Thinking Mathematically (2nd Edition)
J. Mason, L. Burton, K. Stacey
Format: PDF / Kindle (mobi) / ePub
Thinking Mathematically is invaluable for anyone who wishes to promote mathematical thinking in others or for anyone who has always wondered what lies at the core of mathematics.
· The text has been updated with 77 fresh problems matched to curriculum topics together with links between those topics and the original problems.
· There is a new preface describing the origins and uses of the first edition
· New chapter correlates mathematical processes with the natural powers that every learner has already demonstrated in learning to speak.
selected and used. Look at the information provided in the next question and try to put it into a convenient form, getting a sense of what each sentence contributes before actually trying to resolve the question. Ladies Luncheon Five women have lunch together seated around a circular table. Ms Osborne is sitting between Ms Lewis and Ms Martin. Ellen is sitting between Cathy and Ms Norris. Ms Lewis is between Ellen and Alice. Cathy and Doris are sisters. Betty is seated with Ms Parkes on her left
Attack Do enough special cases systematically to reach a conjecture. Are you assuming something about the square that is not stated? Start with a dissection and dissect one of the squares. Start with a square and build others around it. ➤ ➤ ➤ ➤ If you have done numerous examples, you will have convinced yourself that numbers like 4, 9, 16, . . . are nice. If you noticed that nowhere does the question say the squares all have to be the same size, then you probably discovered that 4, 7, 10, 13, .
some future time. Sometimes, however, the problem will not let go of you and you become aware of a deeper commitment. There is a sense that it can be resolved, or at least that more can be done. There is no rush, no hot intensity as with the flush of GETTING INVOLVED. Rather, there is a sense of harmony or connection with the problem. It has become a friend. Few of the questions posed in this book so far are likely to have engendered a sharp, clear moment of KEEPING GOING, if only because I have
Mathematically Extend ➤ Try maximizing the occurrence of other angles. ➤ What is the maximum number of right angles on the faces of a tetrahedron? ➤ Try polyhedra with as many faces meeting at right angles as possible. Rolling Coins Place two coins of the same size flat on a table and roll one around the edge of the other, as if they were gears. When the rolling coin has made one trip around the circumference of the fixed coin, how many times will it have revolved around its own centre? Entry ➤
put into a helpful form it was easy to introduce the symbol P for the original price and thereby show that the generalization was true. Generalizing need not stop here. What if the discount and tax rates change? Does the order of calculation sometimes make a difference? IF YOU HAVE NOT ALREADY DONE SO, TRY IT NOW I hope you can see from the shape of the calculation derived earlier that the actual percentages are irrelevant to the argument. Part of the power of symbols in mathematics is to