Solving Quadratic Equation Using Quadratic Formula - Assignment Example

Lesson Plan 01 Topic: Solving Quadratic Equation Using Quadratic Formula Day: Monday Time: One hour 5th September, Number 30Objectives: The objective of this topic is to understand the method to solve quadratic equations in algebra using quadratic formula. Many problems in the social life involve equations to solve the problems, so quadratic formula provides a great platform to understand them and solve them easily. Procedure: The first session of the lesson will be warm up session in which teacher asks students to tell about equations and how to solve those using different methods. Ask them do they know about equations, and difference between expressions and equations. This session should last for five minutes a very warm welcome session. Guiding Questions: The simplest way of solving a quadratic equation is through factorization but there are students who feel problems in solving equations using factorization. The quadratic equation is of the form ax2+bx+c= 0 where a,b, and c are constants with a ≠ 0. The quadratic formula is Let us consider an example and solve it using quadratic formula, x2 + 5 x + 6= 0. Teacher should tell the students on board and explain the procedure using discriminate about the real solutions, imaginary solutions and solutions that does not exist. Students Activity: After explanation teacher should ask the students to solve an example for the best understanding of the concept. E.g. solve x2 + 3 x + 4= 0 using quadratic formula and also with the different methods they already like factorization and completing square method and check whether their solutions are same or different. Teacher should also assign homework to the students so that they have more and more practice of the concepts they have learned. Feedback from Students: After teaching the lesson teacher should ask the students some questions to check whether they have understand the concept or not and take the feedback and discuss the problems with the students. Summary: Quadratic equations are second degree equations with the coefficient of degree 2 not equal to zero. The graph of a quadratic equation is a parabola and they can be solved using different methods but the simplest way of doing it is through quadratic formula. It gives the roots of the equations that are exact values and they can be checked after getting the results by substituting the answer in the original equation (Sivasubramanian, 2009). Lesson Plan 02 Topic: Using Differentiated Instructions in Teaching Day: Tuesday Time: 1 hour Date: 6th September, 2011 Number of Students: 15 Objective: The purpose of this lesson is to discuss the differentiated instructions while teaching factors and fractions with detailed background discussions on the topics. Results have shown that students understand more using differentiated instructions as compare to others but it is also noted that all the students do not understand the differentiated instructions. Procedure: Most of the teachers include contents like factorization, probability and fractions that are not easily understood by the students. Teacher should brainstorm the concepts before the start of the teaching to check whether the students are ready o understand the concept and warm them up. By this way students take active part in the class and can understand the concepts easily and swiftly. Guiding Students: Teacher should give the students the results of survey conducted to understand the differentiated instruction and after that ask them few questions from that survey results. Always try to ask the questions relevant to the topic and try to gather all students to take active part in the discussion. After question answer session, give the students an activity so that you may be able to know about their understanding of the concepts they have learned today. Feedback from Students: Ask the students to write what should be the best method of teaching mathematics concept and take the feedback so that you may be able to know more about differentiated instruction. Summary: The contents of Mathematics are same for college and university students. But how to teach students so that they can not only understand the concept but also take interest in doing problems; many surveys are done and results show that teacher should follow certain steps and manage his way of teaching. The first step should be build up a lesson that teacher need to discuss in the class with the students, make group of students so that all of the students take active part in solving the problem, don’t use extra contents and just concentrate on the course book and finally analyzed the teaching concept (Butler & Lowe, 2009). Lesson Plan 03 Topic: ESTIMATING LATENT VARIABLE INTERACTIONS AND QUADRATICS Day: Wednesday Time: 1 hour Date: 7th September, 2011 Number of Students: 15 Objective: There is a substantial guidance available for the estimation of latent variable interactions and quadratics. Today we understand the way of estimation using EQS and LISREL 8 and after understanding techniques of estimation we take on procedures for convergence and proper estimation. Teacher should ask the students and brainstorm about direct and indirect estimation. This warm up session should not be taking more than five minutes. Procedure: There are two methods of estimation, one is direct and the second one is indirect estimation. Direct estimation summarizes structural coefficient estimates like multiple indicator specification. Teacher should tell the students about direct estimation through LISREL 8 or COSAN. Indirect estimation approaches to structural coefficient estimates but it is not sure that they are available and examples include subgroup analysis. Teacher should describe these two techniques in detail. Give the graphical as well as mathematical modeling of both COSAN as well as indirect estimation approach and after that teacher should conclude the topic with convergence and proper estimates topic. Guiding Students: Teacher should ask the students to model the mathematical approach on their notebooks and tell them the problems they find while doing so and help them guide through the lesson. Feedback from Students: After teaching the concept ask the students some questions related to topics like COSAN implementation of estimation and its different behaviors and check whether students understand the topic or not and discuss the problems if any student have. Summary: Two different approaches direct and indirect estimation techniques are valuable for latent variable interactions and quadratics. These techniques have different problems associated with them that can be solved but a lot of research is needed to discuss the approach. The techniques of estimation have models suited to describe them properly. Review on the Journal Article for the third Lesson Plan The approach used by the journal is accessible and can easily understand by the students. It introduce with the concept, provide the abstract and theory related to the topic, than explain them with appropriate example, every step of it using mathematical and statistical modeling and graphs. The contents are appropriate and can develop scientific way of approaching things in students. A lot of research is still being needed to understand properly the difference between direct and indirect estimation. The approaches used by the journal are valid and provide great improvement in estimating regression coefficient but more work is needed on specification, estimation and interpretation using structural analysis. The journal has provided the specifications that should be done in the future for the best estimation of structural analysis. It has also provided with the tables that have experimental data related to estimation. Mathematics Learning and Teaching Philosophy The method of teaching is very important for the understanding of the mathematical concepts and teacher should know how to approach these concepts. Teacher should vary the learning strategies for the maximum learning of the students, should focus on individual learning process, teaching should be centered by teacher as well as student so it should be a mixture of student-centered and teacher centered, no child should be left without understanding of concept and discussion with the students to understand their problems is the best way of teaching mathematics. This is the best way of teaching mathematics. References Butler, M. & Lowe, K. (2009) Using Differentiated Instruction in Teacher Education. Centre for innovative Mathematics teaching. Ping, R.A., Jr. (1995) Estimating latent variable Interactions and quadratics: Examples, suggestions and needed research. Wright State University, Dayton. Sivasubramanian, M. (2009) Applications of Quadratic Equation Laws to Geometry. European Journal of Scientific Research. ISSN 1450-216X Vol.38 No.2 (2009), pp.157-158 Read More