The method of teaching math in Singapore is called Singapore Math.It has been used in the United States.Singapore Math focuses on developing an understanding of the concepts before teaching them.It uses both a hands-on and visual approach to teaching, and emphasizes a strong sense of numbers and problem solving.
Step 1: The framework of Singapore math can be learned.
You need to understand the philosophy behind the development of Singapore Math before you can teach it effectively.It may take a little while to get used to Singapore Math, since it isn't like the math education you grew up with.The framework of the general philosophy of Singapore Math has five components: Concepts, Skills, Processes, Attitudes, and Metacognition.The development of mathematical problem solving abilities is dependent on these 5 components.Concepts include numerical, mathematical, statistical, probabilistic, and analytical concepts.Skills include numerical calculation, algebraic manipulation, spatial visualization, data analysis, measurement, use of mathematical tools and estimation.Reasoning, communication and connections are some of the skills that are referred to as processes.Beliefs, interest, appreciation, confidence, and perseverance are referred to as attitudes.Monitoring of one's own thinking and self-regulation of learning is called metacognition.
Step 2: Understand the concepts of mathematics.
The students need to learn how they are connected together by learning the mathematical concepts as individual ideas.Students need to be given a selection of materials and examples in order to understand how they are all connected.To be more confident with their mathematical skills, they need to be able to apply the concepts in active mathematical problem solving.
Step 3: You should develop the mathematical skills.
Students need to learn a variety of mathematical skills, including: numerical calculation, algebraic manipulation, spatial visualization, data analysis, measurement, the use of math tools, and estimation.These skills are needed to learn and use the mathematical concepts they are being taught.It's important that students understand why a mathematical principle works, not just how to solve a math problem.
Step 4: Conducted the mathematical processes.
Reasoning, communication and connections are some of the skills that are included in mathematical processes.Knowledge skills are needed to better understand a mathematical problem and the process that is used to solve it.Reasoning is the ability to analyze a mathematical problem and make logical arguments about it.Students learn these skills by applying the same reasoning to different mathematical problems.Communication is the language of mathematics.A student needs to be able to understand the mathematical language of a problem and express concepts, ideas, and arguments in that same language.The ability to connect mathematical concepts together is called connections.It is possible to link mathematical ideas to non-mathematical subjects.The student can make sense of what is being taught in the context of their day-to-day lives if they are able to make connections.The skills that can help a student think the way through a mathematical problem are called thinking skills.The ability to provide a representation of the problem is one of four categories of heuristics.diagram, list, etc.The ability to make a calculated guess, work through the process in various ways, and alter the problem in order to better understand it are some of the skills that a mathematician has.Every day problems and situations are some of the reasons a student develops their mathematical problem solving skills.It's possible to apply representations of data to a specific problem and then determine which methods and tools should be used to solve the problem.
Step 5: Put mathematical attitudes in shape.
There is a reason that math gets a bad reputation.This reputation isn't developed because math is hard.It develops because math can be boring.What child wants to spend a lot of time learning their times tables?The idea of making math fun and exciting is what mathematicians call mathematical attitudes.In addition to fun and exciting, mathematical attitudes also refers to the ability for a student to take a math concept, method, or tool they have learned and use it in their actual day-to-day lives.This type of application happens when a student knows why a concept works and can apply it to other situations.
Step 6: A metacognitive experience is provided.
Metacognition is a concept that relates to being able to control how you think.It is used to teach students how to solve problems.Teaching general (non-mathematical) problem solving and thinking skills is one of the ways in which metacognition is used to teach Singapore Math.When students think through a problem out loud, their minds are focused on the problem at hand.Giving students problems to solve requires the student to plan how they will solve the problem, and then evaluate their solution.Students should be able to solve a problem using more than one method.Students can work together to solve a problem by discussing various methods.
Step 7: The approach can be applied in stages.
Singapore Math does not try to teach a student everything at once.The concepts are introduced in stages.A concrete concept such as manipulating numbers by counting is taught to a student first.The student is taught the concept using pictures.The student is taught the concept using an abstract approach.
Step 8: The concept of number bonding is explained.
Number bonds are similar to families.There are groups of numbers that are related to each other.A fact family is one where the three numbers are related to each other.You can bond two numbers to the third using addition and subtraction.3 + 4 is 7, or 7 + 3 is 4.10 is considered an easier number to deal with than fact families that add up to 10.You can apply the same concepts to multiples of 10 once you learn 10.You can also use multiplication and division with number bonds.For example, where 2 x 4 is 8 or 4.
Step 9: Use branching to destroy numbers.
Decomposing breaks numbers into simpler parts.Branching diagrams are used to understand the concept.For example, decomposing 15 into 10 and 5.A branching diagram has the number 15 with two lines pointing towards a 10 and a 5, similar to a family tree.Students should be taught to break larger numbers into smaller ones.Friendly numbers are 10 and 5.If we wanted to make the number friendly, we would use 20 and 4.What is 15 plus 24?It may be difficult to add the number 15 to 24.Instead of trying to add those two big numbers, we break them down into smaller, friendlier and more manageable numbers.Instead of 15 + 24 we have 10 + 5 + 20 + 4.It's much easier to add 10 and 20 together.It is very easy to add 30 and 9 together to get 39.The above example shows how branching diagrams drawn on paper can be used to solve a problem.
Step 10: Left-to-right addition is what you should start with.
Adding from left-to-right is taught first in Singapore Math, but eventually it will teach addition, subtraction, multiplication, and division using numbers in columns and moving from right to left.Left-to-right addition helps teach place values.The left-to-right addition uses the idea of decomposing a number to make it easier to solve the problem.7,524 could be expanded and written as '7,000 + 500 + 20 + 4'.The place value concept applies to the order of the numbers.A place value is how we view a number from the right to the left.The number 1,234 can be broken down into place values where 4 are in the one place, 3 are thetens, and 1 is thethousands.If we wanted to add 723 and 192 together, we would have to use left-to-right addition.The student can now add numbers with similar place values from left to right.The final step is to add the numbers from all the values together.
Step 11: The area model is used.
The area model for multiplication uses both place values and tables to make multiplication easier.When two numbers are combined, they are first added into the expanded notation.A 2x2 matrix is drawn if the numbers are double-digits.There are 4 blank boxes in the matrix.The expanded numbers are written on the outside of the matrix, one in each column, and the other in the row.Each box contains the multiplication of the number directly above it in the column and directly to the right of it.When all the boxes are filled, the numbers are added together to get the final result.14 x 3 would be expanded to be 10 x 4.One number in each of the two columns would be written above the 2x2 matrix.The 0 and 3 would be written to the right of the 2x2 matrix.The products of the following numbers would be filled with the blank boxes.The 4 products are added together as 0, 30, and 12 which equates to 42.
Step 12: The FOIL method can be used for multiplication.
The FOIL method uses a horizontal method instead of the matrix used in the area model.FOIL stands for multiplication of the first term, O, I, and L.The four resulting products can be added together to get the final result.If you want to use the FOIL method to calculate 35 by 27 you have to first divide the first 30 terms by 20 and then divide them by 7.If you add the four results together you get 955.
Step 13: Dividing by distributive properties.
The method of division uses branching to break a problem down into manageable pieces.A division problem is made up of two things.The divisor is a dividend.A branching diagram shows the distribution of the dividend.The divisor divides each of the branches and then the two terms get added together to get the final result.You can use this method to divide 52 by 4 by decomposing 52 into 40 and 12 using a branching diagram.40 and 12 are divided by 4.40 / 4 is 10 and 12 is 4.10 + 3 + 13 is the final result.
Step 14: You can estimate the answer with rounding.
As a student learns more complicated math problems, it is important to ask them not to solve the problem, but to estimate the answer by rounding some of the numbers.The ability to do mental math is aided by this skill.The rounding is based on place values.It is easier to round 498 up to 500 and then divide 500 by 5, which is 100, without writing down any calculations.The answer is 99 because 498 is a little smaller than 500.
Step 15: It is possible to make a problem easier with compensation.
When you're trying to figure out a math problem, you probably don't have a name for compensation.It is possible to convert a problem to something much easier by changing how the numbers are displayed.By moving the numbers around it makes it easier to calculate the answer in your head.It might take a bit of figuring if you want to add 34 to 99.By changing the problem to something simpler, it can be solved quicker.The new problem would be 100 + 33 if we moved the value of 1 from 34 to 99.The answer is obviously 133.
Step 16: To solve word problems, draw a model.
By their nature, mathematical word problems are not always as easy to understand as mathematical problems with numbers.One way to solve a complicated word problem is to use a systematic process that includes drawing a visual representation of the problem so that it can be easily solved.The first step is to read the full question without paying too much attention to the numbers that are mentioned.The student should try to understand what the problem is saying when they first read it.Take note of the actual numbers when you read the problem a second time.Write down the "who" and "what" the problem is about in Step 2.To help with the modelling and visualization of the problem, draw unit bars of equal length.A unit bar is a rectangular bar drawn on the paper.Take one phrase at a time and read the whole problem.You can use the unit bars to represent the information in the problem.Adding a question mark to the unit bars will represent the final answer you are looking for.Determine what the question mark should be by using the visualization you drew, plus mathematical concepts and skills you have already learned.It's important to write down your calculations so you can check them if you need to.Write the answer in full sentences.The final answer should be in words since it is a word problem.
Step 17: Understand how to model a word problem.
The following example shows how modelling can be used to solve a word problem.You can use your students textbook or materials to practice the process on your own.Helen has 14 breadsticks.Her friend has more.How many do they have?The first step is to read the problem and note that there are two people in it and that it is about breadsticks.Two people have a certain amount of breadsticks.We want to know the total number of breadsticks the people have.To represent the total amount of breadsticks, draw a big unit bar.The unit bar has a line through it.The 14 breadsticks that Helen has are represented by a bar to the left of the line.There is a bar to the right of the line.The question mark is the fifth step.The number represents the entire bar.We want to add 14 and 17 together in order to get the answer.We could use left-to-right addition to solve the problem by breaking the numbers into expanded notation.Helen and her friend have a total of 31 breadsticks.
Step 18: It's not the same as what you learned in school.
The United States introduced Singapore math in the 1990s.If you went to elementary school before the 1990s, you wouldn't have had Singapore Math in the curriculum.You likely needed to memorize and drill the times tables.The actual mathematic concepts are taught in a way that they can be applied to any problem.
Step 19: Allow a child to use the Singapore method.
If you watch a child do math homework, you probably won't recognize the methods they're using.Do not let this affect you or them.You can learn the concept of the Singapore method yourself.You may be tempted to have a child learn some of the drills you taught, but try not to.It may confuse the child at school.
Step 20: A child needs to be able to explain the answer.
The goal was the correct answer to any math problem, regardless of how you got there.In Singapore math the child needs to be able to explain their thought process from start to finish.It is possible that a child's final answer is incorrect, but that they used all the correct concepts to develop that answer.The child understands what they are doing even if there is a simple error in the process.
Step 21: Singapore math materials can be used at home.
Even if a child is learning Singapore math in school, they can still learn it at home.You can use Singapore Math materials to help a child understand and learn math.You may want to encourage your school board to change the curriculum if you find the process successful at home.
Step 22: You can play games with a math component.
One of the best ways to teach a child math is to play games with them.You can do this even if the method of teaching is different.Ask a child to identify shapes of objects you pass in the car.Ask a child to help you calculate the amount of ingredients needed in a recipe that you want to cut in half or double.Asking a child to calculate how fast a car is travelling using facts other than the speedometer is an example.