Having an interest in mathematics, science and technology; I often interact with many learners, students and educators. Over the past few years it has lead to many instances which were extremely thought provoking and simply stimulating to my ever inquiring mind. Examination time and the lead up to these stressful events are periods where many factors and thoughts are revealed. It is easy to just brush these aside and move on. But sometimes it is worthwhile to spend the time and listen. Conversations after an examination often have the following trends; “we were never taught it this way in class” or “our sir / ma’am has never asked questions in this fashion”. It is this type of response that I want to delve into and look at a few possible solutions / answers / discussions to these types of response from students and learners.

Why is this a typical response from a large majority of learners I encounter almost on a daily bases? This has lead me to counter with another question of my own. Is there something really there or is it simply as a result of students not applying themselves correctly? After some investigative digging and soul searching a few possible solutions and points of discussion have come to light.

## Disparity of Content Delivery Among Schools

There is a huge disparity in the way teaching occurs at different schools. A downside to this is that students may sometimes find themselves at sixes and sevens in an examination through no fault of their own. Before I open up a can of worms here, let’s first make it clear that this disparity is **not always** as a result of poor socio-economic circumstances and lack of finances. Over the past few years there has been many instances of schools in previously disadvantaged areas getting their act together. One of the positives coming from this is that educators and principals have the power to change things in pursuit of academic and economic success for our children. Special attention needs to be given in the areas of mathematics and science education as these are two areas of concern in South Africa at this moment in time.

## Recognizing Strengths and Weaknesses in Textbooks

Schools are given a list of prescribed text books to choose from to deliver the prescribed content to their students. As with any type of text, even non-fiction, books have the strengths and weaknesses. Educators and class facilitators are often so focused on getting through the content that they use these books without acknowledging or realizing possible short comings in certain areas. When these areas are critical examination topics, the effect on student understanding and examination readiness may be irrevocably tarnished.

In many subjects, especially in the area of mathematics and science, there are basic principles and theorems which are vital in the understanding of more advanced concepts. Even more important is that many of basic principles and theorems are not isolated to specific topics in mathematics, but often traverses over a number of topics. Some textbooks acknowledge these concepts and the way they occur in different topics in mathematics. Many educators easily miss or pay insufficient attention to the broader application of some of these principles and theorems which cut across multiple topics. One the the causes of “we were never taught it this way in class” or “our sir / ma’am has never asked questions in this fashion” at the end of a grueling external examination.

## Honing the Skill to Recognize Concepts

One of the areas / approaches which requires much needed further attention is finding ways of enlightening our students about the basic principles and theorems which occur across different topical areas in mathematics. In this regard learners should have the ability to recognize these candidates wherever they occur. Often it is like the case of the chameleon who is able to merge into its background by changing its colour. At the end of it all, it is still a chameleon and retains its unique biological properties. The same goes for these mathematical principles and theorems. Irrespective of where they are encountered, they still retain their mathematical properties and characteristics. The way students need to approach them will remain exactly the same.

Examination, tests, tutorial and tasks are useful ways of exploring student understanding of underlying intricacies in mathematics. Unfortunately, educators and facilitators can easily become one dimensional in the way they set questions and design tasks. It becomes the norm to test basic principles within the topics that introduce these principles to learners for the first time. This has the danger of creating the expectation with students that it is the only way they will encounter these types of questions in tests and examinations. The end result is that come an external examination where topic integration is the order of the day, students and learners come horribly short.

Educators and facilitators do not need to have this one dimensional approach in delivering content and testing the understanding of concepts. There is tons of assistance out there able to assist them in developing and expanding their repertoire of setting test and examination questions. One of the obvious avenues to investigate would be to study tests and examinations set by other workers and institutions within the field of mathematics and science. It does not mean we have copy and rehash the questions word for word, as this could lead to infringement of copyright set by the original examiners. Use these resources as references to set similarly styled questions.

## In Conclusion

Here I have only exposed a few ideas and have hopefully stimulated some points of discussion which could assist us in preparing our students more holistically in the understanding of basic concepts and theorems in mathematics and science. The effect would have a multifaceted advantage. Students and learners will have a deeper understanding of the concepts they have learned during the delivery of the content. Among other things, they would also be more confident, and more successful in sitting external examinations, In this regard I especially think of students who have to sit for their final examination at the end of grade 12. So let us play our part and assist them in joining all the dots they encounter in mathematics and science examinations and tutorials in the future.

Keith Williams

20 September 2018