Archive for January, 2006

A Research Paper for Paraeducator II Class

Saturday, January 28th, 2006


Among students who are classified as learning disabled, arithmetic difficulties are as common as reading problems. Some studies suggest that 6% of school age children have significant math deficits. Such students may respond to repeated failure by not trying to learn anymore and by lowered self-esteem. As such students reach adulthood, their math illiteracy will handicap them in daily living, and will limit their job prospects. What are some of these math disabilities?

One disability involves mastering basic number facts in all four operations (addition, subtraction, multiplication, and division). Such students need help with thinking strategies, not just fact practice. Mathematical reasoning is the goal, not mindless computation. The use of a pocket facts chart can be helpful. Eventually, students will hopefully note a pattern to these facts. Much practice in small doses is helpful. A small number of facts should be presented for mastery at a time, and practice should be interactive, with active engagement by the student. It can be helpful for the student to chart his/her own progress. Another helpful strategy is to ask the student, “How do you remember (math fact)?” Have him drill himself using his own strategy.

The brain tends to remember material that:
• It is ready for.
• Has meaning.
• Can be arranged in patterns.
• Can be linked to previously learned information.

Another math disability involves the student being reliably unreliable in paying attention to operational signs, borrowing/carrying appropriately, and in sequencing steps in complex operations. Such a student may not be very disabled, in reality. He may have a good grasp of math concepts, but have weak lower level skills. Graph paper or lined paper turned sideways can help the student organize written work on a page. This is an aid in properly aligning columns of numbers for addition/subtraction, and for division problems. The teacher and Para educator can partner with the student to help him develop his/her own compensations for this disability.

Other students do have good informal math understanding, but have difficulty with the formal procedures, language and symbols of math. This informal/formal gap is a factor in the majority of math learning problems. Such students need many experiences with concrete materials, or manipulatives, which they can physically hold, move, and group to make strong connections between informal and formal math. Such children are not really helped by the practice of using workbooks. Students must become demonstrators of math ideas, not just problem answerers. To truly succeed in math, understanding must be connected with the symbolic representations of math. If students do not see the connection between real things and more abstract mathematical principles, they will not look for patterns or meaning. They will view math as a collection of unconnected facts to be memorized, but not understood. To establish the connection between math and meaning, the practice of estimation can be used. The student can then note whether his final answer really makes sense.

Math disability may arise from a misunderstanding of the language of math. Some students with language deficits may react to math problems as signals to do something, rather than as mathematical sentences to be read for understanding. For such students, the teacher should slow down the pace of delivery in presenting concepts, offering explanations, giving directions and asking questions. Information should be given in small chunks. Students should be encouraged to read and say problems before and after computing them, and to ask themselves, “Does this answer make sense?” It can be helpful for students to play teacher and explain their understanding of the math problem to others. Also, students who work on math in small groups are more likely to ask necessary questions.

A rare math learning disability is associated with visual-spatial-motor organization. Such students have tell-tale accompanying weaknesses: a poor sense of their body in space(clumsiness), disorganization, and difficulty understanding non-verbal social signals of gesture and facial expressions. These students need repeated experiences with real materials that can be felt, seen and moved around. They also learn well verbally.

Some students have developed emotional blocks which keep them from really thinking about math. Such students need many opportunities to see themselves as successful thinkers. If the student can be helped to see that math is not so much computation as it is problem solving, or thinking, he or she can be helped to overcome anxiety. The teacher and Para educator should work with the student to define his strengths, and then use those strengths to teach the student those concepts he/she finds to be difficult.

In Your Child’s Growing Mind, author Jane Healy, states:

Most people think of math as arithmetic, the study of numbers, and the rules or operations such as addition and multiplication that we use to manipulate them. Guess again! Mathematics is a much greater science of relationships, which uses numerical symbols to describe fundamental truths about our universe. The numbers or symbols on a page represent powerful abstract concepts – but they are rooted in concrete experience. (page 322)

This quote emphasizes what has already been stated. To help a student who is experiencing difficulties with math, math must be tied to real life, to concrete experience. The student must also be helped to see that math makes sense. It is not a grab-bag of facts to be memorized. According to Jane Healy, the child must develop two separate abilities to experience success in math:
1. The ability to comprehend relationships, to reason abstractly and to solve problems.
2. The ability to follow rules, to analyze, to compute accurately, to observe carefully, to form educated guesses, and to maintain an orderly line of thinking in problem solving.

Younger students can engage in play activities which help to build mathematical brains. Some of these activities involve:
• Small objects to count and arrange.
• Board games and dice, to learn the following of rules.
• Sorting and classifying hobbies.
• Unit blocks, patterns, and toy clocks to manipulate.

The child’s active, physical involvement in these real activities is essential, since most people learn by doing (active), not from watching it happen (passive). This is a way to teach children from the bottom up, rather than by presenting abstract rule systems too early. The more varied the experiences, and the more first-hand meaning the experiences have to the student, the more likely they will form a basis for advanced reasoning necessary for math.

Students can also be helped to overcome math difficulties by working with them to develop problem-solving skills:
• Encourage questions.
• Ask open-ended questions and welcome creative responses.
• Provide toys and games that encourage play the child creates himself.
• Show the child how to estimate.
• Practice “guess and test”, the forming of hypotheses.
• Take time to listen to the child’s ideas.
• Model adult problem-solving.
• Help the child to tolerate some uncertainty as he finds the best solution to a problem, or tests a hypothesis.

Certain facts and skills need to become automatic for a student to succeed in math. To build automaticity, the following are important:
• Motivation and involvement by the learner.
• Repetition.
• Novelty.
• Presentation through looking, saying, hearing, touching, and body movement. The more senses that can be involved in the learning process, the better.

Finally, families can help children overcome math learning disabilities and build a strong mathematical foundation by involving them in some of the following activities:
• Family games.
• Cooking.
• Shopping.
• Money-managing (allowance).
• Music lessons.
• Hobbies involving collecting and exploring nature.
• Measuring and weighing.
• Using maps and following directions.
• Calculator games.


“Wright, C. Christina. “Learning Disabilities in Mathematics.” LDOnLine. October, 1996. WETA, Washington, D.C. January 28, 2006.

Rosner, Jerome. Helping Children Overcome Learning Difficulties. New York: Walker Publishing Company, Inc., 1993.

Healy, Jane. Your Child’s Growing Mind. 3rd ed. New York: Broadway Books, a division of Random House, Inc., 2004.

Thank You, My Family!

Monday, January 9th, 2006

I am still resting quite a bit, due to a sprained ankle. My family has been working hard, though, to keep the home fires burning, so that I won’t fret and get up too soon.

First,I would like to recognize Rebecca. Let me tell you what Rebecca did today:

  • All of the laundry for nine people was done.
  • Six loaves of homemade bread were baked.
  • Homemade pizza and salad were served for dinner.
  • Her work for homeschool was done.
  • Dishes were unloaded from the dishwasher and reloaded twice.

How is that for a hardworking young woman?

Seth and Lydia took my turn vacuuming the house today, and did their schoolwork. Lydia helped Rebecca prepare the nummy dinner.

Rick continued to work hard providing for our family. He took time out of his busy schedule to come upstairs to see if I needed/wanted anything. Very sweet indeed. 🙂 He took Debra to and from school, and picked Kayla up from the bus stop. Transporting people hither and yon is usually my responsibility.

Sarah and Kayla were at work, and Michael and Debra were at school. They were busy in their own callings, so were not available to let their talents shine on the home front.

I hope to be up soon, as a fully-functioning hard-working mom. In the meantime, Thank you, dear family for working so hard and for doing such a great job!

Our Times Are In God’s Hands

Saturday, January 7th, 2006

James 4:13: Go to now, ye that say, To day or to morrow we will go into such a city, and continue there a year, and buy and sell, and get gain:
Jam 4:14 Whereas ye know not what [shall be] on the morrow. For what [is] your life? It is even a vapour, that appeareth for a little time, and then vanisheth away.
Jam 4:15 For that ye [ought] to say, If the Lord will, we shall live, and do this, or that.

On Thursday, January 5th, I was hurrying through my usual domestic routine. I glanced at the clock, noting that the mail had probably been delivered. Quickly, I stepped outside and inhaled a deep breath of the fresh, rain-cleansed air. My mind was intent upon fetching the mail and returning to my daily tasks. Whether it was wet leaves on the gravelled driveway, or mud, I’m not sure, but one moment I was striding confidently along, and then I was momentarily parallel to the ground, before landing on my stomach, with intense pain in my left ankle. My first thought was, “Have I sinned against the Lord in any way? Is the Lord getting my attention?” So, I worshiped the Lord in prayer, asking Him to search my heart. That was edifying and comforting.

Next, I tentatively tried to get up, but found my injured ankle was not responding. What to do? Our driveway is long, and the family was inside. So, I started crawling slowly, painfully, up the driveway, in my now soggy skirt. My husband caught sight of me once I was up the driveway, and ran outside with a look on his face that seemed to say, “Have you gone totally nuts?!” Once he realized my dilemma, he kindly tried to help me to stand upright, but crawling was still best. My husband helped me to put an elastic bandage and an ice pack around the injured ankle. I sat down with my foot propped up, and savored a hot cup of tea prepared by my dear ones.

As I sat there enjoying the hot, sweet tea and started to calm down, I thought of the fact that we are in the Lord’s hands. We are able to do things, even ordinary things that are easy to take for granted, only by His enablement. So then I silently thanked the Lord for the many times He has given me the health and strength to do my work, the work I love, of ministering to my family in the mundane things such as cooking and cleaning and running errands.

Well, it is now Saturday evening. After crawling upstairs to my bedroom Thursday evening, I have remained here in my bedroom, not able to put weight on the foot. When necessary, I crawl a bit, which must be a hilarious sight! I’ve had much opportunity to read and rest. My dear family have been cleaning and cooking and caring for one another and for me. I have told them, and now tell you, how very much I appreciate their loving service. I am now more thankful to the Lord for my usual ability to stand upright, and for the many times I have moved easily about, doing my work.

I am scheduled to have the injured ankle x-rayed on Monday morning. If a cast is necessary, it cannot be placed on a swollen ankle, thus the delay. Though I cannot yet put weight on the foot, I can tell it is getting well. I am thankful to the Lord for His healing hand, and also for His using this incident to remind me how dependent upon Him I truly am for life and breath and all things.

Acts 17:25 Neither is worshipped with men’s hands, as though he needed any thing, seeing he giveth to all life, and breath, and all things;