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Techniques to develop concepts rather than memorization in mathematics within time frame at primary secondary levels
The document discusses innovative teaching methods in mathematics aimed at promoting understanding over memorization, particularly in primary and secondary education. It critiques traditional teaching methods, emphasizing the need for interactive approaches such as inquiry-based learning, cooperative learning, and the use of mathematics labs, alongside techniques for assessment and evaluation. The focus is on fostering an engaging educational environment where students actively construct knowledge and apply it in real-world contexts.
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Techniques to develop concepts rather than memorization in mathematics within time frame at primary secondary levels
- 1. TECHNIQUES TO DEVELOP CONCEPTSRATHER THAN MEMORIZATION IN MATHEMATICS WITHIN TIME FRAME AT PRIMARY/SECONDARY LEVELS SAMREEN SHABBIR, TGT, FG PUBLIC SCHOOL NO.1 (GIRLS) BAHAWALPUR CANTT.
- 2. In traditional educationcontext, the teacher is the sender or the source. The educational material is the information or message. The student is the receiver of the information. The delivery medium chalk-and- talk” method. In such a lecture students assume a purely passive role and their concentration fades off after 15-20 minutes. ANALYSIS OF TRADITIONAL METHOD OF TEACHING
- 3. LIMITATIONS Teaching in classroomusing chalk and talk is “one way flow” of information Teachers often continuously talk for an hour without knowing students response and feedback. The material presented is only based on lecturer notes and textbooks. There is insufficient interaction with students in classroom. More emphasis has been given on theory without any practical and real life time situations. Learning from memorization but not understanding.
- 4. INNOVATIVE METHODS OF TEACHING Ihear and I forget. I see and I believe. I do and I understand. - Confucius The empires of the future are the empires of the mind.- Winston Churchill
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- 6. APPROACHES IN TEACHINGAND LEARNING MATHEMATICS Approaches INQUIRY TEACHING DEMONSTRATION APPROACH DISCOVERY APPROACH MATH-LAB APPROACH PRACTICAL WORK APPROACH (PWA) INDIVIDUALIZED INSTRUCTION USING MODULES BRAIN STORMING PROBLEM-SOLVING COOPERATIVE LEARNING
- 7. INQUIRY TEACHING Inquiry Teachinginvolves providing learners with content-related problems that serve as the foci for class research activities. The teacher provides/presents a problem then the learners identify the problem.
- 8. THE STEPS INTHE PROCESS OF INQUIRY • Present specific problematic situation. • Encourage observation for developing a statement of research objectives • Ask students for observation and explanation • Encourage the testing of the hypothesis • Develop tentative conclusion and generalization • Debrief the process
- 9. DEMONSTRATION APPROACH Demonstration Approachis a teaching strategy in which the teacher engages “in a learning task other than just talking about it”.
- 11. DISCOVERY APPROACH Discovery Learningis “International Learning” . Both the teacher and the learner play active roles in discovery learning depending upon on the role that the teacher plays, this can range from guided discovery (needs strict supervision) to free or pure discovery (very little supervision needed)
- 12. MATH-LAB APPROACH The MathematicsLaboratory Approach is a method of teaching whereby children in small groups work through an assignment/task card, learn and discover mathematics for themselves.
- 13. PRACTICAL WORK APPROACH(PWA) Thelearners in this approach, manipulate concrete objects and/or perform activities to arrive at a conceptual understanding of phenomena, situation, or concept. The environment is a laboratory where the natural events/phenomena can be subjects of mathematical or scientific investigations.
- 14. INDIVIDUALIZEDINSTRUCTION USING MODULES Theapplication of Individualized Instruction permits the learners to progress by mastering steps through the curriculum at his/her own rate and independently of the progress of other pupils.
- 15. BRAINSTORMING It is ateaching strategy in which the teacher elicits from the learners as many ideas as possible but refrains from evaluating them until all possible ideas have been generated.
- 16. BRAINSTORMING USUALLY OCCURSIN 4 PHASES 1) problem identification, 2) idea generation, 3) idea evaluation, and 4) solution implementation and evaluation.
- 17. PROBLEM-SOLVING Problem-solving can bestbe defined as a learner- directed strategy in which learners “think patiently and analytically about complex situations in order to find answers to questions”. A problem is defined as a “situation in which you are trying to reach some goal, and must find means for getting there”.
- 18. PROBLEM-SOLVING When using problem-solvingfor the first time: select a simple problem that can be completed in a short amount of time. Consider learners’ interest, ability level, and maturation level. Make sure resources (materials or equipment) are available. Make sure that learners are familiar with brainstorming before you implement problem- solving.
- 19. COOPERATIVE LEARNING Cooperative learningis helpful in eliminating competition among learners. It encourages them to work together towards common goals. It fosters positive intergroup attitudes in the classroom.
- 20. COOPERATIVE LEARNING •eliminates competitionamong learners. It encourages them to work together towards common goals. •It fosters positive intergroup attitudes in the classroom. It encourages learners to work in small groups to learn.
- 21. COOPERATIVE LEARNING ■ Agroup of pupils carrying out activities under the supervision and guidance of a teacher. ■ Pupils exchange ideas through discussion with the aim to solve a problem or to carry out a project together. ■ Teacher monitors pupils’ behaviour and provides task assistance. ■ Teacher evaluates pupils’ learning outcome and helps them to formulate a conclusion.
- 22. INTEGRATIVE TECHNIQUE The IntegratedCurriculum Mode (Integrative teaching to some) is both a “method of teaching and a way of organizing the instructional program so that many subject areas and skills provided in the curriculum can be linked to one another”.
- 23. CONSTRUCTIVISM ■ Pupils constructtheir own knowledge by testing ideas and approaches based on their prior knowledge and experience . ■ Teacher should engage pupils’ curiosity and create interest in gaining new knowledge . ■ Teacher should lead pupils to explore and investigate by using systematic inquiry. ■ Teacher should help to explain the concept involved and make connection to their previous experiences.
- 24. SELF ACCESS LEARNING ■Pupils access learning materials and acquire knowledge and skills independently. ■ Learning materials are created based on the pupils’ needs, interests, level of achievement and learning style. ■ Teacher should provide pupils with learning skills and train them to self access learning. ■ Teacher should guide the pupils when needed.
- 25. FUTURE STUDIES ■ Teacherleads pupils to understand the most important issues, problems and opportunities they may face and teach them the skills they need to continue to look ahead on their own . ■ In future studies approach, teacher provides pupils with the necessary techniques for becoming independent thinkers and lifelong learners
- 26. Steps of lessonplanning were adopted as given by Carin and Surd (1981) 1)Statement of the problem. 2)Previous knowledge. 3)Concept to be developed. 4)Specific objectives. 5)Teaching aids. 6)Presentation.(how to present subject matter) 7) Questions of Discussion 8) Investigative activities of students. 9) Observation table made by the students. 10) Generalization 11) Open questions. 12) Teacher activity.
- 27. Evaluation Procedures Testing Procedures Informal and StandardizedTests Individual and Group Tests Oral , Essay and Objective Tests Speed , Power and Mastery Tests Readiness and Diagnostic Tests Verbal, nonverbal and Performance Tests
- 28. a. Achievement Testinclude simple quizzes on the work during single period to full-scale examinations c. Inventory tests often referred to as pre- and post- tests and are used to determine the improvement of the students e. Speed tests are tests wherein a student is required to complete as many tests or problems in a predetermined time b. Diagnostic tests attempts to locate areas of misunderstanding or areas where teaching has not taken place to enable suitable remedial instruction to be given d. Individual tests require careful questioning and observation of the reaction of an individual and needs an expert to administer f. Power tests require a student to do as many problems or tasks out of a set of increasing difficulty g. Sociometric Tests which test sociability of students require them to select or identify their classmates whom they like very much Types of Tests for Evaluation Purposes
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