MATHS300: How To Write A Maths Report

MATHS300

Learning to Write a Maths Report

Lesson Plan

Each MATHS300 lesson serves two purposes. On the one hand it is a professional development experience offering opportunity to try something new, hopefully in conjunction with your staff, in the knowledge that the notes record the successful experiences of your colleagues elsewhere. On the other hand it is a well trialed lesson plan which provides clear information about 'what to do in maths tomorrow'.

Years: K - 12

Time: 1 - 2 lessons

This lesson is used after students have explored the 'iceberg' of a problem and have related it to the Working Mathematically process. Some Schools use this as a poster displayed in the classroom. Others ask students to paste it to the inside cover of their maths journal.

The lesson can be adapted to any year level. It can also be used following any problem solving investigation. You may like to first use this lesson plan by putting it in the context of Maths300 Lesson 17, Eric The Sheep.

Readers who do not have access to Maths300 can find teachers' notes about Eric the Sheep at:
http://www.blackdouglas.com.au/taskcentre/iceberg.htm

Publishing in the depth described would not necessarily follow every investigation. Consider perhaps two or three times per year as a class, and three or four times as a personal requirement in middle school years.

In this text, the lesson is embedded in the story shell used by one teacher who related it to exploring the Mathematics Task Centre Home Base web site. Such a story line suggests a reason for the students to learn to write for an external audience. Other teachers may not be in a position to use the lesson exactly as here, but the story shell is readily modified. Perhaps:

contacting another school by fax or letter

writing for the school newsletter

linking to mathematical history and adopting the approach of writing to a friend or colleague as did the mathematicians of earlier centuries.

Web-based student problem solving teams offer another reason for writing mathematics. Several schools have set up such opportunities, and in some cases this has been a consequence of using common materials from the Task Centre Project.

Preparation

You will need:

quantities of paper for drafting; half page pieces (A5) work well
large poster (butcher's) paper - optional

Introduction

After class yesterday I was telling one of the other teachers how pleased I was with the way we worked on ... . She told me there is a home page for problem solving on the World Wide Web, so I looked it up last night.

Write up the address of the Task Centre Home Base the board, viz:
www.blackdouglas.com.au/taskcentre

You might like to look this up at home. You click on the logo to start and then one of the links is called Iceberg Information. Our problem wasn't there, so, since you did so well with it I thought we could plan a report today and submit it for others to use after we write it up.

Addressing the Audience

Ask students what they think someone on the other end of a computer link would need to know about 'our problem'? Make a blackboard list of responses which are likely to include such things as:
- what it's about
- the answer
- how we got it
- what else we found out
Accept all suggestions and encourage respect for the contributions of others.

Great. Now could you think of some headings which would help us organise what we will write? A heading should be just three or four words which clearly tell you the sort of things which will be in the section.

Accept suggestions which approximate your version of the following main stages:
- The Problem
- What We Did
- What We Found Out
- New Problems

Preparing the Text

OK, let's deal with these one at a time. What are the important parts of the problem which we will need to repeat for our internet contacts?

Develop a blackboard list.

Now I'll give you a couple of minutes to write out your personal version of the problem - just the problem, not its solution. We'll choose one to be uploaded onto the home page.

To select the wording to be used, group the students in sixes and ask them to select the version from their group which they think is most clearly constructed. The emphasis is on consensus and justification rather than competition. That will leave about four or five submissions, depending on class size, from which the final selection can be made later.

Now what shall we write about what we did?

Put the heading on the board, discuss the types of things which could be found under this heading, and list points made by the students.

Some teachers use butchers' paper charts in this planning phase.

Encourage judgement about what is relevant and what is irrelevant information to include, eg:

Is it important that another class realises that the our problem can be acted out?

Is it important to know which person played which part?

Also encourage the use of language from the Working Mathematically process. Phrases like:
- collecting and organising data
- seeking and seeing patterns
- acting out to solve the problem and making a table
- making and testing hypotheses
are likely to be important.

Team Work

Now let's try to work together to compose some proper sentences which capture all this information. Angela could you think of a sentence which would start us off?

Continue publicly building up a paragraph or two in this way as a composite of the students' suggestions.
(Since this will have to be taken away from the current classroom to be typed up as a computer file, the idea of using charts seems sensible. Alternatively, someone can be chosen as scribe.)
As the construction of the text continues, it may also become apparent that it is not always possible to usefully separate What We Did from What We Found Out. Personal writing style preference can also play a part here. It is important to acknowledge and value potential differences while emphasising the key elements which need to be present regardless of the individual style applied.

This seems like a good paragraph to us, but perhaps we know the problem too well. How could we test our writing to see if it is clear enough?

Asking this question is an opportunity to encourage students to:
1. Re-read their work as if they were on the receiving end of the computer. Would they really be interested in this problem if these words were their first introduction to it?
2. Ask an 'outsider' to comment on their writing before submitting it. Perhaps a colleague could be invited to check the writing.

Enacting the Learning

The next steps are What We Found Out and New Problems sections. Again write the headings and record students' suggestions as to what should be included under each one. However this time, following class discussion, ask the students to individually prepare a piece of writing for these sections; perhaps as homework. Collecting these will not only provide 'entries' for the home page submission, but will provide feedback on the learning which has occurred and may provide direction for the next lesson.
Arrange a process for considering submissions and selecting for the various parts of the final report. 'Splice' these and display the text for final consideration.
Discuss the possibility of adding photographs, scans, drawings or sample student work to enhance and illustrate the text.
Make it clear that you have worked on this report as a team to prepare students for writing their own problem solving reports in the future.
At this point you might consider showing an Eric The Sheep report as a Power Point presentation. This version is from Heath, Rainer, Nathan and Tom of Ivanhoe Grammar School, Melbourne. Certainly it is part of the process of Working Mathematically to publish problem solving reports, but it is also part of the curriculum to learn to publish in a variety of formats. Smarter teaching combines these requirements and leads to achieving several learning objectives simultaneously.

Note
The PP presentation may show automatically in your browser. If not, right click, save to your computer and open from there.
Summarise the lesson by asking students what they think are the key points to consider when preparing a good report. Record these and later duplicate them for the students to insert in their problem solving journals.
As soon as possible after this lesson, publish the class report in line with the story shell situation in which you first developed it.

Notes

The alternative to integrated use of 'learning to write lessons' into the maths curriculum seems to be requests such as Write me a report of what you have done. Without modelling in a manner similar to that above, why should we expect any response other than ones such as We did the Eric The Sheep problem and it was fun and I liked it.
As for any learning experience it is unlikely that one 'modelling' lesson will be sufficient for all students to value the key points. However, it was the experience of trial teachers that even one lesson of this sort lifted the quality of the written reports.
Some faculties plan this type of lesson into the early parts of their problem solving program at every year level to encourage a growing sophistication in the writing. In systems where senior secondary students are expected to prepare substantial assignment work for external assessment, such planned skill development, which can begin in primary school, serves the senior students well.
Maths300 has a world-wide audience, so your story shell might be to write for the Classroom Contributions section of any lesson on this site. Many lessons have submissions already, but not many have submissions from students. Material can be sent to by email to Doug Williams for consideration.

email: Doug.Williams@curriculum.edu.au