The Number line: 3 THINGS YOU NEED TO KNOW
A particularly powerful tool that supports students’ understanding of numerous mathematics concepts is the number line (Gersten et al., 2009).
Young children can use BEAD STRINGS and LINEAR NUMBER TRACKS as EARLY number lines as notched versions can be confusing for young learners if they land between the numbers as they are counting.
A bead string can be linked together and so has the potential to represent numbers in a structured and linear way. Not only does it represent individual numbers but also illustrates the way numbers are related in a logical structure.
NUMBER PATHS
Children are given the opportunity to begin moving from counting sets (i.e. individual objects like candies, toy cars, bugs, etc.) to the very early stages of linear measurement through the use of “number paths” on their developmental trajectory towards the eventual use of the much more abstract number line.
In a number path game, children build confidence as they practice counting, use one-to-one correspondence, and learn that numbers come before and after other numbers. Having experience with a visual model like a number path will help young children be prepared for later mathematics learning. It may help bridge understanding to number lines.
While this is slightly more abstract than counting say actual dinosaurs or donuts, it is much less abstract than looking at a line with notches on it.
Show Me…
Ask children to “show 4 on the number path”. What we are looking for is children showing that 4 includes 4 squares and not just the last square. This builds on the idea of cardinality.
Moving from BEAD STRING and NUMBER PATH representation to that of a number line (points/notches labelled) can still be challenging (Askew, 2016).
HERE ARE 3 IMPACTFUL WAYS TO USE THE NUMBER LINE...
2. Include explanations and ample practice using the number line. Because some children may not be familiar with the number line representation, there needs to be multiple opportunities for students to practice using the number line (Dougherty, Flores, Louis, & Sophian, 2010).
"There is evidence that training children to use the number line more competently may support mathematical development, especially in arithmetic and in particular through the use of number tracks in games (but not when the number tracks are circular, only when linear). Construction of a linear number line allowed students at age 6 to solve a wide range of maths problems more successfully."
3. Compose high-level questions that challenge all children to think and talk about the maths they are doing (Thornton, Langrall, & Jones, 1997). Kazemi and Hintz (2014), as well as the National Council of Teachers of Mathematics (2014), suggested that Children's mathematical reflections may be increased when asked questions that require them to think deeply about mathematics, such as, “Why do you think that?” and “How do you know?” These open-ended questions provide children with the opportunity to explain their thinking and reason about the mathematics.
A FINAL THOUGHT...
Systematically incorporating visual representations like the number line into mathematics early and continuing throughout the primary years will not only support the development of children's understanding of increasingly complex maths concepts but also equips children with a mathematical tool that can support their thinking over time.
Did you use this in your classroom or at home? How impactful was it? Don't forget to post in the comments. Math IS Visual. Let’s teach it that way.
Thank you for all you do to support your children's number journey. Thank you for watching and listening.
Love, Janey x