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Learning Mathematics Differently, Learning A Different Mathematics.
Assignment 1 for Math 361 Mathematical Education - 2011
Date : 19/10/2016
Learning mathematics differently, learning a different mathematics.Unfortunately my memory does not allow me to recall as far back as I would like it to. For this reason I will concentrate my analysis on the education I received since around the age of fourteen, when I started my first year of Liceo Scientifico. A “Liceo Scientifico”, literally translated as “Scientific School”, is an Italian secondary school where emphasis is given to the studies of “scientific” subjects such as mathematics, physics, biology and chemistry. As such, five hours a week were dedicated to study of mathematics throughout the five years I attended the school. This was more than given to any of the other ten subjects. I was delighted since mathematics was my preferred subject. Also, I believe that the extra time allowed the whole class to keep up with more difficult topics while still completing the enormous syllabus we had.Since Italian students are to choose their ideal direction of studies at the age of fourteen, it is to hope that those attending a Liceo Scientifico consider themselves good at maths. This comes across in the classroom in a much positive way. There is no particular fear towards maths as may be experienced in another type of school and this makes a great difference to the progression of the class. It means that the teacher can proceed at quite a high pace without losing many students along the way.Having observed how mathematics is taught in the British education system and discussed teaching methods with education professionals, I have noticed how more and more attention is being given to include the following six elements listed in The Cockcroft Report (1982, p.71) in lessons:exposition by the teacher discussion between teacher and pupils and between pupils themselves appropriate practical work consolidation and practice of fundamental skills and routines problem solving, including the application of mathematics to everyday situations investigational work. The manner of teaching mathematics in the Italian system may seem old fashioned compared to the English system in the sense that a typical lesson consists in exposition by the teacher and very little participation from the pupils. Not once do I remember doing any discussions, problem solving or investigational work in one of my maths classes at school. However, I found that in my first year of university I was more prepared than most of the other students on the course and was able to understand the new topics introduced quickly and in depth. Having said this, I do believe that the elements listed above should be adopted by all teachers to prevent mathematics to be viewed as arbitrary and therefore be learnt via memorising and rote learning. Here I am using the word arbitrary as is described by Linda Haggarty (2002): something is arbitrary if you can only know it to be true by finding it out from another source. Clearly the mechanics of mathematics are not arbitrary since they can be worked out from prior knowledge. I suppose it is the teacher’s role to introduce an activity that encourages pupils to investigate and build upon what they already know as true to discover mathematical properties new to them.I was not lucky enough to have a teacher who assumed the role stated above, but I recognise that this has not yet become necessary in Italian Licei Scientifici in order to obtain good student performance. The teaching I experienced was very effective in its environment. It is true that we were informed of mathematical properties as facts to be learnt by memory (Haggarty (2002) refers to these as received wisdom), but every fact was accompanied by a formal proof and it was left as our responsibility to make sure we understood the logic behind it. Haggarty (2002, p.55) recognises that:It is possible for students to use their awareness to try to work out for themselves why this received wisdom is true. If a student succeeds then this becomes a necessary fact and rightfully returns to the realm of awareness.This type of learning would not suit every student as it requires a certain predisposition towards mathematics and the willingness to understand more. Another student may simply treat it as arbitrary and something to be memorised. However, I believe that if the student is willing to put in that extra work, a in depth understanding of mathematics can be achieved.I found this method of teaching particularly beneficial as it forced me to develop a more independent attitude towards learning. Although this may sound contradictory since in class learning was based on the exposition by the teacher, more work was required to be done at home, the amount of which varied from student to student. I find this very similar to the way I am currently learning mathematics at university and this relates back to how I found myself well prepared in my first year.I understand that my experience is limited to that of a school frequented by students who probably consider mathematics as one of their priority subjects, and therefore have a strong initiative to look into the reasoning behind the facts exposed to them. This has lead me to ask myself whether pupils would perform better if their attitude towards maths was more positive. There are of course those who have the natural capacity to do well at maths no matter how little effort they put in. In other cases the student may have to put in a lot more effort to understand the intricacies of mathematics, so the problem reduces to convincing the student that this effort is worthwhile. This can be partly induced by the teacher, but I believe greater responsibility lies with the parents and the students themselves. The Cockcroft Report (1982) agrees that parents can have a great influence on their children’s attitude towards learning and should therefore be involved in their education and try to comprehend the importance of mathematics. Perhaps the whole cultural view of mathematics needs to change before we can expect pupils to perform better at school.
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