Working Mathematically 1: Teacher Resource Book (Series: Maths World).
Author: Lloyd Dawe
Contributors: Jody Crothers, John Dowsey, Andy Edwards, Lisa Patterson, David Tynan, Jill Vincent, Neville Windsor.
Published: David Tynan, MacMillan
Education Australia Pty. Ltd., 2007
135 pp., spiral-bound soft cover
Working Mathematically 2: Teacher Resource Book (Series Maths World)
Author: Lloyd Dawe and contributing
author: Monique Miotto.
Published: Ingrid Kemp. MacMillan
Education Australia, 2009.
169 pp., spiral-bound soft cover
The Working Mathematically Books are a fantastic resource and an invaluable aid for the classroom teacher of mathematics. The Author Lloyd Dawe sums up his main purpose. "He feels there is a real need throughout Australia for original tasks to supplement the worked examples that are the daily bread of most students."
The main attribute of these books is the vast amount of work that has been done for the teacher. There is more information, questions and challenges than you will need to provide a great lesson to a classroom of middle ability students. By reading and preparing for only a few minutes you will master the key ideas. Then you will be able to help your students work through a stimulating discovery lesson, involving real-life mathematics.
Each of the tasks in these books has an "Introduction"; the working mathematically learning activity, called "Try this!" ("Learning activities" in Book 2.); a "Challenge" section as well as "Teacher Notes" and "Answers" ("Solutions" in Book 2.)
Each Book has 20 tasks that are reproducible for your students. My favourites from Book 1 were "How big is the Moon? ", "Radio Frequencies", "Catching and storing Rainwater" and "Getting the most out of your tyres." Several that caught my eye from Book 2 were "Tap water and bottled water: what's the difference?", "How do you find the centre of an earthquake?" ,"Fermat, prime numbers and Pythagoras", "Fireworks on New Year's Eve", "The survival of the Antarctic blue whale" and "Melanoma: is it a worry for teenagers?".
Each task certainly involves mathematics and many of the tasks also have cross-faculty links to Science, Geography and History as well as to global environmental issues. There are several tables in each book so that teachers in each state can easily match each task topic to particular syllabus references.
Book 1 is recommended for Years 7, 8 and 9 while Book 2 is recommended for years 9 and 10. I feel that the Book 1 material could also be used with all ability level students in Year 10. Book 2 would also be totally appropriate to supplement the work in a senior non-calculus course (General Mathematics in NSW.)
As the author says: "The tasks will motivate students by increasing their knowledge and developing their understanding of mathematical concepts." "Each task is designed to challenge junior secondary students to think, communicate and work mathematically."
Here is a short list of some practical uses I would recommend. These occurred to me as I worked through most of the tasks.
* The main feature of the tasks is that they show the reading teacher how to design and develop a lesson. You will soon be able to use an interesting fact or a newspaper article to improve standard textbook lessons!
* A great source of extension material for independent learners or individuals seeking to extend their knowledge.
* An interesting collection of homework exercises rather just completing the current classwork.
* Adjustable time length lessons. There is enough material for a fifty minute lesson, an eighty minute lesson or the challenge can be completed for homework.
* A good historical introduction to topics; e.g., you could introduce Coordinate Geometry through the task "The French Connection from Algebra to Geometry." The brilliant ideas of Descartes have lead us to the amazing GPS (Global Positioning System) technology that we use today.
* You may choose to discuss only the key concept of a task to end your lesson or start a new topic.
* Relief or casual teachers can be given a good lesson to reinforce the current topic.
* A yearly program of "Rich Tasks" or homework for a high ability class of students; e.g., the top class in a comprehensive school or for all classes in a selective school.
* Getting students comfortable calculating and using formulas with real applications; e.g., from the "Secret of a beam balance", we learn to use momentum (m) = force (f) x distance (d).
* Explaining definitions; e.g., "A conjecture is a statement that appears reasonable but has not been proven." No, this example was not Goldberg's Conjecture, but students were challenged to make up their own conjectures about adding fractions up to a limiting sum. There is even a good explanation of Euclid's "Proof by Contradiction" to show that the set of primes is infinite.
* Introducing Higher Order Thinking. There are well explained examples of limits and convergent series that will prepare students for the theoretical aspects of senior calculus courses.
The teacher's biggest decision will be how much to do with each task. Go with the flow of your student's interest and if they want more give them more. Make sure that you do not bore them by making them do everything as they will lose the impact of the interesting facts and key ideas of each task. You do not have to do everything because there is plenty of great material there!