Background
SLC is the first examination which is conducted from national level for our students. In B.S. 2067, 397759 students participated in this examination but only 55.5 % students passed this exam. Mainly major subjects like mathematics, English and science are subject where many students fail. Over all subject-wise judgment nationally is not fair in number but one truth is true that day by day students’ fail rate in mathematics comparatively to other subject is rising highly. There are several reasons but one important reason is our traditional teaching method. Very old and traditional and parroting way of teaching learning method cannot cover the coverage of mathematics and finally students are going to be weaker and weaker day by day from junior class to senior classes.
Mathematics is also a language, it has its’ own symbols and terminologies with some specific meaning. Mathematics learning depends upon chain where learners’ pre-knowledge plays vital role. When students have some difficulties in previous concept, ultimately, it harms to learn and innovate new concept. In Nepal, only after 10 -12 years school education, students’ achievement is checked in so-called standard form but before that many students fall in trouble and gone in dark sky. SLC result is made only the way to check every one like teacher, student and school. At that time when someone pupils fail in mathematics then every type of charges is under that specific teacher or school which is very unfair. So that every mathematics teacher should think a new way of positive solution, which here is going to discuss as another teaching method “Constructivism in Mathematics Class Room”.
Introduction
Constructivism is taken as a learning theory but still there is a debate that it is a learning theory or it is a model of knowing which uses learning theory to correlate some known and unknown concepts in class room. Any way, we use it in mathematics class room very effectively with better conceptual and coverage learning. Here students participate directly and teacher remains as a guide or facilitator. Students are encouraged to participate in class room activities, correlate their pre-knowledge, construct new knowledge and accept it. A mathematics deal on logic, for logical experiments, society is needed, so, mathematics class is taken as a society. That’s why social constructivism is also a theory where learners gather, talk, discuss, do experiments and find out the conclusions. Development of mathematical proofs should be socially agreed, mathematical knowledge is also a part of society. In psychological constructivism, learner participates according to his or her past knowledge, their psychological interests and development stages. The main difference between social and psychological constructivism is the focus of learner, both say knowledge is built in brain. In social constructivism, influences from society, peer group and other external factor affect in learning process but in psychological constructivism, learners mind set, development stages and nearly surroundings affects.
Major principles to facilitate constructivism learning are as follows (According to Brook and Brook 1993):
a. Posing problems relevance to students: Students do activity but it does not mean that they do what they want. Teacher move the students in planning, so teacher is always be in preparation.
b. Structuring learning around primary concepts: Teacher manage the class room environment according to students’ pre-knowledge and get knowledge in depth with big picture.
c. Seeking and valuing students’ point of view: Teacher is always ready to listen students’ view so that it can direct the experiment or discussion towards objectives according to their interest.
d. Adopting curriculum to address students’ suppositions: Teacher is flexible to go with students’ support to get success. It is really difficult to manage for teacher.
Constructivism approach believes in knowledge. The creation of knowledge and its application is the main focus point of this approach. Here nature of knowledge required for teacher and student is defined as follows (Hendry, 1996):
1. Knowledge exists in the mind of people only: classroom, black board, teacher, books etc are only tools; student must work out in mind to get knowledge.
2. The interpretation gives according to knowledge: When teacher ask any query in classroom discussion then students reply according to their previous knowledge, teacher explain the materials and theories on existing norms and values.
3. Knowledge can never be certain: Knowledge of teacher is not fixed, when new environment comes then person defines accordingly.
4. Knowledge is constructed through perceptions and action: Knowledge of teacher and student is changing day by day according to the person’s perception-action about this content.
5. Construction of knowledge requires time and energy: Construction of knowledge is not easy task but it gives satisfaction and pleasure after getting. It needs more effort and contribution of the learners’.
Constructivism approach allows the students how they interact on mathematical relations within and with other disciplines, teacher does not dominate the class, students are encouraged to go deeply through possible solutions. Teacher, let them to search the better way of solution, use them in society whether they use calculator or computer or paper pencil which does not matter. Constructivist philosophy do focus on how and what new knowledge is integrated by using pre-knowledge by the help of teacher, books etc.
Role of teacher
According to behaviorist that teachers are the tellers of truth, as a transmitter, math teacher knows many things about mathematics but constructivist wants to change the role of teacher from transmitter to facilitator. Teacher creates positive environment of class room by asking favorable questions, organize students’ work carefully in prompt. So teacher must be in plan before taking class. Every required material and their uses should teach before starting the lesson like some time teacher should guide the use of graphic calculator or protractor. Class room must be managed properly in sound and friendly environment, lesson plan and materials should be student favorable. Teacher’s main role is in planning that how to involve and way out them in correct direction and diversity of their out puts, activities, interests should be taken easily by teacher.
According to Perkins and Smerdon, a constuctivist teacher has the following characters:
- Encourage and accept student autonomy and initiatives.
- Use raw data and primary sources as far as possible along with manipulative, interactive and physical materials.
- Use cognitive terminology such as “classify”, “analyze”, “create” etc when framing task.
- Allow student response to drive lessons, shift instructional strategies and alter content.
- Inquire students’ understanding before sharing their own understandings.
- Encourage student in dialogue or activity with teacher and students.
- Encourage to ask thoughtful and open-ended questions with teacher and students.
- Allows time to think, create relationship and construct metaphors after asking questions.
- Summarize the discussion or activity according to students’ thought which is true.
Role of student
Students in constructivism approach learn in resourceful environment, a lot of materials within class room direct them in new knowledge. They actively collect the information, assemble them by using their pre-knowledge and try to gist it. May be they do mistakes but it does not hinder them. In Nepal, we may say our class room is not well managed with materials but constructivist approach suggests to use local manipulative materials. Teacher with apple or bread for fraction, rope for number line, marbles and stones for algebraic addition, black board for rectangle and parallel line etc are enough materials.
Students work in group or individual to identify the problem, built hypothesis, collect information and give conclusions. They actively engage in activity, encourage others and make good example of society. They give strong voice on their own logic but accept and respect others view as well can enjoy in diversity of responses and encouraged to drill, draw, write and other form of expressions. Really students are like social being in sense.
Main problem in mathematics and its solution
Nepal with low mathematical practical knowledge gives many negative effects in society and unusual problems arise because of different reasons. Here main problems among many in mathematics teaching-learning process are focused as follows with solutions from constructivist view.
Math-anxiety
According to Piaget, Pre-operational stage (two to six years) is the main age to learn language but that language is associated with some physical object. At this time children have some characters like egocentric, reversibility, no conservation skill and no logic skill. We teacher teach them by lecture method so that they never enjoy mathematics, feel boring and dry subject. From this stage we send our children far from mathematics then they never encourage to learn mathematical skills. Teacher should use local materials and correlate mathematics with daily life by playing or enjoyable way according to their development stage. Manipulative materials should use in the beginning to learn the concept and inter-relate this skill in another place without using these materials is true learning because learning should be transferable. Math anxiety starts from pre-operational stage and cumulate in higher ages.
Basic Mathematics skill Achievement
Our classes X students feel difficult to add some fractions by using LCM. Where is the problem? They never make their true conception about vector except definition and some calculations then how do they understand theories in physics? Basic mathematics skill must be taught thoroughly with good conceptions so that they can construct new concepts like bricks in wall of a house. If finding median is needed to teach in t-test in statistics then it is not possible to use constructivism approach. Mathematics is a chain, if student have gap in junior knowledge then senior classes’ effort is useless. So, basic concept of mathematics is built by constructivism, not effective by other method.
Problems to use constructivism approach in class room
- Expert role in mathematics class changes to facilitator role which transformation is very hard for teacher.
- Noise level of your class room is obviously increased which may be problem for our traditional schools.
- Students may be undisciplined because their role also been changed.
- Class room teaching takes much time. If students have lack of previous knowledge then it is about to impossible to use this approach.
- Teacher must be well plan to motivate the class room activity in well path concept in subject matter.
- Lack of infrastructures.
What constructivist mathematics is not?
Here student participate directly but it does not mean that students ‘discover’ new math knowledge. Piaget used one term ‘Reflective Abstraction’ which means power of generalization and abstraction from reflecting on one’s actions. Example: When a boy learns counting from 1 to 10 now and you give first 10 oranges then he can count easily, if you add 2 more then either he counts 11, 12 or again starts from 1. If he already had some experience in reflection of counting breads or marbles, he is able to solve the problem by imagining them in his mind otherwise he cannot. If a teacher uses material but does not try to use reflective abstraction, it means connection between object to image and picturing in child’s brain is not complete so that lacking of connection between object to word/concept/theory gives no meaning.
Criticism
Constructivism has some criticisms. Mathematics needs drill and practices but constructivism approach does not believe on it. Mathematical formulas are discovered by Discovery Method then why should say constructivism instead of Discovery? All mathematical problems cannot solve by students then there is no alternative than teacher for this solution, here constructivism does not work. Some says that constructivism makes student slow.
Conclusion
Decision to choose teaching approach is in teachers’ hand but some factors determine before to select the teaching approach in the class room like number of students, nature of subject matter, physical structure etc. Using only one approach in the class room is tedious and boring, no one want same taste always. Constructivism approach is better to use in junior level and in the conceptual teaching in mathematics. Very few fundamental mathematical concepts are made really understandable to school children by other than this approach.
