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.

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.

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.

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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**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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