A critical comment on any one mathematics textbook of grade 8

Introduction:

The textbook is valuable when it is used properly so the textbook is designed in such a way that it can be used properly. Appraisal of textbook can be taken as the answer of what should be included in the textbook? What types of textbook should be there? Is it appropriate in academic, physical and psychological point of view?

For the appraisal of mathematics textbook, I have taken the textbook of grade 8 published by curriculum development centre (CDC), Ministry of Education (MOE) and printed by Janak Shiksha Samagri Kendra limited. The presented compulsory mathematics textbook of graded 8 had been written by Dr. Santoshman Makey, Harinarayan Upadhaya and Sunma Tuladhar in 2053 B.S and later on it has been modified by Dr. Siddhi Prasad Koirala, Bhojraj Sharma, Salikram Bhusal, Barun Prasad Baida, Indira Aryal and Nirmala Gautam with the current modified curriculum of Nepal. The first edition of that book was in 2053 B. S and the last edition of the book is of 2061 B.S. The appraisal of textbook from Academic, Physical and psychological point of views are presented below respectively.

Academic Aspects: In this aspect mostly the structure of content, organization of content, presentation, rigor, vocabulary, correctness, theorems and proofs, generalizations, illustrations, example, teaching methods and teaching materials, exercise and review, reference and index etc. are evaluated. The presented textbook of grade 8 has some strength however it may not be free from some shortcomings also. Saying about the strength of the book it is written by well qualified and experience teacher whose aims of writing the textbook is very genuine. The strength and weakness of the textbook are presented below as follows:

Strengths of the textbook:

Ø The language used in the textbook is very simple and clear.

Ø It is written in desired curriculum.

Ø Here are not so many examples so it has helped to the student to get adequate opportunity through initiative and independent effort.

Ø Here are the sequence and consistency in organization of the subject matter.

Ø The way of writing the textbook is interesting and comprehensive.

Ø Here is not any irrelevant subject matter.

Ø The textbook satisfies the demand of examinations also.

Ø The proof presented on the textbook is appropriate for the maturity of the student.

Ø The vocabulary used in the textbook is appropriate and suitable.

Ø The homework and assignment can easily be given from the textbook.

Ø The illustrations presented on the textbook are simple.

Ø The exercise and their answer are given on the textbook is simple.

Ø The exercise and their answers are given on the textbook appropriately.

Ø It enables to give the new knowledge to the student.

Ø The subject matter is presented in simple to complex form.

Ø The level wise organization of the subject matter is genuine.

Ø It is sufficient to give the fundamental bases for the next class.

Weaknesses of the textbook;

Ø The steps of solving the problem are not given sufficiently so that the normal student can't understand clearly the problems in some pages of the textbook. We know the textbook should be written in such a way that the normal student can understand the matter from self study also. Here are given some steps to solve the problem which can't be understood by students even the teacher may get the problem in understanding the matter. For example in the lesson 'Square root and cube root' the method of finding the square root from division method is very complex. The direction and steps given in the textbook are quite difficult and complex to understand. So there is less probability of understanding the problem and steps given in the textbook for the student of grade 8. Even the vocabulary given in the textbook is not suitable. We know the symbols and terms used in the textbook must be those which are popular so that they may have no confusion. All new term should be clearly and accurately defined but authors has not concerned in this unit.

Ø The subject error as well as printing mistake is not avoided carefully.

Ø There are not included few difficult exercise to challenge the most intelligent student.

Ø There are not sufficient provision for practice and review; it may not meet the demand of students' ability and interests.

Ø There are not sufficient suggestions to improve the study habit.

Ø It does not facilitate to use the inductive, analytic, heuristic, laboratory method.

Ø Here are presented the suitable proof of the theorem but it has not given any alternative proof of the student.

Physical Aspects:

It is an aspect of textbook which is commonly important as the academic aspects. The presented textbook of the grade 8 is suitable in looking, easy to carry and of around 200 pages whose price can be said moderately priced. Except this strength, here are given some more strength and weakness as follows:

Strengths of the textbook:

Ø The shape and size of the textbook is suitable for desired class.

Ø It is very easy to carry.

Ø It is easy to fold while studying.

Ø The printing of the book is suitable.

Ø The line spacing of the book is suitable.

Ø The letters used in the textbook is suitable.

Ø The figures sketch in the textbook is appropriate.

The weakness of the textbook:

Ø The cover of the book is not attractive.

Ø The block of the book is not printed properly.

Ø The quality of the book in not good.

Ø Only one color is used in the book.

Ø Very few figures are drawn in the textbook.

Ø The book is prepared keeping the intention to be cheap.

Psychological Aspect:

It is also an important aspect of textbook. The textbook should be appropriate form academic and physical aspect as well as psychological aspect. The textbook should be able to arouse the interest to the students. If the book is suitable from the physical and academic point of view the book will be suitable from psychological point of view otherwise it may not be suitable and appropriate. The presented text book of grade 8 is suitable from psychological point of view how ever it can't free from some weakness. If we can remove the weaknesses of physical and academic aspects definitively the weaknesses of psychological aspect will remove automatically. Comparatively the textbook of grade 8 is suitable with contemporary other books because it is written by well qualified, established and experienced author so as a conclusion we can say the book is appropriate psychological point of view.

Suggestions:

We have already said that the textbook is valuable when it is used properly. The teacher should not feel that his work is confined to transferring the contents of the textbook into the head of students. The textbook shouldn't be used as only source of instructional materials. It should be used as an aid in teaching not a substitute for teaching. Its place in teaching can only be real if the teacher supplements it by his oral exposition. So to be the good textbook the above knowledge should be followed carefully and intelligently meanwhile writing the textbook. Those matter and steps should not be put in the textbook which may arouse the confusion to the students. If we remove the weaknesses of the textbook mentioned in the physical, academic and psychological aspects then the text book will be appropriate and effective.

Ausubel's strategy for meaningful verbal learning and its classroom implication

David P Ausubel was an American psychologist who did his undergraduate work at the University of Pennsylvania (pre-med and psychology). He graduated from medical school at Middlesex University. Later he earned a PhD in Developmental Psychology at Columbia University. He was influenced by the work of Piaget. He served on the faculty at several universities and retired from academic life in 1973 and began his practice in psychiatry. Dr. Ausubel published several textbooks in developmental and educational psychology, and more than 150 journal articles. He was awarded the Thorndike Award for "Distinguished Psychological Contributions to Education" by the American Psychological Association (1976).One of his most significant contributions to the field of and educational psychology, cognitive science and science education learning was the development and research on advance organizers (since 1960). He retired from academics in 1973 and devoted himself to his psychiatric practice.

Main Theme:

1 Student gradually learns to associate new knowledge with existing concept in their mental structure.

2 To insure meaningful teaching necessary to avoid rote memorizing in facts.

Ausubel, whose theories are particularly relevant for educators, although he recognized other forms of learning, his work focused on verbal learning. He dealt with the nature of meaning, and believes the external world acquires meaning only as it is converted into the content of consciousness by the learner. Meaning is created through some form of representational equivalence between language (symbols) and mental context. Two processes are involved

i) Reception which is employed in meaningful verbal learning and

ii) Discovery which is involved in concept formation and problem solving.

Ausubel's work has frequently been compared with Bruner's. The two held similar views about the hierarchical nature of knowledge, but Bruner was strongly oriented toward discovery processes, where Ausubel gave more emphasis to the verbal learning methods of speech, reading and writing. We can study the Ausubel theory into different way which can be considered as the strategy of learning according as David Ausuble.

Subsumption Theory:

To subsume is to incorporate new material into one's cognitive structures. From Ausubel's perspective, this is the meaning of learning. When information is subsumed into the learner's cognitive structure it is organized hierarchically. New material can be subsumed in two different ways, and for both of these, no meaningful learning takes place unless a stable cognitive structure exists. This existing structure provides a framework into which the new learning is related, hierarchically, to the previous information or concepts in the individual's cognitive structure. When one encounters completely new unfamiliar material, then rote learning, as opposed to meaningful learning, takes place. This rote learning may eventually contribute to the construction of a new cognitive structure which can later be used in meaningful learning. The two types of subsumption are: 1. Correlative subsumption - new material is an extension or elaboration of what is already known. 2. Derivative subsumption - new material or relationships can be derived from the existing structure. Information can be moved in the hierarchy, or linked to other concepts or information to create new interpretations or meaning. From this type of subsumption, completely new concepts can emerge, and previous concepts can be changed or expanded to include more of the previously existing information. This is "figuring out". Ausubel is a proponent of didactic, expository teaching methods. From this perspective, expository (verbal) learning approaches encourage rapid learning and retention, whereas discovery learning (Bruner) facilitates transfer to other contexts.

Advanced Organizers:

An 'advance organizer is a cognitive instructional strategy used to promote the learning and retention of new information which is information that is presented prior to learning and that can be used by the learner to organize and interpret new incoming information. These organizers are introduced in advance of learning itself, and are also presented at a higher level of abstraction, generality, and inclusiveness; and since the substantive content of a given organizer or series of organizers is selected on the basis of its suitability for explaining, integrating, and interrelating the material they precede, this strategy simultaneously satisfies the substantive as well as the programming criteria for enhancing the organization strength of cognitive structure. An advance organizer is not an overview, but rather a presentation of information (either verbal or visual) that is "umbrellas" for the new material to be learned. According to Joyce et al. (2000), the advance organizer model has three phases of activity:

Phase I (includes presentation of the advance organizer)

Ø Clarify the aimes of the lesson

Ø Presentation of the advance organizer

Ø Prompting awareness of relevant knowledge

Phase II (includes making links to/from the organizer)

Ø Presentation of the learning task or learning material

Ø Make organization and logical order of learning material explicit

Phase III (strengthening of the cognitive organization)

Ø Integrative reconciliation and active reception learning (e.g. the teacher can ask learners to make summaries, to point our differences, to relate new examples with the organizer).

Ø Elicit critical approach to subject matter (have students think about contraditions or implicit inferences in the learning material or previous knowledge)

The simple principles behind advance organizers are that:

1 Most general ideas should be presented first in an organized way (not just a summary) and then progressively differentiated.

2 Following instructional materials should integrate new concepts with previously presented information and with an overall organization.

Therefore, advance organizers present a higher level of abstraction. They are not just simple overviews, illustrating examples etc. But they share with such techniques the idea, that they must be integrated with other teaching/learning activities. Advance organizers provide the necessary scaffolding for students to either learn new and unfamiliar material (an expository organizer which provides the basic concept at the highest level of generalization) or to integrate new ideas into relatively familiar ideas (a comparative organizer which compares and contrasts old and new ideas). Ausubel contends that these organizing ideas, which may be single concepts or statements of relationship, are themselves important content and should be taught because they serve to organize everything that follows. Advance organizers are based on major concepts, generalizations, principles, and laws of academic disciplines.

Ausubel contributed much to the theoretical body of cognitive learning theory, but not as much to the practical classroom aspects as Bruner and others. Ausubel's most notable contribution for classroom application was the advance organizer. The advance organizer is a tool or a mental learning aid to help students `integrate new information with their existing knowledge, leading to "meaningful learning" as opposed to rote memorization. It is a means of preparing the learner's cognitive structure for the learning experience about to take place. It is a device to activate the relevant schema or conceptual patterns so that new information can be more readily `subsumed' into the learner's existing cognitive structures. Ausubel believed that it was important for teachers to provide a preview of information to be learned. Teachers could do this by providing a brief introduction about the way that information that is going to be presented is structured. This would enable students to start with a "Big Picture" of the upcoming content, and link new ideas, concepts, vocabulary, to existing mental maps of the content area.

The primary idea of Ausubel's theory is that learning of new knowledge is dependent on what is already known. In other words, construction of knowledge begins with our observation and recognition of events and objects through concepts we already possess. We learn by constructing a network of concepts and adding to them. A concept map is a instructional device that uses this aspect of the theory to allow instruction of material to learners of different prior knowledge. Another major concept of Ausebel's theory focuses on meaningful learning. To learn meaningfully, individuals must relate new knowledge to relevant concepts they already know. New knowledge must interact with the learner's knowledge structure. Meaningful learning can be contrasted with rote learning which also can incorporate new information into the knowledge structure but without interaction. Rote memory is fine for remembering sequences of objects (i.e. lists of structures) but does not aid the learner in understanding the relationships between the objects. Meaningful learning, therefore, is personal, idiosyncratic and involves recognition of the links between concepts. Both rote and meaningful learning may be achieved no matter what instructional strategy is used. Either reception learning (passive listener with teacher-directed agenda) or discovery learning (active learning where the learner chooses information to be learned) may result in meaningful learning. Therefore, its not necessarily how information is presented but how the new information is integrated into the old knowledge structure that is crucial in order for meaningful learning to occur. A third key idea of Ausubel's theory is that concepts are of different depth. That is, concepts can range from the very general to the very specific. Furthermore, general concepts include (subsume) less general concepts which include most specific concepts. As such, concepts can be progressively differentiated by their level of specificity. In order to learn meaningfully, concludes Ausubel, the learner must discern the level of new concepts and then place them within progressively inclusive levels of specificity in their knowledge structure. The primary idea of Ausubel's theory is that learning of new knowledge is dependent on what is already known. In other words construction of knowledge begins with our observation and recognition of events.

Educational Implications:

1 Reception learning is important as most of school learning involves presentation of concepts rather than their discovery.

2 Abstract concepts can be taught effectively by presenting subsumes and help pupils grasp higher order relationships between abstractions.

3 Since Meaningful Verbal Learning depends on critical ability and readiness to receive, teacher should make use of the adequate pedagogical techniques such as precise and accurate definition of concepts, giving similarities and differences between related concepts, and enabling learners to define in their own words.

4 Since single concepts are easier to retain rather than to remember many specific items, subsumption begins during cognition. Hence, clear, relevant subsumers (advance organizers) should be provided.

5 When we teach separate chapters one after the other, children have to learn details of the topic before acquiring inclusive subsumers as generalizations. This adversely affects learning and retention. Advance organizers (subsumers), therefore, facilitate meaningful learning and its retention.

6 Developing thinking skills in students requires specific instruction and practice rather than application. Teachers should address analysis, evaluation and synthesis using advance organizers that encourage students to operate at higher levels of abstraction. Strengthening cognitive structures helps students retain information longer, and subsumptions provide students with basic structures on which to build new concepts.

7 Before teaching new mathematical concept teacher should motivate the student and relate the new concept with pre existed knowledge. For example to teach about height and distance in class ten the teacher must remind to the student about sin, cos, tan, cosec, sec, cot and other condition of trigonometry.

8 Teaching materials should be used in classroom teaching and teacher should demonstrate it in very well manner.

9 Teacher should explain a lot as much as possible to give the subject matter to the student.