I Don't Get It ... MATH HINTS

Below are some hints for helping a child who has difficulty with arithmetic. These are hints for a child who has hit the wall. A child who constantly says he hates math. A child who may have already failed a year of math.  She may demonstrate little or no awareness of the patterns in math, be unable to remember procedures, and see no relationship between numbers let alone the relationship between daily lessons. The suggestions below are not the way to teach a math class. They are for the individual child who needs more than after school tutoring at the local strip mall math center.

1. 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. 
2. 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. 
3. 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.  
4. 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

   Play with the cards. First have the child call out the number of dots as quickly as possible. Make a second set and play matching games with the cards, as well as memory games. What does this do? It helps children quickly recognize a pattern. Instead of calling out the number have the child call out even or odd.  This is a good game for 6-8 year olds who are having trouble with numbers or for the older child who isn't sure about evens, odds, or primes. I have seen children in 4-5th grade who really could not visualize a number. They may have been working on defining a prime number, but they could not tell if 22 was an even or odd number.  
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.
6. 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.
7. 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.
8. 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".
9. 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. 
10. 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. 
11. 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.

Remember when people are having problems learning new material the ability to learn by just being there seems to vanish. The ability to refer to past knowledge seems frozen out of the brain by fear or confusion. Slow down.

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.

Teaching vs. Paperwork

Many years ago I went back to school to get certified to teach special education. In the U.S. teaching certification credentials are given by each state, but much of special education consists of following ....  federal laws! So a majority of the class time was focused on learning the national laws that apply to this field. What I received for my time and money was a brief overview of the various teaching methods one might use in the various types of special education, and an in-depth study of the federal laws that apply to special education students.

When I completed the course of study and satisfied the other requirements, I decided to look for a job. After checking out several public schools I decided to teach in a private school. Why? Because at that time I wasn't not impressed at the working conditions for special education in public schools. Most of the resource rooms I checked out consisted of many children going in and out while the resource teacher (also expected to deal with behavior problems that might arise in other classrooms) helped them with modified work. There was very little time for remediation and interruptions were more common than those in the regular classroom. I am sure there were some excellent resource rooms out there, but obviously the teachers in those situations decided to stay put. I spend almost ten years in a private school for children with learning differences. My classes never exceeded eleven students. When I started working at that private school the focus was on the children's needs, and the school had a successful record of remediation as well as modifications.

Special education in the public school still seems to have its problems. This article attributes the difficulty in finding and keeping special education teachers to  the large amount of paperwork required.  People who love to teach seldom make enough money to hire an admin assistant. That causes the reams of paperwork that accompany teaching a child under the federal Individuals with Disabilities Education Act (IDEA) to fall into the teacher's workload. It also means that the teacher realizes that if anyone may be sued, due to a parent's dissatisfaction on how their child is being or not being taught, it usually includes the teacher. This is one reason certification for special education focuses on how to fill out paperwork rather than how to teach. Finally large amounts of paperwork and meetings are two reasons that many qualified teachers (teachers who may have been excellent at working with children with special needs) leave the field fairly quickly. Thus schools find themselves unable to comply with the federal mandate requiring certified special educators.

Because of the establishment of  IDEA there are many children receiving an education in public school who would have been sent home 50 years ago. There is a now place in schools for children with physical, mental, emotional, and learning differences. There is an expectation that these children can learn.  But in an effort to be all things to all children the in-the-trenches art of teaching is being watered down. I understand the need for paperwork in an attempt to insure that the intent of the law is followed - although many a parent with an excellent Individual Education Plan (IEP) in their file cabinet will tell you that they doubt that the plan is really being followed. But an over abundance of paperwork, schedules, and due dates means that less attention can be giving to the act of teaching. Good teachers lose the joy of teaching, good schools find themselves unable to meet federal mandates for certified special education teachers, and students . . . well, too many students find themselves unable to read the paperwork that assures them their individual needs will be met.