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Techniques used in Authority teachingTelling which is definedstating an understanding without justificationby analogyby demonstrationLESSON 3backInteraction and discussionsInteraction is created by asking questions in order to provide means for active instead of passive participation.LESSON 3backDiscoveryLESSON 3techniques where learners are not given everything by the teacher but they have to work out the rule and meaning by themselves.nextLaboratoryLESSON 3done through experimental activities dealing with concrete situations such as drawing, weighing, averaging and estimatingnextTeacher-controlled presentationThe teacher uses educational technology such as films and filmstrips, programmed materials, and audio materials. LESSON 3nextElements of a discovery experience Motivationprimitive processan environment for discoveryopportunity to make conjectures a provision for applying the generalization.backMathematical activities based on problem solvingGeneralizationAbstractionconcept building LESSON 3STRATEGIES IN TEACHING MATHEMATICSProblem solvingConcept attainment strategyLESSON 3Problem solvingTeachers task:Make sure students understand the problem. The students will lose interest in a subject they do not understand. The question presented may not even present a problem.Ask the following questions:1 Do the students understand the meaning of the terms in the problem?2 Do they take into consideration all the relevant information?3 Can they indicate what the problem is asking for?4 Can they state the problem in their own words?LESSON 3Help the students gather relevant thought materials to assist in creating a plan. Assist the students in gathering information by helping them analyze the given conditions.Provide students with an atmosphere conducive to solving problems.Once the students have obtain the solution, encourage them to reflect on the problem and how they arrived at the solution.Encourage them to present alternate ways of solving the problem.LESSON 3Theoretical basis of problem solving strategiesConstructivismCognitive theory Guided discovery learning Metacognition theoryCooperative learningLESSON 3Constructivismthis is based on Bruners theoretical framework that learning is an active process in which learners construct new ideas or concepts based upon their current/past knowledge.Cognitive theorythe cognitive theory encourages students creativity with the implementation of technology such as computers which are used to create practice situations.LESSON 3Guided discovery learningtools engages students in a series of higher order thinking skills to solve problems.Metacognition theorythe field of metacognition process holds that students should develop and explore the problem, extend solutions, process and develop self-reflection. Problem solving must challenge the students to think.Cooperative learningthe purpose of cooperative learning groups is to take each member a stronger individual in his/her own right. Cooperative skillsforming groupsworking as a groupproblem solving as a groupmanaging differences24STEPS OF THE PROBLEMS SOLVING STRATEGYRestate the problemsSelect appropriate notation. It can help them recognize a solution.Prepare a drawing, figure or graph. These can help understand and visualized the problem.Identify the wanted, given and needed information.Determine the operations to be used.Estimate the answer.Solve the problems.Check the solution. Find a way to verify the solutions in order to experience the process of actually solving problems.OTHER TECHNIQUES IN PROBLEM SOLVINGObtain the answer by trial and error.Use an aid, model or sketch.Search for a patternExample: find the 10th term in a sequence that begins, 1,2,3,5,8,13. this approach is an aspect of inductive thinking-figuring a rule from examples.Elimination strategyConcept Attainment StrategyAllows the students to discover the essential attributes of a concept.Enhance students skills in:Separating important from unimportant information.Searching for patterns and making generalization.Defining and explaining concepts.Concept Attainment StrategyStepsselect a concept and identify is essential attributes.present example and non-examples of the concepts.let students identify or define the concept based on its essential attributes.ask the students to generate additional examples.SAMPLE ACTIVITY: Defining proper fractionThe following are proper fractions;1/5,2/5,3/5,4/5,1/8,2/8,3/8,4/8,5/8,6/8,2/3,2/4,2/10,12/15,3/7,25/43,78/79The following are not proper fractions:5/5,6/5,7/5,8/8,9/8,9/9,10/9,11/9,14/16,15/16,16/16,17/16,20/21,22/21,34/35,35/35,36/35(expected answers: 4/6,5/6,7/9,8/9,14/16,15/16,20/21,34/35)A proper fraction is ____________.(expected answer: a proper fraction is a fraction whose numerator is less than the denominator)NEXTbackEffective use of the concept attainment strategy:successful when:Students are able to identify the essential attributes of the concepts.Students are able to generate their own examples.Students are able to describe the process they used to find the essential attributes of the concept.CONCEPTS FORMATION STRATEGYThis strategy is used when you want the students to make connections between and among essential elements of the concept.StepsPresent a particular question or problems.Ask students to generate data relevant to the questions or problem.Allow the students group data with similar attributes.Ask students to label each group of data with similar attributes.Have students explore the relationships between and among the groups. They may group the data in various ways and some groups may be subsumed in other groups based on their attributes.