The magic of the number line

It didn’t take long for me to step outside the traditional Montessori boundaries – this is only the third post! With due respect to Maria Montessori, she can be viewed as a pioneer in the use of number lines in the classroom – a look at the ticketed squared and cubed chains confirms that they are indeed number lines. However, a more traditional number line (from 1-10 or from 1-25) is not part of most Montessori classrooms.

Below is the ticketed 5-squared chain from the Montessori mathematics area:

Research into mathematics learning, particularly in the case of children lagging behind their peers and/or exhibiting learning disabilities, has proven that the use of number lines has been very effective.

The most compelling study is one by Siegler (2009), who investigated the case of low-income children lagging behind in numerical development. Interestingly, this study tested the impact of using a mathematically precise number line with the numerals 1-10 compared to a similar line with colours for each of the squares. With four sessions of 15 minutes each, the children using the number line with numerals were able to advance in mathematics learning to the level of their more well-off peers, while the children using the coloured line did not advance. The reason that the number line works is that children tend to have an internal number line that is logarithmic instead of linear and repeated exposure to a mathematically precise linear number line serves to “correct” their internal number line. What does it mean that their number line is logarithmic? If asked to place 5 on the number line, a child would place it close to 10 instead of in the middle.

Is the number line an effective teaching and learning tool? Absolutely! After reading about Siegler’s research in early 2011, I created a quilted number line for the classroom and the children and I have been using it frequently for the past year. The results are very encouraging.

Below is the quilted number line:

Here are three ways to play the number line game:

1. Play as a race from 1 to 25 with one die. We use buttons for pieces. Learning that four dots on the die means 4 is called subitizing – and this game helps the children learn to subitize very quickly. Children tend to learn to subitize before they learn the numerals 1-6. There are many variations on this game: the winner is the one to reach the end first; play until all reach the finish line; or one must roll the exact number to end on the final square of the number line.

2. Play the race with + and – cards. Using small cards with the numbers +0, +1, +2, +3, +4, +5, +6 and -1, -2, -3, -4, -5, -6 play in the same ways as above. To make these cards, I typically make 4 each of the cards except the -3, -4, -5, cards, of which I make only 2, and the +1 and +2 cards, of which I make 6. The children tend to be very interested in this, particularly in the way that the positions can change so quickly. Clearly this is a more advanced game than the one with the die, since children need to know the numbers 0-6 and understand the concept of + and -.

3. Building a number line to 25. I make tiles (using craft foam) for the numbers 1 to 25 and the children build their own number line from left to right with the tiles.  As a self-correcting tool/reference point, the quilted number line is set up a distance away. If a child is stumped as to which number comes next, he/she can walk over and count up the number line. This works very well to reinforce the patterns in our number system. When the child is done, the quilted number line can be brought over and each tile placed on the number line as a check.

The number line has facilitated mathematical learning in our classroom, particularly for children for whom the traditional Montessori materials did not provide enough of a bridge from the concrete (quantity) to the symbolic (numbers) for building an understanding of the numbers to 0-10.

Many of the parents in my school purchased one of the quilted number lines when I sold them as a fundraiser last year. If anyone is interested in purchasing one, please get in touch.

References:

Siegler, R. S. (2009), Improving the Numerical Understanding of Children From Low-Income Families. Child Development Perspectives, 3: 118–124.

Teri Courchene, Riverdale Montessori

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About Teri Courchene

Instructor at U of T School of Continuing Studies, Math tutor. Education: CSC, MEd (OISE), AMI Montessori Diploma (FME), MA Economics (Queen's), BA Economics (UWO)
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