Using newspapers as a resource for challenging activities

Helen J. Forgasz, La Trobe University

Introduction

Problem solving, problem posing, and mathematical investigations - both individually and collaboratively - have been promoted in recent Australian mathematics curriculum statements and policy documents. As part of the mathematics program, teachers have been encouraged to present ‘real world’ problems situated in contexts that are familiar to students. This perspective was reinforced by the Australian Association of Mathematics Teachers (AAMT, 1996):

Finding stimulating and challenging examples is not always easy. The daily newspaper is a readily accessible, frequently overlooked, resource.

In A mathematician reads the newspaper, Paulos (1995) maintained that newspapers should ‘enhance our role as citizens and not reduce it to that of consumers and voyeurs’ (p.3). An unappreciated way in which newspapers can fulfil that responsibility ‘is by knowledgeably reflecting the increasing mathematical complexity of our society in its many quantitative, probabilistic, and dynamic facets’ (Paulos, 1995, p.3). As well as broadening students’ perspectives on the applicability of mathematics in their everyday lives, activities based on daily events reported in the press have the potential to stimulate curiosity, tap mathematical creativity, reinforce mathematical knowledge, and foster communication and presentation skills. However, newspaper articles need to be suitably chosen. In devising mathematical activities, the mathematical backgrounds and interests of students need to be considered.

In this paper, suggestions for selecting and appropriately using suitable newspaper articles to promote mathematical thinking are discussed. Sample questions based on selected offerings are provided. Examples include some activities for individual work; others appear to lend themselves better to paired or cooperative small-group settings.

Selecting articles - devising activities

Newspaper articles are often well suited to an integrated curricular approach. That is, the same article could be used as stimulus material for a problem or investigation in history, geography and/or science as well as mathematics. From time to time, and when possible, an interdisciplinary activity should be considered. An indirect outcome of such endeavours would be to challenge the perception, often developed by children, that knowledge is compartmentalized into distinct non-overlapping domains.

Considerations for selecting articles on which to base activities

I have written previously of the need for students to be ‘exposed to a variety of worthwhile mathematical activities set in a range of different contextual settings’ (Forgasz, 1995, p.399). It is important that mathematics be perceived as an ‘inclusive’ discipline. To promote this perception it was suggested that the contextual settings of activities reflect gender balance, not gender neutrality, and that ‘consideration should be given to the needs, interests and sensitivities of all students’ (p.399). Some students (often boys) react negatively to activities that do not interest them. Teachers should not be taken in by this behaviour. Intervention is needed to minimize such reactions and their consequent effects.

The following considerations should help in the search for suitable newspaper articles that cater for the interests of all students:

knowledge of students’ personal interests;

significant happenings in the community, for example, Olympic games, census data, school/other elections;

curricular content areas that might be linked meaningfully, or that may require reinforcement.

Once an article has been chosen (or brought to the attention of the teacher), a worthwhile mathematical activity that promotes mathematical thinking needs to be devised.

Promoting mathematical thinking; using and assessing activities

Challenging mathematical tasks have often been part of the mathematics teacher’s repertoire. However, the ways in which they have been included in the teaching program, and the importance attached to them, are what teachers are being asked to question and change. ‘Problem solving’ has sometimes been presented as a standalone unit; puzzles and challenging tasks have been given to students who finish routine work quickly, or as homework assignments. Students often do not consider these activities to constitute ‘real maths’ which they understand to be routine ‘drill and practice’ exercises from the textbook (the chalkboard or worksheets) and ‘formal tests’. Integrating challenging mathematical activities across content areas (strands) and validating them (including assessment) as worthwhile, serious components of a mathematics education, appear to conform to the spirit and directions envisaged in more contemporary Australian curricular documents.

There are many kinds of challenging mathematical activities: for example, problem solving, problem posing, investigations, and extensions to routine skills-based tasks. The aims of activities can also vary: for example, to introduce topics or skills, to reinforce knowledge, to demonstrate applicability, or to provide alternative perspectives. Newspaper articles on which to base one or many of these types of activity can be found.

Students will be attuned to the importance teachers attach to challenging activities, and their efforts will often conform to perceptions. For example, activities are unlikely to be taken seriously if they are tacked on to the end of a topic, if the products are given only a cursory glance, of if they are never assessed. When activities are considered worthwhile, mainstream mathematical pursuits in the classroom, students will respond accordingly. Their efforts can amaze. The final product of challenging tasks and the presentation of students’ work can take many forms, such as, individual reports, a group report (including some form of accountability for member inputs), verbal reports to the class, class debates, or a combination of these.

In the next section, sample activities based on three newspaper articles are presented. The motives underlying their selection, and a range of other potential activities stemming from them, are suggested.

Article 1

The ‘Odd Spot’ in the Age on 26 December, 1995 (p.1) read:

This short newspaper clipping might serve myriad purposes and be used by teachers in various ways. Examples serving as an introduction to the topic, estimation, are as follows:

How did the children reach this figure?

What would they need to have known to get an answer?

What assumptions might they have made?

Estimate how many books there are in the school library.

Estimate how many red cars there are in Victoria.

Estimate how many registered cats there are in Melbourne.

Article 2

1996 was an Olympic year and an activity based on world record times seemed appropriate. The graphic shown in Figure 1 appeared in the Age Good Weekend (13 January 1996, p.20), accompanying an article about Alexander Popov. It presented numerous possibilities for activities based on curricular content at different grade levels, using different mathematical tools (some dependent on availability), skills and knowledge bases.

Activities (and extensions) based on the information shown in Figure 1 are suggested below.

Selected world record times for the men’s 100 m freestyle are represented on Figure 1.

Suggested points to discuss with the class:

Before beginning an activity, brainstorm opinions, and discuss the factors that might have contributed to the improved times for the 100 m swim over the years.

When students have completed one of the suggested activities (or a teacher-devised activity), a discussion of the portrayal of the world record times in the diagram might follow. Ask students to consider if the diagram is deceptive in any way.

Suggested activities

Mensuration

1. (a) Calculate the average speeds for each of the swimmers in (and ).

(b) If all the swimmers were in the same race, how far behind the winner would each of the other swimmers be when Popov completed the 100 m?

Modelling (graphing, using a spreadsheet)

2. (a) Use a spreadsheet to plot a graph of the world record times (y-axis) against the year (x-axis). Find the equation of the curve of best fit (up to Year 8, I would suggest ‘the equation of the straight line of best fit’).

(b) Use the model to predict what the 100 m world record was in:

(i) 1800 (ii) 1500 (iii) the year 0

(c) Use the model to predict what the world record will be in:

(i) 2000 (ii) 2300

(d) What can you say about the limitations of this model?

(e) How could the model be improved?

Possible extensions (or alternative activities)

It has been said that world record times for the women’s 100 m freestyle have improved at a greater rate than for the men’s 100 m freestyle. Investigate. What are the implications of the findings?

The Excel spreadsheet, graph and line of ‘best fit’ for the men’s 100 m freestyle as represented in the graphic from the Age are shown below (Figure 2):

 

For younger students who may not yet have encountered linear graphs, the mensuration activity may be more appropriate. If a spreadsheet program is not available for the modelling activity, ‘traditional’ graphs could be plotted, lines of ‘best fit’ approximated, and the data extrapolated to answer the suggested questions. Creative teachers and curious students will undoubtedly present a range of alternative, challenging activities based on the same data.

Article 3

A regular daily feature of the Age is the weather information section (see Figure 3). The data included on the page have enormous potential for many inter-disciplinary activities (science and geography, in particular) as well as many mathematical investigations. Collection of a sequence of these pages - daily for a month - will provide sufficient data for trends (and some cycles) to emerge.

Based on the data from a sequence of weather pages, structured or more open investigations can be devised. Examples are suggested on page 13:

From data gathered for one month: Structured activity: The sun and the moon (and planets)

From the data for one month:

Open investigations (with written and oral reports)

1. Working in pairs, select an aspect of the weather information page that interests you (for example, tidal movements; daily temperatures in Melbourne and/or around the world; times at which the sun, moon and/or planets rise and set). Investigate the data for the month. Present your findings on a single sheet of cardboard (more instructions may be required here). Be prepared to discuss your findings, and how you arrived at them, in a five-minute class presentation.
2. If a picnic were planned during the month for which you have data, what would be the most likely prediction for the day’s weather? Write a script for a radio broadcast of the day’s weather report. Be prepared to show (in written form) how you reached your conclusions and to explain your findings in a five-minute class presentation.

Some general tips and recommendations

Not every activity devised from newspaper articles will be totally successful. For each activity developed:

monitor and judge the curricular relevance and the educational outcomes;

get feedback about students’ enjoyment of the activity and what they learnt from it;

ditch disasters. Consider modifying less successful aspects of other activities;

although an excellent store of activities will be built up over time, make a point of using a current/recent newspaper article regularly.

Final words

To avoid classroom boredom and to promote critical, analytical mathematical thinking, variety in the mathematics classroom is essential. Lessons based on newspaper articles have the potential to fulfil a number of goals of contemporary mathematics curricula. They should form one of a number of teaching strategies at the disposal of the competent, confident teacher.

References