Linked Questions

46 votes
18 answers
12k views

How to explain the flipping of division by a fraction?

This question is inspired by @DavidButlerUofA's discussion of "$\div \frac{2}{3}$ as $\times \frac{3}{2}$" in "Are fractions hard because they are like algebra?" Q. How can one best convey to ...
Joseph O'Rourke's user avatar
18 votes
8 answers
2k views

What is the right feedback for incorrect cancellation?

Here are three "cancellations" seen during algebra simplification, two of which are invalid. (1) $\frac{x + 6}{6} = \frac{x+6\hspace-1.2ex\diagup}{6\hspace-1.2ex\diagup} = x$ (2) $\frac{6x ...
Chris Cunningham's user avatar
31 votes
4 answers
4k views

Books about elementary mathematics written like a good undergraduate textbook

I've never seen any really good expositions of elementary mathematics (middle school or earlier). A good college-level textbook, written for people with an interest in mathematics, reads like a novel ...
Jack M's user avatar
  • 1,337
7 votes
10 answers
2k views

How to explain fractions to 7 year old kid

I am finding it difficult to convince my kid that 2/4 and 1/2 are same. As per the kid, 2/4 is more than 1/2 since in first case the boy gets 2 candies out of 4 and in second case he gets 1 candy out ...
NotAgain's user avatar
  • 171
12 votes
8 answers
4k views

How to teach sum of fractions to students?

I think almost every middle school student in my country has learned sum of two fractions in this non reflexive way (I'm included when I was kid), doing the following steps: They calculate the lcm. ...
user26832's user avatar
  • 573
18 votes
4 answers
2k views

Are fractions hard because they are like algebra?

It occurs to me that to really understand the ways that people work with fractions on paper requires a good grasp of the ideas that numbers have multiple representations and that expressions can be ...
DavidButlerUofA's user avatar
13 votes
4 answers
562 views

Analyzing an answer to the following problem: Give meaning to $\frac{4}{5} + \frac{2}{3}$

Case: Exam Problem given to student at university: Give a problem/context illustrating the operation $\frac{4}{5} + \frac{2}{3}$ Answer by student: Anna and Beatrice buy flowers for grandpa for his ...
Improve's user avatar
  • 1,881
6 votes
6 answers
586 views

What are the essential mathematics skills that uni based STEM math educators want high school to teach students?

The question in the title mostly covers the question I want to ask. After seeing a number of questions here on ME and having taught/TA'd a number of introductory math classes, I wonder what people ...
DRF's user avatar
  • 1,018
11 votes
3 answers
2k views

How to engage low-level students?

I'm a recent graduate in my first year of teaching. I teach secondary students, and I have found that some low-level students are not listening in class. They seem to have given up and stopped trying. ...
EXL's user avatar
  • 311
2 votes
3 answers
378 views

Is it possible to understand decimals without understanding fractions?

It is common for students to come unstuck by there inability to manipulate fractions (eg calculating gradients, algebraic fractions, etc) yet these same students can handle decimal numbers competently....
pdmclean's user avatar
  • 957