MAED 5351 Whole Numbers Rational Numbers and Operations

This report represents the techniques and methods of teaching the chapter of mathematics “Ratio and Proportion” to the students of a classroom through “Thinking Through a Lesson Protocol”(TTLP). The format of the lesson plan is an integral part of teaching and learning process. In the report, we are elaborately discussing the background information, relevant information, reflection and summary of the teaching process of the chapter “Ratio and Proportion” delivered to the 7^th grade students.

Introduction:

The objective of the report is to teach the idea of “ratio and Proportion” to the seventh grade students of the school. The classroom contains 30 students of ages 10 or 11. Now, among them, one student is handicapped in leg. Various learning charts are used and set of questions is valued over answers in this classroom where an ambient atmosphere exists. It is assumed, that students are aware of all the mathematical operations like addition, subtraction, multiplication and division.

Teacher is aware of the condition of the class and his priority would be to teach this topic playfully to the students. His approach must be helpful and collaborating towards the entire class irrespective of their merit.

In the following, report describes particularly the effective method and technicality of teaching the students. The report also appreciates the teacher to involve the students in various extra curriculum activities at the time of teaching the chapter (Jalon and Arias, 2013).

Background Information:

Aim of the teaching:

This report incorporates the co-learning of many students along with teachers. Students can practice to identify the objectives of instructions, improving mathematical techniques and sequencing mathematical tasks. Teacher would also be able to develop students’ competence effectively by chapter related extra curriculum activity, teaching research activities and deepening the understanding of teaching (Lamon, 2013).

Outcomes:

The students would be able to handle the mathematical ideas and decisive approach to enter to the world of real numbers from whole numbers. In addition to the learning, the students could apply this concept to the field of basic algebra. The knowledge of Ratio and Proportion could influence them to relate several situations in real life.

A method of assessment of students’ learning:

Group participation and curriculum activities, observation and participation are the crucial factors of the assessment. Teacher can invite the students to share their knowledge by wall magazines, math journals of the class, observational games.

Other items and accessories:

An interactive whiteboard, wall hanging tables, math journals are truly essential to deliver lesson to the students. Besides, teacher needs a computer lab to show the different operations and attributes of ratio and proportion to the students after completion of topics.

Relevant Information:

Method of teaching:

In TTLP format, teacher’s standard of choice is TEKS where the teacher mainly depends on classified textual format and documents. TEKS means Texas Essential Knowledge and Skills. TEKS format mainly was introduced to bring the multicultural education system in America (Casas, 2013).

Firstly, teacher can deliver a speech about any story related to proportion. Teacher could invite first boy of the class and ask him to tell a number. Again, we could ask last boy of the class to tell another number. Then, he or she would write those two numbers in the white board and affix a proportional sign between them. Finally, teacher would inform students that it is the standard form of proportion. Lastly, teacher could define that what ratio is.

At the next step, he would tell students to reduce some proportions to their reduced form. Suppose a student tells a number 6. He should put the next number 8 and write it as 6:8. Then, he could advice them to reduce the value to 3:4 with the concept of greatest common divisor. He would not discuss the previous chapters but revise the knowledge in other way. The general idea to develop is that these two quantities change at the same rate. Then, he can write two ratios in divisible form. It is a new approach to write proportion. They would get a chance to improve and revise the cross-multiplying.

Teacher could have another approach to divide students in many groups. They are randomly given a task to observe two variable tables, where these two variables’ columns are filled with related data that are proportionally allocated like hours and distance covered by a train, number of pens and the cost of pens, dollars and meters in the taxi-fare (Ekawati,Lin and Yang, 2015). After studying tables and equivalent rates, the students would get prepared to tackle word problems on Ratio and Proportion. Teacher should choose simple ones at first, and let students think in the hope that they might well come up with an answer by their own.

The next step is to provide the knowledge of proportion and the true relation between proportion and ratio. He would tell the students that the main difference is units. Ratio is unit-free whereas the proportion could be dependent upon units. Teacher should provide the relevant preliminary definitions on ratio and proportion.

He can justify our teaching in the way that real life aspects of “Ratio and Proportion” are applicable to our teaching. Suppose, a teacher could tell that he went to market to buy 1 kg of potato at rupees 10, next day again 2 kg of potato at rupees 20. The teacher could ask the student that what it is going to be the total cost price tomorrow if he would buy 5 kilograms of potato.

If the concept of proportion is more or less clear to all the students, then they can think about inverse proportion. He would provide the idea of increment of one variable with the increment or decrement of another variable. As an example, he can cite the time and the number of workers problem. Teachers should form balanced groups (in terms of abilities) and advice the students to find different ideas about this topic from the mathematics textbook (Carrillo et al., 2013). The teacher should make sure that the student is able to solve the basic problems on Ratio and proportion and understand what is actually happening to the topic. After the group work of the students, the teacher should provide an independent activity to each student to express their response and ideas (Assessment, 2013).

After finishing the lesson:

The teacher can spend this time playing math quiz with the students on the interactive whiteboard and award the students with appreciation. Teacher can ask some inherent questions from the discussion to the students as well (Boyle and Kaiser, 2017). Teachers should relate facts from student’s day-to-day life; comprehend and conceptualize the specific topic “Ratio and Proportion” discussed.

Expected outcome of the lesson:

The teacher should get evidence that the students have learned properly at the end of the day. He or she could playfully call the students to the white-board to solve some easy sums. He or she would continuously guide the student to solve it. As he or she is the mathematics teacher of the class, teacher should be aware of different IQ level of different students. Teacher should be more caring toward the student who is comparatively behind others. If the student succeeds to solve any hard problem of “Proportion”, teacher would request others to clap to encourage that student.

After the scheduled time of class:

The teacher should spend this time responding to any clarifications from students after scheduled time of the class. He or she can also provide a one-minute individual activity and award whoever performs according to the teacher’s expectations. The students with the help of teachers should stick the charts and wall magazines that they have prepared during the lesson on the classroom notice board. In addition, the teacher should explain the expected outcomes of the chapter to the students (Furlong, 2013).

Concluding the lesson:

The teacher could take the help of reasoning and communication with the students in each segments of curriculum. After that, the teacher should carry out a class activity by asking students some problems. For example, “I am thinking two numbers that are divisible by 3, their proportion is 5:7. What are these two numbers?”

Summarization of the whole topic could be helpful to all the students as they can remind the forgotten points. The teacher can let the students express their views and feelings towards the topic. Finally, each student can express their doubts and queries and other students would try to solve it before they leave the classroom.

Conclusion:

Reflections:

One of the biggest obstacle that students face about “Ratio and proportions” is the notion that assuming proportion and inverse proportion are confusing to remind and easy to forget (Boudreaux,Kanim and Brahmia, 2015). Many students find that these are not relating to anything they have read in past. The duty of teacher is to relate or formulate those annoying things that are making students scary. If students are not finding any segment reasonably and logically correct, teacher would guide them analytically. Sometimes, he or she can take the help of algebraic expressions and variables like x or y. Teacher jointly with classroom can arrange a group discussion where all of them can participate and one student can answer or debate with others. It is a new scientific process of learning and overcoming the obstacles. Students are the assets of the class. Therefore, their soulful participation in the process of learning could create a healthy learning atmosphere.

Summary of the lesson:

  The summary of the lesson elaborately justifies the credibility of the teacher if and only if students’ performance spreads out from their core as outcome. Students could perform better in their assignments and exams, if their misconceptions wipes out with the heartiest attempt of teacher. Teacher would help the students with patience although they are not being able to solve the simplest sums. The chapter surly is going to improve the logical and reasoning power of the students along with the math solving ability. If students find interest in the chapter, it is sure that teaching and learning process is successful.

References:

Assessment, W. S. B. P. (2013). Conceptual Framework.

Boudreaux, A., Kanim, S., & Brahmia, S. (2015). Student facility with ratio and proportion: Mapping the reasoning space in introductory physics. arXiv preprint arXiv:1511.08960.

Boyle, J.D. and Kaiser, S.B., 2017. Collaborative Planning as a Process. Mathematics Teaching in the Middle School, 22(7), pp.406-419.

Carrillo, J., Climent, N., Contreras, L. C., & Muñoz-Catalán, M. D. C. (2013). Determining specialised knowledge for mathematics teaching. In Proceedings of the CERME (Vol. 8, pp. 2985-2994).

Casas, M., 2013. Designing an AntiRacist Curriculum For Middle School Students in Texas via The Texas Essential Knowledge and Skills (TEKS) and Latino/Latina Critical Pedagogy. Journal of Border Educational Research, 7(1).

Díaz-Aguado Jalón, M. J., & Martínez Arias, R. (2013). Peer bullying and disruption-coercion escalations in student-teacher relationship. Psicothema, 25(2).

 Ekawati, R., Lin, F. L., & Yang, K. L. (2015). DEVELOPING AN INSTRUMENT FOR MEASURING TEACHERS’MATHEMATICS CONTENT KNOWLEDGE ON RATIO AND PROPORTION: A CASE OF INDONESIAN PRIMARY TEACHERS. International Journal of Science and Mathematics Education, 13(1), 1-24.

Furlong, C. (2013). The teacher I wish to be: Exploring the influence of life histories on student teacher idealised identities. European Journal of Teacher Education, 36(1), 68-83.

Lamon, S. J. (2013). More! Teaching Fractions and Ratios for Understanding: In-depth Discussion and Reasoning Activities. Routledge.