LD OnLine

Strategies to Facilitate Math Concepts and Homework

By: Regina G. Richards (2008)

One Tuesday afternoon, I received a frantic call at my educational therapy clinic. It was Sammy's mother. Sammy was one my clients and usually we worked on reading on Saturdays. Sammy's mother exclaimed, “I just picked Sammy up from school and he's pretty hysterical. It's hard to understand what he saying, but it seems he doesn't understand the words his teacher's using in math. He saying he's going to flunk math because of these words. Can you help?”

Sammy was in luck. I happened to have a canceled session in one hour. I suggested that Sammy's mother take them out for a snack to help him calm down and then bring him to my office in an hour. I felt it was important for Sammy to calm down before our session, because a student who is upset or anxious effectively “closes the door” on any learning that might otherwise take place.

Sammy arrived at the appointed time and although he was somewhat calm, I could tell that he still felt anxiety about these “words” that the teacher used in his math class. I decided to start our session by reading Sammy a story. When I explained this to him, his eyes lit up and he was delighted.

As I walked to my bookcase, I spoke with Sammy about Camelot and King Arthur and we talked about knights and their ladies. Sammy was delighted and enchanted with Camelot. I pulled out a book by Cindy Neuschwander called Sir Cumference and the First Round Table.

Sammy and I got comfortable and I began to read the story. In summary,

King Arthur was King in Camelot. There was a problem so the King called his bravest knights for a meeting. Sir Cumference brought his wife, Lady Di, from Ameter, and their son, Radius.

The knights had a meeting and they sat at a long rectangular table but everybody had to shout. The carpenter made a square table but then the people at the corners were very crowded and began to whisper. The carpenter tried a variety of different table shapes: diamond, parallelogram, triangular, and oval. However, there was a problem with each.

The knights were discouraged, especially Sir Cumference. He decided to go for a ride in the forest with his family. Radius notices a fallen tree and proclaims, “See, Father! There's your table!” A picture in the book shows Lady Di, from Ameter, standing next to the fallen tree. She reaches from one end to the other, right in the middle. The carpenter cuts a cross-section of the trunk to make into a tabletop and Sir Cumference tells him, “Leave the bark on the outside edge. I like its rough feel.”

The carpenter makes a table, they use it for the next meeting with the knights and everyone is happy. King Arthur is delighted with his new table and thanks Sir Cumference, Lady Di, and their son, Radius.

The King proclaims, “Because Lady Di of Ameter has a reach that is equal to the distance across the table, we will name this measurement for her. We will call it the diameter.”

“Radius may be small, but he has tall ideas. Let's call the small measurement from the center of the circle to its edge the radius.”

The King then reminds everyone that it was Sir Cumference's idea to leave the bark on the outside edge of the table. He names the outside edge of a circle after him and calls it, “the circumference.”

When I finished the story, Sammy was all excited. He exclaimed, “Now I get it! I see what the words mean!” I noticed that he said, “I see” and pointed this out to him. I explained that sometimes words alone were not enough for him. He needs to remember this and not get upset but find a way to help himself “see” what the words mean. I told him, “You know, Sammy, you could even go to your teacher and tell her that you need to “see” what the words mean and ask her to show you or draw you a picture. Or, you could try to draw your own and then ask her if that's what the words mean.”

We then reviewed the meaning of the words circumference, diameter, and radius. Sammy was excited that he understood.

I happened to have some round mint patties in my freezer and so, to reinforce the concepts, I pulled out a mint patty and some thin red licorice candy strips. I asked Sammy to take the licorice and, using the mint patty, show me the circumference of the circle. He outlined the circumference with the red licorice. He then cut another piece of licorice to show the diameter and another for the radius of the circle.


Licorice candy strips Round mint patty
Fig. 1 — Materials to demonstrate circumference, diameter, and radius

We had only 10 minutes left in our session but Sammy was very comfortable with these three words that were so important to his math lesson. We then reviewed the formulas for circumference, diameter, and radius. I told him he had to memorize a term called “pi:” pi = 3.14. I promised him I would read him another story next time called Sir Cumference and the Dragon of Pi. We practiced a few calculations.


The teaching elements

“Our brains are meaning-making machines, searching for matches to previous experiences.”

— From Quantum Teaching: Orchestrating Student Success by Bobbi DePorter, Mark Reardon, and Sarah Singer-Nourie


What were the key teaching elements that I used in my session with Sammy?

First, he needed to be more relaxed so that he could “open the doors” to new information. Part of achieving relative calmness is learning to accept our mistakes or the fact that we may initially have difficulty. We need to accept this without “crashing.”

Second, I know that learners need to hook new information to existing and familiar information. I had to find a way to hook the vocabulary words to something that was familiar to Sammy. I knew that he could not begin to understand how to manipulate the formula until he had a deeper understanding of these words. Having a deeper understanding of the important words enabled him to create a concrete hook so that he had less of a tendency to confuse the words.

Third, I used the extremely critical teaching principle that applies to all new learning with students: experience before labels. I helped Sammy experience the meaning of these words and the related concepts.

“Experience before labels”

As parents, we can use these principles to help our children feel more relaxed and competent with their homework, especially in math. As teachers, we can use these principles as we present concepts to broaden our reach to our students.

Following are a few additional activities we can use to help our students experience the meaning of concepts before they apply and use them. Readers interested in additional ideas may find them in the books listed in “other helpful resources” at the end of this article.


The importance of words

As demonstrated in the above scenario, it is critical that students understand, at a deep level, the meaning of the words they will be using. You can assist your students by exploring the morphology, or meaning of word parts, related to important conceptual terms.

Following are some word parts relevant for the area of math:


Word part Meaning
equi- equal
multi- many
poly- many
quad(r)- four
sub- under; down
-gon figure having certain number of angles
-lateral side

Here's a way, from my book The Source for Learning and Memory, to help students explore the meaning of math words:


Measuring

Measuring mnemonics

Mnemonics are memory tools and students can use mnemonics to help them learn and recall many different ideas and concepts. Following are some examples from my book LEARN: Playful Strategies for All Students of mnemonics to help with measurement terms.


Meter — “A meter measures 3 ft. 3 / It's longer than a yard, you see”

Liter — “A liter of water's / a pint and three-quarters”

Kilogram — “2 1/4 pounds of jam / weighs about a kilogram”

Fahrenheit and Centigrade — to convert, take away 30 and halve it

Centigrade to Fahrenheit — double and add 30


Note: These are approximations. The technical method to translate Fahrenheit to centigrade is to subtract 32, multiply by five, and divide by nine.

Body measuring

To help your student grasp the concept of various measurement sizes, have her compare the term to some part on her own body. Some examples from The Source for Learning and Memory follow:


Adding and subtracting

Using 2 rulers

This technique helps students who have difficulty learning and remembering math facts for addition. For some students, it is more concrete than adding objects.

Use two rulers that have numbers written very clearly, or create your own using cardboard. What is important is an even sequence of numbers, rather than the exact measurement.

Two tan rulers
Fig. 2 — Using the two rulers

Using the two rulers to add 3 + 4, follow these steps:

Color coding columns

Color coding is useful if your student has difficulty keeping his numbers straight, i.e., lining up the ones-column and lining up the tens-column.

Color coding colums
Fig. 3 — Color coding columns

To make it easier and more concrete, place a green arrow of the ones' column to indicate “start”.

As your student progresses and increases her understanding of the use of columns, omit the color for the tens' column and only use the green for the ones' column. Eventually omit all of the color.


Multiplying and dividing

Patterns

Multiplication facts follow a specific pattern. It is useful to show your student some of the easier patterns, especially if you discuss with her why the pattern works. Provide experience by using manipulatives (counters such as beans) to practice and explain the pattern.