Name: Problem-solving strategies
ISBN: 9780387982199

Problem-solving strategies

Problem-Solving Strategies is a unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. The discussion of problem-solving strategies is extensive. It is written for trainers and participants of contests of all levels up to the highest level: IMO, Tournament of the Towns, and the noncalculus parts of the Putnam competition. It will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week," "problem of the month," and "research problem of the year" to their students, thus bringing a creative atmosphere into their classrooms with continuous discussions of mathematical problems. This volume is a must-have for instructors wishing to enrich their teaching with some interesting nonroutine problems and for individuals who are just interested in solving difficult and challenging problems.

What Hacker News says

qsortJul 2022

(not parent, but I used to do that thing as well and you might find this helpful)

It depends on their age and skill level. It goes without saying that younger kids need more guidance if they aren't extremely motivated.

This is worth looking into: https://artofproblemsolving.com, it's kind of the go-to website for the competitive math community. There are a lot of free high-quality resources on the wiki, and they sell courses and books.

A couple classic books: https://www.amazon.com/Art-Craft-Problem-Solving-3E/dp/11194... https://www.amazon.com/Problem-Solving-Strategies-Problem-Bo...

And obviously, competition problems! For example, this is the AMC: https://amc-reg.maa.org/default.aspx; competition websites usually have an archive of past editions freely available. Studying past problems is the meat and potatoes of actual competition training. Make sure they are age appropriate, because the difficulty level ramps up VERY fast.

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dragon96Jun 2022

Regardless of which text you choose, I recommend writing proofs (full sentences and all) for the solutions that were harder to come by, or you feel difficulty expressing clearly. And if you can, get some feedback on the proofs. (Happy to take a look at a few if you DM me)

The process of writing will hopefully help you:

  - build awareness of when your arguments are not airtight or when you make false assumptions
  - modularize your thinking 
  - become more fluent with logical "vocabulary"

As for books, my personal favorites were Problem Solving Strategies (Engel) and Art and Craft of Problem Solving (Zeitz). They're both really approachable, have plenty of examples, and will give you a different perspective on what math can be about.

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newsoulMay 2022

After reading all the comments I am sharing my choices

1. The foundations of mathematics by Stewart and Tall

2. Problem Solving Strategies by Arthur Engels

3. Journey into Mathematics by Rotman

4. Concrete Mathematics by Knuth et al.

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strstrNov 2021

Bunch of problems like this are in the book "Problem-Solving Strategies" by Arthur Engel [1], I believe even including this particular one. Fun book.

[1]https://www.google.com/books/edition/Problem_Solving_Strateg...

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yaksha13Jul 2020

Problem-Solving Strategies by Arthur Engel. It's more than a textbook and not easily absorbed. The book + the internet is a powerful combination for not just learning cool math skills but building mental models/ problem framing lenses that will benefit them later in life

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newprintAug 2019

There are numerous books devoted to Olympiad preparation, there are websites completely devoted to Olympiads, there are freely available problems sets (with complete solutions). To name the few: Hungarian Problem Books, Problem-Solving Strategies, Challenging Problems in Algebra, books by Titu Andreescu - a former US IMO coach, who published a lot of books on math and IMO prep, http://www.cut-the-knot.org/

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