DIFFICULTIES OF HIGH School STUDENTS IN MATHEMATICS   

"According to the investigation, high school students find difficulty in solving mathematical word problem due poor reading comprehension. The reason for this may be students' negative attitude towards the subject, wrong interpretation of the problem or limited vocabulary to understand word problem".  

              

                        Mathematics is the study of topics such as quantity, structure, space & change.  There is a range of views among mathematics and philosophers us to the exact scope and definition of mathematics.  A problem in mathematics is a problem that is amendable to being represented, analyzed and possibly solved with the methods of mathematics.

                     A word problem is a mathematical exercise where significant background information on the problem is presented as text rather than in mathematical rotation.  Word problem are an integral part of the mathematics curricular.  Word problem in mathematics often pose a challenge because they require that students read and comprehend the text of the problem, identify the questions that needs to be answered and finally create and solve a numerical equation.  Children are often overwhelmed by word problems not because they cannot solve these but because they do not comprehend the problem statement due to a language barrier.  As a result they often wait for the teacher to solve the question in numerical form otherwise they misinterpret the problem statement and come up with wrong answers. Mostly the problem is they have poor reading comprehension due to which they find difficulty in solving word problems.

Difficulties of students in solving mathematical word problem

The difficulties encountered by the students in solving mathematical word problems are

Ø Limited vocabulary to understand word problem in mathematics.

Ø Lack of technique in solving word problems.

Ø Lack of methods used by teacher to read word problem.

Ø Poor reading comprehension.

Ø Students doing rote learning.

Ø Negative attitude towards the subject.

Ø Lack of interest in subject.

Ø Lack of concentration.

Ø Wrong interpretation of the problem.

Ø Lack of reinforcement and motivation.

Objective

1.  To know the difficulties of the students in solving mathematical word problem.

2.  To identify the reasons behind the difficulties of the students.

3.  To analyze their performance before and after the remedies given.

4.  To suggest remedial measures to improve on the basis of their performance.

Hypothesis

           From the above objective it has been hypothesized that the students find difficulty in solving mathematical word problem due to poor reading comprehension.

METHODOLOGY

Method

         Method used was action research.

Sample

       The sample for the present investigation consists of 16 students including 3 girls and 13 boys of class VIII of Govt. H. S. S. Thrickodithanam.

Tool Used

         For this investigation, a diagnostic test was conducted in sample class.

Procedure

         A pre-test was conducted among 16 students of class VIII to know about their difficulties on that basis they are given remedial measures and then again conducted a post-test.

                The tests were conducted in regular classroom periods and in extra classes on mathematical word problem.

Data Collection

            Diagnostic test was administered on students of class VIII. Then located the area of difficulty and proper remedial instruction were given to rectify their problem in group.

Table

Duration of period	Action to be taken	Procedure & tool used
Regular classroom period	Orientation of the students regarding the problem.	By distributing a sheet of paper in which some simple word problems given and said to read it and just only write what is given in it.
2 days	Directing the students to write on the given sheet at their home.	Requesting the teacher of the same class not to give heavy in their subject for these two days and the parents to let them free.
Regular classroom period	To collect sheets from the students.	Collecting the sheets by taking help of the monitor of the class.
2 days	Evaluation of sheets and division of the class into 3 groups - good, average and poor on the basis of their skill of solving word problems.	Evaluation of the skill of solving word problem on the basis of set criterion of the students.
1 week	Selecting good specimen paper of word problem for students.	Referring other textbooks, guides and math text available and collecting good specimen from other math teacher.
Extra class period	Distributing the collected specimen to the 3 groups of class already divided.	Classify the specimens according to the level of difficulty into 3 groups so that they can be given separately to students with good, average and below average.
2 days	Drill work practice or exercise.	Now students given problems and said that this time not only identify the given items but also try to solve it.
2 days	Proper checking of notebooks (collected by students)	The teacher will do this work in free period.
Regular classroom period.	Giving more problems and solving in class and checked by teacher.	Students are given more question and said to solve it in the class. Then teacher check the improvement of the students.
1 week	Giving previous years question papers.	Students are given previous years question papers to solve.
Regular classroom period	By organizing a mathematics test.	The teacher will conduct the test among students on solving word problem.

Findings And Result

               From the study, it was clear that students of class VIII has difficulty in solving mathematical word problem due to poor reading comprehension.

Conclusion

           Many students find difficulty in mathematics. There are many areas in mathematics that is difficult for students and the reason for it is that they are not able to understand the methods of teaching. So to know about what are the difficulties that high school students are facing, a teacher should conduct an investigation to solve it. Hence to know the reason of difficulty that high school students have in solving mathematical word problem, an investigation is conducted and the result shows that students has difficulty in solving mathematical word problem due to poor reading comprehension.

   REFLECTION ON MY EXPERIENCE AS A MATHEMATICS TEACHER DURING  SCHOOL INTERNSHIP PROGRAM

         I went to Govt. H. S. S. Thrickodithanam for school internship program on 20 June 2016 as a mathematics teacher. It was a good experience as I was able to know about the students more and to know about school systems and the responsibilities of a teacher.

          My first class didn't go well as I was nervous and had fear that how students will accept and welcome me. But later on as the classes went, I become more comfortable and confident in front of my students. I was allotted class VIII - C and IX - C, the English medium section of the high school.

         I tried my level best for making my class more effective and interesting. There were many good and bad experiences during my internship program, which made me to reflect on myself.

          In the first class, students where divided into four groups and class was taken according to the lesson plan. At first students participation and responses were less but later on as the classes progressed, everything came under control and students actively participated in school activities. There were 16 students in class VIII - C including 3 girls and 13 boys. In IX - C , there were 19 students including 4 girls and 15 boys.

           During the internship program, there were many activities conducted in school and we actively participated in them all. I also took part in organizing Mathematics club inauguration.

            Then on August 15, 2016, there was a flag hosting and we all participation in the ceremony. Then on 7 September 2016, school organized Onam celebration in which we actively participated. We took part in preparing food and judging the Onam games. I was one of the judge in judging "Athapoove" competition. Students actively participated in all activities and made the program a grand success. We were also surprised and happy on seeing their talents. Then on 26 September 2016, school organized a school exhibition in which students presented their creative work in which we also helped them. Then on 7 October 2016, there held school youth festival ( school kalolsavam) in which I was a co-ordinate member with the school teachers of Green house. I actively participated in all activities and co-ordinated all the activities of the house and supported it.

  

           This internship program gave me many good experiences. I was able to know how to handle students and how to control a classroom. This not only made me to know a classroom but also helped to know that what are the responsibilities of a teacher towards the school and also students. I am happy that I was a part of it.

Euclid

                                                  



Euclid (sometimes called Euclid of Alexandria), was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323 - 283 BC). His elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics especially geometry from the time of its publication until the late 19th or early 20th century. In the elements, Euclid deducted the principles of what is now called Euclidean Geometry from a small set of axioms. Euclid also wrote on  perspective, conic section, spherical geometry, number theory and rigor.

Contribution of Euclid in mathematics:

1. Euclidian geometry states that sum of the angles of a triangle is 180 degree.
2. Euclid formulated a method to find out the H.C.F.
3. He gave a proof that prime numbers are infinite.
4. It was Euclid who first proved root of 2 as a transcendental number.

Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and has been credited as the founder of the movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived so very little reliable information is known about him. He was born on the island of Samos, and traveled, visited Egypt and Greece, and maybe India, and in 520 BC, he moved to Croton, in Magna Graecia, and there established some kind of school or guild.

Pythagoras made influential contribution to philosophy and religion in the late 6th century BC. He is often reverted as a great mathematician and scientist and is best known for the Pythagorean theorem which bears his name.Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important. It was said that he was the first man to call himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato, and through him, all of Western philosophy.

Contribution of Pythagoras in Mathematics:

1. The sum of the angles of a triangle is equal to two right angles.
2. The theorem of Pythagoras for a right angles triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. The Babylonians understood this 1000 years earlier, but Pythagoras proved it.
3. The constructing figures of a given area and geometrical algebra. For example they solved various equations by geometrical means.
4. The discovery of irrational numbers is attributed to the Pythagoreans, but seems unlikely to have been the idea of Pythagoras because it does not align with his philosophy the all things are numbers, since number to him meant the ratio of two whole numbers.
5. The five regular solids (tetrahedron, cube, octahedron, icosahedron, dodecahedron). It is believed that Pythagoras knew how to construct the first three but not last two.
6. Pythagoras taught that Earth was a sphere in the center of the universe, that the planets, stars, and the universe were spherical because the sphere was the most perfect solid figure. He also taught that the paths of the planets were circular. Pythagoras recognized that the morning star was the same as the evening star, Venus

Bhaskaracharya

Bhaskara (also known as Bhaskaracharya), (1114 - 1185), was an Indian mathematician and astronomer. He was born in Bijapur in modern Karnataka.

Bhaskara and his works represents a significant contribution to mathematical and astronomical knowledge in 12th century. He has been called the greatest mathematician of medieval India. His main work SIDDHANTHA SHIROMANI, (Sanskrit of "Crown of Treaties") is divided into  four parts called LILAVATI, BIJAGANITA, GRAHAGANITA and GOLADHYAYA, which are also sometimes considered four independent works. These four section deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treaties named KARANA KAUTUHALA.

Bhaskara's work on calculus predates Newton and Leibniz by over half a millennium. Hes is particularly known in the discovery of the principles of differential calculus and its application to astronomical prob;ems and computations. While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhaskara was a pioneer in some of the principles of differential calculus. He was perhaps the first to conceive the differential coefficient and differential calculus.



Some of Bhaskara's contributions to mathematics include the following:

• A proof of the Pythagorean Theorem by calculating the same area in two different ways and then canceling out terms to get a + b = c.

• In Lilavati, solutions of quadratic and cubic indeterminate equation are explained.

• Solutions of indeterminate quadratic equations (of the type ax + b = y).

• Integer solutions of linear and quadratic indeterminate equations (Kuttaka). The rules he gives are (in effect) the same as those given by the Renaissance European mathematicians of the 17th century

• A cyclic Chakravala method for solving indeterminate equations of the form ax + bx + c = y. The solution to this equation was traditionally attributed to William Brouncker in 1657, though his method was more difficult than the chakravala method.

• The first general method for finding the solutions of the problem x − ny = 1 (so-called “Pell’s equation “)was given by Bhaskara II.

• Solutions of Diophantine Equations of the second order, such as 61x + 1 = y. This very equation was posed as a problem in 1657 by the French mathematician Pierre de Fermat , but its solution was unknown in Europe until the time of Euler in the 18th century.

• Solved quadratic equations with more than one unknown, and found negative and irrational i solutions.

• Preliminary concept of mathematical analysis.

• Preliminary concept of infinitesimal Calculus, along with notable contributions towards integral calculus .
• Conceived differential calculus, after discovering the derivative and differential coefficient.

• Stated Roll’s theorem, a special case of one of the most important theorems in analysis, the mean value theorem. Traces of the general mean value theorem are also found in his works.

• Calculated the derivatives of trigonometric functions and formulae.

• In Siddhanta Shiromani, Bhaskara developed spherical trigonometry along with a number of other trigonometric results.