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"?...
- 9,184
15
votes
What are some "deep" questions to explore in elementary school math?
Here is a game I stole from Marty Weissman:
You start at zero on the number line. You are allowed "hop" forward or backwards by $6$ and "jump" forwards or backwards by $10$. Which ...
- 24.3k
12
votes
How to deal with a talented 11-year-old pupil?
Here in the U.S. there's been a rise in the last decade of "math circles"; extracurricular math clubs with students of the same age, with some amount of play/competitiveness to hone their interest.
...
- 24.3k
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, ...
- 5,762
11
votes
How to deal with a talented 11-year-old pupil?
I might disagree with several implicit hypotheses: that mathematics is only a school subject; that the there is a single linear course through it; that the main option is just the speed with which one ...
- 14.2k
8
votes
What are some "deep" questions to explore in elementary school math?
Following up on David Raveh's comment, geometric manipulatives would offer
a wealth of interesting questions.
(1) Polydrons.
(2) Snap / Linking cubes.
(3) Tangram puzzles
- 29.5k
7
votes
Mathematics exam -- How to keep brain functioning through a four-hour exam?
Having one's mental abilities fall off after about 90 minutes is consistent with having eaten 20 - 30 grams of sugar before the exam started, but not having eaten any starch at that time.
Can you ...
- 3,148
7
votes
Mathematics exam -- How to keep brain functioning through a four-hour exam?
Take some periodic breaks. Yes, you can't finish it if you take breaks, but you can't finish it if you don't take breaks. Think of it as an optimization problem. Volume is rate times time. If your ...
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7
votes
How to deal with fast students without neglecting weaker ones
When I taught high school, I offered each students a choice between doing two different worksheets, making it clear that one worksheet had many problems at a low level for lots of practice and only a ...
- 3,996
7
votes
what is a good student grouping in this situation?
I don't have any solid suggestions regarding these two students. I would have no concerns about the gifted student, and I might speak with the anxious student to put them with others they are most ...
- 20.1k
7
votes
What are some "deep" questions to explore in elementary school math?
As a child I was fascinated with numbers. As part of our fourth-grade curriculum we were familiarized with conversion to and from, as well as performing basic arithmetic in, different bases. I ...
- 291
6
votes
Extension activities in Algebra II
Edit [12.16.17]: A write-up concerning a few of the problems below was accepted for publication in NCTM's grades 8-14 journal, The Mathematics Teacher. It is slated for publication in Fall 2018, but a ...
- 18.4k
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 ...
- 20.1k
6
votes
Kid, 8 years old, developed a new calculation algorithm
It is highly unlikely that your child has developed a new algorithm for solving an interesting problem, but it is possible. It is a very good sign that they developed something that was new for ...
- 6,730
5
votes
Mathematics exam -- How to keep brain functioning through a four-hour exam?
While it is true (as @Jasper suggests) that your issue might be partly metabolic/biochemical, also it is simply the case that human beings cannot operate in a very intense mode for very long. In ...
- 14.2k
5
votes
Curriculum for Advanced 6th Graders
Beast Academy is a new(ish) curriculum, meant for math-loving students, from the Art of Problem Solving folks. It has 4 levels for each 'grade' (from 2nd to 5th), and each level has a Guidebook and a ...
- 20.1k
5
votes
Splitting the students by abilities
If you are not going to formally split the classes (with different exams, class names, etc.), I would advise just teaching to the basic level. [But I like Adam's idea to add ungraded extra hard ...
- 277
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 ...
- 51
4
votes
How to deal with a talented 11-year-old pupil?
Permit me to support paul garrett's response,
not-necessarily-textbook math books written by real mathematicians about real mathematics
with an unusual suggestion:
Skiena, Steven S. Calculated ...
- 29.5k
4
votes
Teaching arithmetic operations ($+ - \times \div$) to a 3 year old
Maria Montessori pioneered the study of childhood education, and the materials she developed for mathematics remain state-of-the-art. In this article the author encourages taking an actual lesson ...
- 157
4
votes
What are some "deep" questions to explore in elementary school math?
Matte-LIST is one resource we suggest to our students. In Norwegian. https://www.mattelist.no/
I think some of the tasks there are from Youcubed, but I have not looked deeper into it. In English. ...
- 6,730
4
votes
What are some "deep" questions to explore in elementary school math?
NRICH has a lot of resources. I usually go through adding 1 to the number in the URL until I find an interesting-looking problem, like Geoboards or Cereal Packets.
Here's an extract from the end of ...
- 221
4
votes
What are some "deep" questions to explore in elementary school math?
When I was around this age (I dont remember exactly when, but I could read but only slowly) my parents introduced me to a book "What Is the Name of This Book?" by Raymond M. Smullyan. It is ...
- 141
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 ...
- 7,485
3
votes
Mathematics exam -- How to keep brain functioning through a four-hour exam?
I have had to work on 4- to 6- hours math an physics tests for four years in total in my curriculum, and I train student or 5-hours long math tests. I will not attempt to be as thorough as other ...
- 9,079
3
votes
Effects of early study of advanced books
Sorry if this sounds simple, but I think the biggest consideration is efficiency (maybe a bit related to the missing Y issue). If you study books that are too hard, it may take you longer than a more ...
- 277
3
votes
Math Scholarships for the highly advanced
I don't know about scholarships in the USA, but here's an alternative: Consult a maths department at some university (maybe college is more appropriate in USA?), preferably one that is close enough ...
- 6,730
3
votes
What are some "deep" questions to explore in elementary school math?
Some more:
Why does division by zero not work?
Why is the order of operations important in math?
(Necessity for a standardized order to get consistent results)
Why are there infinitely many prime ...
- 139
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