- Math is a subject that builds on past knowledge. Slow down and give a child time to play with and learn new knowledge before moving on.
- Break a procedure into small components and see what a child is missing. If you are working with a child trying to learn how to add mixed numbers and she does not realize that when the numerator (number above the line) is larger than the denominator that the number is greater than one -- you need to backtrack.
- Working with fractions means heavy work with concrete items. I always have paper available and draw constantly when teaching fractions. Operations with fractions often produce numbers that don't make sense to a child. For example: multiplication of fractions produces a smaller number and division a larger one. This is counter intuitive for many children. Sometimes a child just needs different words to understand why this is so. A child might understand an explanation along with a physical representation showing that when we multiply a fraction we cut (don't use the word divide) the number by the number given. For example: 1/2 times 1/2 is cutting 1/2 into half making two 1/4s. Division of fractions is really asking how many 1/2s are in a half. There is only one, so the answer is 1. Having an explanation is magic for some children. For others it only confuses the issue, so a quick run-through explanation should be followed by the "how to get the answer procedure." A procedure may be all a child is able to deal with at the time.
- For children who seem confused with working with numbers you might have them make number cards. Get blank playing cards and have a child put dots on the cards. Use at least ten cards to represent the digits 0 through 9. The cards are set up so there are two rows of dots.
Example of child-made number cards
Note: 9 is represented as three 3's and as 4 and 5
- Help students learn how to figure out basics with their fingers. This is to get a feel for the numbers and to use fingers quickly if needed. It is useful to a tactile learner. It is amazing how many children who are having difficulty in 2nd - 4th grade math have to count before they can hold up 7 fingers.
- Use number lines and hundreds charts to show patterns and the directionality of numbers. Some children find one more useful than the other. There are a number of activities on the Internet on the use of number lines and hundreds charts. Start with the easier ones to see what you child knows. Point out patterns and how the numbers change in different columns.
- I create songs and stories to help students remember procedures. I have a great division song for the child who doesn't remember where the numbers go. I use stories when teaching a child how to regroup to add or subtract. Under a place value chart we place a street with houses or stores. Each house has an address and each place only accepts items grouped like their address. When we add, our house gets too full and we have to give some numbers to the neighbor, but only in a set of 10s or 100s. Sometimes one must go to a neighbor to borrow a ten when you subtract. Later on in an addition problem one must return that ten. I am sure mathematicians gasp in disgust at teaching math this way, but these students probably will not grow up to be engineers, mathematicians, or find any need for high level math. All they want to do is get out of 4th grade.
- Practical math usually is fun. Gardens, cooking, decorating a room, or sewing, help a child use math. This is a good way to learn the concept of "measure twice, cut once".
- Use math terms with explanations. I say: "look at the denominator, the bottom number, and tell me if it is the same as the numerator, the top number." Using math terms with the explanation exposes the child to the terms, but helps them understand what you are talking about even if they don't know the vocabulary.
- It is essential to understand a child's learning style. Some students need to draw things out for themselves, others find that confusing. Some need the reasons why, others need to slowly learn a procedure before learning why.
- Teach the child how to use examples that are shown in the book. Some children don't understand what an example problem has to do with what is expected of them. Point out an example, show how it can be used as a model, and teach them how to create their own examples. It they are unsure what to do with a problem such as 1/2 + x = 3/4, show them that in the case of 5 + x = 9 it's easy to see that you take 5 from 9 for an answer of 4. I have found this way of understanding is often developmental, so while the 2nd grade student may not be able to generalize the knowledge, a 3rd grader might have an "aha!" moment.
One a different note: I have written a chapter book for children who are having problems in school. Swute's Stories is about a little mouse who didn't quite "get" school. Fortunately his parents helped him find his special talent. Finding that talent took time but for the little mouse's happiness it was well worth the effort.