Teaching Kindergarten and Preschool Math

The way math is presented to children makes a tremendous difference in their success as learners, as well as your success as an educator. Children need to take part in activities that encourage them to experiment, to investigate, and to record their observations.

Preschool and kindergarten students always need to have things to move around or manipulate in order to make sense of math concepts. In the education world these are called "manipulatives" and there are a great assortment of these available, such as blocks, counters and pattern blocks. Give children ample time to play with the manipulatives in order to satisfy their curiosity about the materials before attempting to use them to teach a math concept. Introduce new math vocabulary as the children play, as this will help them when they participate in teacher led experiences.
Keep structured lessons short to begin with and do not assume the children understand your expectations. Spend a week teaching proper use of materials and proper cleanup. Teach the children to use mats to identify and define their work area.

The following steps work well when teaching young children. First, demonstrate the math activity two or three times before you give the children materials. You will quickly lose the children's attention if you pass the materials out first. Second, give materials to the children and ask them to try the activity. Check to see all have understood the concept and are experiencing success. Assist children that are having difficulty.

After a few days of the same or similar lessons, record your math experience as the children observe. Keep it simple. For example, after a lesson making repeating patterns print the words, I made a pattern. Say, "I used a red block, a blue block, a red block, a blue block." Draw the pattern and color the blocks. Pass out paper and have the children draw what they did and record words using their knowledge of letters and letter sounds. Recording the activity gives children an opportunity to share and solidify their knowledge.

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Effective Way to Teach Mathematics - A Guide For Tutors

Mathematics can be considered as the most problematic subject area among average students. Not all students are able to grasp the concept of their math subjects as easily as how brilliant student are able to do so. This is the reason why home tuition will mostly cover math subjects. Thus, private tutors must develop a skill on how they will be able to deliver the concept of the subject matter in a manner that can be understood by their student easily.

In order to make teaching mathematics effective, teachers must follow the most important principle of teaching math to keep them on the right track. Teachers need to make everything about the concept make sense. Let's face it math can really be very complex. Your teacher can teach you the steps and procedures on how to solve a certain math equation but fails to make you understand why these steps actually work.

More often than not, math teachers will only focus on the how of the concept rather than the why. Meaning, the students may grasp the procedure and solve certain problems but loose on the concept or their ability to understand why the procedure is working. For instance, a child may be able to learn the procedure or the how to multiply but is not able to understand the concept or why the formula works. This kind of learning is very superficial and can be forgotten over time. But, if the teacher is able to let the student understand the concept behind the formula, then it can be considered as learning the subject matter as whole. The understanding of the procedures and the concept may vary from one student to another. Thus, the teacher must be flexible with how he relays the subject matter.

Teaching tools is another factor that needs to be considered to. Making use of different tools to make teaching more effective must also be given priority. With the innovations in technology, so many teaching tools have been developed. From abacus to calculators, textbooks to e-books, even games are utilized to make understanding easier. However, teachers must effectively use the resources efficiently and effectively. Teachers can start from the basics. As time goes by, they can now add more tools to aid them in their teaching strategies. You need not grasp every tool all at once. You can utilize each tool one at a time, taking in to consideration how your students are benefiting from each tool.

You see, every child has a unique learning potential. Thus, it is very important for educators to identify how their students are responding to their way of teaching. Thus to make teaching effective, it is the responsibility of the teacher to use variations on their styles and they must be flexible enough to adapt on the learning capacity of their student. This goes especially true among those who are providing home tuition. They must be very keen in observing whether their manner of delivering the subject matter is effective or not.

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Singapore Math Methods and Beliefs

At least for me, Math is one of the most difficult subjects to teach a child. This is especially true if you are homeschooling and you need to be the math teacher. When I started teaching my children, I was worried I would never be able to teach them how to be really good at math considering it isn't exactly my strong point.

I was very blessed to come across a program called Singapore Math. I was amazed at how differently they taught math compared to all of the other math programs I have come across. In fact, Singapore Math has been teaching me right along with my children. The concepts are presented in such a way that everyone can learn.

Singapore is known for having the highest math scoring students in the world. Singapore Mathematics teaches your child the exact same way and gives them the head start they need to become math geniuses. I became a believer of the Singapore Math curriculum when I saw the results in my own children.

They caught on very quickly with Singapore Math compared to the other math we had tried. They understood the material better, and still know how to effortlessly apply what they learned last year. That is proof of a great math curriculum.

I have found that there is a huge difference in the way Singapore Math teaches my children how to think about math. Sure, they learn to memorize things like any other math curriculum, but with Singapore Math, children learn to think about problems in several different ways.

For example, with the very small children, this curriculum will show them a sequence of numbers like 3, 4, 5, and 6. With these numbers, they will have to memorize them and decide if the sequence goes forward or backward. Other sequences will have numbers missing, and the child will decide which numbers are missing, where they go, and if the sequence goes forward or backward.
This requires the student to focus on thinking about the numbers rather than taking the easy way out by just memorizing them. While other programs teach you how to do math, this program teaches you how to understand math. The colorful pictures and entertaining characters really add a nice element to the material as well.

One of the Singapore Math methods I truly enjoy is the way they present math problems to my children. Most math curriculums give children a problem to learn how to solve. In order to help them solve it, they will show children how to place the problem within a formula.

With Singapore Mathematics the children learn each and every step of a problem, which gives them a greater understanding of how math works. They will then be provided with the problem as a whole, and this ensures that they are already familiar with the individual parts of the problem, so the entire problem is not overwhelming to them.

Singapore Math is just great for parents who want to raise intellectual thinkers. Children who understand the concepts of mathematics from the inside out can more easily solve problems and figure out answers to other types of problems. This is the reason that the Singapore curriculum is my first choice, and will continue to be as my children grow.

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Which Homeschool Math Curriculum Is Best?

Many parents usually ask the question of which math homeschool curriculum would be best for their children. Which curriculum has the most resources? Which has the best textbooks? This one comes with a lot of math worksheets and quizzes, why don't the others? There are a lot of questions and a lot of great curricula to choose from, but it's often hardest to determine which would fit their child's specific needs the best. This is why it's important to establish a foundation to build on when it comes to picking the right math curriculum for your children.

There are a lot of popular curricula offered on the market today and they all target different learning styles. One of the most popular curricula out there for both classroom and homeschool teaching is Saxon. This type of curriculum provides an approach that is very similar to the approach of an ordinary Math textbook used in classrooms. Each new lesson typically contains exercises which would help the student understand a specific topic better. On the completely opposite end of the learning spectrum would be Math-U-See. This curriculum is heavily video oriented, and is targeted towards visual learners allowing the child to visualize the topics of the subject first. This is a much more creative way of helping a child who doesn't particularly like math learn Mathematics.

If you've done any research into math curriculum then you've come across Singapore Math, which is a mastery-based type of curriculum. The focus of this type of curriculum is the memorization of certain topics and methods which are important to mastering the subject. Of course, there are still other curricula that are also preferred by parents such as Abeka Math and Miquon Math. All of these are tried, true and proven effective, which still leaves the question which one is the best?

Here are the two main determining factors in choosing; first is the teacher and the second is the student. The teacher should be an important factor in choosing the best math homeschool curriculum for the child. Yes, the teacher. Curriculum is a tool and an effective teacher is the key to learning. A teacher does more than provide a book, a teacher must be able to relay the information from the book in such a way that the child will understand it.

Great! More work to do, right? Math doesn't teach itself, teaching is always part of the equation for homeschooling, that part is no different than in a classroom. The trick is being enthusiastic about teaching the subject matter. If you hate the curriculum how is your child going to enjoy it? If you can't make a more rigid curriculum fun then choose a curricula that is designed to be more interactive and engaging to benefit the both of you.

In choosing which curriculum would be best for your child, identify your child's learning method. Does your child tend to me more visual, auditory or a memory based learner? For instance, many parents end up buying Saxon, Horizons and Singapore Math programs because their children are so different in how they learn. They all work well, but typically, children who are more language oriented and don't really care much for math tend to prefer Horizons. Children who are typically stronger in math prefer Singapore. Saxon and Horizons are fairly similar in approach, so many parents end up combining Singapore with either of those programs as Singapore is more of a critical thinking method.

It's true, choosing a good math homeschool curriculum can be quite a tedious task, but to answer to the ultimate question of which curriculum is best... it would have to be a combination of curriculum. No, that's not a cop-out, combining multiple methods ensures a better understanding and more well-rounded education and that's what your really researching isn't it?

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The School Math Curriculum - How Children Learn Maths

Many parents worry that teaching math through play and the medium of Cuisenaire Rods will somehow confuse their child if the school he/she attends adopts a more formal or different approach. The fact is that it is universal math concepts that are being taught using the rods to provide children with a deeper understanding of the structure of number and our number system than would otherwise be possible. These concerns are of course irrelevant if you are homeschooling your children.

This approach teaches universal math concepts in a way that is totally child-centered. Children discover math is creative and fun. Concepts are discovered through play, games and open-ended challenges. Sometimes the hardest part for parents to accept is that 'maths is fun'. As a consequence children will always associate Math with a pleasurable, creative and constructive experience that they enjoyed.

This is often a world away from the memories of most of us.

This method is designed to complement the way children learn best and because of this children's learning is invariably accelerated compared to children exposed to more traditional and formal methods. Children are naturally kinesthetic/tactile learners and this reflects the dominant methodology which is truly multi-sensory as visual and auditory learners are also well provided for.
Math need no longer be a source of stress and conflict in the home.

Math related surveys consistently reveal that Math is probably the most hated subject on the school curriculum. One of the most iconic figures of the 20th Century - Barbie's - first words were '"Math is tough" following concerns raised in the US regarding the lack of math achievement by girls. The National Network For Child Care posed the question "What Can We Do?" in their newsletter. Back in 1982 a major report 'Mathematics Counts' was produced as result of a committee of enquiry into the teaching of Mathematics in schools in the UK under the chairmanship of Dr W H Cockroft. Some of the findings were alarming. When adults were interviewed the report observed how "... even an apparently simple and straightforward piece of mathematics could induce feelings of anxiety, helplessness, fear and even guilt..."

I question how much has changed.

A positive introduction to Math is absolutely crucial and what better way than through play? Just give the rods to a child of any age and he/she will do what they do best - play. Play is one of the most powerful motivational forces in the world. Learning should always be fun - structured, but fun. Most of our learning is non-conscious and incidental. For example children who use the rods regularly will 'know' their number bonds to 10 at a very early age without having to 'count' on their fingers.
Play is the harvesting of experience that will feed the growth of the child's understanding and further development. Play creates a positive learning environment. Directed activities can be introduced alongside Free Play to reflect children's particular interests. There are no limits to the possibilities. For example children can be asked to:

• Create a star ship.
• Build Cinderella's Palace
• Produce a mosaic floor pattern etc.

It can be useful to keep a digital camera handy as children are often very reluctant to break up their creations. In fact it is a very good idea to treat their constructions as you did when they painted their first picture, as unique works of art. Photographs can also serve as a record of your child's progress. Play stimulates that most important attribute of the brain - our imagination.

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Solving Math Problems

A good math education needs to start very early, as early as in elementary school. However, it is rather clear that students are not learning math in a way which will help them love it, hence often times, they try to look for help with math.Consequently, it is not unusual that students simply turn away from math, and don't end up assimilating basic mathematical skill which would help them tremendously in the professional lives, in almost every single area.

It is not a mystery that the main reason why students have little affection for math is because of a deficient methodology lacking in meaningful math problems. One capital mistake is the tendency to entice memorization instead of critical math reasoning, which certainly leads to failure, since memorization doesn't provide the reach that true mathematical understanding does. With this kind of teaching method, it does not help the students that much with math. Take for example the case of Pythagoras Theorem.

The Pythagorean Theorem in geometry says that, for a triangle in which one angle is a right angle (having 90 degrees or also known as a right angle), the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two other sides of the triangle. In equation form, it is often expressed as a2 +b2 = c2.

We can say that regardless the appealing appearance of the formula, instead of memorizing it, it would be obviously more productive to discuss how the formula is derived, or at least why it is plausible that it is true. He or she might talk on the history of the theorem, and might need to illustrate some drawings. In addition, presenting it in a story-like manner would make math more interesting for kids. As we probably have experienced before, a good story usually makes it up for a difficult concept, because it makes math much more enjoyable.

Another fun mode of educating kids in mathematics is through online games. There are quite a big number of websites which offer interactive games that help your kid understand the concepts of mathematics while at the same time, making learning an enjoyable experience. Not only free material is available online. Sometimes, quality material can be purchased at reasonable prices, which could really make a difference. Math doesn't get any easier with all the resources available nowadays.

In today's world it is clear that not all the responsibility of math learning is on the teachers. Parents too play an important role in the development of a kidýs learning process. There was one parent in California who was struggling to teach her kid about the various denominations of the dollar. Instead of just letting her daughter memorize how the coins look like and how much it is equivalent to, she set up an imaginary "toy store" wherein she tries to "buy toys" from her kid. This creativity and ingenuity did not only allow the kid to learn fast, but also made her understand the idea far better than the typical classroom scenario.

For mathematics to be entertaining, and to help you deal with math with your kids, mathematics should be presented in such a way that kids would remember the concepts and formulas easily. Creativity is the key, aside from having a full understanding of the principles behind.

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How to Solve Easy Math Word Problems

Frank Howard Clark said, "I think the next best thing to solving a problem is finding some humor in it." What Mr. Clark would like to convey with this is that the way to solving easy math word problems is by having fun with the problems. And in having fun with them, there are two simple steps in solving math word problems:

Step 1: Translate the words into a numeric expression or equation

Math word problems can be converted into a series of expressions or equations containing a combination of mathematical expressions. To be able to translate these word problems you have to follow these steps:

1. Read the problem very well and in its entirety. Get the full perspective of the problem. Reading it in full will give you an idea of what the real problem is.

2. List all the factors provided. Make a list of all the given variables including units of measurement if available. Having all these information available will show you if you need to do any conversion like from miles to kilometers, pounds to kilograms, etc.

3. Define what needs to be answered. Be sure to know what you are looking for or what the problem needs to answer.

4. Organize your solution. Provide the procedures or steps you will take to find the answer to the problem. Showing the step-by-step procedure will help you track all the variables and expressions you are using.

5. Be aware of the key words. In translating and solving the problem, you should be aware of the basic key words in translating words into algebraic equations, such as:
Addition: added to, increased by, more than, sum of, total of, combined with
Subtraction: decreased by, subtracted from, less than, difference of, reduced by, fewer than
Multiplication: multiplied by, times, product of
Division: divided by, quotient of, remainder of, percentage, ratio of, per
Certain key words suggest specific mathematical operations that should be done to the given factors or variables.

6. Plot the expression or equation. Plot the expressions or equation properly following the order of operations.

Step 2: Solve the mathematical equation

To solve a mathematical equation, follow the order of operations by level:

• compute first all those inside parentheses or the innermost expressions
• compute those with exponents, raised to a power or root of
• multiply or divide from left to right
• add or subtract from left to right

It would be easy to solve the equation by writing down the answers for each level before going to the next level. Here is an example:

X = ((2 * 3) + (3²) + (20/4) - (2 * 6)) * 2 + (3 * 8) - (4 * 5)
X = ((6) + (9) + (5) - (12)) * 2 + (24) - (20)
X = (6 + 9 + 5 - 12) * 2 + (24 - 20)
X = (8) * 2 + (4)
X = 8 * 2 + 4
X = 16 + 4
X = 20

From the sample equation above you will the order operations that were followed in solving the equation.

With these two simple steps to follow there is no need for you to just stop and stare and pray for divine intervention to be able to solve a math word problem! Now you can safely say that Math is easy and that it isn't hard to solve math word problems.

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Special Learning Strategies For Elementary Mathematics

Many children experience anxiety related to mathematics to a certain extent, and this may begin as early as kindergarten. This anxiety can result in poor academic performance in math, many misunderstandings in math content and procedures, and negative attitudes toward math. Obtaining a math tutor may be helpful for many students, but often, parents who have a general understanding of learning strategies for mathematics can provide equally effective help. The following information can help parents, teachers, and tutors provide a basis for mathematics learning for elementary school students.

Understanding the Learning Progression

First, we need to consider how children best learn. Think about very early learning for children and the idea of "cat". When toddlers see a cat, their parent says, "cat", and pats it, to give the child the name for that object. Soon, the toddler knows what a cat is, from seeing it, touching it, and hearing the name for it. Later, the child draws a picture, points to it, and says "cat". Eventually, as a child grows, he is able to associate the spoken word "cat" with a mental picture of the animal. This learning progression, from concrete (the real cat) to semi-concrete (the picture) to abstract (the spoken word) is an example of how children learn mathematics as well. To teach a child about triangles, first they need to interact with real triangles - touch them, trace them, see them. This is where manipulatives play a large part in mathematics instruction. Children use hands-on manipulatives to learn the characteristics of math concepts (like a triangle), or use them to show procedures (like adding 4 blocks and 3 blocks). The first learning strategy to use when teaching children new mathematics content, therefore, is to go to the manipulatives.

Learning the Underlying Rules

A second strategy that is helpful for students when learning mathematics is to memorize necessary facts, vocabulary, and rules. Much time is spent in the 1st and 2nd grade with students learning addition and subtraction facts, and an equivalent amount of time is spent in the 3rd and 4th grade with learning multiplication and division facts. Even with this practice time at school, many students have difficulty committing these facts to memory. It is critically important that students memorize these, however, as most later mathematics learning is dependent upon the quick and accurate recall of math facts. Think how difficult it would be for children to add 358 to 472 if they did not have a firm grasp of addition facts? Likewise, how would a student find a common denominator for two fractions if they could not recall basic multiplication facts? There are many, many ways that these facts can be practiced. One way is the "tried and true" flash cards. A variation of traditional flash cards is 3-sided flash cards. When studying multiplication facts, for example, write one factor in one corner, one factor in another corner, and the product in the final corner. When using these flash cards, cover up the product with your finger, so that the child can see the two factors, and practice multiplying them together. When studying division facts, put your finger over one of the smaller numbers, so they can see the large number and one of the smaller numbers. They have to divide to determine which number is covered. For example:

On your triangle, write 2, 3, and 6 - one number in each corner. When practicing multiplication, cover the 6, so that the child sees 2 and 3, and multiplies them together to get the answer of 6. When practicing division, cover the 2, so that the child calculates 6 divided by 3, to determine the answer of 2.

Helpful Shortcuts
Another strategy that is effective is teaching students the steps of a procedure by using mnemonics. For example, the first letters of Please Excuse My Dear Aunt Sally stand for the steps of the order of operations (parentheses, exponents, multiply, divide, add, subtract). The "family list" of Daddy, Mother, Sister, Brother, Cousins, Relatives indicates the steps for long division (divide, multiply, subtract, bring down, compare, repeat or remainder). Strategies such as these help students remember procedural steps so that they can perform them consistently.

For conceptual learning, like "What is an equilateral triangle?", children learn through the processes of explain, elaborate, illustrate. In this situation, a child should define the equilateral triangle (explain), tell what that means in his own words (elaborate), and draw a picture of it (illustrate).
As with any other type of learning, mathematics strategies can only be learned through consistent application and multiple opportunities to practice. You will know that children have become proficient in the use of the strategies when they are able to independently apply them to mathematics problems they encounter in school.

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