
Cornell's Good Questions Project has a great question bank for conceptual questions.
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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7
votes
Source of conceptual, multiple choice calculus questions
The Calculus textbook of Hughes-Hallett, Gleason and McCallum et. al. includes ConcepTests that are rather good for this purpose. Sorry this is not a free online resource, but I hope it helps.
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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 ...
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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 ...
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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 ...
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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, ...
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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) ...
- 5,952
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 ...
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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 ...
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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 ...
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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, ...
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5
votes
Source of conceptual, multiple choice calculus questions
Though not nearly as good as some of the other suggestions here, the practice exams for AP Calculus contain decent problems. The sample multiple choice ones are buried inside the "AP Calculus Course ...
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5
votes
Source of conceptual, multiple choice calculus questions
I tend to download testbanks for Pearson's TestGen application (requires instructor account at Pearson, available for almost any text they produce) and hunt through them for conceptual questions for ...
- 23.6k
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 ...
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