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23 votes

The effectiveness of "honors" classes

My undergrad university had an honors math program and the point was to prepare students for top graduate programs in math. The content was far more rigorous/intense than the regular classes, which I ...
Justin Skycak's user avatar
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
  • 9,639
16 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 ...
Steven Gubkin's user avatar
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. ...
Daniel R. Collins's user avatar
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 ...
paul garrett's user avatar
  • 14.7k
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 ...
Opal E's user avatar
  • 4,043
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 ...
Jasper's user avatar
  • 3,178
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 ...
guest's user avatar
  • 188
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 ...
Sue VanHattum's user avatar
  • 21k
7 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
Joseph O'Rourke's user avatar
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 ...
Benjamin Dickman's user avatar
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 ...
Tommi's user avatar
  • 7,318
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
  • 21k
6 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 ...
njuffa's user avatar
  • 311
6 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 ...
BagiM's user avatar
  • 161
6 votes

The effectiveness of "honors" classes

This can play out very differently depending on the setup of the educational system that you're in. When I was an undergrad at Berkeley in the 80's, honors classes were much more rigorous than ...
kjhgsldkjh's user avatar
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
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 ...
Sue VanHattum's user avatar
  • 21k
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 ...
paul garrett's user avatar
  • 14.7k
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 ...
guest's user avatar
  • 287
5 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. ...
Tommi's user avatar
  • 7,318
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 ...
Joseph O'Rourke's user avatar
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 ...
wizzwizz4's user avatar
  • 221
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
  • 8,224
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 ...
Benoît Kloeckner's user avatar
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 ...
guest's user avatar
  • 287
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 ...
BigMistake's user avatar
3 votes

What are some "deep" questions to explore in elementary school math?

Take whatever questions the child has found interesting to study, and expand upon them. Some directions will be more fun than others: pay attention to that. For the questions you've mentioned: What ...
wizzwizz4's user avatar
  • 221

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