Many children feel that mathematics is difficult. The reasons may range from lack of practice to ineffective methods of doing homework. If a child continues to find math difficult then he or she may be suffering from mathematics anxiety. Math anxiety refers to feelings of tension and anxiety that arise when you try to solve math problems. Children may loose their self-confidence due to math anxiety. Therefore, it is necessary to treat it. Here are some tips with which children can become familiar with mathematics and relieve their anxiety:
Some of the causes for math anxiety are negative experiences linked with math. Besides, the usual class room teaching methods are sometimes not effective in teaching everything about mathematics. Understanding the reasons behind math anxiety can be one of the first steps to overcome your fear.
Kids should not feel tense about mathematics. In fact, it is an easy subject that involves numbers and calculations. They should remember that there is nothing difficult in math. A common mistake that most students commit is that they try to memorize mathematical concepts. The best approach is to solve all the math problems on a piece of paper to understand the basic idea behind each problem. This can also help in clearing up any confusion that a child may have. Things start getting clearer when children write their solutions on paper.
Parents and teachers can assist their children by creating a positive environment at school and home. Children should not be blamed if they fail to do well in math, this will only increase their math related fears. Instead, their failures should be tolerated. If a child repeats a mistake, make sure that he or she practices solving the particular problem so that he feels confident doing it. Teachers and parents can support children by providing positive response to their mistakes. Kids should know that doing mistakes is okay because it is an important part of learning. Teachers can boost the student’s confidence by showing them both their mistakes and plus points.
It is important to provide satisfying answers to the children’s math problems. Since math is not only about memorizing certain steps and procedures, it is also about understanding the concepts behind various problems. Children must understand why they solve problems with various steps to reach the right answer. The teachers must stress upon the importance of accurate working along with the correct answer. Normally, a child understands the mathematical procedures but makes a mistake in addition or multiplication calculation. Therefore, they end up with the wrong answer in their assignment or test. Wrong answers can often discourage children. However, these kids must understand that they know math and they have made simple calculation mistake. Teachers are advised that they should encourage their students by giving them credit for their working, so that they don’t get depressed by their performance.
Parents can play a great role in helping their child overcoming the fear of math. One of the great ways of relieving match anxiety is through games and household activities. Many children will happily participate in these games, unaware of the fact that they are solving math problems that gives them fear and anxiety. You can play many games with your children including cards and Dominoes. Few of the popular games are Yahtzee, Battleship and Connect four. Cooking and sewing are two household activities that can improve your child’s mathematics. Children can also take part in home repairs and all those activities that involve problem solving and measurements. Make sure that your children use their mathematical skills in solving those problems. You can boost their confidence by rewarding their good performance.
By: Kelly J Thomas
Posts Tagged ‘Teaching Methods’
How to Relieve Math Anxiety?
March 23rd, 2010INDUCTIVE AND DEDUCTIVE METHODS OF TEACHING
January 2nd, 2010INDUCTIVE AND DEDUCTIVE METHODS OF TEACHING
Students have different intellectual capacities and learning styles that favour or hinder knowledge accumulation. As a result, teachers are interested in ways to effectively cause students to understand better and learn. Teachers want to bring about better understanding of the material he/she wants to communicate. It is the responsibility of the educational institutions and teachers to seek more effective ways of teaching in order to meet individual’s and society’s expectations from education. Improving teaching methods may help an institution meet its goal of achieving improved learning outcomes.
Teaching methods can either be inductive or deductive or some combination of the two.
The inductive teaching method or process goes from the specific to the general and may be based on specific experiments or experimental learning exercises. Deductive teaching method progresses from general concept to the specific use or application.
These methods are used particularly in reasoning i.e. logic and problem solving.
To reason is to draw inferences appropriate to the situation.
Inferences are classified as either deductive or inductive.
For example, “Ram must be in either the museum or in the cafeteria.” He is not in the cafeteria; therefore he is must be in the museum. This is deductive reasoning.
As an example of inductive reasoning, we have, “Previous accidents of this sort were caused by instrument failure, and therefore, this accident was caused by instrument failure.
The most significant difference between these forms of reasoning is that in the deductive case the truth of the premises (conditions) guarantees the truth of the conclusion, whereas in the inductive case, the truth of the premises lends support to the conclusion without giving absolute assurance. Inductive arguments intend to support their conclusions only to some degree; the premises do not necessitate the conclusion.
Inductive reasoning is common in science, where data is collected and tentative models are developed to describe and predict future behaviour, until the appearance of the anomalous data forces the model to be revised.
Deductive reasoning is common in mathematics and logic, where elaborate structures of irrefutable theorems are built up from a small set of basic axioms and rules. However examples exist where teaching by inductive method bears fruit.
EXAMPLES: (INDUCTIVE METHOD):
1) MATHEMATICS:
A) Ask students to draw a few sets of parallel lines with two lines in each set. Let them construct and measure the corresponding and alternate angles in each case. They will find them equal in all cases. This conclusion in a good number of cases will enable them to generalise that “corresponding angles are equal; alternate angles are equal.” This is a case where equality of corresponding and alternate angles in a certain sets of parallel lines (specific) helps us to generalise the conclusion. Thus this is an example of inductive method.
B) Ask students to construct a few triangles. Let them measure and sum up the interior angles in each case. The sum will be same (= 180°) in each case. Thus they can conclude that “the sum of the interior angles of a triangle = 180°). This is a case where equality of sum of interior angles of a triangle (=180°) in certain number of triangles leads us to generalise the conclusion. Thus this is an example of inductive method.
C) Let the mathematical statement be, S (n): 1 + 2 + ……+ n =. It can be proved that if the result holds for n = 1, and it is assumed to be true for n = k, then it is true for n = k +1 and thus for all natural numbers n. Here, the given result is true for a specific value of n = 1 and we prove it to be true for a general value of n which leads to the generalization of the conclusion. Thus it is an example of inductive method.
2) LANGUAGES:
A) Development of a story from a given outline is an example of inductive method because the student may develop any story from the given outline (specific) based on his/her imagination.
B) Writing a letter to his father describing a particular event of his life, is an example of inductive method because, the event and the language (use of words) differs from student to student (general) while the format of the letter is always specific as it always starts with “Respected Father”, then is the body of the letter and finally the closure is done by “your (loving) son/daughter” followed by name.
C) Writing an essay on “the book I like most”, is an example of inductive method because while the format of essay i.e., introduction followed by body and finally, the conclusion, always remains the same (specific) but the book and the reasons for liking it and the words used differ from individual to individual (general).
3) CHEMISTRY:
Elements in the periodic table are divided into several groups which have similar properties and electronic configurations etc. Thus if the properties of individual elements in a group like chemical reactivity, melting point, boiling point, ionization energy etc. are known the properties of the elements of the entire group can be predicted with very few exceptions. Thus it proceeds from specific to general and so is an example of inductive method.
4) PHYSICS:
By noting the amount of work done in lifting a body from the ground to a height h, we can derive the relation between the potential energy of the body (P.E.) with the height attained by it from the ground, which is P.E. = m g h, where, g = 9.8 m/sec2, the acceleration due to gravity acting vertically downwards. The height being specific, it proceeds from specific to general and so is an example of inductive method.
5) BIOLOGY:
a) Morphological and anatomical characteristics can be studied in particular plants with prominent characteristics, such as Lemna (Duckweed), Eichhornia (water hyacinth) hydrilla, Opuntia, Accacia, Calotropis (AK); for understanding the ecological adaptations of plants into three groups on the basis of plant water relationships as Aquatic (Hydrophytes), Terrestrial (Xerophytes, Mesophytes) and Halophytes. As it proceeds from particular to general, therefore it is an example of inductive method.
b) The children are explained the consequences of depletion of resources like coal, petroleum and then let them reason the need for conservation of resources and methods for it. As it proceeds from particular to general, therefore it is an example of inductive method.
6) ECONOMICS:
By studying the factors affecting inflation which are specific, like the supply and demand of goods in an economy etc, we can predict as to whether the rate of inflation will rise or fall during a given period of time (general) which ultimately gives an estimate of the cost of living in an economy and calculating the cost of living index number, the govt. is able to decide regarding the extent of increase in the dearness allowance (DA).
EXAMPLES: (DEDUCTIVE METHOD):
1) MATHEMATICS:
A) We have an axiom that “two distinct lines in a plane are either parallel or intersecting” (general). Based on this axiom, the corresponding theorem is: “Two distinct lines in a plane cannot have more than one point in common.” (Specific). Thus this is an example of deductive method.
B) We have a formula for the solution of the linear simultaneous equations as and(general). The students find the solutions of some problems like based on this formula (specific). Thus this is an example of deductive method.
2) LANGUAGES:
A) Writing a summary of a passage known as précis writing is an example of deductive method because for the given passage (general) we always have certain key points which are included in the summary (specific).
B) Explaining a poem in prose with reference to context is an example of deductive method because the poem being given (general), we always try to pen the specific idea or thought of the poet in prose. Hence it is an example of deductive method.
3) CHEMISTRY:
The experiment of salt analysis is an example of deductive method because here, we firstly perform the preliminary test also known as dry test (general) to ascertain as to which group it may probably belong. The group being ascertained, we proceed to perform specific confirmatory test to identify the particular salt. Thus it proceeds from general to specific.
4) PHYSICS:
By using the properties of semi-conductors (general), we make several instruments like diodes and transistors which have (specific) uses like the light emitting diode (LED) is used in remote control instruments; the photo diode is used for counting the exact number of people present in a stadium at a particular interval of time. As it proceeds from general to specific thus this is an example of deductive method.
5) BIOLOGY:
a) This method can best be made use of in the study and understanding of diseases where the symptoms and precautionary measures of various diseases caused by bacteria, virus and other organisms can be explained and children are asked to identify the same on the basis of their understanding.
b) Classification of animals into chordate and Non-Chordate on the basis of their differences. Since, the differences are general in nature, and the classification as mentioned above is particular in nature, it proceeds from general to particular. Thus this is an example of deductive method.
The examples cited above are not exhaustive. Many more examples can be given and from variety of subjects as well.
Logic and Problem solving are two more areas where these methods find extensive usage.
The major task of logic is to establish a systematic way of deducing the logical consequences of a set of sentences. In order to accomplish this, it is necessary first to identify or characterize the logical consequences of a set of sentences. The procedures for deriving conclusions from a set of sentences then need be examined to verify that all logical consequences and only these are deducible from that set.
From its very beginning, the field of logic has been occupied with arguments, in which certain statements, the premises, are asserted in order to support some other statement, the conclusion. If the premises are intended to provide conclusive support for conclusion, the argument is a deductive one. If the premises are intended to support the conclusion, only to a lesser degree, the argument is called inductive.
A logically correct argument is termed “valid”, while an acceptable inductive argument is called cogent. The notion of support is further elucidated by the observation that the truth of the premises of a valid deductive argument necessitates the truth of the conclusion. It is impossible for the premises to be true and the conclusion false. On the other hand, the truth of the premises of a cogent argument confers only a probability of truth on its conclusion: it is possible for the premises to be true but the conclusion is false. For example let the premise is: “All teachers are scholars” and the conclusion be: “There are some scholars who are not teachers”. Let the premise be true then obviously, the conclusion is false. Hence it is a cogent. Again let the premise is “no policeman is a thief” and the conclusion be “no thief is a policeman”. Let the premise be true then the conclusion is also seen to be true. Thus it is a valid (deductive) argument.
Problem solving is another area where inductive and deductive processes may be used.
In inductive thinking, one considers a number of particular or specific items of information to develop more inclusive or general conceptions. After aspirin was synthesized, for example, some people who swallowed the substance reported that it relieved their particular headaches. Through induction the reports of these specific individuals were the basis for developing a more inclusive notion: “aspirin may be helpful in relieving headaches in general”.
“Deduction” is reasoning from general propositions –or hypotheses-to more specific instances or statements. Thus, after the general hypothesis about the effectiveness of aspirin had been put forward, physicians began to apply it to specific, newly encountered headache cases. The deduction was that, if aspirin is generally useful in managing pains in the head, it might also be helpful in easing pains elsewhere in the body.
Although a person may deliberately choose to use induction or deduction, people typically shift from one to the other depending on the exigencies of the reasoning process.
Finally let me compare these two methods.
S.NO
INDUCTIVE METHOD
DEDUCTIVE METHOD
1.
It gives new knowledge
It does not give any new knowledge.
2.
It is a method of discovery.
It is a method of verification.
3.
It is a method of teaching.
It is the method of instruction.
4.
Child acquires first hand knowledge and information by actual observation.
Child gets ready made information and makes use of it.
5.
It is a slow process.
It is quick process.
6.
It trains the mind and gives self confidence and initiative.
It encourages dependence on other sources.
7.
It is full of activity.
There is less scope of activity in it.
8.
It is an upward process of thought and leads to principles.
It is a downward process of thought and leads to useful results.
To conclude, we can say that inductive method is a predecessor of deductive method. Any loss of time due to slowness of this method is made up through the quick and time saving process of deduction. Deduction is a process particularly suitable for a final statement and induction is most suitable for exploration of new fields. Probability in induction is raised to certainty in deduction. The happy combination of the two is most appropriate and desirable.
There are two major parts of the process of learning of a topic: establishment of formula or principles and application of that formula or those principles. The former is the work of induction and the latter is the work of deduction. Therefore, friends, “Always understand inductively and apply deductively” and a good and effective teacher is he who understands this delicate balance between the two. Thus: “his teaching should begin with induction and end in deduction.”
By: prabhat marwaha
