26 April 2016
Teaching of maths concepts to students in schools is like being taught how to ride a horse over several years where the learner never gets to ride the horse until the last year. In the first year you can pat the horse, in the second year touch the bridle. Slow, disjointed, boring, laborious with poor maths students as an outcome.
Most students fail to see connection between maths concepts from one year to the next. Given each concept is only ever done for a few lessons in a few weeks in a year and then left for a whole year, what should we expect!
It has been shown that exposure to maths concepts, well ahead of their introduction in school, such as Pythagoras’ Theorem, algebra and trigonometry has a profound effect. I call this ‘jump-ahead’ maths and easily applies to those concepts that can stand in isolation to some degree, without prior knowledge. Good teachers revise from previous years and jump ahead to let them know where they are heading in the next few years. Makes perfect sense!!!
Smart, analytical students already know concepts, often without being taught. Born that way! And good on them. However, given most of us are visual dominant learners it is understood that the majority of students learn by diligent application – doing the same thing many times, applying themselves, studying, setting out visually and remembering. Dragging it out of the dark recesses of the mind to use when needed again.
Those who have difficulty in maths are those who:
- have poor self-worth
- articulate hopelessness
- fail to see connection between concepts from one year to the next
- operate in the ‘present’ with little attention to future
- fail to hold memory
- exhibit indicators of anxiety and ‘blind in the mind’ issues
- exhibit indicators of brain dysfunction inclusive of processing disorders, dyslexia, autism…
- have poor visualisation/memory storage
- gravitate towards association with likeminded students.
Very few things are learned in life by doing just once. Yet this is the way maths is taught in school. Do a bit on topics for a few weeks a year over several years and students are expected to connect the various ‘add-ons’ and progress their knowledge and understanding. Often there is no time to even cover the concept in detail if there are other school happenings such as sporting carnivals, excursions… cutting into the weekly schedule. The maths curriculum is mapped out in advance at the beginning of the year, across the 4 terms and 10 weeks in each term.
Exposing students to concepts… ‘jump ahead maths’… that will be introduced in future years in school, gives the learner time to do it many times and to be wiser and more mature when it is introduced in class.
This applies particularly to the concepts in maths where concepts build on each other like the foundations of a pyramid effect. Each adds greater understanding, allowing it to be applied to problem solving and the student’s mathematical communication and justification.
The joy and amazement shown on students faces when something is introduced in class that they recognise is amazing!! To see them actually know and understand, even if only partially, is an educator’s delight!! It is the immediate transformation of an individual. Someone who recognises that they are ahead and not behind, probably for the first time ever. Answering questions in front of classmates is an immediate boost to self-esteem, self-identity, self-perception and opens the mind to many, higher-level career possibilities.
Maths rules the world. If you are good at the various concepts in maths, their importance and connectivity to future learning, you can do anything.
If you are good at maths, the perception by teachers and peers is that you are smart. Teachers believe that. The correlation is that kids who are good at maths have better self-esteem and complete other subject areas more diligently… and have the choice of many, many professions.