Howard Gardner, a professor at Harvard University, suggested that intelligence was not simply made up of linguistic and mathematical ability, but was in fact made up of eight different intelligences. These intelligences included verbal-linguistic, logical-mathematical, musical, spatial, bodily/kinaesthetic, intrapersonal, interpersonal and naturalistic. Some psychologists have argued that a ninth intelligence could be considered – the existential intelligence, or spiritual intelligence where a personal asks questions and likes to think about questions. However, most people do not include this intelligence in their tests. This article is mainly based on an article by two South Africans, E. Gouws and A.M. Dicker which was published in Africa Education Review (8:3) in 2011, which is called Teaching Mathematics that addresses learners’ multiple intelligences.

In both the Trends in International Mathematics and Science Study and the Progress in International Reading and Literacy Study, of all the countries tested, South Africa performed the worst. Shardlow (2011) stated that students found mathematics “disconnected, uninteresting and hard”. Perhaps by addressing the way students learn – as one example by catering to the students different intelligences – learners might begin to enjoy maths. This article will look at how the different intelligences are manifested and how teachers might use this information to align their classes and lesson plans with these different forms of intelligence.

### Verbal-linguistic intelligence (or word-smart) people

feel the need to communicate with others. These kinds of students will enjoy verbal tasks such as word problems, and working in groups. They learn by writing and hearing or reading. Ask them to explain their reasoning and thought processes, as well as involve them in discussions about the solutions to questions.

These learners need to work from words to symbols – for example from a story sum to an equation. Suggestions for activities in class would include doing group work; asking learners to make a speech about a particular mathematics topic (e.g. the history of mathematics, where numbers come from, why calculus is important and so on); asking students to partner with other students to explain the work to them; creating a maths class dictionary – where students write down words in mathematics that they don’t understand and other students can write up the correct definition for those words, each individual class could have their own poster with the words that that class struggles with. Another suggestion might be to ask the students to write down the steps for a sum (be it long division or finding the factors of a cubic function) line for line in their own words as a useful tool for studying.

### A logical-mathematical (or logical-smart) person

understands mathematics concepts very quickly and can become bored when the teacher needs to explain the same concept again in different ways. These learners are logical, deductive and inductive thinkers and enjoy working on puzzles that require logical thinking. To draw these students into the maths lessons use colour to help them understand patterns, use different contexts – for understanding real-life maths, integrate other subjects into mathematics – for example ask them how a parabola might apply to science, or where the compound interest formula could be used other than in the bank and so on.

Gouws and Dicker suggest that the students should be diverted from “everyday written tasks to exploring, studying, investigating, categorising and classifying”. Explore where a particular mathematics topic can be used or ask students to find solutions before the topic is started. Study and investigate applications of mathematics in real-life, for example, examine the way a roller coaster is designed or try to design an equation for the rate at which coffee cools (basic first year calculus textbooks may have the answer – try Smith and Minton, Calculus, Early Transcendental Functions). Teach students the link between graphs and how they apply to other mathematics – for example parabolas and factorising – by understanding one, understanding of the second task can be more easily understood.

Challenge those students who are ahead of the class to come up with their own questions or find questions that will challenge them and their understanding of that particular maths topic. Another suggestion might be to give students a warm up exercise before continuing the lesson – for example in the Learning and Teaching Mathematics June 2013 issue, Mark Rushby suggests a warm up activity for grade 7’s using four numbers to make 24, using any mathematical operation. This is quite a nice way to solidify the students’ concept of BODMAS.

### Musical intelligence (or being music-smart)

occurs when a person is able to identify pitch, tone, rhythm and emotional expression in music. These children (or adults) tend to tap or drum their pen on their desks and may even hum or sing during lessons particularly when they are forced to sit still. According to Gouws and Dicker, there is a distinct link between music and mathematical patterns. In other words, sometimes people who have musical intelligence tend to do well in mathematics and vice versa.

Students can learn rhymes in order to help them remember the order of operations or counting in groups of threes, or fours and so on. Musical notes can be used to teach fractions as they are based on wholes, halves and quarters. A suggestion for older students might be to link each topic with a particular song – work a summary into the chorus for example, so that students can “silently” hum the tune to themselves while writing exams in order to help them remember important points about a section.

### People who have spatial intelligence

(or who are picture smart) think in terms of pictures or graphics – they learn through graphs and diagrams. Students who are picture smart might struggle in a lesson which is purely verbal. These learners are able to represent concepts and ideas through drawings, sculptures and other representations. Using colour in a lesson for example – drawing graphs (their shifts up and down or changes and transformations) in different colours on the same set of axes might help these students to grasp the transformation of graphs.

Visual stimuli for these learners are very important – so try to incorporate pictures and diagrams into their lessons. One suggestion by Gouws and Dicker was to present the students with colourful flash cards. Another suggestion they make is to incorporate paper folding into your lessons which they suggest is helpful for teaching multiplication and fractions. When teaching the volume and surface area of a cylinder, I like to use a toilet roll to explain the concept that the length of the tube unrolls to become a rectangle. The length of the rectangle is obviously the circumference of the circle at the top of the cylinder (unwind and re-wind a length of toilet paper from the roll to demonstrate this concept), and the height of rectangle is the height of the cylinder – as can be seen from the toilet paper. This concept can really help students to intuitively understand the concept of surface area and volume of a cylinder anywhere from grade 8 when they first learn the formula to matric when they need to know these types of formulas for calculus.

Another suggestion from the article is to use overlapping transparencies to explain for example, shifts in graphs (a great idea for teaching trigonometry graphs), or teaching the equivalency of fractions. Gouws and Dickers also suggest that students use diagrams wherever necessary to help them see the problem – for example for basic division – draw the three friends who each receive sweets – once students understand the concept of sharing they can begin to do the diagrams in their minds instead of on the paper.

### Those people who have a bodily / kinaesthetic intelligence

(or who are body smart) tend to be the most restless of all the students in the classroom. They feel a need to move. They have the ability to use their bodies to express and explore ideas and to understand concepts. A very obvious example of this might be counting on their fingers. Younger students can use beans or counters to express counting in groups or division – they need to be able to move or order objects (or themselves) in order to understand a particular concept.

A great exercise for body smart learners might be to use the learners to explain exponents. Have one learner volunteer to stand in front of the class (however doing this outside might be easier as it requires some space). This learner has two hands and thus can hold onto two friends – have the two friends come up and the first learner latch his or her hands onto their shoulders. This makes 2. Now get another 4 learners to latch onto the second set of learners hands, followed by 8 and then 16. Learners should be able to see the pattern. The first learner is counted as 0 – anything to the power of zero is one. The first set of two learners is counted as one. Two to the power of one is two, and so on. Another great way to incorporate this idea is to use it to explain the sum of geometric terms or even how geometric sums are determined. Gouws and Dickers suggest charades as a way to include body-smart learners.

### Intrapersonal intelligence

(or being self-smart) occurs when a person has the ability to understand themselves and they are able to set goals and identify their own feelings. These learners tend to daydream and can be very quiet in class. These students are self-disciplined and have good self-esteem. These learners tend to prefer to work alone. To encourage these learners to enjoy mathematics suggest that they try to use the knowledge they have already gained to solve problems presented to them that are increasingly challenging, suggest that they look at the different learning areas and see how they are connected to each other. Ask learners to look at and explain how they got to the answers they did.

### On the other hand, learners who have interpersonal intelligence

(who are people-smart) tend to spend a lot of time in class talking with other students. They tend to comment on other students problems even when this is not relevant to them. These students are very good communicators and thrive in groups. These students learn best through discussions and working with other people. To help these students – pair them up with another student who is either weaker or stronger than they are the pairs to help each other through a problem. These learners enjoy group work so projects and are a great way for them to enjoy mathematics. Draw them into debates about the current topic you are focused on and ask them to explain where this would be used in real-life. Ask these students to do a speech on a particular topic or get them to help teach a lesson with you by giving them a particular role to play in the lesson.

### Finally, naturalistic intelligence

(or being nature-smart) is having the ability to recognize patterns in nature, they are able to identify natural objects and then use this information effectively. These students enjoy naturals sciences (biology) and they enjoy being in the great outdoors. These students want to be outside and battle to focus when they are inside. Gouws and Dicker suggest that teachers use nature in their explanations about mathematics or explain how the concept applies to the outside world – for example, a centipede has 1 leg on either side (2 legs) count in twos to find the number of legs the centipede has. Another suggestion when explaining exponential growth is to use the growth of bacteria, or using logs to find out how long it would take the bacteria to double.

Although the application of the different intelligences in the classroom and trying to find ways to apply it might seem daunting in the beginning, once you start the process you will find that the ideas start to flow. Özdemir, Güneyu and Tekkaya (2006, 74 as found in Gouws and Dickers article) are of the opinion that learners should be given the opportunity to “engage all [8] of the intelligences” and allow these students to discover how their intelligences help them to learn.

There are two websites (if you have access to a computer lab with internet access) literacy works and bgfl which allow the students to answer either scaled questions or yes/no questions (respectively) that then tests where their different intelligences lie. The first website’s feedback is verbal and gives suggestions for how the students can use their abilities to learn. It gives their top 3 intelligences with the top score being a 5.

The second website’s feedback is a graph which shows comparatively where their multiple intelligences lie – great for spatial intelligence learners. The pbs website suggests that learners who are involved through their multiple intelligences will become more actively engaged students. They suggest that these learners will learn how they learn and that this will teach them to continue learning throughout their life span. They also suggest that teachers set rules and boundaries for the learners so that lessons do not become out of control but instead are fun and exciting. These students need to know what is expected of them and how they will be evaluated.

We wish you best of luck in applying this theory and would love to hear how you used the different intelligences in your class. Use our contact us page to let us know and we will post your stories below this article to inspire other teachers.