54 votes

The concept of infinity for a 5 year old

This does not directly concern the $\infty+1=\infty$ issue and I am not certain that I understand what you mean by his previous understanding of mathematics, but I wanted to give the following ...
orion2112's user avatar
  • 1,007
36 votes

In what curricula are "rectangles" defined so as to exclude squares?

I cannot answer the OP's question about cross-cultural/international perspectives, but here is a historical perspective that may be helpful. The issue here (whether the category "rectangles"...
mweiss's user avatar
  • 17.4k
33 votes

Children's counting problems: Is this question phrased correctly?

I don't think there's anything wrong with the wording; it's clear what is being asked. Your example with the three dollars is also not always the way we speak in everyday language. If you ask someone ...
Thierry's user avatar
  • 1,527
26 votes

The concept of infinity for a 5 year old

First of all, regardless of age, people need to understand that "infinity" is not a number, and not a placeholder for a number, but an attribute of them (i.e. the fact that you can increase numbers ...
AnoE's user avatar
  • 848
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
  • 17.4k
20 votes

How to answer a three-year-old the question "Why is $2+6$ the same as $4+4$"?

I'm nearly sure I did this with my child when she was young. First, establish that she understands that a number, like three, is equal to $1+1+1$. Hold three fingers up and ask her "how many is this"?...
Nick C's user avatar
  • 9,436
20 votes

Children's counting problems: Is this question phrased correctly?

When we describe counts in natural language, there's almost always an implicit "exactly" when phrasing like this. We use phrases like "at least 4" when we want a more general ...
Barmar's user avatar
  • 369
19 votes
Accepted

The concept of infinity for a 5 year old

On a piece of paper, he started with writing 10, then 100, then 1000, .... and he stopped after writing 40 zeros with 1. Then he came to me and said, "I understand infinity now; infinity is a number ...
QMC's user avatar
  • 779
17 votes

The concept of infinity for a 5 year old

I'm not sure why the two basic things adults seem to say about infinity are "infinity is not a number" and "∞+1=∞", both of which are at best misleading. (Infinity doesn't name a number, but it does ...
Henry Towsner's user avatar
16 votes

The concept of infinity for a 5 year old

Speaking as someone who was that kid, you might be able to explain $\infty + 1 = \infty$ via the Hilbert hotel. Imagine a hotel that has an infinite number of rooms, one for every number. Imagine the ...
James_pic's user avatar
  • 261
16 votes

Children's counting problems: Is this question phrased correctly?

Perhaps "shows" instead of "has". If you asked me to show you 4 apples, I can't think of a logical argument in favor of me grabbing 5 apples and smiling smugly.
Aeryk's user avatar
  • 8,013
11 votes

Children's counting problems: Is this question phrased correctly?

Nearly every test like this includes instructions to choose the "best answer" to cover exactly this scenario. This looks like it's part of a test of basic counting skills, and in that ...
Jason E's user avatar
  • 111
10 votes
Accepted

Why do so many children's book confuse discs with circles?

Mathematics, as any other field of inquiry, has specific terminology. The rest of the world is not obliged to use the same technical terminology. Note that this also happens within mathematics; not ...
Tommi's user avatar
  • 7,015
9 votes

In what curricula are "rectangles" defined so as to exclude squares?

There is a model of how people progress towards abstract reasoning through the subject of geometry called the Van Hiele model. The model describes five levels: visualization, analysis, abstraction, ...
user52817's user avatar
  • 10.8k
9 votes

The concept of infinity for a 5 year old

My son, also 6 yo, regularly talks about millions and billions and infinity. Obviously, large numbers have some attraction to children of this age. I try to explain that infinity is not a number. ...
rexkogitans's user avatar
8 votes

Children's counting problems: Is this question phrased correctly?

I showed this question to my three-year old son. His response - because he counted the apples one by one in each picture, passing "4" each time - was B, C and D. Hence, we need to take into ...
Nardya's user avatar
  • 81
7 votes

The concept of infinity for a 5 year old

I am going to answer your question by suggesting a couple of books which might be fun to read with your son: The Phantom Tollbooth by Norton Juster. The book is a rather surreal adventure trip ...
Xander Henderson's user avatar
  • 7,988
6 votes

How to answer a three-year-old the question "Why is $2+6$ the same as $4+4$"?

Blocks work well for thinking about addition. Have her count out 8 blocks, and then ask her about all the addition problems that have 8 blocks as the answer. A lovely children's book which looks at ...
Sue VanHattum's user avatar
  • 20.3k
5 votes

Teaching a child time and hours in a digital world

My experience: In the early 2000's, I had my first child ($\approx$ 5 yrs) help me "build" an analog clock (it was just a paper model, no gears). We would occasionally set it to the correct time (...
Nick C's user avatar
  • 9,436
5 votes

The concept of infinity for a 5 year old

There is a well-known Christian hymn, Amazing Grace, whose last lyric captures the idea of (countable) infinity quite well, and may be more effective to a five year old because it includes a context ...
Michael Joyce's user avatar
5 votes

In what curricula are "rectangles" defined so as to exclude squares?

I just came across this discussion https://news.ycombinator.com/item?id=16605831 which reminded me of your question. The perspective isn't exactly math and isn't exactly not-math but rather, a ...
Adam's user avatar
  • 5,673
5 votes

How to answer a three-year-old the question "Why is $2+6$ the same as $4+4$"?

A good answer to this question is one that (is correct, and) she finds convincing. As kids are growing up and making sense of the world around them, experimentation is often one of their key sources ...
yomplex's user avatar
  • 51
4 votes
Accepted

What's the word for addition and subtraction without borrowing or carrying over?

This topic seems to be called "Bridging 10s" or "Making 10s": http://www.helpingwithmath.com/by_subject/addition/making-10-1oa6.htm I'm not sure that you will find many discussions about the utility ...
Opal E's user avatar
  • 3,986
3 votes

Teaching a child time and hours in a digital world

Have you considered buying an analog watch for your child? My parents got me one for my sixth birthday and I was able to use it to tell time. I would think the child could also use it to learn to ...
Amy B's user avatar
  • 8,017
3 votes

The concept of infinity for a 5 year old

My children both learned about infinity at around four to five years old (now 5 and 7). For both of them it was fairly straightforward; it came about with my eldest when he was talking to other kids ...
Joe's user avatar
  • 161
3 votes

The concept of infinity for a 5 year old

I would start by saying something along the following lines... "You're asking some very grown-up questions for someone that's only 5. Are you ready to do some really, really, grown-up thinking about ...
ChrisA's user avatar
  • 1,224
3 votes
Accepted

Teaching three-year-old subtraction using the number line

The following is anecdotal and rambling, but I think it goes a good way towards addressing the question (from a personal point of view). My daughter and I play a variant of the card game War to work ...
Xander Henderson's user avatar
  • 7,988
3 votes

The concept of infinity for a 5 year old

I've no idea whether this would work, but would relating it to forever hekp? Infinity is like forever but for nunbers. Doing something for a week and then forever is the same as just doing it forever. ...
timtfj's user avatar
  • 571
3 votes

The concept of infinity for a 5 year old

I suppose one problem is that your son looks at $\infty$ the same way he looks at $10$. But infinity is not a natural or real number, even though it has a symbol and can be used in "equations" like $\...
Peter - Reinstate Monica's user avatar

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