58 votes

Is there a virtue to learning how to compute by hand?

The following response is written with elementary-to-high-school mathematics in mind. A lack of a decent number sense really does encumber making sense of and parsing word problems, as well as the ...
ryang's user avatar
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27 votes

Is there a virtue to learning how to compute by hand?

I find the ability to estimate calculations quite useful and I think you need to be able do do calculations to estimate them. If you are keeping a grocery budget, I would suggest you should know what ...
Ross Millikan's user avatar
25 votes

Is there a virtue to learning how to compute by hand?

Yes! But the virtue doesn't lie in being able to do the calculation but in gaining a feel for numbers as well as algorithmic thinking. I teach Computer Science freshmen and one of the first things we ...
ljrk's user avatar
  • 449
25 votes

What is the rationale for distinguishing between proper and improper fractions?

added Oct 6 The reason mixed numbers are found in US education is that mixed numbers are found outside of school in the US, so the children need to learn to understand them. Mixed numbers are found ...
Gerald Edgar's user avatar
  • 7,489
22 votes
Accepted

How do you coach students who often make small errors?

Ask the student to "talk through" their calculations Having a student verbalize their calculation may force them to pay more attention (or a different kind of attention) to their work that ...
Mike Pierce's user avatar
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22 votes
Accepted

Are there research studies that attempt to determine the value of a "Growth Mindset?"

Psychologist Carol Dweck's "growth mindset" theory has become a popular solution and intervention technique in (mostly American) schools of all ages. We might say that it's become the new ...
Daniel R. Collins's user avatar
21 votes

Are kindergartners supposed to be steered from squares being rectangles?

Kindergartners are generally at an early stage of geometric development, in which shapes are recognized by how well they resemble prototypical images, rather than by whether or not they conform to a ...
mweiss's user avatar
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21 votes

Is there a virtue to learning how to compute by hand?

I taught at the elementary and high school levels. At times we used calculators and at times we didn't. Students benefit from experience both ways. Students need to learn that calculators are only a ...
Amy B's user avatar
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19 votes
Accepted

Examples of vocabulary that have different meanings in Mathematics compared to "everyday" English

This is a problem for some English language learners: The triangle on the left is also a right triangle.
JRN's user avatar
  • 10.8k
18 votes

What is an intercept?

This is a case where you might be looking for a distinction that's pretty subtle. By definition, the y-intercept occurs at x=0. In one notation, it's literally f(0), where the x is explicitly offered....
JTP - Apologise to Monica's user avatar
17 votes
Accepted

Midterm in Mathematics Courses

"Cheating Lessons" by James M. Lang argues (and has many references to back up) the claim that smaller, more frequent, lower stakes assessment both improves student learning outcomes and decreases the ...
Steven Gubkin's user avatar
16 votes
Accepted

Gender and groupwork

Here is one article in PNAS. The final sentence quoted below is a summary: "creating small groups with high proportions of women [...] is one way to keep women engaged [...]" Dasgupta, Nilanjana, ...
Joseph O'Rourke's user avatar
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
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Does the "how old is the shepherd" phenomenon occur for more relatable word problems?

Note (Feb 2018): There is an alleged "Chinese math problem" (see, e.g., WaPo article) going around about the second example problem below (cited to Reusser 1988, but can be found in Reusser 1986, as I'...
Benjamin Dickman's user avatar
15 votes

What is the quantitative data on effectiveness of "modern" teaching methods?

Consider a paper from this year: Setren, et. al., "Effects of the Flipped Classroom: Evidence from a Randomized Trial", Annenberg Institute at Brown University (2019). In their introduction, the ...
Daniel R. Collins's user avatar
14 votes

How do you coach students who often make small errors?

I used to have this problem. What helps me more than anything is: Solve it two different ways if you can and make sure they agree If you are finding a general formula, test it on some examples If ...
causative's user avatar
  • 241
13 votes

Examples of vocabulary that have different meanings in Mathematics compared to "everyday" English

"In general" or "generally" In mathematics, if we say a specific result holds in general, we mean there are no exceptions to the result. In every-day non mathematical discussions, if someone makes a ...
user6626's user avatar
  • 131
13 votes
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What is the correlation between students' contentment and educational quality?

From Clark, Richard, Paul A. Kirschner, and John Sweller. "Putting students on the path to learning: The case for fully guided instruction." (2012): Even more disturbing is evidence that when ...
Daniel R. Collins's user avatar
13 votes
Accepted

Separating the roles of "teacher" and "assessor"

A question that occurs with a project like this (broader than one department, as you put it) would be: Who is qualified to make those assessments? Probably not any other department at a particular ...
Daniel R. Collins's user avatar
13 votes

Is there a virtue to learning how to compute by hand?

I attended the Computer based math educational summit back in 2016 and found their ideas interesting. I agree with some of their points and disagree with others, but it is certainly interesting to ...
Ferenc Beleznay's user avatar
12 votes

What are some good books on mathematical pedagogy?

In The Teaching Gap, James Stigler and James Hiebert analyze research from the TIMSS studies. Part of their conclusion is that much of our experiences of classroom culture are deeply imprinted in us, ...
Sue VanHattum's user avatar
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11 votes

What is the rationale for distinguishing between proper and improper fractions?

I do not know of any relevant research. Here are my own not-research-informed ideas. Most people refer to fractions as parts of a whole. If someone says "I lost a fraction of a pound on my diet&...
Steven Gubkin's user avatar
10 votes

A study comparing effects of calculator usage on later math skills?

Studies such as Suydam (1979) indicate that there is not an adverse effect. However, most of the cited studies on the effects go back to the late 70's or early 80's. Anecdotally, as a high school ...
J. Plencner's user avatar
10 votes

Examples of vocabulary that have different meanings in Mathematics compared to "everyday" English

This can get quite some list… Here are a few: function: a mapping in mathematics vs. a "feature" a "purpose" and "functionality" in everyday language root: e.g. a point where a function is zero vs. ...
Dirk's user avatar
  • 2,992
10 votes

Examples of vocabulary that have different meanings in Mathematics compared to "everyday" English

The term "statistically significant" is significant in this regard. In the previous sentence, the first example of "significant" means "unlikely to have occurred by chance", and the second denotes ...
CopOnTheRun's user avatar
10 votes

Literature on learning from errors in mathematics

You might be interested in systematic errors. From page 14 of Kurt VanLehn's "Mind Bugs: The Origins of Procedural Misconceptions" (MIT Press, 1990): Systematic errors appear to stem from ...
JRN's user avatar
  • 10.8k
10 votes
Accepted

request for evidence about class perspectives in math word problems

Yes, there is evidence for the claim; for example, consult the following: Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219-...
Benjamin Dickman's user avatar
10 votes
Accepted

Apply the inverse operation on both sides, or know the inverse function?

I'd say both: they must know the inverse function, and that it's being applied to both sides. This then connects up with the fundamental properties of equality. As a teacher of many algebra courses (...
Daniel R. Collins's user avatar

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