How Maths is Made Difficult
Maths becomes difficult when the natural progression of how children learn maths is not followed. This progression is often designated by ELPS:
E for Experience
L for Language
P for Pictures
S for Symbols
Typically the maths books jump directly to sequence # (3) and, then immediately move to sequence # (4).
Without proper guidance in Experience (sequence #1) and development of the necessary language (sequence #2), we are naive to expect that a student would directly comprehend from pictures (#3) and would effortlessly graduate to the symbols (#4).
We start talking about a room being 20'x30' without realizing that a student has no experience of what is meant by measuring of a room. Their estimation of 1" or 1' and things being 5" or 5' do not build in their minds the picture of the relative sizes. These are symbols without meaning. Their feeling of time and estimation of the passage of time is weak. Word problems often create the biggest hurdle. This is most often due to lack of comprehension and understanding of (i) lack of experiential feel and (ii) lack of appropriate language.
For e.g., the operation minus can be phrased in world problem as subtracted from, decrease by, lesser than, difference of, and so on. However, the synonymous use of these phrases in some contexts makes sense and in others do not. This creates a huge word barrier.
We make maths harder when we ignore the importance of E and L. We must in order to make maths easy for the students give them a feel and intutive understanding of all the measure through physical experience and explicit development of language.
This may not have been a big problem about 50 years ago, when people were used to do so many things by their hands. By age eight most children had obtained experience of using tools like hammer, pliers, nose pliers, saw, hand drills, tester, manual weighing machines. They had already observed people repairing watches with their precision tools, carpenters making furniture, plumbers repairing and threading GI pipes and using pipe wrenches for tightening and opening pipes, digging with hand showels, welding etc. Normal maintenance in the house was done manually by people from the household or was done by workers coming to the house and doing the repair, maintenance. Making of cheeze, ghee, washing soap, dahi (curd), lassi was done at home by hands. Juices were extracted through manual machines, qeema was grounded by hand, spices were grounded by hand, and chutneys and so many items were processed at home.
All these exposures gave a child of a feel and experience of forces at work, friction, resistence, circular motion, transfer of motion from one plane to another, push, pull, passage of time, estimation, calculation, conversions, translations, transformations and other physics, maths and chemistry concepts. Armed with these experiences they had a head start and for them to pick up from sequence #2 to #4 was straight forward.
However, in today city life and even in the village life this exposure has become minimal with the available of automatic devices, packaged food, bottled water, disposable furniture, disposable watches and many other stuff. E and L must now be introduced first.
Another problem is in communication and in understanding the intent of mathematical questions. One of the classic examples is that of a teacher asking a student how many halves are there in three and a half ( 3 1/2). The student may give an answer which can be one or seven depending upon how he understands the question. However, the teacher may overlook the ambiguity in the question and with may mark the answer of the student wrong, because only one answer can be right. A student going through several such mistakes may errorneously conclude that using his mind is a dangerous activity. He then starts trying to foresee what the teacher wants, or looks for clues or simply starts guessing. He looses his confidence and thinks that maths is unpredictable.
This loss of confidence in a student's ability to use his mind is the fundamental reason for maths anxiety.