54 votes
Accepted

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 ...
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  • 1,012
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"...
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  • 16.1k
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 ...
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  • 1,234
25 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 ...
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  • 699
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"?...
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  • 7,686
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 ...
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  • 321
18 votes

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 ...
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  • 761
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 ...
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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.
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  • 6,350
15 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 ...
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  • 16.1k
15 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 ...
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  • 251
12 votes

Teaching arithmetic operations ($+ - \times \div$) to a 3 year old

My immediate response is 'wait a few years'. I've spent a fair amount of time with 3 year olds, and most of them are busy learning how to be a person in their own right, how to have a conversation, ...
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  • 5,540
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 ...
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  • 111
10 votes

Mathematical problems for preschoolers

To supplement the "games not problems" answer above (I love that answer): Certain games provide interesting opportunities for discovery...even if you don't know anything about the rules! An example ...
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  • 5,887
10 votes

Learning counting and addition: fingers or in their head?

Edit (May 2016): From The Atlantic is: Boaler, J. & Chen, L. "Why Kids Should Use Their Fingers in Math Class." Apr 2016. Link. "Evidence from brain science suggests that far from being “...
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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 ...
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  • 4,544
9 votes

Mathematical problems for preschoolers

Addition/subtraction by measurement I'm not sure whether this is at all what you had in mind, but here comes anyway. When I was something like 2-3 years old my Dad taught me to add and subtract ...
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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, ...
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  • 7,565
8 votes

Are there any video games/app to teach children at age 3-4-5?

Not formally an answer (so if you have one, do not let this prevent you to post it), but I think challenging the implicit assumption that it would be good to have your kid use any such software ...
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8 votes

Mathematical problems for preschoolers

A good math curriculum to check out for Pre-K to K is Big Math for Little Kids. You can find some information about it in this interview with co-developer Herb Ginsburg. Ginsburg is also working on ...
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8 votes

Fun games for children

Another great game is Rush hour. It requires the important but in my opinion underemphasized skills of nonverbal problem solving, working backwards and trying all possible options.
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  • 2,906
8 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. ...
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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 ...
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  • 81
7 votes

Fun games for children

I think Set is a great commercial game. There's a daily instance of the game that can be played at the same website I just linked to.
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  • 2,906
6 votes

Are there any video games/app to teach children at age 3-4-5?

(Migrated from the comments.) Here are three specific suggestions: Teachley (company page) Tiggly (company page) Bedtime Math (wikipage) I mentioned the first two in an earlier answer to MESE 750; ...
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6 votes

Mathematical problems for preschoolers

Symmetry Suppose the blue line is a mirror, how the figure would look like in it (i.e. put the blocks at the right side to recreate the left side)? The purpose of this problem is to train pattern ...
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  • 8,729
6 votes

Mathematical problems for preschoolers

Odd one out There is a bird, a plane, a square with a hole and a cloud, which one does not fit? The purpose of this problem is to highlight that explanations are as important as answers. In ...
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  • 8,729
6 votes
Accepted

Learning counting and addition: fingers or in their head?

I was working with a student (high school level, algebra) and she blushed when she realized that she was counting on her fingers in front of me. She quickly told me her friends made fun of her. "35 ...
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6 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 ...
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