8/10/2019 hbmt 4303.docx

1/12

FAKULTI PENDIDIKAN DAN BAHASA

SEMESTER SEPTEMBER 2014

HBMT 4303-V2

TEACHING OF UPPER SECONDARY MATHEMATICS PART II

NAMA : SITI MASNI BT. AHMAD

NO. MATRIKULASI : 790522025694001

NO. KAD PENGENALAN : 79052202 - 5694

NO. TELEFON : 013 9112225

E-MEL : sitimasni.ahmad@yahoo.com

PUSAT PEMBELAJARAN : SG. PETANI LEARNING CENTER

8/10/2019 hbmt 4303.docx

2/12

1.0 Introduction

Mathematics is an interesting subject and it should be an enjoyable experience for the

students to learn it. However, in reality either students at the school level or advanced

studies in college or universities facing difficulties to achieve such experience in the class.

Moreover, the students perceived that Mathematics subject is a difficult and complicated

to be learned especially an advance version as in Malaysia we have Additional

Mathematics. Statements such as "Mathematics is a killer subject", "I hate the teacher

who is teaching us Mathematics, she is very strict", and "Why do I have to do so many

exercises in Math class". So often, since we stepped into school's life, there is one of the

stigmas that will be inherited by most of us which is Mathematics's teacher is always

fierce and very strict with students. As we growing up and maturing ourselves from

primary school students until secondary school students, some of us are still carrying that

stigma which somehow affecting their performance in Mathematics subject. When the

statistics for big exam such as Sijil Pelajaran Malaysia showed a declining in

performance, we started to finger point each other as a way to avoid the shame. Who is at

fault for this matter? The so called strict teacher? Education system? The spoiled students?

It might be the combination of those three and maybe so much more reasons that

constraining the effectiveness of students especially in Malaysia to learn Mathematics.

We often heard that one of the effective ways to create a good learning and teaching

environment is by creating two-ways communication between the teacher and his

students. The communication between the two parties are important not only to build an

enjoyable surrounding in learning new thing but also to reduce the stress and tense of

handling some difficult chapters and formulas in Mathematics. According to Nor'ain et.al

(2011), teaching and learning should show an active and dynamic classroom as students

thinking, exploring and applying what they have learned. But the big question mark is, is

it dynamic and active enough to attract the students to learn the topic? In Mathematics,

topics such as differentiation and integration are considered as moderately difficult for

some students and very tough for weaker students. In finance world, there is no worries

for the 'some students' as they could perform well in their exams, but the risks are more

for the weaker students as these students will generally being the left out among their

colleagues because they always get low grades for this subject which at the end of the day

8/10/2019 hbmt 4303.docx

3/12

will affect the overall performance for the school as many students failed to deliver good

results for Mathematics subject.

As an educator, the teacher has a big responsibility to change this situation and what

sort of changes are required to cater the problems? As for this paper will focusing on two

topics which are differentiation and integration, a more specific question is needed. What

is/are the best teaching methods that can help the students to learn differentiation and

integration more effectively? Therefore, to answer the questions, the paper will review

three teaching methods with other supporting literatures to show the strengths for each of

these methods. After that, a dynamic and creative teaching method will be proposed in

teaching the students on differentiation and integration. Lastly, a teaching activity will be

provided to show the structure of daily lesson for this two topics of interest.

Before stretching the discussion to a deeper part, an introduction to the concepts for

both topics are necessary as an icebreaking for the newcomers who had zero knowledge

on this area and also as a refreshment for the one who already used to the concepts for

each topic being discussed.

1.1 Differentiation

Differentiation is the term used to for the process of finding the rates of changes or

derivatives of a function with respect to one of its variables. This is equivalent to finding

the slope of the tangent line to the function at a point. It usually denotes as dy/ dx which

means that "the first derivative of y with respect to x." There are three commonly used

ways to express the definition of the derivative as showed in Figure 1.

Figure 1: Expressions of derivative definition

8/10/2019 hbmt 4303.docx

4/12

1.2 Integration

It is the term applied to the operation of finding a function when given its derivatives.

Integration is a contradiction to differentiation as differentiation is an operation to find the

derivatives where the function is given while the integration involves the inverse

operation. It can be used to find the areas, volumes, central points and etc.

2.0 Teaching Methods

Around the world, there are many approaches being used by the educators to teach on

differentiation and integration chapters which also known as the ingredients of Calculus 1.

In order to conduct an effective teaching for the students, the most suitable method must

be adopted by a teacher. The traditional method that usually being used by most of

teachers is the lecture method. This method takes the form of presentation where the

instructor should have the knowledge on the topic that will be presented and must know

how to organize and deliver the lecture. According to Kadry and Shalkamy (2012),

lecture method is used to introduce new topics, present graphical subjects, summarize

ideas, present coding, display the main points of the lecture, and show the relation

between the theory and the practice. Though this method is widely used by most of

teachers in schools but is it effective enough to teach the students on a more advanced

Mathematics topics such as differentiation and integration? Therefore, this section will

discussing on three teaching methods which been proposed by researchers in teaching

differentiation and integration topics.

2.1 Microsoft Excel

Besides products from Apple, almost all technology devices such as desktops, tablets,

laptops and notebooks will install Microsoft Office to run their works. One of the

branches for Microsoft Office is Microsoft Excel. Excel is an electronic spread sheet

software where the end user can use it to store and structure their data in a tabular form. It

allows the user to do any arithmetic application and utilize a huge set of mathematics to

build the formula. Microsoft Excel is useful because it offers a wide range features that

consist of calculation, draw graphics, create formulas, and solve equations and many

mathematical functions. According to Hammer (2000) and Mykytyn (2007), this method

8/10/2019 hbmt 4303.docx

5/12

has been found to enhance the student knowledge as it incorporates aspects of

experiential and problem based learning. The teacher must have the skills and also

knowledge on using the Excel to teach it to the students. It might takes time for the

teachers to master the steps and procedures involved in using the Excel to solve the

problems on differentiation and integration but its worth their efforts if the students really

take it seriously in the classroom. The observations by the researcher showed that the

Excel-based learning provides benefit for the students in three ways (Jiajuan and Martin,

2008).

1.The hands-on approach of solving Excel problems throughout the class improves the

students ability to stay focus. The teacher will set the time to solve a question and the

students must listen carefully to the explanation for each concepts and steps in using the

Excel so that they will not being the left out from the lesson.

2.The use of visual approach through Excel graphing and other procedures seems to be

effective learning approach for our students. According to Kadry and Shalkamy (2012),

the visual approach improves the percentage of concentration of the students and they are

able to produce result or the answers in a short time.

3.Students entering into more advanced quantitative analysis courses are more efficient

in Excel techniques and hence enhance student learning

Research by Kadry and Shalkamy (2012) prolonged the benefits of using Excel to

teach integration and differentiation as follows:

1. The students understand the topics in calculus very well in an attractive way

2. The students get more experience and knowledge in Excel which will be using it in

the future.

2.2 Computer Algebra System (CAS)

Historically, Computer Algebra System or CAS already being introduced to the

world of computer technology on 1970s and also on microcomputers around 1980s. As

the technology is becoming more advanced, it is now accessible as CAS calculators that

have increasing demand from the secondary school students. CAS calculators capabilities

include graphics calculator together with capabilities for symbolic algebra. It has abilities

to perform algebraic procedures including calculus, drawing graphs, and others. CAS

8/10/2019 hbmt 4303.docx

6/12

calculators' model which is known as T1-92 have excellent graphical and numerical

capabilities as well as a symbolic algebra capability that allows manipulation of symbols

according to certain algorithmic procedures which enable a wide range of tasks including

differentiation to perform very quickly and precisely. The data analysis shows that the

CAS activities is supporting the student learning on derivative concepts. The functional

CAS assisted the students to learn formulation competencies that related with graphical,

symbolic, and numerical representation of differentiation while the pedagogical CAS

activities seems to assist the students at learning on some of the interpretation

competencies and formula competencies. The study found that the chance to enhance

students' understanding can be achieved through few reasons such as the teachers have

deep mathematics knowledge, skillful, confidence and willingness to use CAS. From

students perspectives, it helps them to do a quick and accurate performance of wide range

of numerical, graphical and symbolic procedures as it can simultaneously performing two

works in a split screen features.

2.3 Graphing Calculator

As technology is getting advanced day by day, it is tactical-wise to adapt one of the

technologies that can be used in the classroom by the students. The technology does not

need to be too advanced but the functions of the device and its features are good enough

to improve students' performance in the class. Calculator is one of the essential gadgets in

Mathematics classes because most of the topics involving big numbers and complicated

functions which explained why we have to rely on calculators instead of using other

traditional tools such as paper and sempoa. There are varieties of calculator available in

the market that serving the needs of students especially the upper secondary students and

the college students. One of the popular calculators among the students is graphing

calculator. According to Kor and Lim (2004), graphing calculator is a hand-held ,

powered by battery that is equipped with functions to "plot graphs, give numerical

solutions to equations, and perform statistical calculations, operation on matrices, and to

perform more advanced mathematical functions such as algebra, geometry, and advanced

statistics." The graphing calculator is not only useful because it enables the students to

solve the mathematical problems by engaging themselves in doing the mathematics

8/10/2019 hbmt 4303.docx

7/12

(Noraini et. al, 2011), but also forming a better understanding among the students of the

mathematics involved and are motivated to solve any complex problems by using the

device. This has been proven by many studies throughout the world in this particular tool

in assisting the students to enhance their understanding on differentiation and integration

topics. Alkhateeb and Wampler (2002) found that the use of graphing calculator increased

the performance of the students in a test compared to the students who did not use it for

the test. In addition, a similar study had been conducted by Tiwari (2007) who found that

students that are using graphing calculator have higher tendency to achieve conceptual

understanding and problem solving abilities in both topics. For this particular paper, the

model that will be utilized is TI-Nspire. The feedbacks from the students after they used

TI-Nspire:

1.

Colorful and clear screen

2. Fast and flexible to work with

3. Manage more difficult tasks

4. Learn and understand Mathematics better

5. Mathematics is more interesting and fun when working with TI-Nspire

However there are also some difficulties in using this calculator which are listed as

follow:

1.

Hard to start using TI-Nspire

2. Takes time to learn TI-Nspire

3. Difficult to use different tools

4. When you work with pencil and paper you understand better

Overall, the researcher found that the graphing calculator stimulates mathematical

thinking and also helps the students to visualize the abstract and complex concepts. Last

but not least, it allows the students to enjoy the learning process and makes the teaching

more fun and meaningful.

8/10/2019 hbmt 4303.docx

8/12

3.0 Teaching Materials

After a thorough discussion and literature reviews being made in earlier sections,

there is a need to construct the best teaching material that can be used to teach the

students on both topics that have been the limelight for this paper which are

differentiation and integration. All of the teaching methods being discussed in previous

sections show the influences of technology to the education nowadays. We cannot argue

the contributions of these technologies on enhancement of teaching and learning

environment especially in Malaysia where the government is encouraging the efforts to

adapt and adopt more technologies in education system. It has becoming a national

agenda to increase the quality of education among Malaysian students especially the new

generations. It is rather impossible to rely just on teachers' skills and knowledge in

achieving the goal of our government. Therefore, by using teaching aids along with the

knowledgeable and trained teachers, the goals are very likely to be achieved as the

government and other non- government organizations cooperatively working together to

support them.

It might be a traditional way to teach the students, but so often it serves the purpose

very well. Lecture method has been used by many educators at all level around the world

despites many devices and alternatives have been introduced to replace this method.

Lecture method allows the teacher to teach the students important concepts for a topic.

However, in order to make the method working more efficiently it must be combined

with another method which is discussion method. The lecture method usually only

involve the teacher and its teaching materials such as text books and whiteboard in

teaching the students without any active participation by the students and most of the time

only the teacher is talking in front of the class. By combining lecture and discussion

methods, the teacher will encourage the students to participate in the class and they will

having more opportunities to ask any doubts that they have and share their answers to the

whole class. This is called as student-centered approach as the teacher will only facilitate

the students on each topic instead of 'feeding' everything to them. This approach will

allow the students to understand each concept rather effectively. According to Kadry and

Shalkamy (2012), the target of the instructor is to draw out what the students understand

instead of spending the entire class period to tell them about the topics. But, there is

8/10/2019 hbmt 4303.docx

9/12

8/10/2019 hbmt 4303.docx

10/12

4.0 Teaching Plan

The following table describing the lesson plan for this topic and each learning

objectives must be achieved at the end of the lesson to show the effectiveness of

TI-Nspire on students understanding for topic Integration and differentiation.

Daily Lesson Plan

Topic: Probability I

Subtopic: Probability concepts

Date: 19t

November 2014 (Wednesday)

Time: 9 am - 11 am

Learning Objectives:

1.Students learn how to use graphing Students

can define the concepts of Differentiation

2.Students can define the concepts of

Integration

3.Students can differentiate each concepts

4.Students can give examples for each terms

5.Students able to solve differentiation and

integration problems by using the TI-Nspire

Teaching Outline:

1.Teach the students how to use the graphing

calculator

2.Lesson on Introduction to the concepts of

Differentiation and Integration

3.Discussion on both topics

4.Solve the questions related to integration

and differentiation.

Classroom Design

Materials:TI-Nspire, Mathematics textbook

Warm up:Teacher will guide and explain the features and functions of the graphing calculator.

Lesson:Topic review by teacher and detail explanation on both topics which are integration and

differentiation

Activities:

a.Students will solve simple problems by using paper and pencil method

b.Students will solve problems by using graphing calculator

c. Solve the exercise for this topic

Closing: Students will be given homework for both topics.

8/10/2019 hbmt 4303.docx

11/12

5.0 Reflective Report

The teacher must have the necessary knowledge and skills on handling the graphing

calculator. This is vital because he or she needs to explain it to the students clearly so that

they will understand the explanation which is useful for them to use it in solving the

problems related to topic of integration and differentiation. The students should fully

focused on the guidelines from their teacher and fully utilized the graphing calculator to

increase their ability to provide the solutions on each exercises rather quickly and pin

point accuracy. The usage of this calculator is hoping to reduce the issues related to

teachers' problems in teaching both topics to their students. The traditional lecturing

method which basically teacher-centered learning process usually will create a gap among

the students who are not that quick to absorb all the knowledge given by the teachers.

Therefore, the graphing calculator is a good choice to cater this problem because it can

solve most of the mathematical problems in a short time.

However, there are two adjustment that can be made to improve the efficiency of

using graphing calculator among the students in learning integration and differentiation.

Firstly, the teacher should ask the students to learn about the features and functions of the

graphing calculator at their home instead of doing it in classroom because it could be time

consuming if they did it in the classroom. The teacher just need to give them a brief

explanation on it and let the students do their own exploration of that calculator as a

homework. Besides that, the usage of TI-Nspire should be nurtured at earlier stage of

learning mathematics subject. This will allow the students to be well-prepared when the

want to use the calculator in future time. Its an important decision to be decided by the

teacher and school if they want to buy the graphing calculator or the normal scientific

calculator because it is quite costly to purchase both type of calculators. Therefore, the

purchase of graphing calculator will allow the students to be very well-skilled on many

topics for Mathematics subject. In conclusion, the graphing calculator is a useful

handheld device in improving teaching and learning process in teaching two topics which

are integration and differentiation.

8/10/2019 hbmt 4303.docx

12/12

Reference

Alkhateeb, H., &Wampler, J. (2002).Graphing calculators and students' conceptions of

the derivative.Perceptual & Motor Skills, 94(1), 165.

Hamer, L. (2000). The Additive effects of Semistructured Classroom Activities on

Student Learning: An Application-Based Experiential Learning Techniques.Journal

of Marketing Education 22(1), 25-34.

Jiajuan, L., & Martin, L. (2008). An Excel-Aided Method for Teaching Calculus-Bases

Business Mathematics. College Teaching Methods & Styles Journal. 4 (11).

Kadry, Seifedine, & Shalkamy, M.E. (2012). Toward New Vision in Teaching Calculus.

Lim Chap Sam and Kor Liew Kee 2004. Teaching statistics with graphical calculators in

Malaysia: challenges and constraint.Micromath. 20(2): 30-33.

Mykytyn, P. Educating Our Students in computer Application concepts: A Case for

Problem-Based Learning. Journal of Organizational and End User Computing; 2007,

17(1), 51-62.

National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation

Standards for School Mathematics. Reston, VA: National Council of Teachers of

Mathematics.

Norain Mohd. Tajudin, Rohani Ahmad Tarmizi, Wan Zah Wan Ali, & Mohd. Majid

Konting. (2011). The use of Graphic Calculator in Teaching and Learning of

Mathematics: Effects on performance and metacognitive awareness. American

International Journal of Contemporary Research, 1(1), pp. 59-72.

Tiwari, T. K. (2007). Computer graphics as an instructional aid in an introductory

differential calculus course, International Electronic Journal of Mathematics

Education, 2(1), 35-48.