Reading the Numbers: Everyday Mathematical Literacy
Students need literacy as well as quantitative skills to be successful especially as society becomes more technology-dependent. The emphasis on building children’s numeracy skills should match the efforts of writing and reading intervention efforts. Just as students who are exposed to early literacy activities are more confident in reading so too are students more confident in math when they are exposed early on to numbers and mathematical relationships. 22% of adults in the U.S. don’t have the basic math skills for an entry level job. They can’t successfully add fractions, work with measurements or mentally estimate a tip. They are functionally illiterate when it comes to numbers.
We learn the language of math the same way we learn any language by exposure, immersion and interaction. Some of reading and arithmetic is memorization. We learn some multiplication facts like word chunks 5×10=50, 100÷25=4. Then there are sight-words like and, the, and any just like there are some math facts that should just be learned on sight: 6×8=48, 7×8=56. However, there is more to reading than just decoding and there is more to math than calculation procedures. Once you know that 10×8=80 and 7x8=56 you can mentally regroup 17x8 as (10x8)+(7x8) which is 80+56 or 136. A 15% tip on a $30 meal is 10% plus 5% or $3 plus half that, $1.50, and all together that is $4.50. Understanding that a number represents a quantity means never having to laboriously count again.
Students might be resistant in middle and high school to use number lines or color chips, but it’s important to scaffold student’s learning from concrete to more abstract models like number lines or drawings to the most abstract representations of numbers and variables. It’s even more important that students be able to understand and explain mathematical concepts in numbers, drawings and words. It’s always easier to remember a mathematical “rule” if it makes sense. For example, the zero exponent rule says that any number to the zero exponent is one: x0=1. This rule can easily be confused with x•0=0. A simple demonstration can clear up the confusion. When you fold a piece of paper, the sections double exponentially. If you fold it once, it creates two sections or 21. If you fold it twice, there are four sections or 22. If you fold it three times, there are 8 sections or 23. No matter how many times you fold the paper, though, it started as one piece of paper. That is why x0=1 and not 0.
As money becomes more electronic, it becomes increasingly important to have a fully developed number sense that can keep track of all the abstract amounts. When I was a young girl, my mom taught me how to count back change and she always gave me the task of paying for the gas. As I got older, I took more responsibility in planning the weekly menu and I went to the grocery store with her. While I never enjoyed shopping, it was important to have these concrete experiences with money. Children experience this less and less as more purchases are made with debit or credit cards. That makes it all the more important to give children a concrete experience with time and money. Many banks offer special savings accounts for children. Teachers also have a lot of freedom to suggest different after-school activities; they could partner with local banks and help students practice creating and managing budgets. Classes can engage in their own class economic systems either as part of the curriculum or as part of a classroom management system. As the yearbook supervisor, I include marketing and budgeting in our after-school activities. Even though they put a lot of effort into making the book, I help them understand that the books don’t pay for themselves and I encourage them to budget and save for their own yearbooks. Mathematical and financial literacy is essential and these are just a few suggestions.
Math, more than any other subject, tends to get characterized as an innate-ability rather than an effort-based subject. However, success in math is about exposure, practice and hard work. Show that you value math achievement even if you feel you are not good at math. Engage in age-appropriate math conversations in everyday activities inside and outside of the classroom:
- count objects by joining (add/multiply) and separating (subtract/divide)
- measure time in multiples of 15, 30, 60, 12 and 24
- use money in multiples of 25 and with decimals in tenths and hundredths
- estimate the cost of a meal or a tip
- add, subtract, multiply and divide fractions in cooking
- convert inches to feet in physical measurements
- multiply by 7 and add quantities of 2, 3, 6 and 7 in football
- determine the time it will take to drive a certain distance at a certain speed
- use proportions to determine the cost to fill the gas tank
- create budgets and spreadsheets to manage money
Overall, the three most important factors in numerical fluency are a strong concept of numbers as quantities, concrete and abstract understanding of mathematical principles, and engaging with math in daily activities. This will strengthen and improve a student’s number fluency and mathematical confidence more than rote memorization and procedures.
This article is sponsored by Western Governors University, a non-profit, accredited, online university. WGU's Teachers College offers multiple online degree programs for current teachers or those looking to become teachers. To find out more, please visit www.wgu.edu/wisecareers_teachers.