TEACHING MATHEMATICS IN PRE SCHOOL AND YEAR ONE

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In the context of teaching and learning, a model that is getting attention and focus of study for researchers and experts of mathematics and science education is a model based on 'understanding of construction' (Constructivism) (Mohd Nor, 1995). According to this model is a person of knowledge developed by the individual based on a unique experience. Mathematical concepts can not be transferred from teachers to students in the form of complete or perfect. Students need to develop a concept for the product of their own and may not, but teachers may not develop a particular concept to students. The main role of teachers is to provide a learning environment appropriate to allow students the opportunity to actively construct mathematical concepts to be taught (Ellerton & Clements, 1993; Von Glasersfeld, et. Al. 1992; Nik Azis, 1996; Mohd Nor, 1995; Ibrahim, 1994 ). Construction concept involves three processes, namely participation, reflection and abstraction (Nik Azis, 1996). Mathematics education in KBSM is demanded of teachers in each practice teaching and learning.

Constructivism is a theory of knowledge and learning that interest, motivate and facilitate students' understanding. In addition, constructivism suggests that children actively construct knowledge based on prior knowledge of the child. Construction of knowledge can be generated through games and experimentation as well as cooperative learning. When children collaborate, they share the idea of the construction process. Indirectly, the child can construct new knowledge as a result of self-learning. Children are encouraged to submit ideas and theories to solve the problem. In mathematics education, children usually are taught using concrete objects that they acquire the experience that used to be associated with the learning of mathematics will be studied next.

It's worth taking the time to convince kids that subtraction is the same as addition, just turned around. This means that teaching subtraction as a continuation of addition. Any time a child masters an addition fact, reinforce the companion subtraction fact in fun and conversational ways. Use walking games to "add two" walking two steps, or to subtract. Have fun with "subtract 1" or "minus zero" to cement these skills early on, since confusion of this type can challenge a child for a long time.

Besides, we can reinforce the language of subtraction in several ways. Students need to be taught that "the big guy comes first" meaning the larger number comes first when writing subtraction equations. Children who are finding subtraction difficult often make that particular error. They aren't well grounded in the concept that the larger number is written first - a quandary which can make story problems a mystery for them. Use the term "difference" and "how many left" for the answer regularly so children absorb it into their math language. Remind students often that subtraction makes things smaller. Demonstrate taking away items from a child while verbalizing a subtraction sentence. Clarifying this early in the development of subtraction skills makes learners ready to comprehend the concept of reasonableness of an answer.

Even though there are many subtraction games available in the market and internet but the best subtraction games are those which you can incorporate in your daily life. You can teach subtraction to kid while doing your day to day chores. For example, we may use his toys to teach him subtraction. By doing this exercise over and over again, we teach kid the concept of subtraction in a fun and entertaining manner. But make sure that we don't overdo the subtraction games as it will only make the child hate the subject. Also, remember not to overburden the child by playing the subtraction games with objects which are too many in numbers. For example, teacher can play subtraction games with fruits like apples or banana, but don't ask the kid to start counting grapes as the sheer number of grapes in a bunch will confuse him. Subtraction games are a great help for both parents and child as they make the task of studying subtraction very easy.

Teaching and learning mathematics involves two stages of manipulating the internal concepts of mathematics and mathematics as a tool to use symbols and labels (Amin, 1993). For most students, the concept is not available. This means that they learn to manipulate symbols empty, without knowing any meaning or label something without substance in it.

Teaching and learning begins with the manipulation of concrete materials, and followed by representatives of the next picture is translated into symbols (digits) as the final answer. Brownell (1930, in Swetz & Team, 1988) found that, with the recovery process in question involves the rejection of two two-digit number, if children are taught to understand the meaning of mathematical terms, they can do less with more efficient operations from children who just memorize the rules alone. He further suggests that children are taught 'arithmetic mean' conscious understanding of development as well as counting skills.

As a result, a thorough and precise lesson plan has to be developed to ensure that children can learn subtraction without fear to learn subtraction facts, and by having fun to develop confidence in their math abilities by insert some games playing to present subtraction as a fun activity.

2.0 Objective

As a pre-school and year 1 mathematics teacher, It is imperative and crucial to ensure that lesson on subtraction and to be developed in a fun and interesting way so to stimulating and exciting the student in classroom. There are three fun ways of teaching subtraction to be discussed in this paper

3.0 Ways to Teach Subtraction

3.1 Count Back

To figure out 15 - 3, children start with 15 and count back 3 numbers: fourteen,

thirteen, twelve.They could visualize this as jumping back along the number track.

This strategy works well when subtracting~l, 2, or 3.

For an instance, 10 minus 3 would be

10 take away 1 is 9

It's the verbal equivalent of "counting on your fingers" one by one backward for arithmetic.

3.1.1 Modification and Justification Lesson Plan

Title : Subtraction count back Race

Primary Subject : Math

Level : Primary Year 1

MATERIALS REQUIRED:

Screen, projector and laptop with internet connection

Two boxes

Index cards with a number, 1-10, written on each (two sets)

Wide-open space, preferably on the grass

At least 10 subtraction questions with answers between 1 and 10

Online courseware from www.hbschool.com/activity/count_back_numberline/

LEARNING OBJECTIVE:

By the end of this session teachers will:

• understand what is involved in helping young children to count and

calculate.

For each group

• A pile of small objects to count (e.g. counters, coins, paperclips or dried

beans)

ACTIVITY:

A few subtraction problems are given to students to work in the heads. This will be a "warm up" for their minds.

With whole class together check for understanding: Ask students to show the answers to the subtraction problems given by holding up the corresponding number of fingers.

Students will be divided into two teams.

Each group will get a game packet that contains all the materials you will need to play the game. (Demonstrate the following as you speak) The way the game is played is that the first person spins each spinner (spin both spinners). The spinning wheel have number on it which represent the student number, if the needle stick on that number then the student have to anwer the question. When everyone has gone, whoever has the largest number circled gets a point. After four rounds, whoever has the most points in your group is the winner. Let's try one together."

An online courseware from www.hbschool.com/activity/count_back_numberline/ will be projected by teacher to present a subtraction problem on the screen to the students who, upon seeing the question, must run down to their box, locate the index card with the correct answer on it, and return to the teacher in the quickest amount of time.

Have individual students come up and guide them through the steps.  It is a good idea to pick a student  from each group to do the demonstration.

Allow the game to begin.  You will need to visit each group to make sure they have the concept.  Once they get it, they seem to really enjoy the game! 

The teacher then the correct answer and the counting back way to students.

CLOSURE (Final check for understanding before independent practice):

Enquiry one of the students to explain the game to the others.

Ask the students to suggest things that should be kept in mind when playing this game (good sportsmanship, trying your best, being a supportive team member, etc).

Ask all the students to do the worksheet (see worksheet at the attachment) given to them as homework.

Ask the students if they have any questions and who like to play again..

3.1.2 Discussion

Teaching methodology adopted here is cooperative Learning.Pembelajaran koperatif merujuk kepada kaedah pengajaran yang memerlukan murid dari pelbagai kebolehan bekerjasama dalam kumpulan kecil untuk mencapai satu matlamat yang sama (Slavin, Cooperative learning refers to teaching methods that require the students from various abilities to work together in small groups to achieve a common goal (Slavin, 1982). Sasaran adalah tahap pembelajaran yang maksimum bukan sahaja untuk diri sendiri, tetapi juga untuk rakan-rakan yang lain. The target is the maximum level, not only for themselves, but also for other partners. LimaGanjaran diberi kepada individu dan kumpulan dalam pelaksanaan kaedRewards are given to individuals and groups in the implementation of this method. Individu dalam kumpulan dikehendaki menunjukkan kefahaman masing-masing dan memainkan peranan berbeza bergilir-gilir. Pengajaran sebaya memainkan peranan yang sangat penting menurut cara Jigsaw.

Children are like sponges. They absorb every bit of information that is given to them, especially if it is presented in a fun and easy to learn way. Lesson will not get bored easily will attract students attention and interest on learning mathematics.

This lesson which is taken from internet as a resource has been modified little bit so to varied the activity. This is where the question is presented on the screen from LCD projector instead of just read it aloud. This is due to the key to success is teaching math is through visual aids--in other words, explain the problem and the solution in concrete ways the student can actually see. Visual learning will be much more fun and effective than all the workbooks and memorization in the world. The online courseware makes the lesson more fun and attracting with colourful appearance. The online courseware can be used as drill and practice as well.

Students participation also ensured in the activity.

3.1.3 Courseware's Appearance

3.2 Take Away

A method of taking one number away from another.

For instance,

If you have 5 apples

and you subtract 2,

you will be left with 3.

This would be written: 5 - 2 = 3

3.2.1 Modification and justification Lesson Plan

Title : Subtraction as Take Away

Primary Subject : Math

Level : Primary Year 1

LEARNING OBJECTIVE:

The students will begin subtracting by acting out the words to a song.

MATERIALS REQUIRED:

Materials Required: 5 monkey puppets, 1 alligator puppet, dry erase/chalk board, Dr. Jean & Friends CD

Screen, projector and laptop with internet connection

Online courseware from http://www.ictgames.com/targettakeaway.html

ACTIVITY:

Step 1:

Activity Time: 20 minutes

Concepts Taught: Subracting Concrete Objects

Procedure: Before the lesson make 5 monkey puppets and one alligator puppet. I use small laminated drawings attached to popsicle sticks.

Teach students the song "Monkeys and the Alligator" using the Dr. Jean and Friends CD.

"(Five) little monkeys swinging from a tree,

Teasing Mr. Alligator, "Can't catch me."

Along came Mr. Alligator quiet as can be

And SNAP that monkey right out of that tree."

(Repeat song with four, three, two, one.)

After students are familiar with the song, select 5 students to hold the monkey puppets and 1 to be the alligator. Have everyone sing the song together, taking away one money each time.

Write out subtraction problems on the board to go along with each verse of the song.

5 - 1 = ___

4 - 1 = ___

3 - 1 = ___

2 - 1 = ___

Use the puppets to solve each problem. The alligator should serve as the subtraction sign. Just as alligators took the monkeys away, the subtraction sign takes numbers away. After students have mastered subtracting by one, you can continue using the puppets to solve more difficult problems. The alligator should help students remember to take away instead of add.

Step 2: Game Playing as Enhancement

Teacher uses cooperative learning to further enhance the students' understanding about the day's lesson. Students are divided into three groups and each group is called A, B and C. Teacher gives each group an envelope that contains four questions. Students are required to answer all the questions in four minutes and write down their answers on the manila cards provided. After four minutes, all the answers must be attached on the whiteboard. Teacher gives marks for each group and displays the marks.

Teacher gives quiz papers to the students. Teacher observes the students while they do the quiz. Teacher discusses the answers of the quiz questions with the students by using online software from http://www.ictgames.com/targettakeaway.html.

CLOSURE

Teacher asks students to make a conclusion about the topic learnt that is subtraction using take away. Teacher gives homework from the worksheet.

3.2.2 Discussion

The children explore subtraction through problem solving with manipulative, such as puppet, which help students make connections to numbers concretely. Thus they begin to discover the symbolic nature of manipulative and, by extension, of number. The plan develops the language for discussing and recording subtraction situations that will give meaning to the algorithm in a concrete way. After that, we use children themselves as analogy method to make them more clear and understanding the concept by letting them hands-on.

This lesson is very suitable and powerful because it link the activity to the daily life such as counting snack that still left after been eaten. A real connection is the cornerstone of learning, because when a student internalizes the concept they have learned it - not before. Worksheets are only good in rote memorization of a math concept and math facts, which is good on a certain level - some mental math applications. The online courseware can be used as drill and practice as well. This gives them a better understanding besides using the standard worksheet subtraction problem. Students will find this fun and a lot less boring than worksheets.

3.2.3 Courseware's Appearance

3.3 Difference

A method of find the difference between two numbers by comparing.

For instance,

3 - 2 = 1 The difference between 3 and 2 is 1

3.3.1 Modification and Justification Lesson Plan

Title : Subtraction as difference

Primary Subject : Math

Level : Primary Year 1

LEARNING OBJECTIVE:

Students:

understand the effects of subtracting whole numbers

use a difference methods and tools to compute

To be able to demonstrate simple subtraction and to solve simple number problems

Understand subtraction 'difference' and use the related vocabulary

Use the symbol '=' to represent equality;

MATERIALS REQUIRED:

Any of the activity sheets below, with the bingo cards cut out. (To print bigger bingo cards, enlarge the sheets onto A3 before cutting them out.) See appendix.

Activity sheet level 1 (a and b)

Bingo cards for simple addition with number spots (a) or numbers (b) to 6.

Activity sheet level 2 (a, b and c)

Bingo Cards for simple addition (or subtraction) with numbers between 1 and 10.

Screen, projector and laptop with internet connection

Online courseware from http://www.ictgames.com/numberlineJumpMaker/index.html

ACTIVITY:

Step 1:

Explain the rules of the game of Bingo to the class and reiterate that the step must use difference way in subtraction. On level one, all of the numbers need to be marked since there are only four squares. On level three, a straight horizontal, vertical or diagonal line would be sufficient.

Ask one student to write down the questions for each game on the board. Call out questions until a pupil calls "Bingo!"

If simple subtraction is the focus (Cards on activity sheet level 1) ask questions such as:

The Difference of 2 and 1 is?

The cards on activity sheet level 2, enables harder calculations of simple subtraction:

The difference between 8 and 3 is?

Step 2: Game Playing as Enhancement

Teacher uses cooperative learning to further enhance the students' understanding about the day's lesson. Students are divided into three groups and each group is called A, B and C. Teacher gives each group an envelope that contains four questions. Students are required to answer all the questions in four minutes and write down their answers on the manila cards provided. After four minutes, all the answers must be attached on the whiteboard. Teacher gives marks for each group and displays the marks.

Teacher gives quiz papers to the students. Teacher observes the students while they do the quiz. Teacher discusses the answers of the quiz questions with the students by using the online courseware called a number line demonstrator from http://www.ictgames.com/numberlineJumpMaker/index.html.

Each correct answer, scores one point for their team. The team with the most points at the end of the game receives a reward from the teacher.

CLOSURE

Teacher asks students to make a conclusion about the subtraction as difference method. Teacher gives homework from the worksheet.

3.3.2 Discussion

In order to create an environment in which cooperative learning can take place, this lesson is designed to actively involve every student in class learning activity. Group learning methods encourage students to take greater responsibility for their own learning and to learn from one another, as well as from the instructor (Terenzini & Pascarella, 1994). By playing bingo game which is very familiar with student are suitable to use as a tool to learn. Students will find it very interesting in learning. Besides, mini competition is also used to make the environment more challenging. The way of subtraction as difference will show on the screen projected from LCD projector by using online courseware. One way is to use an interactive online computer game that involves critical thinking skills to develop a greater understanding of subtraction.

3.3.3 Courseware's Appearance

Numberline Jump Maker

4.0 Conclusion

The key to teaching subtraction so most students understand and retain the information they are learning is to make it real. A real connection is the cornerstone of learning, because when a student internalizes the concept they have learned it - not before. Worksheets are only good in rote memorization of a math concept and math facts, which is good on a certain level - some mental math applications. However to truly memorize a math concept, a students needs to understand it first.

The road to learning subtraction is pitted with sinkholes full of students who could never make the connection of subtraction and what it all means to them. We all know that the opposite of subtraction is addition and common strategy is to subtract through addition. This method is used for learning subtraction, for example "36 minus 12 is 24" or "12 plus 24 is 36." Great the student just proved that he/she can memorize, however does the student really understand? Students need to understand first, if they are to learn.

Besides strategies above to help you teach subtraction, students' learning style has to be determined first. For example, if your student is a visual learner, she will learn best with pictures and written problems. Audio learners are more likely to retain information they hear, so repetitive definitions and rhyme schemes are helpful tools. Those who learn best with their hands are kinesthetic, and physical objects like marbles or candy work well for number sense. If pair addition and subtraction as opposites is a context for your child, use interchangeable words like take away and minus. Increase your math vocabulary in every conversation with words, including how many, more than, less than, leftover and remainder. Use subtraction in daily activities, including grocery shopping, banking or sorting mail. Last but not least, the best way to teach a whole class is to use a varied pedagogy to suit with students' varied learning styles that is included visual, audio, and kinesthetic aspect in the teaching pedagogy.

In conclusion, the children learn mathematics through the experiences and perceptions of an item. In addition, children can improve thinking by creating a new concept. This means that knowledge can be considered as a collection of concepts and actions are useful according to the conditions and time required.

REFERENCES

Slavin. R. E. "Cooperative Learning: Student Teams" 2nd Ed. Washington, DC: National Education Association, 1987.

Slavin, R. E. "Cooperative learning." Review of Educational Research, 1980, 50, 315-342.

Slavin, R. E., and Karweit, N. "Cognitive and Affective Outcomes of an Intensive      Student Team Learning Experience." Journal of Experimental Education, 1981, 50, 29-35.

http://www.ictgames.com/numberlineJumpMaker/index.html.

http://www.ictgames.com/targettakeaway.html

www.hbschool.com/activity/count_back_numberline/

http://www.lessonplanspage.com/printables/PMathPESubtractionRace1.htm

http://illuminations.nctm.org/LessonDetail.aspx?id=L192

www.bbc.co.uk/schools/laac/numbers/ch3.shtml

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