LESSON PLAN

Major/Faculty                         : Mathematics Education / Mathematics and Science

School Unit                               : SMK Muhammadiyah 3 Klaten Tengah

Program / Vocational             : Health / Nursery

Subject                                      : Mathematics

Class / Semester                     : X / 1

Time Allocation                       : 15 minutes

Standard of Competence         : 1.       Solving problems related to the concept of real numbers operation.

Basic Competence                     : 1.2.     Applying the operation on exponential

Indicators                                      : 3.1.1.    Mention the properties of the exponential of positive integers.

                                                   3.1.2.  Simplify the forms of numbers in the exponential of  positive integers.

                                 

I.          The Purpose of Learning

a.       Students are able to mention the properties of the exponential of positive integers.

b.      Students are able to  Simplify the forms of numbers in the exponential of  positive integers.

II.            Topic

Definition of Exponential

Exponential is multiplication repeated with the number itself.

Example :

·         4⁷ = 4 × 4 × 4 × 4 × 4 × 4 × 4

·         (-3)⁴ = (-3) × (-3) × (-3) × (-3)

·         =  

·          =      

Definition : aⁿ = a × a × a × . . . × a

 

                   Its repeated until n factor

with,

a are called as cardinal number

n are called as exsponent

aⁿ are called as exponential

Look this example !

^·          (-4)³  this is an example of positive exponential because the exponent is positive.

^·          3^-4  this is not an example of positive exponential because the exponent is negative.

The properties of exponential operations.

1.      Integer with positive exponent.

For a  R, m, and n is integer, so we can apply the following properties :

a.       Look this example :

1.      3² × 3⁵ = (3 × 3) × (3 × 3 × 3 × 3 × 3)

= 3 × 3 × 3 × 3 × 3 × 3 × 3

= 3⁷

2.      4⁴ × 4² = (4 × 4 × 4 × 4) × (4 × 4)

= 4 × 4 × 4 × 4 × 4 × 4

= 4⁶

From two example above, so :

a^m × aⁿ = (a × a × a × . . . × a) × (a × a × a × a  . . . × a)

    Its repeated until m factor   Its repeated until n factor

= a^m+n

So we can get the properties  :  a^m × aⁿ = a^m+n

After we konw about the properties of exponential a^m × aⁿ = a^m+n  , now try to simplify the following exponential !

1.      6⁵  6³ = . . .

2.         = . . .

3.       2⁸ = . . .

4.      9  27 = . . .

III.          Teacing Method

a.       Expository

IV.          Learning Scenario

No	Teacher activity	Students activity	Time Allocation
A.     Opening
1.	The teacher greet the students (good morning students, assalamualaikum wr.wb) and ask students to pray. The teacher checking on school attendance with ask to the students “who’s the absent today ?” . The teacher look into the students, with observe whether the students prepare their school equipment or not.	Students answer the greeting (good morning mom, wassalamualaikum wr.wb) and then praying. The students answer “none mom”. The students already prepare their school equipment.	2 minutes
2.	The teacher explain that today we will study about  “The properties of  Integer with Positive Exponent ” and write that topic on the whiteboard.	The students listened what teacher’s said and they write the topic “The properties of  Integer with Positive Exponent ” on their own book.	0,5  minutes
3.	The teacher gives apperception about topic who will learn today. Remember about real number system (especially integer) and operates two or more integer. Teacher gives motivation to student about problem related to the properties  of  integer with positive exponent in daily life  .	The student pays attention to what is learning submit.	1,5 minutes
B.     Main Activity
1.	Start the lesson, teacher writes down example of  integer with positive exponent. 47 = 4 × 4 × 4 × 4 × 4 × 4 × 4 (-3)4 = (-3) × (-3) × (-3) × (-3) Then the teacher writes down 2 example of again and asks 2 student to formulate it and writes down it is whiteboard. = . . .  = . . .	Student pays attention to example given by teacher, then student asked by advance to the fore soon writes down its the formulation is whiteboard.	2 minutes
2.	Teacher invites student to define meaning from exponential, that is : Exponential is multiplication repeated with the number itself. Or we can write, Definition : an = a × a × a × . . . × a                  Its repeated until n faktor with, a are called as cardinal number n are called as exsponent an are called as exponential	Student can define meaning from exponential with their own language.	1 minutes
3.	The teacher gives two examples. ·          (-4)3  this is an example of positive exponential because the exponent is positive. ·          3-4  this is not an example of positive exponential because the exponent is negative. Then the teacher explain that today we will study about  the properties of  integer with positive exponent .	Student pays attention to example and explanation from the teacher.	1 minutes
4.	Teacher writes down 2 the problem of multiplication of  integer with positive exponent  in the whiteboard. 1.      32 × 35 = . . . 2.      44 × 42 = . . . Teacher invites student to elaborate example of the problem together and explains how to make simplify the problems.	The students make a note what teacher’s write on the whiteboard. Student elaborates example together with the teacher.	2 minutes
5.	Teacher writes down formula from both examples and challanges student to conclude first at  integer with positive exponent .   am × an = (a × a × a × . . . × a) ×            Its repeated until m faktor                  (a × a × a × a  . . . × a)    = . . .             Its repeated until n faktor Teacher enquired " was properties mentioned by one of the student have been correct or had not ?".	There is student giving conclusion from formulation given teacher that is am+n. The teacher said “correct”.	2 minutes
6.	The teacher gives 4 question and the students must finised that question with   properties of exponential  am × an = am+n . 1.      65  63 = . . . 2.         = . . . 3.       28 = . . . 4.      9  27 = . . . Student asked to do 1 problem beforehand and completed does the problem, asked to write down result of their work front of class.	The students make a note and do that exercise in their own book. There is student is going forward to the fore class to write down result of their work.	1 minutes
C.      Closing
1.	Teacher said about   the properties of  Integer with positive exponent  which have been studied today . Teacher asks student to did 3 problem which had not have time to be done the  (as homework) and will be discussed in next meeting . Teacher also informs that next meeting will study the properties other exponential.	Student pays attention to what is learning submit. Student pays attention to what is learning instruct.	1 minutes
2.	Teacher closes Iesson by inviting student to pray together. After praying teacher to terminate Iesson by saying greeting at student. The teacher greet the students : “assalamualaikum wr.wb., good morning students”	Student prays together and answers greeting from teacher. Students answer the greeting : “wassalamualaikum wr.wb., good morning mom”	1 minutes

V.          Medias and Sources

a.       Medias                                     :  Markres and whiteboard.

b.      Sources                       : Heryadi, Dedi. 2007. Matematika untuk SMK kelas X (Teknologi, Kesehatan, dan Pertanian). Jakarta: Yudistira.

VI.          Assessment

A.      Assessment Technique          : Written test

B.      Form Of Instrument               : Eassy

C.      Instrument of Assessment

a.       Cognitve

Simplify the following exponential !

1.      6⁵  6³ = . . .

2.         = . . .

3.       2⁸ = . . .

4.      9  27 = . . .

b.      Affektive

No	Student	Aspect assessed
		participation			appreciate
1.
2.
3.
4.
5.
6.
7.
8.
9.

Explanation :

1.      Participation

1                      =  Less                        (doesn’t give an idea)

2                      =  Medium       ( sometimes give an idea)

3                      =  Good           (often give an ide)

2.      Appreciate

1                      =  Less                        (laughs at friend who is replying is wrong)

2                      =  Medium       (just silent when their friend answer some question)

3                      = Good                        (pass an opinion from answer which have been laid open their friend)

D.     Key of Answer

No	Key of Answers	Score
		Right Answer	Wrong Answer	Didn’t Answer
1	Question : Simplify the exponential  65  63 ! Answer : 65  63 = 6 (5+3) = 68	2,5	0,5	0
2	Question : Simplify the exponential   ! Answer :     =	2,5	0,5	0
3.	Question : Simplify the exponential   28 ! Answer :  28 = 23  28 = 2(3+8) = 211	2,5	0,5	0
4.	Question : Simplify the exponential   27 ! Answer :  27 = 32  33 = 3(2+3) = 35	2,5	0,5	0

                                                                                                          Yogyakarta,     April 2012

      

Supervising Teacher Subject Mathematics                                                                   Student

                                                                                                                                  Yustia Rahmawati

            NIP                                                                                                  NIM : 09301244005

Developing and Managing the Design of Innovative Teaching Learning of Mathematics in Junior/ Senior High School

Introduction

Mathematics is a subject that is considered difficult for most students. Difficulties experienced by students is an understanding of concepts. Sustainable concepts in mathematics between the new material with old material sometimes not understood by students. So if teachers teach new material, old material sometimes been forgotten by the students, but such materials are interrelated.

To overcome this problem needed good developing and managing the design of innovative teaching learning of mathematics in junior/ senior high school.

Content

Developing and managing the design of innovative teaching learning of mathematics in junior/ senior high school is really important, because with good developing and managing the teaching learning process would be a good and the purpose of teacing learning of mathematics will be achieved.

            Here is the developing and managing the design of innovative teaching learning of mathematics in junior/ senior high school :

1.      Formal Document

Formal document start from the curriculum who made by Goverment of  Indonesia (GOI). From Goverment of  Indonesia, continued to provincial governments, distric, and school. Curriculum in Indonesia is KTSP, in that curriculum, the learning will be described details and materials through Standarad of competencies, Basic competencies, object,  and indicators.

2.      Approach/Design

Find innovative learning design is one way to make the students easier receive the lessons. Approach/design consist of constructivist, realistic mathematics, problem based lerning, cooperative, contextual learning.

3.      Method

Developing and managing various method of teaching. Method of teaching learning is the way for a teacher tobe acceptable to raise the material to students well.

Some of teaching method are :

a.             Lecture method

Lecture method is one of method of teaching learning where the teacher is a center of the class and explain all of the material to the students.

b.             Discussion method

Discussion method is one of method of teaching learning where the teacher make same small group of the students and they discuss about some topic and they must present their task.

Discussion  methods  are  effective  in  getting  the trainees to think constructively while interacting with  the  rest  of  the  group.  Conduct  discussions with  large  or  small  groups;  however,  small  groups are  more  desirable.  You  can  control  and  direct a  small  group  more  easily  than  you  can  larger groups  of  10  or  more  trainees.  If  a  group  is extremely  large,  break  it  into  smaller  groups  or teams  with  a  discussion  leader  for  each  team. The  use  of  the  terms  class   discussion   and directed   discussion   in  this  text  refer  to  a method  in  which  you  direct  and  control  the  verbal exchange  of  the  class.  To  use  this  method,  first lay  a  suitable  foundation  for  the  discussion  by asking one or more challenging questions. Then stimulate   the   trainees   to   discuss   the   basic questions;  finally,  guide  the  discussion  to  a  logical conclusion.

c.             Inquiry method

Inquiry can be considered a philosophical approach to teaching ­ teaching any number of subjects, not just science ­ or can be considered a mere method. In the background here, I will discuss the philosophy of inquiry, and in the method, show one step-by-step process for helping you to start your students carrying out their own inquiry activities.

Note the words I have avoided. I have not used the word “experiment”, or the word “laboratory”. A laboratory is a place where an experiment is carried out. A laboratory report is the record of that experiment. An experiment is a contrived situation in which one variable is tested against another. Although much of science research is carried out using experiments, other inquiries are not experiments.

d.             E-Learning method

E-learning method is one of method of teaching learning where learning is done via internet, like blog, e-mail, facebook, twitter, other social network, and some refferences from internet.

e.              Demonstrasion method

Demonstratasion method is one of method of teaching learning where the teacher make demonstration about the topic

f.              Presentation method

Presentation method is one of method of teaching learning where the teacher present some topic with power point, flash animation, and video.

g.             Teaching aid method

Teaching aid method is one of method is one of method of teaching learning where the teacher use teaching aid to explain the topic, so the students will be easier to recive that topic.

h.             Tutorial method

Tutorial method is one of method is one of method of teaching learning where the teacher make same small group of the students, and in this group one of student explain the material to other member at that group.

i.               Contextual / teaching learning practice

Contextual / teaching learning practice is one of method is one of method of teaching learning where the students adnd the tacher practice the material out of the class.

For example : measure tall the building

4.      Teaching Materials

Teaching material consist of :

a.       Lesson Plan

A lesson plan is a teacher's detailed description of the course of instruction for one class. A daily lesson plan is developed by a teacher to guide class instruction. Details will vary depending on the preference of the teacher, subject being covered, and the need and curiosity of children. There may be requirements mandated by the school system regarding the plan.

Many formats for a lesson plan :

1.      Title of lesson.

2.      The teachers should determine the topics to be studied today.

3.      Time required to complete the lesson.

4.      List the teaching materials.

5.      Formulate learning objective.

6.      Choose the method of teaching learning of mathematics.

7.      Arrange the steps of learning activities

8.      Mention the source / learning media that will be use

9.      Determine assesment teaching

If the lesson plan can be implemented well, then learning will be in accordance with the planned.

b.      Students worksheet

Worksheet is not collection of problem, but worksheet is a facility from teacher to students so they can construct the formula their selves.

Good worksheet is a worksheet who made by the teacher of mathematics it self and in accordance with a predefined lesson plan.

c.       Handout

A handout is something given freely or distributed free. It can refer to materials handed out for presentation purposes or to a charitable gift, among other things.

During the Great Depression, many people lived entirely on handouts of one kind or another. The term became especially popular among hobos, who developed a system of signs and symbols to describe the nature, quantity, and availability of handouts.

In more recent times, the perceived ineffectiveness of simple welfare schemes has given the term a negative connotation. "Give a hand up, not a handout" is a common remark among proponents of workfare or other welfare-to-work systems. As the issue of homelessness has become more visible and controversial, handouts to panhandlers are more often frowned upon by those who believe the behavior encourages homelessness. The term "government handout" is often applied to both welfare systems as well as corporate welfare or pork. The implication is that a handout is unearned and undeserved, unlike a "donation" or "contribution".

Handouts may also refer to short, usually single-page assignments distributed in high school or college.

d.      Text book

A textbook or coursebook is a manual of instruction in any branch of study. Textbooks are produced according to the demands of educational institutions. Although most textbooks are only published in printed format, many are now available as online electronic books.

Students seek relief from rising prices through the purchase of used copies of textbooks, which tend to be less expensive. Most college bookstores offer used copies of textbooks at lower prices. Most bookstores will also buy used copies back from students at the end of a term if the book is going to be re-used at the school.

Once a textbook is purchased from a retailer for the first time, there are several ways a student can sell his/her textbooks back at the end of the semester. Students can sell to the college/university bookstore, fellow students, or a number of online Web sites or student swap service.

e.       Teaching aid

A teaching aid is a tool used by teachers, facilitators, or tutors to help learners improve reading and other skills; illustrate or reinforce a skill, fact, or idea; andrelieve anxiety, fears, or boredom, since many teaching aids are like games.

Used the teacing aids have many purpose , there are : provide variety of activities, provide variety of learning method, provide of context and learning atmosphere, clarify understanding of material.

Obstacles in it’s implementation are need more a lot of time, requires creativity and skill of teacher, requires more cost, requires a commitment of school.

With the use of teaching aid, learning mathematics will be more interest and make students quickly understand the subject being taught.

Conclusion

So, there are a many developing and managing the design of innovative teaching learning of mathematics in junior/ senior high school, that must be done in learning for learning mathematics in accordance with what is expected by the teacher and students can also understand very well. Developing and managing the design of innovative teaching learning of mathematics in junior/ senior high school start from the formal document, approach/design, method, and teacing materials.

Formal document consist of curriculum who have Standarad of competencies, Basic competencies, object,  and indicators.

Find innovative learning design is one way to make the students easier receive the lessons. Approach/design consist of constructivist, realistic mathematics, problem based lerning, cooperative, contextual learning.

Some of teaching method are lecture method, discussion method, inquiry method, E-learning method, demonstrasion method, presentation method, teaching aid method, tutorial method, contextual / teaching learning practice.

Teaching materials consist of lesson plan, students worksheet, modul, handout, text book, and teacing aid.

Reference

http://www.usask.ca/education/coursework/mcvittiej/methods/inquiry.html

http://navyadvancement.tpub.com/14146/css/14146_73.htm

http://en.wikipedia.org/wiki/Handout

http://en.wikipedia.org/wiki/Textbook

The Way Of Mathematics Teaching In The School

Introduction

            We can think or imagination about mathematics. And talking mathematics have same way. This way is like having an imaginaton line that divides between traditional teaching and innovative teaching. In the schools, both of methods are often in teaching learning activities. And they also have different characteristics. What are the characteristic of both methods is that many schools are using it ?

Content (about innovative and traditional learning)

Between traditional teaching and innovative teaching there is an imagination line. There's a line in the world (in our imagination), a world system in which there are things that distinguish between two things. The things in the world include the characteristics, religion, phylosophy, paradigm, theorities, design, scheme, models, program, aktivities, and example.

We know that our self is world, but we need to characteristic to different with other. Only who have a lot of experiences we can find our charactheristic. We are trying to analyse about traditional and innovative teaching. Both the teaching is often applied in the school.

About Innovative Teaching Learning

We have four pillars of education, there are learning to know , learning to do, learning to live together, learning to be. Learning goal of innovative are wisdom (values) , knowledge (internalized), information, and data (discrete). Curriculum need for : facilitator of the learning process, which is individualized and allows time to complete the learning cycles.

Innovative Teaching Methods : Cooperative learning, action research, role play , participate learning, seminar adnd discussion, paper persentation, case studies, projects, field visits, brain stroming, guided self-study, internship.

In innovative teaching, the teacher as a facilitator for the students. The paradigm (system) is construc of knowledge by the students. Moreover, the pros of innovative teaching method in teaching help a lot where there is a centered classroom which is created by the teacher and accepted by the students. In innovative teaching, students are aware of their learning process through the computers. Thus with the help of computers teachers prepare their work in their thumb drive and present it to the class through slides show which is an easier way. And students can do their studying and their work all in the computer without depending 100% on their teacher in schools. Innovative teaching is a long term and the process such as mathematics is students himself.

About Traditional Teaching Learning

  Traditional teaching is concerned with the teacher being the controller of the learning environment. Power and responsibility are held by the teacher and they play the role of instructor (in the form of lectures) and decision maker (in regards to cirriculum content and specific outcomes). They regard students as having 'knowledge holes' that need to be filled with information. In short, the traditional teacher views that it is the teacher that causes learning to occur (Novak, 1998).  

Learning is cheifly associated within the classroom and is often competitive. The lesson's content and delivery are considered to be most important and students master knowledge through drill and practice (such as rote learning). Content need not be learned in context. (Theroux 2002, Johnson &Johnson 1991).

In traditional teaching, the teacher totally control his/her students. The paradigm (system) is transfer of knowledge by the teacher. Traditional lerning still adopts the behaviorism, consider the students as an empty vessel, just as an investment education is not a requirment.

            Conlusion

            So, innovative lerning and traditional learning is totally different. In the schools at our country, the teacher sill predominantly used the traditional lerning because they are sometimes reluctant to make innovations in learning. They prefer to used traditional lerning they think it is easier and less complecated. But if teachers are willing to use innovative learning, the students will not fell bored in mathematics learning and teacing aid because the method used is more diverse, it can help students understand the lesson. Indeed the teaching methods should be balance because it both brings good intentions in educating a person for the better future of everyone. Thus it sends out the same message even in different way but yet it is useful.

            Refereces

http://www.scribd.com/doc/3272989/Innovations-in-Teaching-Learning-Process-Indore

http://rickatz.blogspot.com/2008/04/traditional-teaching-vs-modern-teaching.html

http://ehlt.flinders.edu.au/education/DLiT/2002/environs/scott/tradteac.htm

How To Practice A Good Teaching Learning Of Mathematics

To understand about mathematics, of course we must study mathematics intensively. School is one of the educational institutions that teach mathematics intensive. And as a prospective  teacher, we must to know how to teach mathematics so that students can easy to understand what we teach. So, to be a good teacher we must practice a good teaching lerning of mathematics. But how to pactice a good teaching lerning of mathematics ?

Teaching lerning of mathematics have a groove. Start from fundamental concept that is the nature every / each meaning the teaching learning of mathematics. In learning of mathematics, we have to learn to the maximum, which is studied extensively (widest extent) and intensively (deep inside). And then we must develop any aspect in teaching learning of mathematics, for example student develop. To develop student’s creativity there should be an interaction, interactions can occur between students and students, students with teachers, and students with the environment. Direct interaction  can be done in a one way and two way. Interactions can also be done through technologies such as blog, website, social network, etc.

 Teaching learning process have a many factors, there are :

1.      Educational facilities

Educational facilities are becoming increasingly specialized. For example, we have come to understand that classrooms intended for pre-schoolers are fundamentally different from those that best serve high school seniors or the training of mid-career professionals.

Students experience the provision of  adequate educational facilities, e.g.

accommodation (lecture theatres, tutorial  / seminar rooms), technology, libraries,

and other support for teching lerning.

2.      Teaching media

Teaching media in mathematics is teaching aid. A teaching aid is a tool used by teachers, facilitators, or tutors to help learners improve reading and other skills; illustrate or reinforce a skill, fact, or idea; andrelieve anxiety, fears, or boredom, since many teaching aids are like games.

3.      Teaching method

Method of teaching learning is the way for a teacher tobe acceptable to raise the material to students well. There are many teaching methods that can be used by teachers, a good method will create a good learning as well.

4.      Psycological aspects

Psycological aspects such as the readiness of students to receive learning also affect the learning process.

5.      Syllabi ( coming from the curriculum)

syllabus is used as a reference for teaching.

6.      Lesson plan

A lesson plan is a teacher's detailed description of the course of instruction for one class. A daily lesson plan is developed by a teacher to guide class instruction. Details will vary depending on the preference of the teacher, subject being covered, and the need and curiosity of children. There may be requirements mandated by the school system regarding the plan.

7.      Students worksheet

Good worksheet is a worksheet who made by the teacher of mathematics itself and in accordance with a predefined lesson plan.

8.      Assessment

Assessment of teaching and learning is the process of evaluating  the quality and appropriateness of the learning process, including teacher and pedagogic approach.

9.      Teaching learning resources

Teaching learning resourcess used to add a reference of what we learned.

10.  Paradigm

Phylosophy à teories à paradigm

Next groove of teaching learning of mathematics are the object and the framework, references and concert model, and understanding. The object is a content of teaching learning of mathematics and the framework is a scheme of teaching learning of mathematics. About references and concert model, references can be research, book, logic, our mind, and publication, while concert model can be experiences. And the last is understanding or knowledge, we can get them from references.

The last groove of teaching learning of mathematics is spirituality, if the spiritual path has been achieved then we can find the world of mathematics in yourself.

           So to pactice a good teaching lerning of mathematics all aspect of learning must be met. Starting from the fundamental concept, the factor effect of teaching lerning, understanding, and spiritulity.

Reference : http://sydney.edu.au/ab/policies/Good_Prac_T&L.pdf