THE TTT METHOD

Learners face many difficulties in mathematics. The abstract nature of it often scares learners. Many learners try to recall the work of the teacher, often with not much success. One main challenge for a mathematics teacher is to take away the difficulties learners have, to let them enjoy the mathematics, to show them the beauty of it without boring them and to give them enough tools and skills.

General Educational theories talk about teaching from the concrete to the abstract.

Montessori and Dewey put much stress on the concrete level. They translated this to a playing level. Learners will develop from the playing level to more abstract levels when they are ready for it.

Van Hiele developed this idea by using the playing level as a start, not as an aim on itself or as an end. From the playing level learners have to go on to a level of putting in words what they discovered during the playing. Finally they should formulate possible theories using each other during discussion and using knowledge they have already.

In mathematics these theories can be summarized by three words:
 

Touch------------------->Talk------------------>Think

First learners need to play around with materials like coins, cubes, geo-boards etc. (touch). Using this playing they need to talk together about what they discovered (talk). Finally they need to put these ideas into a framework of existing knowledge, expanding their knowledge (think).

Seeing and touching will help to develop intuitive mathematics versus formal mathematics. From intuitive ideas learners can share these ideas, test them and finally formulate possible theories. The teacher needs to help the learners with materials for the touch level and with ideas how to explore these materials. The teacher needs to provide possibilities to share ideas and test these. Finally the duty of the teacher is to guide the learners by asking questions. These questions should help to put learners on the right track or to divert them from a wrong path. The teacher should avoid putting the learners on a track they do not yet see themselves.

Many teachers are afraid to work in the above way. They reason that playing is fine but not enough. The learners will not develop enough skills to use their mathematics in appropriate ways. Mathematics has theories that need to be learned. Many learners are not able to conclude from their playing. There is a danger that the learners do not develop beyond the touch level. Other dangers teachers are afraid of is that the above method takes too much time and makes the learners undisciplined. As there are many topics to be covered it will be wiser to give examples how to use theories and let the learners develop skills by offering them much practice in exercises.

Teachers using the TTT or Hand, Mouth, Brain method as it is also called, argue as follows:

Many people who have been taught mathematics have not learnt much during these lessons. They still cannot use fractions, percentages. They have no idea what x was all about. Many never managed to pass the mathematics examinations. This proves that formal mathematics only provides for a small group of learners. In life people come across many problems that need to be solved. Most people will look at the problem touch it, talk about it and come up with solutions. Education should use this natural method of solving problems and should train learners to use the natural method better. They also say that more time spent on playing will pay off at the end when theories will be remembered much better. There will not be much need for revision. Learners will learn more when they enjoy the learning.

Education in the future needs to produce learners who will be flexible, independent, adaptable to change, responsible. The job market will change tremendously, no job security will be offered in the future. Predictions say that the future employee will change jobs every three years. Knowledge will not be stagnant, employees will need to learn many new skills on the job. Computer skills are one example education need to take notice of. The society does not need people who only can recall what they have learnt, it will need people who also can develop themselves by using information around them, who look for new solutions. Mathematics education needs to be in the forefront of this changing technological world.

Good examples of the TTT method are seen at the Rhodes University in South Africa. They produced a reader called Rethinking Mathematics Education. The TTT method is a good example of Learner Centred Education introduced in Namibia.

We as the writers of this module believe in the TTT method as a way to teach mathematics. We believe in intuitive mathematics as opposed to formal mathematics. We do not believe in recall methods or the cookery book method.

This module will often use the TTT method to explain things. It will ask you to try it out in your lesson and to think about the above method.
  Examples of the above method can be taken from almost all topics in mathematics:
Number concepts and patterns can be explored using geo-boards, small cubes, coins, 100 boards.
Geometry can be developed using geo-boards, cutting and pasting figures, cutting nets of three dimensional figures.
Statistics can start to collect data in very physical ways, display the data in pictographs and stem and leaf.
Units can be compared to lengths, areas and volumes.
Algebra can be connected to geometry in the form of area's, length, volume of tiles.
Probability will be taught as part of fractions using coins, dice, arrow boards, bags with bottle tops.
Transformations can be done using triangles on geo-boards rotate, translate, reflect, enlarge them.
Trigonometry can be seen as working with ratio's. Ratio's are fractions. Fractions can be shown and touched in many ways.
 
 

Examples of the above method can be taken from almost all topics in mathematics:  Number concepts and patterns can be explored using geo-boards, small cubes, coins, 100 boards.  Geometry can be developed using geo-boards, cutting and pasting figures, cutting nets of three dimensional figures.  Statistics can start to collect data in very physical ways, display the data in pictographs and stem and leaf.  Units can be compared to lengths, areas and volumes.  Algebra can be connected to geometry in the form of area's, length, volume of tiles.  Probability will be taught as part of fractions using coins, dice, arrow boards, bags with bottle tops.  Transformations can be done using triangles on geo-boards rotate, translate, reflect, enlarge them.  Trigonometry can be seen as working with ratio's. Ratio's are fractions. Fractions can be shown and touched in many ways.