Making logical-mathematical EFL learners talk
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 different intelligence types, i.e. verbal-linguistic, logical-mathematical, visual-spatial, bodily-kinaesthetic, musical-rhythmic, intrapersonal, interpersonal, naturalist, and, possibly, existentialist intelligence (Gardner 1983, 1993, 1999). 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 purpose of this paper is to describe four communicative activities 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 enjoy activities that involve word puzzles, problem solving and critical thinking, completing brain teasers, finding patterns, categorising and classifying words and objects, sequencing information, and asking 'why' questions (Gardner 1993, 1999; Berman 2002; Christison 2005; Puchta & Rinvolucri 2005; Palmberg 2010).

ACTIVITY ONE: COUNTING FROM 1 TO 21

Revise the numbers from 1 to 21. Next, ask the learners to work in pairs and tell them that each learner must add either one or two numbers to an accumulating list of numbers starting from 1. The one who is forced to say 21 has lost. This activity (taken from Palmberg 2007; 2009) provides young learners (and beginners of any age) with a motivating reason for reciting numbers.

A typical dialogue can go like this:

Learner A: One,
Learner B: two, three,
Learner A: four, five,
Learner B: six, seven,
Learner A: eight,
Learner B: nine, ten,
Learner A: eleven, twelve,
Learner B: thirteen,
Learner A: fourteen, fifteen,
Learner B: sixteen, seventeen,
Learner A: eighteen,
Learner B: nineteen, twenty,
Learner A: twenty-one.

After of couple of goes some of the learners will most probably have figured out how they can (almost) always beat their partner. Can you?

ACTIVITY TWO: LATERAL THINKING PUZZLES

Tell the learners that you are going to give some background facts about a specific event, and that their task is to provide the full context of the event by asking "Yes" or "No" questions. Make a point of emphasising that they must listen carefully to your answers, since you might also say: "Irrelevant" (or, with younger learners, "It doesn't matter"). If, for example, someone asks if the man (in the example below) is old, the answer is "irrelevant". If a learner asks a Wh-question (Who, What, Where, Why, Which, When or How) you must ask him or her to rephrase the question so that you can give a "Yes" or "No" answer.

Here is a modified version of a lateral thinking puzzle presented on Rinkwork's "Brain Food" website:
http://www.rinkworks.com/brainfood/p/latreal1.shtml

Background:
A man is trying to sleep. He takes the phone and calls 345. A voice says "Hello." The man says "Thank you" and puts the receiver down. Now he can sleep. Why?

Solution:
He is a guest at a hotel and someone in the neighbouring room was snoring. By waking the person up he made the snoring stop.

Finish your example (you may have to help the learners a little bit to make them understand the idea). Next, divide the learners into groups of three. Give one of the learners in each group a piece of paper containing a lateral thinking puzzle, and ask him or her to read out the background information to his or her group and then be ready to answer questions. The "Brain Food" website has more than fifty puzzles of various levels of difficulty to choose among, but be warned, some of them are rather morbid.

(For a variation on this see the Tip 'Building up a narrative':
http://www.developingteachers.com/tips/pasttips144.htm)

ACTIVITY THREE: SCRAMBLED INSTRUCTIONS

Revise the relevant vocabulary. Next, divide the learners into pairs and give each pair a piece of paper containing these twelve sentences taken from Romijn and Seely (1981):

[ ] Eat the toast
[ ] Plug in the toaster
[ ] Push the lever down
[ ] Put some jam on the toast
[ ] Put the bread in the toaster
[ ] Put the toast on a plate
[ ] Spread some butter on the toast
[ ] Spread the jam around with a knife
[ ] Take out a slice of bread
[ ] Take out the toast from the toaster
[ ] Wait for a little while
[ ] Watch the butter melt

Ask the learners to read through the sentences and arrange them in a (chrono)logical order. Tell them to indicate the correct order by filling in the figures 1-12 in the brackets: "1" for the activity that comes first, "2" for the one that comes next, and so on.

When the learners have agreed on the correct order, ask them to look at the sentences as they are listed on the handout and, taking turns, tell each other why the first sentence ("Eat the toast") must or cannot come before the second one ("Plug in the toaster"); why the second one must or cannot come before the third one ("Push the lever down"), and so on. (For more inspiration along these lines, consult the "Practice" section of a website entitled "Multiple Intelligences for Adult Literacy and Education", maintained by Literacyworks.)

(See also the past Tip 'Action':
http://www.developingteachers.com/tips/pasttips35.htm)

ACTIVITY FOUR: MYSTERY SENTENCES

Prepare yourself for the activity by writing short sentences (so-called "mystery sentences") such as:

- "I don't like strawberries."
- "My new shoes got wet yesterday."
- "Action films are the best."

Give each student a slip of paper (each containing a unique sentence) and tell them to walk around in the classroom and talk to as many classmates as possible about a topic suggested by the teacher. Their task is to engage in any on-going conversation (or start one of their own) while trying to include their personal mystery sentence as naturally as possible at an appropriate place. Ask them to make notes of all mystery sentences they think they've spotted.

After ten minutes or so, stop the activity and let the students decide who managed most successfully to include his or her mystery sentence without being spotted.

(For a variation see also the past tip 'Strangers on a train':
http://www.developingteachers.com/tips/pasttips19.htm)

References
Berman, M. (2002). A Multiple Intelligences Road to an ELT Classroom. Carmarthen: Crown House Publishing.
Christison, M. A. (2005). Multiple Intelligences and Language Learning. A Guidebook of Theory, Activities, Inventories, and Resources. San Fransisco: Alta Books.
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.
Gardner, H. (1999). Intelligence Reframed. Multiple Intelligences for the 21st Century. New York: Basic Books.
Literacyworks. "Multiple Intelligences for Adult Literacy and Education". http://literacyworks.org/mi/home.html
Palmberg, R. (2007). "Twenty-one reasons for counting." IATEFL Voices 194 (p 12).
Palmberg, R. (2009). Activities and exercises for logical-mathematical learners of English. Karperö: Palmsoft Publications.
http://www.vasa.abo.fi/users/rpalmber/MI-LML.htm
Palmberg, R. (2010). Basic Multiple Intelligences for EFL Teachers. Karperö: Palmsoft Publications.
http://www.vasa.abo.fi/users/rpalmber/MI-LML.htm
Puchta, H. & M. Rinvolucri (2005). Multiple Intelligences in EFL. Cambridge: Cambridge University Press & Esslingen: Helbling Languages.
Rinkworks. "Brain Food".
http://www.rinkworks.com/brainfood/p/latreal1.shtml
Romijn, E. & C. Seely (1981). Live Action English. Book 2. Oxford: Pergamon Press.

*This is a paper version of a workshop held at the 7th International AzETA Conference in Baku, November 2010.

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.

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