Why so many high schoolers say “I hate mathematics”. There are many reasons, I have found some possible causes. I hope by making some corrections in the way we teach mathematics, may be, there will be fewer high schoolers hate mathematic.
One of the problems is: Mathematician, educators, epistemology, cognitive psychologist are too busy to teach Kindergarteners mathematic. It is a big mistake to believe that every adult is qualified to lay the foundation of the concept of mathematic for a five-year old child.
Mistake one:
Parents teach children to memorize the sequence of number. From there we jump to counting. In term of concepts, there is a big gap between the sequence of number and counting the number of objects. Sequence describes an order. Counting describes the amount. Adult teaches children to count does not explain the gap between sequence and amount. The child has to make that transition. Some of them stuck there.
How the sequence and amount is related and how are they different.
( It should involve gross motor muscles, each count should correspond to each gross motor movement: pointing, touching, picking it up, move it with her hand from one place to another or carrying it from one place to another.) counting the building, of course we can not move the building, but we move the finger, or our bodies. Make counting an action, not reciting the sequence.
In sequence: four preceded five. The first one reaches the finish line is better than the second one. In quantity, five is heavier than 4.
Mistake two:
number is used to represent order as well as among of objects. We have the order sequence as the first, the second, the third, the fourth, the fifth, the sixth, the seventh, the eighth, the ninth, the tenth, the eleventh. Except the oder of First, second, third, fourth and fifth, the rest of the order is similar to number. It creates confusion. Confusion is the cause of “ I am not good at mathematic. I hate Mathematic”
Counting is role memory of sequence, we use the sequence to add the amount of the objects. “ what is the number after the number six?” “seven”. This is the sequence.
Think about a practice example: A father point his finger to the basket where are some apples. He asked “how many apples in the basket?“ she counted it, she said six. Then the father give her one more apple. He asked her how many apple in your basket? She quickly said: “ seven”. Is that from the role memory of the sequence: the number after six is seven. Would it be different if her father asks her to counter it aloud starting from one…”
Should we not teach the children the sequence of number at all or should we let the children discover themselves.
This group of apples is call having six apples, this group of apples is call having seven apples, this group of apples is called having eight apples, etc. let the child discover that the group of eight apple has one apple more than the group of seven apple.
The common error of Teaching children mathematics: too much teaching and too little is leave for children to discover. Confusing sequences and quantity.
Mistake three:
Counting objects verse counting intervals. Object is discrete. It is touchable, movable, and it has weight, shape and textures. But interval doesn’t. How many hours are between 1 o’clock and 3 o’clock?
If the child is confused by this problem. Teacher should not told her the answer. The child may not be ready to deal with time intervals yet. Intervals: time interval and distance interval, temperature interval, are more abstract than object. My personal experience, I have trouble of answering the question correctly: how many fence poles is needed to put up a fence of 100 feet, if fence poles are placed 10 feel apart. The correct answer is 11 not 10. Tricky questions are not good for laying the foundation for children.
Mistake four:
Counting objects require the concept of “one“. An adult asks a child, pointing to the fruit in the basket: “how many are there? (there is one apple and one orange) the child look confused. Rightfully, he should feel confused. The adult told the child that there are two. The adult imprinted the wrong answer onto the child’s mind. The question should not be: “how many are there?” it should be: “how many pieces of fruit are there?” But does the child at that age has the ability to place the apple and orange into the category of “Fruit”. It requires the ability of abstraction. If not, it lays a foundation of confusion for the child. Before certain age, the child doesn’t have the ability to ignore the difference between an apple and an orange. In her mind, an apple is an apple, an orange is an orange. She can not add them together. The child was right, but if she accept the adult’s answer, she might become confused. “ Mathematic is not as simple as I think., sometime my thinking is right, sometimes my thinking is wrong and for no reason.”
The counting of “one” require ability of abstract thinking, ignore the irrelevant attributes of the objects. The adult who teaches children counting often ignore the difficulty a child face: she needs to know what is the relevant attribute and what is the irrelevant attributes. Otherwise: apple is apple, orange is orange.
Another example of how the concept of one could cause confusion. A teacher give the child one box of mango, and then he give the child one more mango and then ask the child “ how many mangoes do you have.” How to apply the formula: 1+1=2.
One box of mango plus one piece of mango equal to what?
The concept of one has to make a judgement that this one is the same as that one. So each one of them can be counted as one.
The concept of one was rarely explained to the child, nor the adult understand how the child come to the conclusion that each one of those could be considered as one. Even though some apple is greener than the other, some apple is smaller than the others.
Do not challenge the child nor confuse the child with the abstraction concept which the child has not developed.
Sequence is on the time dimension, quantity is on the dimension of shape and weight.
2, 3, 4, 5, in the sequence dimension, number 4 does not indicate it has more mass than number 3. But in term of quantity, 4 has more mass/weight than 3. So let the child feel the weight of quantity of 4, and the quantity of 5. 5 is heavier than 4. Five mangoes is more than four mangoes.
If we remove this confusions, perhaps less high school student would say they hate mathematics.