Reading tasks for logical-mathematical language learners
by Rolf Palmberg


Introduction and aim

We are not all the same. According to Howard Gardner, creator of the Multiple Intelligences (MI) Theory, we all have personal intelligence profiles that consist of combinations of eight or nine different intelligence types. An important message of the MI Theory is this: if education is to work as effectively as possible, teachers should take into account their learners’ MI profiles rather than ignore them (Gardner 1983, 1993).

The aim of the present paper is to give examples of reading tasks that are particularly attractive to logical-mathematical language learners. Such learners, according to Gardner’s MI Theory, are particularly fond of logical reasoning and numbers. They especially enjoy tasks that involve problem solving, finding patterns, categorising words and objects, completing brain teasers, and asking ‘why’ questions. The tasks presented below therefore go beyond what Neville Grant refers to as “plain sense reading”, i.e. the ability to understand what is stated in a text, or simply, the ability to “read the lines” (Grant 1987).

TASK ONE – jigsaw reading

The first task is based on the principle of jigsaw reading, but it has an additional twist. The teacher starts by pre-teaching (or revising) the most relevant vocabulary items in the sample text ‘The Window’ (taken from Berman 2008; see Appendix 1). Next, s/he divides the class into groups of three to four learners. Each group is given a copy of the text, which – just like a real jigsaw puzzle – has been cut into pieces (there are seven pieces, each constituting one of the first seven paragraphs – the last paragraph should not be handed out). The learners’ task is to arrange the paragraphs (marked A-F for reference purposes) into their correct order, and, within each group, to come up with a suitable ending to the story.

After each group has presented their ending of the story, the teacher reveals the correct order of the paragraphs (which is D-A-F-B-E-C-G) as well as the original ending (the missing eighth paragraph). If there is time, the learners are encouraged to discuss the moral of the story or to decide which group has the best ending.

TASK TWO – deductive reading

The second task requires learners to be able to draw inferences from a text, i.e. to “read between the lines” (Grant 1987). The teacher hands out a modified version of ‘Monologue 9’ (Mortimer 1980 p. 18; see Appendix 2), a text that was originally written to test learners’ listening comprehension ability. The learners’ task is to read through the text individually and answer twenty comprehension questions. It is a good idea to translate the questions into the learners’ mother tongue before handing them out. In doing so, the teacher can better judge whether the learners have in fact understood the text.

When the learners have answered the questions, they are asked to compare and discuss their answers in pairs or in groups of three or four.

TASK THREE – projective reading

As suggested by Grant, teachers should give learners ample opportunity to practise their projective reading skills, i.e. their ability to relate a text to their personal opinions, knowledge, imagination, and/or experience (Grant 1987). However, learners’ eagerness to “read beyond the lines” can sometimes go too far. The purpose of the third task is to show learners that there is a limit to the number of inferences to be drawn from their own experience when reading a text – things are not always what they appear to be.

The teacher hands out a text entitled ‘Have you been to Greece?’ (Palmberg 2009a, 2009b; see Appendix 3) and tells the learners to read through the text. They are asked to work individually and write down everything they know about Michael and also their first impression of him as a person. Having done that, they are invited to compare and discuss their facts and impressions in pairs.

Next, the teacher displays the following background information on an OH transparency:

“Michael has just returned from a week’s holiday in Hawaii. He never drinks alcohol, but in order to cope with the hot sun he had to drink lots of mineral water every day. He has visited Greece only once, when he was a little boy of three. The t-shirt he’s wearing is a gift from his sister who visited Greece some time ago.”

The learners are now asked to discuss any presumed facts that proved in fact to be false assumptions. How, in their opinion, could these misunderstandings have been avoided in the first place from a language and/or reader point-of-view?

TASK FOUR – reactive reading

The purpose of the fourth task is to keep learners alert while reading, i.e. to make them react. The task is based on a teaching idea suggested in Britten (1983) and this is how it works. The teacher takes a familiar text (one that has been introduced to the learners during an earlier lesson) and prepares a text version where all nouns have been deleted and replaced with one single (but irrelevant) word, e.g. ‘sausage’. The sentence ‘The man went into the forest and saw two birds’, taken from an imagined text, would thus read: ‘The sausage went into the sausage and saw two sausages.’

The learners’ task is to recreate the original text, either orally or in writing. If they like the activity (and most of them inevitably will), they can be challenged to prepare similar tasks at home (to be used later in class). The ‘sausage’ version of Britten’s idea was first presented in Palmberg and Palmqvist (1988) and further elaborated on in Palmberg (2009b).

TASK FIVE – combined deductive / projective reading

The fifth task is a blend of deductive and projective reading. The teacher displays five sentences on an OH transparency, one sentence at the time. After each displayed sentence, the learners are asked to write down a short answer to the question: ‘Who is Mary?’ Having done that, they are asked to share their thoughts in pairs.

1. Mary was on her way to school.
2. She was worried about the maths lesson.
3. Last week she couldn’t control the class.
4. It wasn’t fair of the maths teacher to leave class responsibility to her.
5. After all, it’s not part of a/n xxx’s duties to teach.

After the fifth (and final) sentence, learners have to guess Mary’s occupation. (She is a school secretary.)

‘Mary’s Puzzle’ originates from Sanford and Garrod’s book Understanding Written Language (1981); the suggested classroom method is from Blom, Linnankylä and Takala (1988). Since the five sentences in ‘Mary’s Puzzle’ are cleverly designed, most learners will no doubt revise their thinking several times during the task, which will, under favourable conditions, result to an intensive exchange of opinions (see also Palmberg 2009b).

References

Berman, M. (2008). “The Way of the Kabbalist”. http://www.hltmag.co.uk/jan08/sart01.doc.
Blom, L., P. Linnankylä & S. Takala (1988): Tekstien avaaminen luokassa. Jyväskylän yliopisto. Kasvatustieteiden tutkimuslaitoksen julkaisusarja B. Teoriaa ja käytäntöä.
Britten, N. (1983). “Reactive Reading”. Practical English Teaching 3:3 (34-35).
Gardner, H. (1983). Frames of mind. The theory of multiple intelligences. New York: Basic Books.
Gardner, H. (1993). Multiple intelligences. The theory in practice. New York: Basic Books.
Grant, N. (1987). Making the most of your Textbook. London & New York: Longman.
Mortimer, C. (1980). Dramatic Monologues for Listening Comprehension. Cambridge: Cambridge University Press.
Palmberg, R. (2009a). “The Greek T-shirt - facts vs. assumptions”. http://edition.tefl.net/ideas/reading-ideas/greek-t-shirt/.
Palmberg, R. (2009b). Activities and exercises for logical-mathematical learners of English. Karperö 2009: Palmsoft Publications. http://www.vasa.abo.fi/users/rpalmber/.
Palmberg, R. & O. Palmqvist (1988). ”Varying text revision”. Practical English Teaching 8:3 (35-36).

Biodata

Rolf Palmberg is a Senior Lecturer at the Department of Teacher Education at Åbo Akademi University in Vaasa, Finland, where he has taught EFL methodology since 1979. His publications comprise a number of books and papers mainly in the fields of applied linguistics and EFL methodology.
He is also the author of a range of CALL programs and Java applets, available at: http://www.vasa.abo.fi/users/rpalmber/download.htm His non-academic interests include geographical enclaves and tripoints.

APPENDIX 1

THE WINDOW

Two men, both seriously ill, occupied the same hospital room. One man was allowed to sit up in his bed for an hour each afternoon to help drain the fluid from his lungs. His bed was next to the room’s only window. The other man had to spend all his time flat on his back. The men talked for hours on end. They spoke of their wives and families, their homes, their jobs. And every afternoon when the man in the bed by the window could sit up, he would pass the time by describing to his roommate all the things he could see outside the window. [D]

The man in the other bed began to live for those one-hour periods where his world would be broadened and enlivened by all the activity and colour of the world outside. The window overlooked a park with a lovely lake. Ducks and swans played on the water while children sailed their model boats. Young lovers walked arm in arm amidst flowers of every colour of the rainbow. Grand old trees graced the landscape, and a fine view of the city skyline could be seen in the distance. [A]

As the man by the window described all this in exquisite detail, the man on the other side of the room would close his eyes and imagine the picturesque scene. One warm afternoon the man by the window described a parade passing by. Although the other man couldn’t hear the band – he could see it in his mind's eye as the gentleman by the window portrayed it with descriptive words. Then unexpectedly, a sinister thought entered his mind. Why should the other man alone experience all the pleasures of seeing everything while he himself never got to see anything? It didn't seem fair. [F]

At first thought the man felt ashamed. But as the days passed and he missed seeing more sights, his envy eroded into resentment and soon turned him sour. He began to brood and he found himself unable to sleep. He should be by that window - that thought, and only that thought now controlled his life. [B]

Late one night as he lay staring at the ceiling, the man by the window began to cough. He was choking on the fluid in his lungs. The other man watched in the dimly lit room as the struggling man by the window groped for the button to call for help. [E]

Listening from across the room he never moved, never pushed his own button which would have brought the nurse running in. In less than five minutes the coughing and choking stopped, along with that the sound of breathing. Now there was only silence - deathly silence. [C]

The following morning the day nurse arrived to bring water for their baths. When she found the lifeless body of the man by the window, she was saddened and called the hospital attendants to take it away. As soon as it seemed appropriate, the other man asked if he could be moved next to the window. The nurse was happy to make the switch, and after making sure he was comfortable, she left him alone. Slowly, painfully, he propped himself up on one elbow to take his first look at the world outside. Finally, he would have the joy of seeing it all himself. He strained to slowly turn to look out the window beside the bed. [G]

It faced a blank wall! The man asked the nurse what could have compelled his deceased roommate who had described such wonderful things outside this window. The nurse responded that the man was blind and could not even see the wall. She said, ‘Perhaps he just wanted to encourage you’.

APPENDIX 2

MONOLOGUE 9

Frank thought he was just ordinary. His face was ordinary. So were his clothes. Not like the man sitting next to him. There was something odd about his mouth. He tried not to catch his eye. He might start a conversation. Interesting that he was just in front of him in the queue. They looked in his bags and pockets – even made him remove his shoes. Now people were starting to get their blankets down. He guessed everything would be quiet in an hour. Then he would act. They had looked in his briefcase too. But they didn’t find anything. He put his hand into his pocket. Marvellous how small they can make them these days, he thought. If he were sitting in funny mouth’s seat, he could probably look down and see the mountains gleaming in the moonlight. He smiled to himself. Then he went over his speech again. He must not forget what his demands were.

Questions (modified)

      1.   Where does this take place?
      2.   What time of day is it?
      3.   What word does Frank think best describes him?
      4.   ‘There was something odd about his mouth.’ Who does the word ‘his’ refer to?
      5.   ‘He tried not to catch his eye.’ Who is ‘he’?
      6.   ‘He might start a conversation.’ Who is ‘he’?
      7.   ‘… he was just in front of him in the queue.’ What is the ‘queue’ referred to in the text?
      8.   ‘They looked in his bags ...’ Who are ‘they’?
      9.   ‘They looked in his bags ...’ Who does the word ‘his’ refer to?
    10.   ‘… even made him remove his shoes.’ Explain this remark.
    11.   ‘… people were starting to get their blankets down.’ What were they planning to do?
    12.   ‘Then he would act.’ What does Frank intend to do?
    13.   ‘They had looked in his briefcase too.’ Who does the word ‘his’ refer to?
    14.   ‘But they didn’t find anything.’ Explain this remark.
    15.   ‘He put his hand into his pocket.’ Why does Frank do so?
    16.   ‘Marvellous how small they can make them these days.’ Who are ‘they’?
    17.   ‘Marvellous how small they can make them these days.’ Who or what does the word ‘them’ refer to?
    18.   Who is ’funny mouth’?
    19.   ‘Then he went over his speech again.’ What is the ‘speech’ referred to in the text?
    20.   ‘He must not forget what his demands were.’ What are the ‘demands’ referred to in the text?

Answers (modified)

      1.   In a plane.
      2.   Late evening or night.
      3.   Ordinary.
      4.   The man sitting next to Frank.
      5.   Frank.
      6.   The man sitting next to Frank.
      7.   The queue for the security control at the airport.
      8.   Airport security guards.
      9.   The man sitting next to Frank.
    10.   The security guards also checked the man’s shoes.
    11.   They were getting ready to go to sleep.
    12.   Hijack the plane.
    13.   Frank.
    14.   The security guards found nothing prohibited or suspicious.
    15.   He checked that his weapon was still in his pocket.
    16.   Arms manufacturers.
    17.   The type of weapon that Frank had.
    18.   The man sitting next to Frank.
    19.   What he was going to say to the air personnel.
    20.   The sum of money he planned to demand from the airline company.

APPENDIX 3
 
HAVE YOU BEEN TO GREECE?

It is December. Michael is standing in the arrival hall at Helsinki airport, tanned and relaxed. He is wearing a white T-shirt with a red text saying Kos, Greece. Peter, an old friend from long ago, sees him and walks up to him.

“Hi, Michael. Have you been to Greece?”
“Yes, I have.”
“How was it?”
“To be honest, I can hardly remember anything at all.”
“You must remember something. What was the weather like?”
“It was raining non-stop every day.”
“Then how can you be so tanned?”
“I spent five or six hours in the sun every day last week.”
“Have you had a lot to drink lately?”
“Indeed I have. Several litres every day.”

Peter shakes his head and walks away.

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