Levels of Headings

There are three levels of headings:

1. Centred, Upper and Lower Case, not Italics, Bold.

2. Not Indented, Upper and Lower Case, Italics, not Bold. (Text does not run on from heading.)

3. Indented 6 (begin typing on 7th), first letter of first word upper case, remainder lower case, italics, not bold. If heading continues to next line, then this is not indented. Text runs on from heading.

Sequencing

1. Where brief categories or points are described, use a colon followed by (a) with text following . . . ; (b) . . . ; and (c) . . . . Text is "run on"--not a new line for each point.

2. Where paragraphs are needed to make points, then use setting out as in this description of sequencing. (Indent 6, type numeral on 7th, followed by a period.

Quotations

In-text quotations. Use double quotation marks, and at the completion of the quotation, the closing quotation mark comes after a full stop or comma (except if the reference is given in brackets, in which case the quotation marks come before the first bracket). For example: In other research he has demonstrated that "children come to school already knowing a lot about one-half" (Hunting, 1987, p. 46).

Display quotations. (To be used for quotations containing 40 words or more) In this case, no quotation marks are used, and the display quote is indented 7 throughout. Normally, it is introduced by saying something like:

Hunting (1987) has asserted:

In schools in Victoria and the United States of America . . . (at least 40 words; use one-and-a-half-spacing)

Immediately after the quotation, the page number(s) are given in brackets, e.g. . . . knowing a lot about one-half. (p. 46) Note that the full stop closing the quotation is given before the page reference.

Display quotations should not be right justified. (The (1989) book edited by Nerida Ellerton and Ken Clements, entitled School mathematics: The challenge to change, and published by Deakin University does have right justification for display quotes--it does not follow APA on that point.) Normally, display quotations should be used sparingly, although Higginson in Chapter 1 of School mathematics: The challenge to change uses them extensively to good effect. Observe, for example, how he has presented the excerpt from C.S. Lewis on p. 8.

When you omit words in a quotation use exactly 3 dots (not .. or .... etc.). You should only omit words from a quotation if the meaning intended by the original author is maintained.

Captions. These should be beneath the Figure, and centred. The word "Figure" should be in italics, followed by the Figure number and a period; then a brief expression describing the Figure should be given (with the first letter of the first word in upper case, the other letters in lower case, except for proper names); a period should be placed at the end. For example:

Figure 5. Conceptual scheme for instruction on rational numbers.

Captions. These should be above the Table, and flush on the margin (i.e., not centred). The word "Table" should be in ordinary Roman print (not italics), followed by the table number.; on the next line a brief expression describing the Table should be given (with the first letter of main words in upper case, and the whole caption in italics; there is no period at the end of the caption

For example:

Table 5

Modes of Communication in the Classroom (From Del Campo and Clements, 1987, p. 12)

The table itself. Tables should never have vertical lines. But the use of horizontal lines is encouraged. Do not use upper case typing for words in the Table, except for first letters.

Your 1996 assignment tasks in EDGS 646 ask you to use APA style in your written presentations. Perhaps your best guide to the style is to found in the Mathematics Education Research Journal (published by the Mathematics Education Research Group of Australasia) and in a book which Nerida Ellerton and Ken Clements edited, School mathematics: The challenge to change. Most of the chapters in that book are very close to APA.

Note, however, that it is not easy to learn the style--the American Psychological Association's style manual is over 200 pages long, and even those experienced in the use of APA style sometimes cannot remember all the details. So, in order to assist you with the task I've prepared the following brief summary of important aspects of APA style.

l. Paragraphing--indent the first word 6 spaces (type on seventh). It is a good idea to use a tab on your word processor.

2. List of authors in text--alphabetical ordering not chronological. (e.g see bottom of p. 67 of School mathematics: The challenge to change).

3. Headings and subheadings. Note that throughout the book School mathematics: The challenge to change three different levels of headings have been employed. Examples of these can be found on page 108 of the book. (Line 28 is a main heading, line 29 is a major side heading, and line 3 is a minor side heading. With minor side headings, the text "runs on.")

4. Notice how Table and Figure captions are presented (see p.178 and p.180, respectively, of School mathematics: The challenge to change).

5. Notice how ." is used (and not ".) at the end of line 3 on page 52 of School mathematics: The challenge to change. Generally speaking, note that ," (and .") not ", (and ".) are used. However, for other punctuations the inverted commas precede the punctuation mark (for example "; and ": and "?).

If, however, a reference is given after an in-text quotation, then the quotation marks are followed by the bracketed reference(s) and then by the comma, full-stop or other punctuation mark. For example, you might have:

As one writer has claimed, the period from 1900 to 1905 witnessed "some remarkable reforms in both primary and secondary education in Victoria" (Clements, 1989, p. 36).

6. Sometimes, in citing joint authors, you use the word "and" and sometimes you use "&." You would write "White and Jones (l984, p. l7) have claimed that ...," but if, after making some point, you wanted to use the White and Jones reference to support what you've said, you'd put (White & Jones, l984, p. l7). Notice in the first case "and" separates White, Jones, whereas in the second case "&" does.

7. Tables should never contain vertical lines as column dividers.

8. The reference list should be placed at the end of your assignment, and should provide details of all books, papers, theses, etc., to which reference has been made in the text (and only these). The reference list should be preceded by the centred, major heading: References, and should not be called a bibliography.

9. Note that in School mathematics: The challenge to change Ellerton and Clements made at least one mistake in trying to achieve true APA style--Throughout the lists of references they did not insert a space after an author's initials. One should write, for example, Ellerton, N. F., & Clements, M. A. (1991) and not Ellerton, N.F., & Clements, M.A.(1991).

Some examples of how you should set out references in APA style are now given. Please pay particular attention to (a) the position of every comma, full stop, and colon; (b) where spaces are placed; (c) whether letters are upper case or lower case; (d) when and how page references are given; (e) the use of "&" rather than "and"; (f) the fact that the place of publication is placed before the name of the publisher; (g) what is in italics and what is not.

Casey, D. P. (1979). An analysis of errors made by junior secondary pupils on written mathematical tasks. Unpublished M.Ed. thesis, Monash University.

Harris, P. (1989). Contexts for change in cross-cultural classrooms. In N. F. Ellerton & M. A. Clements (Eds.), School mathematics: The challenge to change (pp. 79-96). Geelong: Deakin University.

Hunting, R. P. (1981). The role of discrete quantity partition knowledge in the child's construction of fractional number (Doctoral dissertation, University of Georgia, 1980). Dissertation Abstracts International, 41, 4380A-4381A (University Microfilms No. 81-07919).

Kidric, M., & Galvin, B. (1989). Having fun with story book maths at Wonga Park Primary School. Prime Number, 4 (1), 3-5.

Lean, G. A., Clements, M. A., & Del Campo, G. (in press). Linguistic and pedagogical factors affecting children's understanding of arithmetic word problems. Educational Studies in Mathematics.

McCauley, C. (1989). Teachers may be retrained to teach maths. Age, 17 January, p. 37.

Victorian Ministry of Education (1988). The mathematics framework P-10. Melbourne: Ministry of Education (Schools Division).

von Glasersfeld, E. (1988, July). Environment and communication. Paper presented at the Sixth International Congress on Mathematical Education, Budapest.

Wheatley, G. H., & Bebout, H. (1990). Mathematical knowledge of young learners. In L. P. Steffe & T. Wood (Eds.), Transforming children's mathematics education: International perspectives (pp. 107-111). Hillsdale, NJ: Lawrence Erlbaum.

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© 1996: The University of Newcastle: Faculty of Education

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