Ctet mathematics pedagogy part 2

This is the second Part of CTET Mathematics Pedagogy. In this part we will discuss Problem of Teaching Mathematics, Error Analysis, Diagnostic and Remedial Teaching.

1. CTET MATHEMATICS Mathematics Pedagogy Part - 2

2. This is the second part of Mathematics Pedagogy. In previous part we discussed Nature of Mathematics, Need of Mathematics in Curriculum, Language of Mathematics, community of Mathematics and communication. In this we will discuss Problems in Teaching Mathematics in context of teacher and students, Evaluation, Error Analysis, Diagnostic and Remedial Teaching.

3. Evaluation “Evaluation is the systematic assessment of the worth or merit of some object.” “Evaluation is the systematic acquisition and assessment of information to provide useful feedback about some object.” Both definitions agree that evaluation is a  systematic  endeavor and both use the deliberately ambiguous term 'object' which could refer to a program, policy, technology, person, need, activity, and so on. The latter definition emphasizes  acquiring and assessing information  rather than  assessing worth or merit  because all evaluation work involves collecting and sifting through data, making judgments about the validity of the information and of inferences we derive from it, whether or not an assessment of worth or merit results.

4. Education Evaluation Educational evaluation  is the  evaluation process of characterizing and appraising some aspect/s of an  educational process . There are two common purposes in educational evaluation which are, at times, in conflict with one another. Educational institutions usually require evaluation data to demonstrate effectiveness and to provide a measure of performance for marketing purposes. Educational evaluation is also a professional activity that individual educators need to undertake if they intend to continuously review and enhance the learning they are endeavoring to facilitate . T he   Joint Committee on Standards for Educational Evaluation published three sets of standards for educational evaluations.  The Personnel Evaluation Standards   was published in 1988,  The Program Evaluation Standards  (2nd edition )  was published in 1994, and  The Student Evaluations Standards was published in 2003.

5. Purpose and Function of Evaluation T o determine the present status of the children in the teaching- learning process. To motivate children for better learning. To provide basis for guidance and counseling to children. To determine the rate of progress of the children. To collect evidence for improvement in curriculum. To diagnose children’s weaknesses and strength for further instruction. To measure the effectiveness of the examination system. To improve the efficiency and success of the teacher. To discover innovative and effective methods of teaching. Classify children in different categories. To improve the teaching - techniques and strategies. To provide basis for remedial teaching on the basis of strength and weakness of the children. To give reinforcement and feedback to both the teachers and pupils.

6. Good Evaluation A good evaluation programme should have following characteristic: It measures the direction and extent behavioural changes. Evaluation is quantitative and qualitative estimation of specific changes in children’s behaviour . Evaluation is diagnostic so that it may provided basis for remedial teaching. Evaluation is a continuous and comprehensive process. Evaluation offers feedback to the entire educational system. Evaluation is pupil oriented Evaluation is activity based. Evaluation used to improve instruction, curriculum, methods and examination etc.

7. Process of Evaluation Selection and Formulation of objective. Defining objectives in terms of behavioural changes. Selection of tools and techniques of evaluation. Use of tools and techniques and making results. Interpretation and generalization of results. Feedback of the results for improvement of teaching-learning process.

8. Formative Evaluation Formative evaluation is generally any evaluation that takes place before or during a project’s implementation with the aim of improving the project’s design and performance. Formative evaluation complements summative evaluation and is essential for trying to understand why a program works or doesn’t, and what other factors (internal and external) are at work during a project’s life. Formative evaluation does require time and money and this may be a barrier to undertaking it, but it should be viewed as a valuable investment that improves the likelihood of achieving a successful outcome through better program design

9. Need and Importance of Formative Evaluation Provides information to teachers for modifying instruction and teaching Helps to prescribe group and individual remedial programmes . Helpful in monitoring pupil’s learning progress. Provides feedback to both the teachers and pupils. It facilities retention and transfer of learning. Enables teacher to change the mode of instruction according to need of the students. It also reinforce the learning of high achievers. Helps in better performance in the simulative evaluation. It can also be used as a self evaluation device by the children. Provides immediate feedback to the children. Helpful in diagnosing child’s strength and weaknesses.

10. Summative Evaluation Summative evaluation looks at the impact of an intervention on the target group. This type of evaluation is arguably what is considered most often as 'evaluation' by project staff and funding bodies- that is, finding out what the project achieved. Summative evaluation can take place during the project implementation, but is most often undertaken at the end of a project. As such, summative evaluation can also be referred to as  ex-post  evaluation (meaning after the event). Summative evaluation is often associated with more objective, quantitative methods of data collection.  Summative evaluation is linked to the evaluation drivers of accountability.  It is recommended to use a balance of both quantitative and qualitative methods in order to get a better understanding of what your project has achieved, and how or why this has occurred. Using qualitative methods of data collection can also provide a good insight into unintended consequences and lessons for improvement. Summative evaluation is outcome-focused more than process focussed . It is important to distinguish outcome from output. Summative evaluation is not about stating that three workshops were held, with a total of fifty people attending (outputs), but rather the result of these workshops, such as increased knowledge or increased uptake of rainwater tanks (outcomes).

11. Formative VS Summative Evaluation   Formative evaluation is qualitative while summative evaluation is quantitative. Formative evaluation is a continuous process while summative evaluation is an event that takes place at the end of an instructional unit. Summative evaluation is formal and takes the shape of quizzes and written tests whereas formative evaluation is informal such as homework and projects. The aim of formative evaluation is to improve upon what has been learnt whereas the aim of summative evaluation is to prove the amount of learning that has taken place.

12. Problems of Teaching Mathematics A sense of fear and failure among a majority of children. A curriculum that frustrates both a talented minority as well as the non-participating majority at the same time. Crude ways of assessment making perception of Mathematics as mechanical computation. Lack of teacher preparation and support in the teaching process Mathematics.

13. Fear and Failure Mathematics anxiety and math phobia are the consequences of that emotional comment. Mathematics is taught in the school in such a way that it alienates the children and causes them to stop attending schools. Such fear of Mathematics is closely linked to a sense of failure. The cumulative nature of Mathematics mainly causes such Fear and Failure. The other main reason is the predominance of symbolic language. When symbols are manipulated without the understanding, then after a certain point children start dissociating from the subject. The language of Mathematics learnt in school is completely different from their everyday speech and becomes a major force of alienation in its own right.

14. Disappointment Curriculum Any mathematics curriculum that prioritizes procedure and memorization of formulas over understanding of concepts, enhances the anxiety and phobia. Mathematics is the subject that sees great motivation and talent even at an early age in a small number of children. These children take to quantisation and algebra easily and carry on with great facility. The curriculum does not offer conceptual depth and thus settles for the minimal use of children’s motivation. The learning procedures may be easy for them, but their understanding and capacity for reasoning remain un- utilised .

15. Crude Assessment The crude method of assessment are the barriers for the effective teaching and learning of mathematics. Those method of assessment encourage perception of mathematics as mechanical computation. In all the subjects except the mathematics, partial knowledge may be tried and demonstrated but in case of mathematics such as perception is easily coupled to anxiety and panic. The evaluation procedure in mathematics has seen a little change in our school over a hundred year or more.

16. Inadequate Teacher Preparation Mathematics education depends very heavily on teacher’s understanding of mathematics and his preparation of teaching mathematics. It is the teacher’s knowing of pedagogic techniques that makes the teaching and learning of mathematics so fascinating.

17. Other Systemic Problems Compartmentalisation This includes very little systematic communication between the high school and college teachers of mathematics. Most of the school teachers have never even seen or interacted with the research mathematics Curricular Acceleration It involves the rapid and frequent change of the course curriculum making the shape of mathematics education as taller and more spindly, rather than broad and rounded. Gender Issue Mathematics is the subject which tends to be regarded as a masculine domain and this perception is further aided by the complete lack of references in text book to women mathematicians. It has been found that the teachers tend to address boys more than girls.

18. Error Analysis The purposes of error analysis are to (1) identify the patterns of errors or mistakes that students make in their work, (2) understand why students make the errors, and (3) provide targeted instruction to correct the errors. When conducting an error analysis, the teacher checks the student’s mathematics problems and categorizes the errors. 

19. Addition and Subtraction Lack of understanding of regrouping Confusion of 1s and 10s in carrying and writing Forgetting to carry 10s and 100s. Forgetting to regroup when subtracting 10s and 100s. Regrouping when it is not required. Incorrect operation (the student subtracts instead of adding or vice versa). Lack of knowledge of basic number facts. Multiplication and Division Forgetting to carry in multiplication. Carrying before multiplying. Ignoring place value in division. Recording the answer from left to right in multiplication. Lack of alignment of work in columns. Lack of knowledge of basic number facts.

20. Fractions Incorrect cancellation. Failure to reduce to lowest common denominator. Ignoring the remainder. Incorrect conversion of mixed numbers to fractions. Word Problems Difficulty in reading. Inability to relate to context of problem. Inability to understand the language and vocabulary of the problem. Difficulty in identifying the relevant and the irrelevant information. Difficulty in identifying the number of steps required to solve the problem. Trouble in doing mathematical operations (addition, subtraction, multiplication, division).

21. Diagnostic and Remedial Teaching Diagnostic Evaluation Diagnostic assessment is a form of pre-assessment that allows a teacher to determine students' individual strengths, weaknesses, knowledge, and skills prior to instruction. It is primarily used to diagnose student difficulties and to guide lesson and curriculum planning. Imagine being a teacher in a new classroom. You begin teaching a lesson only to be met with stares of confusion from your students. When you ask the students if they understand what you are teaching, they reply that they have no idea what you're talking about. Now imagine teaching that same class after conducting a pretest to determine what the students already know about the topic. Which scenario sounds preferable? Which would result in a better experience for both the teacher and the students?

22. Benefits of Diagnostic Assessment Diagnostic assessment benefits both the instructor and the students. First , it allows teachers to plan meaningful and efficient instruction. When a teacher knows exactly what students know or don't know about a topic, she can focus lessons on the topics students still need to learn about rather than what they already know. This cuts down on student frustration and boredom. Second , it provides information to individualize instruction. It may show a teacher that a small group of students needs additional instruction on a particular portion of a unit or course of study. He can then provide remediation for those students so that they can fully engage with new content.

23. Similarly , if a teacher discovers that a group of students has already mastered a large portion of a unit of study, he can design activities that allow that group to go beyond the standard curriculum for that topic through independent or small group study. Finally , it creates a baseline for assessing future learning. It shows both the teacher and the students what is known before instruction has occurred. Thus, it sets a baseline on a topic. As the students move through instruction, they can see what they are or aren't learning, and the teacher can provide remediation or enrichment as needed.

24. Remedial Teaching Remedial education  (also known as developmental education, basic skills education, compensatory education, preparatory education, and academic upgrading) is assigned to assist students in order to achieve expected competencies in core academic skills such as literacy and numeracy. Whereas special education is designed specifically for students with special needs, remedial education can be designed for any students, with or without special needs; the defining trait is simply that they have reached a point of under preparedness, regardless of why. For example , even people of high intelligence can be underprepared if their education was disrupted.