Problem solving


Rationale: While a great deal of ‘problem solving’ ought to happen in regular classrooms, the Internet can theoretically offer some extra benefits to students, including a regular supply of suitably targeted problems, opportunities to share solutions and even opportunities to get professional feedback on their work. [There seems little argument for a set of problems on the web that could just as easily be written in a textbook, with nothing else added.]


Here are some examples:



Problem of the Week


Problem of the Week (POW) was one of the early initiatives of the Math Forum site in the USA, a massive site with many resources of different kinds. Problems are posted at different levels and in different branches of maths, and students can submit answers to these. Good answers are posted on the web and comments on various solutions are offered. In recent years, the cost of doing this has been prohibitive, so that some previously free services are charged for (such as individual mentoring of students), but it is still possible to access the site productively without charge. Explore this page to see how mentoring works and also to look at problems and their (annotated) student solutions. A substantial archive of problems, solutions and commentaries of the past several years is also accessible.



IMO Problems


The International Mathematical Olympiad is a mathematical problem solving competition for school students that has been held each year since 1959. National teams (including Australia) are selected and specially trained for the competition which requires a very high level of problem-solving ability and access to and experience of a suite of mathematical techniques not conventionally taught in schools. On this site, John Scholes of the UK has kindly provided a catalogue of past problems and their solutions. The solutions are very brief and would often be hard for students without substantial mathematical experience to follow. However, a site like this provides access to mathematical work that is rarely available at a typical school to students.



Australian Mathematics Trust


The Australian Mathematics Trust is responsible for the Australian Mathematics Competition, which focuses on problem solving, but at a lower level than the IMO. Organised by the Australian Mathematics Trust and sponsored for many years by Westpac, the AMC is a very large annual competition administered through schools. Other opportunities to learn about problem solving through the Trust are also described on this site, including the Mathematics Challenge. Students who are interested in such activities may learn about them from the web and then discuss their interests with their school.



Word Problems for Kids


This site offers an opportunity for students to solve some word problems, and to get some hints if they get stuck. Unlike many sites concerned with problem solving in mathematics, this is not a competition site (although some of the problems have been modified from competition problems.). Indeed the authors are emphatic: “This is not a test but a set of carefully selected problems which can help you improve your problem solving skills”. Problems are graded by level (Canadian Grades 5-12). The mathematics covers a wide range of areas and all problems have complete solutions as well as hints.


Math TV


This US website for middle school students uses Flash to offer detailed algorithmic help with ‘word problems’, with a new ‘episode’ being produced each week. Students can see how to think about the step-by-step solution of standard problems, with opportunities to be engaged along the way (responding to teacher questions, trying for themselves, etc.) The site features an online calculator and online drawing area. While it doesn’t deal with problem solving in the normal sense of the word, it provides an example of how the web might be used to help students with mathematical tasks, and may be of help to students. Episodes are archived and classified.




The UK-based NRich site has a rich store of problems which are changed monthly. The problems are identified as appropriate to different stages and many contain interactive elements. Problems usually come with notes for a teacher and a hint. The featured solutions from students from around the world provide a nice touch. The site has been going for a decade now, so that the archive of past issues in the left column provides a wealth of interesting problems, well-presented and nicely targeted. The link above takes you to all the problems for This Month, which you can refine to different stages with the links in the left column.



The wonderful PLUS magazine, a companion to the NRich site for more sophisticated students, has a regular Puzzle Page, with an original puzzle each month and solutions in later months. There is also an archive of previous puzzles accessible from the site (Explore the archive at the top of the page). Although one definition of a puzzle is that it is a mathematical problem that doesn’t lead to further mathematical thinking, many of the puzzles on this site will allow students (and their teachers) to engage in mathematical exploration.