“Scientific temper describes an attitude which involves the application of logic and the avoidance of bias and preconceived notions.”
We regularly deal with numbers in our daily life. As parents and teachers we have a responsibility to make our children numeracy aware. We can look for numeracy teaching point of view in ordinary experiences of life.
We find this topic in primary school math text books.
One necessary approach to apply logic and to avoid prejudice is to measure what we can in what we observe. We would reduce uncertainty by knowing the measure of things we use in life. We may be in the market to buy a clothes line, garden hose or a length of cloth. If we do not have a sense of length, we can be lost.
Knowledge about sizes of standard furniture helps us plan furnishing a room. Before we buy a new piece of furniture, we can be sure that it can fit in our home. Spacial planning and laying out items on floor requires measurement of area. We require such knowledge at home, office, school and public places.
I love tools and have a good personal set though I seldom need to use them at home. We do not need ultrasonic laser-guided measuring devices for normal everyday use. Measurements need not be complex as an approximation is adequate in many day-to-day situations. If we “measure with a micrometer, mark with chalk and cut with axe” the steps in the process are not coherent. We do not need micrometer, not even a meter scale or tape to measure many things for our purpose.
Our body parts can serve us well for many requirements of measurements – like they served our ancestors.
We know what a foot is as a measure and as a body part. We can “pace” and know the lengths of rooms, fields, tracks or parks. If we count the paces, the length would be approximately two feet per pace.
In England, horses’ height is measured in ‘hands’, accepted as four inches and defined as the width of a full-grown man’s hand. The phrase “don’t look a gift horse in the mouth” means don’t check for its age by counting its teeth – courtesy requires the recipient to take the horse as-is. When we buy a cow, we count its teeth to know its age – an age old practice in India.
It was common in our villages to talk about depth of a well, pond, or river in terms of “height of a man.” A ‘head-load’ meant 3 stones, which is a little over 19 kg. A person was expected to walk with so much load for a distance of about 3 miles without exhaustion. We do not have to weigh a ‘head-load’ as the person used with carrying goods on head would get a feel of the load.
Home makers measure quantity of water poured in to a vessel by dipping a finger. The distance from the knuckle to the tip of thumb is an inch. You may use other fingers too without much loss of accuracy.
Vendors in most part of the country sell flower garlands by cubit – the distance from the elbow to the tip of the middle finger. Flower vendors do not carry measuring tapes. A cubit is about 18 inches. Biblical references show measure of Noah’s Ark in cubits – 300 cubits long, 50 cubits wide, and 30 cubits deep. Some references show the value of cubit to vary between 17½ to 24 inches.
If we stretch out the hand so that the tip of thumb is as far away as possible from the tip of little finger, the distance is approximately half cubit as is called a “span.”
Width of a finger is a “digit” and is approximately ¾ inch.
Distance between tip of nose to figure-tip of out-stretched hand is about one yard.
“Fathom” is a typical naval unit of measurement. If we stretch our arms to either side of the body as far as we can, the distance between the tips of the middle fingers is a fathom – about 2 yards.
We measure “a handful” of grains, beans and seeds with comfort. Many homes keep aside a handful of rice everyday to donate to poor-homes.
Thus, we have ready measures for 1 inch, 4 inches, 8 inches, a foot, 1.5 foot, 2 feet, a yard, and two yards in our own body. This measuring instrument travels with us wherever we go. Like we can break in to a song when we like without the aid of musical instruments, we can get down to measure things without inanimate measuring instruments.
Speed and Distance
Walking for an hour does not tire a normal healthy person. Walking too is a mode of transportation. The distance-made-good per unit time when we walk normally is highly predictable unless we stop for gossip. It is not much affected by traffic jams and other “rogue walkers.” Walking with normal speed, we cover about 3 miles an hour. This understanding helps us know approximate distances that we often cover. When we promise to meet people we can plan better.
Speed and distance calculations apply when we travel by road or train too. Knowing the distance and the average speed and distance-made-good on our roads, we can plan better. Less is left for chance.
Finance and Accounting
We deal with bills regularly. Our utility bills like electricity, water, and telephone charge us differentially – the more we spend, the higher we pay per unit of consumption. It is similar to tax brackets. It would be an interesting exercise for the children to come out of text books and track the usage and see the effect of lower consumption per unit based on the highest bracket of consumption of the family. Tallying the consumption with various gadgets like electric iron and water heaters would be a good lesson in finance for the children and adults.
Math and Real Life
In Feb 2010 we interviewed a teacher with BSc. B.Ed. qualification and three years of experience in teaching Mathematics in a High School. As part of warm-up talk I asked her how far her home was from the school. It was 5 k.m. Unwittingly I asked a speed and distance problem – “how long would you take to walk the distance?” She answered “40 minutes,” with no idea about the speed at which she walked. Then I asked “How many kilo meters would you cover in an hour at that speed?” The candidate looked blank and also a little offended. She struggled for 5 minutes with paper and pen, could not answer, and gave up. She had scored well in her studies and her students too have been doing very well in their examinations. The teacher would be considered successful and the students bright.
Another candidate told that her son studied in class 6. I enquired the age difference between her and her son. She took time to calculate, using paper and pen, and came with an answer – 13 years. Even Kunti needed to hide the fact of Karna’s birth at age 13. Still I gathered courage and asked the lady at what age she was married. There was no answer and I changed the topic.
I asked another candidate to guess the cost of electricity to iron her cotton saree at home. She just could not get the question, howsoever hard she tried. The concept of power rating of the gadget, cost of electricity per unit, concept of units itself, time taken to iron a saree, etc. were all strange to her. If the question was typically framed in text book, she would have confidently taught the lesson to her students.
More absurd was when I asked a candidate to guess the dimensions of a the window in front of her. Answer was “five.” When I wanted to know the units, it was five centimetres. Again, when I told her we were asking about the area, it was 5 sq. cm.
There are scores of such sad examples. We do not apply the concepts we teach to our own real life. Mathematics or other subjects does not come out text books. We do not prepare children for life, but for examinations and higher studies (whatever that may mean.)
If we map our day to day experiences to the lessons we teach or learn, learning becomes a joyful experience. How can we do this? Not only by teaching the children, but also by thinking aloud in their presence and practicing openly, regularly.
Department for Education and Skills (UK) has beautifully defined numeracy and conveyed its importance.
“Numeracy is a proficiency which is developed mainly in mathematics, but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables.”
To build a society with scientific temper, let us promote numeracy.