Mathematics is “not my cup of tea.” It was irritating to know that I would have to sit through a series of lectures that would improve my skills in teaching mathematics. My first thought was that I wouldn’t learn much from the lectures. How wonderfully wrong I was!
Mathematics is defined as ‘the study of the measurement, properties and relationships of quantities and sets, using numbers and symbols. (n.d. 2004) This definition is a classic example of people’s notion about mathematics – boring, scarey and only for ‘super-brains’.
For countless generations, “mathematics teaching and learning practices…centre on memorisation of facts, and practice of pre-set meaningless procedures, which promote a view of mathematics as lacking creativity, imagination, or critical thought.” Sandra, F., and Len, Sparrow,. (2007).
It was expected of students to not only learn by rote the times tables and equations but also to work on algorithms without really understanding the logic or reason behind what they were doing. Students were not allowed to ask questions as to why they learnt what they learnt and why there was no other way to do what they did. Any questions were either met with stoic silence or a curt ‘it’s always done this way’ remark. This was how I learnt mathematics during my primary as well as secondary education. No wonder, by the time I reached Higher Secondary, I didn’t understand anything about what I was doing in class.
I believe I would have continued hating mathematics if it weren’t for my tenth grade teacher who inspite of limited resources and no access to the latest teaching methodologies, still attempted to make math interesting, logical and realistic. I learnt more about area, time, angles and space from him than I ever did from all the other mathematics teachers both in primary as well as secondary school.
Marilyn Frankenstein has summarised several other people’s and my perception of mathematics in her article ‘Mathematics Anxiety: Misconceptions about Learning Mathematics’. She said that the features of current maths curricula are as follows:
- rote calculations
- memory dependence
- unmotivated exercises
- spurious applications of calculation strategies
- authoritarianism in mathematics education
- tests which assume mathematics can be divided into tiny water-tight compartments
(Frankenstein, M., (1989). pp. 183 – 186)
There are certain questions teachers will have to answer before understanding the teaching methodologies for mathematics and they are:
- Who are our students?
- What are their requirements?
- What are their skill sets?
- What are the learning tools available to them?
- How do they like to study?
- How are they influenced?
- What are the methodologies in which they can be taught?
- How would these methodologies help them?
Before we focus on the current teaching methodologies and resources available to pre-service mathematics teachers, it is of primary importance that we focus on who our students are. Times have changed and it does not make sense to live in the past. We as teachers need to understand whom we are teaching if we have to improve our methodologies.
Though most teachers would not like what I am about to say, I will have to emphasise that we need to look at teachers as ‘knowledge service providers’ and our students as ‘end-users’ or ‘customers’. I am well aware of education being a noble profession but I prefer to think of it as any other industry for quality management purposes. Like all industries governed by the 6 Sigma and Lean Toyota project for service and quality assurance, we will have to make changes to service levels so as to assure quality levels are effectively managed.
Our students are our customers and their world is very different from the one that we live in or grew up in. I liked what Sir Ken Robinson said in a Youtube video played during an Issues lecture, “what are we educating them for?” Their world is changing faster than our own. It is more multi-cultural, multi-lingual and global than ours. Beare predicts the future world of our students in his paper on “From an old world-view to a new” by looking at various factors such as demographics, economic growth, environment, consumer patterns, impacts of consumerism, resource availability, etc in the future. (Beare, 2001, pp. 11-17).
Based on Beare’s statement it is possible to understand that ‘the nature of what is to be studied has also changed’. (Booker, G., Bond, Denise., Sparrow, Len., Swan, Paul.,. (2010). p. 7). There are several reasons why students will have to be proficient in numeracy. These external reasons are as follows:
- intellectual advancement in several arenas requiring an understanding of numbers and their functions
- technological growth both in infrastructural and cyber development
- economical instability requiring better understanding of market figures and functions
- environmental degradation that requires numerical knowledge of replantation and natural resources management systems to circumvent the negative impacts
These are just a few areas where mathematics will play a major role in the future lives of our students. However, as teachers, we will have to ensure that students understand the pervasiveness of mathematics in all walks of life, i.e. ‘an innumerate citizen today is as vulnerable as the illiterate peasant of Gutenberg’s time’ (Steen, 1997)
Students learn differently from before. They have access to better learning management systems and the world of knowledge is literally at their finger tips. Everything that has been discovered or is in the process of being discovered is available to them at the touch of a finger tip. As teachers, we will have to improve our technical skills so that we can use the same tools as our students to teach numeracy.
There is a process to follow when teaching mathematics as stated by Alistair McIntosh in ‘When will they ever learn?’ (McIntosh, A., (1977).) These can be enumerated on as follows:
- Don’t start formal work too early: “It is the experience of many good teachers…it is found to be unnecessary before the sixth year has passed…to do any formal Arithmetic on slates” (Reports, 1895/6)
- Use learning materials and start from practical activities: “…examples of any kind upon practical numbers are of very little use, until the learner has discovered the principle from practical examples.” (Margaret Brown, 1977, p. 10)
- Give children problems and freedom initially to find their own methods of solutions: “If a child be requested to divide a number of apples among a certain number of persons, he will contrive a way to do it, and will tell how many each must have.” (Margaret Brown, 1977, p. 10)
- Children must have particular examples from which to generalise: “When the pupil learns by means of abstract examples, it very seldom happens that he understands a practical example the better for it; because he does not discover the connexion until he has performed several practical examples, and begins to generalise them.” (By a teacher of youth, 1840, p. IV)
- Go for relevance and the involvement of the child: “When children explore for themselves they make discoveries…” (Curriculum Bulletin No.1, 1965, p. 1)
- Go for reasons and understanding of processes. Never give mechanical rules: “…when children obtain answers to sums and problems by mere mechanical routine, without knowing why they use the rule…they cannot be said to have been…well versed in arithmetic.” (Margaret Brown, 1976, p. 16)
- Emphasize and encourage discussion by children: “When children explore for themselves, they make discoveries which they want to communicate to their teacher and to other children and this results in frequent discussion. It is this changed relationship which is the most important development of all.” (Curriculum Bulletin No. 1, 1965, p. 1)
- Follow understanding with practice and applications: “When the pupil learns…he does not discover the connexion until he has performed several practical examples, and begins to generalise them.” (By a teacher of youth, 1840, p. IV)
There are various methodologies for teaching mathematics and they depend on what is being taught. I would prefer to use the same teaching process as the one I used when teaching literacy to young adults/mature age students in India. I will start each lesson with a ‘Lead In’ activity that gives students an idea/clue of what the day’s lesson is all about. Based on this clue/hint, there is the ‘Mathematics for Gist’ activity that focuses on a broad over-view of the topic. The next ‘Mathematics for Specifics’ activity focuses on the appropriate area of learning for that particular day. The learning acquired is then determined on a daily basis through ‘Post specifics-activity tasks’. The assessment/work-sheet will help me to gauge the learning curve of each student in the class.
The one lesson that comes to my mind when thinking about the above process is the one regarding an introduction to algebraic expressions using the ‘Leap Frog’ activity. That was the first time I realised the potential behind teaching mathematics. I had so much fun coming up with the algebraic expression that I realised I would like my students to enjoy learning mathematics too. I had re-discovered the joy of learning mathematics as when I was taught by my favourite mathematics teacher. I believe that it is important for students to move from a general idea to a more specific understanding of the mathematical discipline that is being explored for the day.
Based on what I have just said, I can say that my beliefs are a combination of both ‘Content and clarity’ and ‘Content and understanding’ as stated by Beswick (Beswick, K., 2006, p. 19). I believe it is important to increase my knowledge about the subject. Also, it is important that I should constantly update myself about changes in teaching principles and methodologies. I believe that sequencing of information is important since there is a specific reason why we have been teaching basic algorithms first before moving onto fractions or algebraic expressions. However, I would be glad to hear about alternative solutions from students as well as teachers. I do know that students might not know everything and there will be times when the answers will have to be given to them.
I believe that it is mandatory that ‘pupils are aware of different methods of calculation and are able to choose methods in relation to their effectiveness and efficiency in solving a problem’ (Askew, M. et al, n.d). It is important that I emphasise ‘the complementary nature of teaching and learning and valued classroom activity, which involved pupils working together with other pupils and teachers to overcome difficulties and to reach shared understanding’ (Askew, M. et al, n.d).
The road to being an efficient and effective Mathematics teacher involves self-discovery, self-learning and self-proficiency. If this will enable even one student to love Mathematics and discover maybe the greatest ‘Primary Number’ or even a new method for teaching ‘Mathematics’ then I am willing to make the required changes. Hopefully no student of mine will ever dream about “the final test involves escaping from a nightmare, which is depicted as a lifetime of mathematics problems written on a blackboard” (Swan, Paul., 2004, p. 501) and instead will learn to love this subject as much as I have come to love it.
