Learning to Write a Maths Report
This lesson is used after students have explored the 'iceberg' of a problem and related it to the Working Mathematically process.
How have we worked like a mathematician today?
The lesson can be adapted to any year level. It can also be used following any problem solving investigation. For the purpose of the lesson plan it is assumed that the students have explored Task 45, Eric The Sheep as a whole class investigation.
Publishing in the depth described does not 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. For thoughts about assessment strategies appropriate for evaluating such projects, see the Assessment section of Mathematics Task Centre.
St. Edmund's Junior School, UK, Year 5
The lesson plan is embedded in the story shell used by one teacher who related it to the possibility that someone's report could be submitted to the Publishing section of the Mathematics Task Centre web site. Such a story line suggests a reason for the students to learn to write for an external audience. Other possible story shells are:
- 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. The wide distribution of tasks in schools around the world makes this possible. Schools in Sweden and Australia will not be using exactly the same text book, but they will be using exactly the same task.
You will need:
- quantities of paper for drafting - half page pieces (A5) work well
- large poster/butchers' paper - optional
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 Web, so I looked it up last night.
If you have an electronic white board you could show the Publishing link live.
Our problem wasn't there and since you did so well
with it, I thought we could plan a report today and submit it for other teachers and kids to see what you can do.
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:
Accept all suggestions and encourage respect for the contributions of others.
- what it's about
- the answer
- how we got it
- what else we found out
Great. Now could you think of some headings that will help us organise
what we write? A heading should be just three or four words which clearly tell you
the sort of things in the section.
Accept suggestions which approximate your version of the following main
- 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 we will need to repeat for our audience?
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 submitted to the web.
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. The result will be four or five submissions, depending on class size, from which the final selection
can be made later (perhaps by someone neutral like the Principal).
Now what shall we write about what we did?
- Put the heading on the board, discuss the types of things which should be found
under this heading. Again, list points made by the students.
- Instead of the board you might use butchers' paper at this point.
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
Is it important to know which person played which part?
Also encourage the use of language from the Working Mathematically process. Phrases like:
are likely to be important.
collecting and organising data
- seeking and seeing patterns
- acting out to solve the
problem and making a table
- making and testing hypotheses
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 butchers' paper 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:
- 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?
- 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 the 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 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.
- 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.
- 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 teachers have noticed that even one lesson of this sort lifts 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.