Professional Work
Expository Writing in Relation to the Mathematics Curriculum
One of the responsibilities of active researchers in the various curriculum
areas is to address, for teachers in the classroom, implications of both the
research carried out and the content itself. In terms of the mathematics
curriculum there are still many questions which need addressing. Particularly
for teachers in the middle school, where background in mathematics may not be as
strong as desired, there are issues of the content of the curriculum and how to
make it more relevant to students (through making it more relevant to the
teachers themselves). For all teachers there is the issue of demonstrating and
explaining students’ likely errors in various contexts and looking for ways of
addressing or avoiding them for future students.
Over the years this aspect of the research at the University of Tasmania has
resulted in the publication of a dozen or so articles in state, national and
international professional journals for mathematics teachers. In 1995, articles
relating to some basic aspects of number in the curriculum were collected
together and published under the title “Cautionary Tales: A Collection of
Mathematical Essays for Teachers.” The title reflects concern about assumptions
which are made by teachers, usually do to alack of deeper understand of where
topics lead throughout the curriculum. An example of such an issue is the
question of telling children a mathematical property as if it will be true
“always” when in fact in several years’ time another teacher may have examples
from more advanced arithmetic which contradict the earlier property. Examples of
“adages” which do not hold true in general are the following.
1. Addition makes bigger.
2. Subtraction makes smaller.
3. Multiplication means ‘lots of’.
4. Multiplication makes bigger.
5. Division makes smaller.
6. You can only divide a bigger number by a smaller number.
7. The larger the denominator the smaller the fraction.
8. The longer the number the larger its value.
Hopefully making teachers aware of the difficulties of teaching children “rules”
like the above will contribute to better mathematics education in schools.
Another numeracy issue addressed has been student understanding of basic number
types in the real number system.
As well as addressing issues of basic numeracy, issues involved with statistical
literacy and the chance and data part of the mathematics curriculum have been
addressed. It is planned in the future to collect some of the essays listed
below and others to be written into another volume of “Cautionary Tales.” In
relation to chance and data, issues addressed so far have included the use of
children's literature to emphasise chance language in the classroom, confusion
associated with the decimal point in understanding averages, the need to build
up an understanding of conditional language as a basis for conditional
probability, and the problems associated with sample size when conducting
surveys.
Further to addressing possible traps in the mathematics curriculum, expository
writing can assist in providing suggested activities for classroom use,
particularly in relation to the newer parts of the curriculum. In the case of
chance and data, several articles have been written which make suggestions in
relation to hypothesis testing, conditional probability, graphical techniques in
interpreting data, using the media for problem solving, and integrating the
derivation of probability models into a differential equations course.
References
1. Watson, J.M. (1995). Cautionary Tales: A Collection of Mathematical Essays
for Teachers. Adelaide: Australian Association of Mathematics Teachers. (103pp.)
[ISBN 1 875900 00 4]
2. Watson, J.M. (1989). Howzat hypothesis. Australian Mathematics Teacher,
45(1), 9.
3. Watson, J.M. (1989). Sources for projects with mathematical and social
relevance. Australian Senior Mathematics Journal, 3, 69-82.
4. Watson, J.M. (1991). Exploring data from the AFL grand final. Australian
Senior Mathematics Journal, 5, 23-38.
5. Watson, J.M. (1991). Building probability models in a differential equations
course. International Journal of Mathematical Education in Science and
Technology, 22, 507-517.
6. Watson, J.M. (1992). Fishy statistics. Teaching Statistics, 14(3), 17-21.
Reprinted in D. Green (Ed.) (1994). Teaching Statistics at its Best (pp.
159-163). Sheffield: The Teaching Statistics Trust.
7. Watson, J.M. (1993). Pigs might fly!! Australian Mathematics Teacher, 49(2),
32-33.
8. Watson, J.M. (1993). Introducing the language of probability through the
media. In M. Stephens, A. Wayward, D. Clarke, & J. Izard (Eds.), Communicating
Mathematics - Perspectives from Current Research and Classroom Practice in
Australia (pp. 119-139). Melbourne: Australian Council for Educational Research.
9. Watson, J.M. (1994). Contexts for the consideration of number properties. In
H.L. Chick & J.M. Watson (Eds.), Mathematics and Teaching: Topics for the
Professional Development of Teachers (pp. 121-132). Adelaide: Australian
Association of Mathematics Teachers.
10. Watson, J.M. (1994). Using newspapers to motivate numeracy, chance and data.
In H.L. Chick & J.M. Watson (Eds.), Mathematics and Teaching: Topics for the
Professional Development of Teachers (pp. 142-149). Adelaide: Australian
Association of Mathematics Teachers.
11. Watson, J.M. (1994). Chance and data activities K-8. In H.L. Chick & J.M.
Watson (Eds.), Mathematics and Teaching: Topics for the Professional Development
of Teachers (pp. 242-250). Adelaide: Australian Association of Mathematics
Teachers.
12. Watson, J.M. (1995). Conditional probability: Its place in the mathematics
curriculum. Mathematics Teacher, 88, 12-17
13. Watson, J.M. (1996). What's the point? Australian Mathematics Teacher,
52(2), 40-43
14. Watson, J.M. (1995). Probability and statistics: An overview. In L. Grimison
& J. Pegg (Eds.), Teaching Secondary School Mathematics: Theory into Practice
(pp. 120-139). Sydney: Harcourt Brace.
15. Watson, J.M. (1995). Statistical literacy: A link between mathematics and
society. In A. Richards, G. Gillman, K. Milton, & J. Oliver (Eds.), Flair:
Forging links and integrating resources (pp. 12-28). Adelaide, SA: Australian
Association of Mathematics Teachers. [1995 Hanna Neumann Memorial Lecture]
Reprinted in Reflections, 20(3), 36-45, August, 1995.
16. Watson, J.M. (1997). Numeracy in negative numbers. Delta, 37 (2), 10-13.
17. Watson, J.M., & Chick, H.L. (1997). Irrational beliefs about numbers.
Australian Senior Mathematics Journal, 11(2), 4-13. (N) A1
18. Watson, J.M. (1998). Statistical literacy: What's the chance? Reflections,
23(1), 6-14. [Text of invited keynote to 1997 MANSW State conference]
19. Watson, J.M. (1997, April 19). Ockham's Razor. [ABC Radio Program]. [Script
available at http://www.abc.net.au/rn/science/ockham/or130497.htm]
20. Watson, J.M. (1997, September 15). Putting claims to class test. The Hobart
Mercury, p. 24.
21. Watson, J.M. (2000). Statistics in context. Mathematics Teacher, 93, 54-58.
22. Fenton, P., & Watson, J. (2001). Triangular numbers: Fact or fiction?
Australian Primary Mathematics Classroom, 6(1), 10-14.
23. Watson, J.M. (2002). When 2 + 2 ≠ 4 and 6 + 6 ≠ 12 in data and chance. New
England Mathematics Journal, 34(2), 56-68.
24. Watson, J.M. (2004). Quantitative literacy in the media: An arena for
problem solving. Australian Mathematics Teacher, 60(1), 34-40.
25. Watson, J.M., & Shaughnessy, J.M. (2004). Proportional reasoning: Lessons
from research in data and chance. Mathematics Teaching in the Middle School, 10,
104-109.
26. Watson, J. M. (1999). Lessons from chance and data research II: For the
classroom. In K. Baldwin & J. Roberts (Eds.), Mathematics – The next millennium
(Proceedings of the 17th Biennial Conference of the Australian Association of
Mathematics Teachers Inc., pp. 311-320). Adelaide, SA: AAMT.
27. Watson, J.M. (2002). Lessons from variation research II: For the classroom.
In M. Goos & T. Spencer (Eds.), Mathematics – making waves. (Proceedings of the
Nineteenth Biennial Conference of the Australian Association of Mathematics
Teachers Inc., Brisbane, pp. 424-432). Adelaide, SA: AAMT, Inc.
Contact me...
Faculty of Education
University of Tasmania
Private Bag 66 Hobart Tasmania Australia 7001
Phone: 61-3-6226-2570; Fax: 61-3-6226-2569
Jane.Watson@utas.edu.au