Learning to Write a Maths Report

Learning to write a maths is important because it's part of a mathematician's work.

Working Mathematically begins with an interesting problem. Mathematicians investigate the chosen problem (perhaps over years) and report on the investigation to their peers. Others interested in the problem can then build on what is already known.

Learning how to report has to be taught. Without a model, student response to the expectation of a report is often along the lines of We did this and this ... and it was fun..

The model described below is used after the class has explored the 'iceberg' of a problem, made journal notes as the investigation proceeded and reviewed their work against the Working Mathematically process.

How have we worked like a mathematician?

The model is a lesson in itself, not 'squeezed in at the end' of the investigation lesson. It can be adapted to any year level and any investigation. In the photo, the class is involved in the whole class investigation of Task 45, Eric The Sheep.


St. Edmund's Junior School, UK, Year 5

Publishing in the depth described does not need to follow every investigation. Consider perhaps two or three times per year as a class and additional times as a personal requirement. For thoughts about assessment strategies appropriate for evaluating such projects, see the Assessment section of Mathematics Task Centre.

Green Line

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 to create an external audience are:
  • contacting another school working on investigations and exchanging documents, slides, videos to assist each other,
  • linking to mathematical history and adopting the approach of writing to a friend or colleague as did the mathematicians of earlier centuries,
  • writing for the school newsletter / web site.

Web-based student problem solving teams from different schools are 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 can be using exactly the same task. However time zone and seasonal differences between countries this far apart limit the time available for exchange. For example when Aussie students are expected to be deep into learning in Terms 2 and 3, their Swedish peers are heading to the beach - and vice versa.

Preparation

You will need:
  • quantities of paper for drafting - half page pieces (A5) work well
  • large poster/butchers' paper - optional - and markers

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 web, so I looked it up last night.
Show the Mathematics Centre Publishing section as evidence that it does present student reports.
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 board 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 headings that will help us organise what we write? A heading should be just three or four words which tell you the sort of things 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
OK, let's deal with these one at a time.

Preparing the Text

The Problem
What are the important parts of the problem we will need to repeat for our audience?
  • Develop a list and with student help create a restatement of the problem.
Put the name of our task at the top of your paper and copy this statement of the problem underneath it.
What We Did
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 and again list the students' ideas.
  • Instead of the board you might use butchers' paper at this point.

  • Encourage judgement about what is relevant and 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.

Butcher's paper in a secondary school report writing lesson about Task 147, Garden Beds.
(Maths No Fear, N. T.)

Team Work

Now let's work together to compose some proper sentences which capture all this information.
Angela could you think of a sentence that would start us off?
  • Continue publicly building up a paragraph or two in this way as a composite of the students' suggestions.
  • Suggest including drawings, photographs, graphs from their own journal notes about the investigation.
Now I'll give you time to write your personal version of what we did. You can start with these paragraphs if you want to.

Enacting the Learning

What We Found Out and New Problems
  • Write the headings and briefly record students' suggestions (note form only) for their content.
  • Guided by these notes and their own journal records, students continue with their own version of the report as time permits.
  • As the lesson draws to a close set the expectation to complete the personal report so it can be considered for submission to the web site.
Okay, in this lesson you have been creating a report about our investigation.
We all have the same statement of the problem.
We all had the chance to start What We Did with the same paragraphs and finish it our way.
And we could all use the ideas on the board for the other two sections.
I want you to finish your report and submit it by ...
I'm excited to have a look at them all and then we'll decide which one to select to send to the web site.
  • Collecting these will not only provide 'entries' for the submission, but will provide feedback on the learning and may provide direction for the next lesson.
  • Arrange a process for considering submissions. One way is to get a neutral colleague (perhaps the Principal or an English teacher) to select 5 possibilities. These are then displayed in the classroom and students vote for the one to submit.
If you think this plan is a literacy lesson, you are correct.
Report writing will be included in your school's literacy curriculum in some way.
  • Primary teachers have the opportunity to simultaneously achieve objectives in two major subject areas.
  • Secondary teachers have the opportunity to open a conversation with their language teaching colleagues.
  • As the suggested below, the conversation could also include the digital technology teachers.
Yes it takes time to teach this lesson, perhaps more than one period, and you will have to model more than once, both to consolidate the learning and to confirm that you really do value what you are expecting as the outcome. So make the time ... if you think outcomes like the ones below and others in the Publishing link are worth it.

Next Report Writing Lesson

  • Review the previous lesson by asking students for the key points to consider when preparing a report. Record these and later duplicate them for the students to insert in their problem solving journals.
  • It is part of the process of Working Mathematically to publish problem solving reports, but it is also part of the wider curriculum to learn to publish in a variety of formats. Smarter teaching combines these requirements and leads to achieving several learning objectives simultaneously.
    Suggest that written text is not the only way to present a report. Show examples such as:
    • Eric The Sheep Power Point report. Its authors are Heath, Rainer, Nathan and Tom of Ivanhoe Grammar School, Melbourne.
    • Or a video from our Cube Tube channel.
      Short examples are: Cars In A Garage, Changing The Triangle, Hearts & Loops, Truth Tiles 2, Yellow to Blue
    • Or other examples of written reports, posters, and slide shows from various year levels in our Publishing section.

Notes

  • The alternative to integrated use of 'learning to write' lessons in 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. The posters mentioned above in the Publishing link are examples from the first month of Year 7 in one secondary school. 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.

Follow this link to Mathematics Task Centre home page.