Rickmath

mungkin anda yang tercari-cari cara belajar matematik samada algebra, geometri atau pun statistik di internet yang mana boleh membantu guru, ibubapa serta pelajar sendiri untuk belajar mengenai matematik dengan seronok. satu website yang boleh dikunjungi ialah http://www.ricksmath.com/

Learning statistic

The word "statistics

" is derived from the Latin word "status" meaning condition. The simplest way to understand statistics is to understand it by means of collection, presentation of data and then draw inferences or figures according to the gathered data. Most of the time, information about an object is revealed in terms of data. However, it is not at all possible to draw conclusions from a large amount of data, so the data is pictorially represented with the help of bar graphs, pie charts or pictograph. Some of the basic terms related to statistics are:
Numerical Data: Numerical data is the information given with the help of numbers.
Pictorial Representation or Graph of the Data: The representation of numerical data through pictures or graphs is known as pictorial or graphical representation of data.
Pictograph: Pictograph is a pictorial representation of the gathered data.
Bar Graph: When data is represented in a figure form that resembles a bar, then it is called bar graph.
Bar Graphs in Details

When numerical data is represented in the form of a number of bars, then it is called bar graph or chart. The bars are of uniform width and erected horizontally or vertically. The bars are placed in equal distances from each other. As there are numerous bars to represent a large number of data, each bar represents only a particular value of the numerical data. If two bars represent data of different value, they are of different sizes. The horizontal bars are drawn on x-axis and the vertical lines which show the scale of height of the bars is the y-axis.
Example
Bar graphs or charts provide various advantages, like:
Bar graphs help a lot in easy representation of the data. A bar graph or a chart also helps in drawing a quick conclusion by having just a glance. For instance as in the following figure, a graphical figure would reflect the easy way to show government expenditures in different sectors. The y-axis represents the amount of money spent in million and the x-axis represents the different sectors. By looking at the bar graph, you can easily tell that government has spent the most in the Defense sector.
Test
Represent the number of government companies in different years by means of a bar graph.

Year	Number of companies
2001 2002 2003 2004	80 120 140 180

Pie chart in details
In a particular area, the amount of wheat production for three consecutive years are 20 million in 2001, 25 million in 2002 and 55 million in 2003. When we represent the following figures in the form of a pie, chart, the degree of the angle to represent each of the quantity needs to be calculated.
For instance, the production of wheat:

2001 = 20 million tonnes
2002 = 25 million tonnes
2003 = 55 million tonnes

Therefore, the total amount of wheat produced in these three years are, 20 + 25 + 55 = 100 million tonnes.
Let’s take 100 million tonnes = 360 degree
Therefore, 1 million tonne will be = 360/100
20 million tonne will be = 360/100 x 20 = 3.6 x 20 = 72 degree. (Applying Unitary method)
Similarly, 25 million tonne will be = 360/100 x 25 = 3.6 x 25 = 90 degrees. (by unitary method)
Similarly, 55 million tonne will be = 360/100 x 55 = 3.6 x 55 = 198 degrees.(by unitary method)
The best way to check the result, whether it is correct or not can be done by adding up the three quantities, 72 degree + 90 degree + 192 degree = 360 degree.
If the result of the sum is 360 degree, then most of the time your calculations are fine but in any case if the sum does not result to 360 degree then it is definitely wrong.

A pie chart also known as circle graph is a representation of a circle chart divided into sectors. The circle is divided into various parts and each part or each arc represents a value. The arc length is directly proportional to the quantity it represents. The total value of the data should be represented within 360 degrees because the pie chart is always a circle.
Pie charts are especially effective in places where there is a need to compare between various quantities. Pie charts are a very good analysis tool in case of journalism or business but it is not so effective in case of scientific literature. However, the particular form of pictorial representation of data is widely used and attractive too.
Example
In a survey which represents the percentage of intelligence in a class it is seen that 20% of the students are highly intelligent, 70% of the students are average and 10% are below standard. While analyzing the data, if it is represented in the form of a pie chart then it will be much easier to get a conclusion. The pie chart representing the above data will look like the following:

Test
Represent the following data in a pie chart which gives the number of staffs in different ages in a particular office, which has a total number of 60 staffs. 20 people are below 25 years of age, 30 people are between 25 to 50 age group and there are only 10 people above 50 years of age.
Answer:
By unitary method, we have to take total number of staffs as 360 degrees.
Therefore, 60 staffs represent = 360 degree
1 staff will represent =  360/60
20 staffs (below 25 years) will represent = 360/60 x 20 = 120 degrees
30 staffs (between 25-50 years) will represent = 360/60 x 30 = 180 degrees
10 staffs (above 50 years) will represent = 360/60 x 10 = 60 degrees
Therefore, number of staffs below 24 years of age will represent 120 degree.
Number of staffs between 25-50 years of age will represent 180 degree and number of staffs above 50 years of age will be 60 degree.
Checking:
Three quantities in degree calculated are 120 degree, 180 degree and 60 degree.
Sum of the quantities are 120 degree + 180 degree + 60 degree = 360 degree.
Therefore, the calculation is right.

Mean, Median, Mode
Mean
Mean or arithmetic mean refers to calculating the sum of all numbers in the set and then dividing the numbers by the number of quantities or members. It is very much helpful when you need to draw a summary out of a large collection of numbers. However, don't confuse mean with average as mean is only one of the several kinds of average.
The Median
Getting the median is as easy as getting the 'middle value' in a list of numbers. When you are given with a set of odd quantities, then you need to sort out those numbers into increasing order and find out the middle number. That middle number is the median. However, when you are given an even number of quantity, again you need to sort them out in increasing order. Then you need to find out the sum of the two middle numbers and divide it by two. The result is the median.
Mode
Finding the mode is very easy as all you need to do is to find out the number which occurs most in a given list of numbers. However, if a list contains no number, occurring more than once then that list has no mode. Range of a set of numbers is also easy as it needs you to calculate the difference between largest number and the smallest number of the list.
Example
1) Find the mean of the set {3,7,8}.
The first step is to add the three numbers that is, 3 + 7 + 8 = 18.
The value of the addition is 18.
No. of quantities in the set = 3.
Therefore, the mean is 18/3 = 6.
2) Find the median of the set {4, 2, 6, 12, 5}
The first step would be to sort them in increasing order that is, 2, 4, 5, 6, 12.
The middle number is 5.
With odd rule, the median is 5.
3) Find the median of the set {3, 5, 10, 6, 15, 11}
Sorting the set in increasing order, we get, 2, 4, 7, 5, 9, 11
The two middle numbers are 7 and 5.
Sum of those two numbers = 7 + 5= 12.
Dividing the value by 2, we get, 12/2 = 6.
Therefore the median is 6.
4) Get the mode from the set {2, 9, 3, 9, 2, 6, 12, 9}
Sorting the numbers we get, 2, 2, 3, 6, 9, 9, 9,12…
9 is the mode as it has appeared the most number of times.
5) Calculate the range of the set {3, 5, 29, 14, 9, 11}
The largest number in the set is 29 and the smallest number is 3.
Therefore, the difference is 29 – 3 = 26.
The range is 26.

Algebra

Algebra berasal dari bahasa Arab ‘al jabar’ dan wujud pada kurun 100 masihi lagi. Istilah algebra adalah sebahagian dari cabang–cabang terkenal matematik di mana abjad ‘a, b, c’ dan simbol digunakan bagi melambangkan nilai-nilai nombor tertentu. Salah satu aplikasi matematik algebra ialah penggunaan kalendar di mana tiap-tiap simbol khas melambangkan waktu yang berkait rapat dengan peredaran matahari dan bulan. Antara penggunaannya adalah bagaimana terjadinya janin dan pembesaran bayi di dalam rahim ibu yang tercatit di dalam al Quran dengan penggunaan bahasa kiasan algebra yang indah sekali. Hadith-hadith Rasululullah turut memberikan impak penggunaan algebra bagi mewakili tempoh waktu yang kritikal seperti penglihatan anak bulan (untuk penetapan puasa dan hari raya aidil fitri dan aidil adha).

 Disamping itu, nelayan, ahli pengembara di lautan dalam dan ahli-ahli perniagaan yang termashur seperti Abdul Rahman Al-Auf  dan para matematik greek di kota ROME menggunakan simbol-simbol tertentu seperti ‘V’ untuk nilai hitungan objek sebanyak lima unit, ‘X’ untuk bilangan 10 dan ‘L’ untuk bilangan unit 50. Algebra digunakan di dalam kalkulus yang merupakan sub bidang utama di dalam ilmu kejuruteraan dan Sains Komputer. Keupayaan seseorang didalam memahami asas algebra terbukti dapat membantu seseorang pelajar itu mengaplikasikan dengan jayanya dalam bidang perniagaan, kejuruteraan, pertanian, pertahanan dan lain-lain lagi.

Algebra asas ialah bentuk algebra yang termudah. Ia diajarkan kepada para pelajar yang dianggapkan tidak mempunyai ilmu matematik sebalik prinsip asas ilmu kira-kira. Walaupun dalam ilmu kira-kira, hanya nombor-nombor dan operasi arithmetik (seperti +, −, ×, ÷) wujud, dalam algebra, nombor sering ditandakan oleh lambang (seperti a, x, y). Ini berguna kerana:

• Ia memberikan rumusan umum peraturan arithmetik (seperti a + b = b + a for all a dan b), dan inilah langkah pertama untuk penjelajahan sistematik pada sifat sistem nombor benar.
• Ia memberikan rujukan kepada nombor "tidak dikenali", rumus persamaan dan pelajarannya untuk bagaimana mahu menyelesaikan ini (contohnya, "Carikan nombor x sedemikian hingga 3x + 1 = 10").
• Ia memberikan rumusan fungsi berkenaan (seperti "Kalau anda jual x tiket, kemudian untungan anda akan menjadi 3x - 10 dolar, atau f(x) = 3x - 10, dimana f ialah fungsinya, dan x ialah nombor fungsi yang dijalankan.").

Teachers Need More Knowledge of How Children Learn Mathematics

Teachers need as much scientific knowledge about how children learn mathematics as physicians have about the causes of illnesses. Because of this need, teacher-preparation programs must change. Specific examples from classrooms illustrate this need.

I once wondered why some first graders were getting such answers as 3 + 4 = 4. By watching them, I found out that they were putting three counters out for the first addend and then four for the second addend, including the three that were already out.

Errors of this kind result from prematurely teaching a rule to follow. According to this rule, one must put counters out for the first addend, more counters for the second addend, and count all of them to get the answer. This rule works for children who already know that addition is the joining of two sets that are disjoint. However, the rule is superfluous for those who have constructed this logic, and it causes errors for those who have not constructed it.

Another example of imposing a rule that is either superfluous or premature is teaching counting-on to children who are counting-all. Counting-all refers to solving 3 + 4 by counting out three counters, then four other counters, and counting all of them again ("one-two-three-four-five-six-seven"). In counting-on, by contrast, children say "four-five-six-seven."

With scientific research replicated worldwide, Piaget showed that all children construct, or create, logic and number concepts from within rather than learn them by internalization from the environment (Piaget 1971; Piaget and Szeminska 1965; Inhelder and Piaget 1964; and Kamii 2000). Studying the research leads teachers to understand that addition involves part-whole relationships, which are very hard for children to make and which cannot be taught through practice and memorization. To add two numbers, children must put two wholes together ("three" and "four," for example) to make a higher-order whole ("seven") in which the previous wholes become two parts. When young children cannot think simultaneously about a whole and two parts, they count-all by changing both the "three" and the "four" into ones. Making them count-on is harmful when they cannot mentally make the part-whole relationship necessary to count-on.

When teachers study Piaget's theory and replicate the aforementioned research, they can understand why some first graders cannot count-on. When children have constructed their logic sufficiently to make the part-whole relationship of counting-on, they give up counting-all, just as babies give up crawling when they can walk. I hope that the day will come when teachers entering the classroom and those already in the classroom have as much scientific knowledge about how children learn mathematics as physicians have about the causes of illnesses. To reach this vision, the teacher-preparation programs must change.

Learning Mathematics

Why is it important for my child to learn math?

 Math skills are important to a child’s success – both at school and in everyday life. Understanding math also builds confidence and opens the door to a range of career options.

• In our everyday lives, understanding math enables us to:
• manage time and money, and handle everyday situations that involve numbers (for example, calculate how much time we need to get to work, how much food we need in order to feed our families, and how much money that food will cost);
• understand patterns in the world around us and make predictions based on patterns (for example, predict traffic patterns to decide on the best time to travel);
• solve problems and make sound decisions;
• explain how we solved a problem and why we made a particular decision;
• use technology (for example, calculators and computers) to help solve problems.

 

How will my child learn math?

 Children learn math best through activities that encourage them to:

• explore;
• think about what they are exploring;
• solve problems using information they have gathered themselves;
• explain how they reached their solutions.

Children learn easily when they can connect math concepts and procedures to their own experience. By using common household objects (such as measuring cups and spoons in the kitchen) and observing everyday events (such as weather patterns over the course of a week), they can "see" the ideas that are being taught.

An important part of learning math is learning how to solve problems. Children are encouraged to use trial and error to develop their ability to reason and to learn how to go about problem solving. They learn that there may be more than one way to solve a problem and more than one answer. They also learn to express themselves clearly as they explain their solutions.

At school, children learn the concepts and skills identified for each grade in the Ontario mathematics curriculum in five major areas, or strands, of mathematics. The names of the five strands are: Number Sense and Numeration, Measurement, Geometry and Spatial Sense, Patterning and Algebra, and Data Management and Probability. You will see these strand names on your child’s report card. The activities in this guide are connected with the different strands of the curriculum.

What tips can I use to help my child?

• Be positive about math!
• Let your child know that everyone can learn math.
• Let your child know that you think math is important and fun.
• Point out the ways in which different family members use math in their jobs.
• Be positive about your own math abilities. Try to avoid saying "I was never good at math" or "I never liked math".
• Encourage your child to be persistent if a problem seems difficult.
• Praise your child when he or she makes an effort, and share in the excitement when he or she solves a problem or understands something for the first time.

Make math part of your child’s day.

• Point out to your child the many ways in which math is used in everyday activities.
• Encourage your child to tell or show you how he or she uses math in everyday life.
• Include your child in everyday activities that involve math – making purchases, measuring ingredients, counting out plates and utensils for dinner.
• Play games and do puzzles with your child that involve math.
  They may focus on direction or time, logic and reasoning, sorting, or estimating.
• Do math problems with your child for fun.
• In addition to math tools, such as a ruler and a calculator, use handy household objects, such as a measuring cup and containers of various shapes and sizes, when doing math with your child.

Encourage your child to give explanations

• When your child is trying to solve a problem, ask what he or she is thinking. If your child seems puzzled, ask him or her to tell you what doesn't make sense. (Talking about their ideas and how they reach solutions helps children learn to reason mathematically.)
• Suggest that your child act out a problem to solve it. Have your child show how he or she reached a conclusion by drawing pictures and moving objects as well as by using words.
• Treat errors as opportunities to help your child learn something new.

What math activities can I do with my child?

1.  Understanding Numbers

Numbers are used to describe quantities, to count, and to add, subtract, multiply, and divide. Understanding numbers and knowing how to combine them to solve problems helps us in all areas of math.

Count everything! Count toys, kitchen utensils, and items of clothing as they come out of the dryer. Help your child count by pointing to and moving the objects as you say each number out loud. Count forwards and backwards from different starting places. Use household items to practise adding, subtracting, multiplying, and dividing.

Sing counting songs and read counting books. Every culture has counting songs, such as "One, Two, Buckle My Shoe" and "Ten Little Monkeys", which make learning to count – both forwards and backwards – fun for children. Counting books also capture children’s imagination, by using pictures of interesting things to count and to add.

Discover the many ways in which numbers are used inside and outside your home. Take your child on a "number hunt" in your home or neighbourhood. Point out how numbers are used on the television set, the microwave, and the telephone. Spot numbers in books and newspapers. Look for numbers on signs in your neighbourhood. Encourage your child to tell you whenever he or she discovers a new way in which numbers are used.

Ask your child to help you solve everyday number problems. "We need six tomatoes to make our sauce for dinner, and we have only two. How many more do we need to buy?" "You have two pillows in your room and your sister has two pillows in her room. How many pillowcases do I need to wash?" "Two guests are coming to eat dinner with us. How many plates will we need?"

Practise "skip counting". Together, count by 2’s and 5’s. Ask your child how far he or she can count by 10’s. Roll two dice, one to determine a starting number and the other to determine the counting interval. Ask your child to try counting backwards from 10, 20, or even 100.

Make up games using dice and playing cards. Try rolling dice and adding or multiplying the numbers that come up. Add up the totals until you reach a target number, like 100. Play the game backwards to practise subtraction.

Play "Broken Calculator". Pretend that the number 8 key on the calculator is broken. Without it, how can you make the number 18 appear on the screen? (Sample answers: 20 – 2, 15 + 3). Ask other questions using different "broken" keys.

 

2.  Understanding Measurements

We use measurements to determine the height, length, and width of objects, as well as the area they cover, the volume they hold, and other characteristics. We measure time and money. Developing the ability to estimate and to measure accurately takes time and practice.

Measure items found around the house. Have your child find objects that are longer or shorter than a shoe or a string or a ruler. Together, use a shoe to measure the length of a floor mat. Fill different containers with sand in a sandbox or with water in the bath, and see which containers hold more and which hold less.

Estimate everything! Estimate the number of steps from your front door to the edge of your yard, then walk with your child to find out how many there really are, counting steps as you go. Estimate how many bags of milk your family will need for the week. At the end of the week, count up the number of bags you actually used. Estimate the time needed for a trip. If the trip is expected to take 25 minutes, when do you have to leave? Have your child count the number of stars he or she can draw in a minute. Ask if the total is more or less than your child thought it would be.

Compare and organize household items. Take cereal boxes or cans of vegetables from the cupboard and have your child line them up from tallest to shortest.

Talk about time. Ask your child to check the time on the clock when he or she goes to school, eats meals, and goes to bed. Together, look up the time of a television program your child wants to watch. Record on a calendar the time of your child’s favourite away-fromhome activity.

Keep a record of the daily temperature outside and of your child’s outdoor activities. After a few weeks, ask your child to look at the record and see how the temperature affected his or her activities.

Include your child in activities that involve measurements. Have your child measure the ingredients in a recipe, or the length of a bookshelf you plan to build. Trade equal amounts of money. How many pennies do you need to trade for a nickel? for a dime?

3.  Understanding Geometry

The ability to identify and describe shapes, sizes, positions, directions, and movement is important in many work situations, such as construction and design, as well as in creating and understanding art. Becoming familiar with shapes and spatial relationships in their environment will help children grasp the principles of geometry in later grades.

Identify shapes and sizes. When playing with your child, identify things by their shape and size: "Pass me a sugar cube." "Take the largest cereal box out of the cupboard."

Build structures using blocks or old boxes. Discuss the need to build a strong base. Ask your child which shapes stack easily, and why.

Hide a toy and use directional language to help your child find it. Give clues using words and phrases such as up, down, over, under, between, through, and on top of.

Play "I spy", looking for different shapes. "I spy something that is round." "I spy something that is rectangular." "I spy something that looks like a cone."

Ask your child to draw a picture of your street, neighbourhood, or town. Talk about where your home is in relation to a neighbour’s home or the corner store. Use directional words and phrases like beside and to the right of.

Go on a "shape hunt". Have your child look for as many circles, squares, triangles, and rectangles as he or she can find in the home or outside. Do the same with threedimensional objects like cubes, cones, spheres, and cylinders. Point out that street signs come in different shapes and that a pop can is like a cylinder.

 

4.  Understanding Patterns

We find patterns in nature, art, music, and literature. We also find them in numbers. Patterns are at the very heart of math. The ability to recognize patterns helps us to make predictions based on our observations. Understanding patterns helps prepare children for the study of algebra in later grades.

Look for patterns in storybooks and songs.

Many children’s books and songs repeat lines or passages in predictable ways, allowing children to recognize and predict the patterns.

Create patterns using your body.

Clap and stomp your foot in a particular sequence (clap, clap, stomp), have your child repeat the same sequence, then create variations of the pattern together. Teach your child simple dances that include repeated steps and movements.

Hunt for patterns around your house and your neighbourhood.

Your child will find patterns in clothing, in wallpaper, in tiles, on toys, and among trees and flowers in the park. Encourage your child to describe the patterns found. Try to identify the features of the pattern that are repeated.

Use household items to create and extend patterns. Lay down a row of spoons pointing in different directions in a particular pattern (up, up, down, up, up, down) and ask your child to extend the pattern.

Explore patterns created by numbers. Write the numbers from 1 to 100 in rows of 10 (1 to 10 in the first row, 11 to 20 in the second row, and so on). Note the patterns that you see when you look up and down, across, or diagonally. Pick out all the numbers that contain a 2 or a 7.

 

5.  Understanding and managing data

Every day we are presented with a vast amount of information, much of it involving numbers. Learning to collect, organize, and interpret data at an early age will help children develop the ability to manage information and make sound decisions in the future.

Sort household items.

As your child tidies up toys or clothing, discuss which items should go together and why. Show your child how you organize food items in the fridge – fruit together, vegetables together, drinks on one shelf, condiments on another. Encourage your child to sort other household items – crayons by colour, cutlery by type or shape, coins by denomination.

Make a weather graph.

Have your child draw pictures on a calendar to record each day’s weather. At the end of the month, make a picture graph showing how many sunny days, cloudy days, and rainy days there were in that month.

Make a food chart.

Create a chart to record the number of apples, oranges, bananas, and other fruit your family eats each day. At the end of the month, have your child count the number of pieces of each type of fruit eaten. Ask how many more of one kind of fruit were eaten than of another. What was your family’s least favourite fruit that month?

Talk about the likelihood of events. Have your child draw pictures of things your family does often, things you do sometimes, and things you never do. Discuss why you never do some things (swim outside in January). Ask your child if it’s likely to rain today. Is it likely that a pig will fly through the kitchen window?

Where can I get help?

Many people are willing to support you in helping your child learn math, and there are also many resources available.

• Your Child’s Teacher
• Your child’s teacher can provide advice about helping your child with math. Here are some topics you could discuss with the teacher:
• your child’s level of performance in math
• the goals your child is working towards in math, and how you can support your child in achieving them
• strategies you can use to assist your child in areas that he or she finds difficult
• activities to work on at home with your child
• other resources, such as books, games, and websites

Membina Pemikiran Geometri Murid

Mempelajari ilmu geometri mendedahkan kita tentang kewujudan alam ini dengan mendalam. Mengajar ilmu geometri pula melatih akal fikiran kita untuk menjana pemikiran yang kritis dan terperinci. Terdapat alasan lain kenapa kita harus belajar manipulasi geometri iaitu minat terhadap geometri sentiasa ada apabila kita memerlukan jawapan tentang peristiwa dan fungsi tentang kejadian alam sejagat.

Ironinya, minat terhadap kepelbagaian bentuk dan objek seperti garisan, bulatan, segi tiga, dan segi empat yang begitu dekat dengan kehidupan manusia secara semulajadi selari dengan fenomena memandu di jalan raya, melihat kestabilan bangunan dan lain-lain lagi sering menjadi asas kepada pengembangan terhadap pengetahuan geometri.

Menurut Van Hiele penyelidikannya yang memulakan pada tahun 1950an, pembangunan teori pemikiran spatial dalam geometri mendorong pemahaman serta kemahiran pelajar dengan arahan-arahan yang menjurus kepada aras-aras pemikiran semulajadi geometri pelajar. Teori beliau mempunyai hieraki aras pemikiran bermula pada usia awal kanak-kanak sehinggalah dewasa yang terdiri dari 3 aras pertama yang merangkumi tempoh normal pembelajaran.

•         Aras Pertama adalah Visual di mana tahap ini bermula dengan pemikiran nonverbal. Bentuk dilihat sebagai satu, berbanding daripada pelbagai gabungan bentuk.Pelajar akan menamakan bentuk pada apa yang mereka lihat dan tidak ada penjelasan tentang bentuk tersebut.

•         Aras Kedua adalah Diskriptif. Pada tahap ini,pelajar boleh mengenali dan menghuraikan bahagian-bahagian bentuk. Mereka juga perlu membina bahasa yang sesuai untuk mempelajari sesuatu konsep yang baru.Walau bagaimanapun, pada tahap ini pelajar masih tidak dapat mengaitkan turutan logik dan perkaitannya. Sebagai contoh,pelajar tidak memahami bahawa segitiga sama sisi yang mempunyai 3 sisi yang sama panjang juga mempunyai 3 sudut yang sama besar.

•         Aras Ketiga adalah Deduktif Formal. Pada tahap ini,pelajar dapat mengaitkan turutan logik bentuk. Mereka mampu melihat bahawa ada perhubungan antara satu sama lain dalam suatu bentuk. Mereka juga mampu mengaplikasi serta menerangkan perhubungan antara bentuk dan seterusnya membuat definisi. Sebagai contoh, mereka boleh memahami kenapa segiempat sama adalah juga tergolong dalam bentuk segiempat . Walau pun begitu,pada tahap ini pelajar masih belum mampu memahami peranan aksiom,definisi,teorem dan alihannya.

Bagi sesetengah pelajar,proses pembelajaran berlaku secara aktif serta berkesan melalui permainan. Arahan simulasi dalam geometri serta aktiviti pengayaan boleh diterapkan di dalam aktiviti bermain seperti meyusun mozek serta blok-blok corak mengikut corak tertentu. Dengan menggunakan alatan-alatan ini, secara tidak langsung, kanak-kanak akan mengenal bentuk – bentuk geometri secara tidak formal. Ini kerana geometri ini merupakan suatu seni yang boleh merangsang pemikiran kanak-kanak. Penyusunan blok dan mozek membolehkan kanak-kanak menyelesaikan masalah – masalah bentuk-bentuk yang dikehendaki. Kanak-kanak digalakkan meneroka dengan bebas bahan-bahan geometri dan membuat penemuan secara sendiri ciri-ciri dan struktur bahan. Sementara mereka bermain, murid-murid boleh dinilai oleh guru melalui pemerhatian secara tidak formal cara murid berfikir.

Seperti contoh, penggunaan tangram boleh diajar sejak dari awal peringkat umur murid. Guru boleh menanyakan beberapa soalan seperti apa yang boleh dilakukan dengan kepingan-kepingan tangram tersebut. Guru perlu menggalakkan murid supaya berkongsi dan bercerita tentang bentuk dan gambar yang mereka bina. Secara tak langsung murid meneroka ciri-ciri bentuk dan perhubungan antaranya.

 Ini seterusnya murid dapat memberi tumpuan terhadap ciri-ciri khusus setiap bentuk tangram tersebut seperti bentuk segiempat sama, segiempat tepat dan juga segitiga.

 

Contohnya, dalam suatu permainan, murid menggunakan beberapa kepingan bentuk segitga untuk membentuk segiempat. Guru boleh menggalakkan murid untuk menggunakan kepingan-kepingan yang lain untuk membentuk sesuatu bentuk yang baru. Melalui aktiviti tersebut murid dapat lebih pemahaman yang lebih spesifik terhadap ciri-ciri bentuk. Murid akan sedar bahawa panjang sisi bentuk tersebut adalah sama dan sesetengahnya adalah separuh daripada bentuk yang lain. Mereka juga dapat menyatakan bahawa setiap sudut bahawa apabila dicantumkan bersama akan membentuk bentuk yang lain.

Seterusnya di peringkat yang lebih tinggi, melalui permainan tangram ini, murid diperkenalkan istilah-istilah baru untuk meneroka dengan lebih lagi ciri-ciri bentuk yang baru. Aktiviti ini menggalakkan murid menggunakan istilah-istilah tersebut dalam percakapan dan penulisan mereka tentang pengalaman yang mereka perolehi. Contohnya, semasa guru menanyakan nama-nama bentuk-bentuk, guru boleh memperkenalkan istilah-istilah lain seperti sama sisi, sudut sama, sudut tepat, simetri dan lain-lain. Sebagai contoh guru boleh menanyakan bentuk apa yang mempunyai sudut tempat, apa ciri yang sama dalam semua segitiga,bentuk apa yang mempunyai sisi yang selari dan lain-lain.

Di peringkat seterusnya, aktivti dan tugasan penyelesaian masalah dapat diterap dengan menggunakan soalan terbuka dan boleh diselesaikan dalma pelbagai cara. Matlamatnya adalah supaya murid dapat menggunakan apa yang telah dipelajari dalam menyelesaikan masalah. Murid-murid boleh diberi tugasan mencabar seperti melukis dan membina bentuk-bentuk yang ditunjukkan oleh guru menggunakan kepingan-kepingan tangram tersebut.

Selain daripada itu, penggunaan blok-blok boleh melatih kanak-kanak untuk berfikir secara kognitif melalui penyesuaian bentuk geometri ini. Penggunaan origami juga dapat memberi peluang kepada murid menyelesaikan masalah-masalah geometri seperti paksi simetri, sudut, persamaan bentuk, bucu dan lain-lain.

Kemahiran penyelesaian masalah geometri juga boleh ditingkatkan melalui internet kerana pada masa kini terdapat pelbagai aktiviti interaktif yang membolehkan murid meneroka dan mempelajari tajuk geometri dengan lebih mendalam dengan rasa seronok.

Geometri

Geometri (Greek γεωμετρία; geo = bumi, metria =ukuran) adalah sebahagian dari matematik yang mengambil berat persoalanan mengenai saiz, bentuk, dan kedudukan relatif dari rajah dan sifat ruang. Geometri ialah salah satu dari sains yang tertua. Pada mulanya ia hanyalah sebahagian jasad dari pengetahuan praktikal yang mengambil berat dengan jarak, luas dan isipadu, tetapi pada abad ketiga S.M. geometri telah diletakkan di dalam bentuk aksiom oleh Euclid membentuk Geometri Euclid, yang hasilnya menetapkan piawai untuk beberapa abad berikutnya.

Bidang astronomi, khususnya memetakan bintang-bintang dan planet-planet pada sfera cakerawala, bertindak sebagai sumber-sumber geometri terpenting dari semasa satu setengah alaf berikutnya Menurut Plato Geometri adalah alat atau kaedah yang terperinci untuk  menjelaskan keadaan dua bahagian alam.

Geometri merupakan satu topik yang penting dalam pembelajaran matematik. Ia bukan sahaja merupakan satu penyokong kepada bidang-bidang lain dalam matematik, tetapi juga dalam kerjaya seperti kejuruteraan, arkitek, fizik dan astronomi. Selain daripada mengenali bentuk dan sifat-sifat asas ruang dan bentuk-bentuk konkrit, penerokaan konsep-konsep geometri yang melibatkan penyelesaian masalah dan masalah pengukuran juga diperlukan. 

Geometri merupakan salah satu perkara asas dan penting kepada seluruh sistem matematik. Pembelajaran geometri melibatkan perkara seperti  pembinaan objek daripada suatu ukuran, anggaran serta aksioms, pendedahan kepada banyak teorem-teorem kedudukan serta hukum mekanikal.

Pembelajaran geometri pada awal umur kanak-kanak adalah tidak formal,berbentuk penerokaan,meneka dan menyelesaikan masalah. Ini dapat dilihat, sejak dari bayi lagi, ibubapa sebenarnya telah pun menerapkan pemahaman secara tidak formal kepada kanak-kanak dengan memberikan obejek-objek geometri sebagai alat mainan. Pada peringkat ini, kanak-kanak tidak mengetahui secara saintifik berkenaan geometri tetapi melalui pengalaman mereka bermain dengan alat permainan tersebut telah membina pengetahuan geometri secara tidak langsung.

Melalui sesetengah permainan juga seperti memasukkan bentuk-bentuk geometri seperti segiempat, segitiga dan bulat ke dalam ruang yang disediakan dan penyusunan kepingan-kepingan bentuk-bentuk, kanak-kanak mendapat peluang menimba pengalaman dalam menyelesaikan masalah serta mempelajari konsep geometri darinya.