My math teacher friends and I often talk about the inaccurate and incorrect mathematics that we encounter when out and about that often goes unnoticed by others. But probably one of the two most common ones (the other I’ll reserve for another blog) is related to pricing.
This one drives us crazy for two reasons. The first issue being that there is clearly a lack of understanding of number magnitudes and labeling numbers correctly. Secondly, it’s often fruitless in trying to explain the error. And trust me, whether with others or alone we never pass up the opportunity to explain the error in the hopes that a correction will be made even though explanations are usually met by a blank and clueless stare. But we all know that pictures speak louder than words, so here are some examples of inaccuracies that we often see.
(Photos: Courtesy of Margaret Bangerter)
Do you get the point (pun intended) of what ruffles our mathematical feathers? Yes, the incorrect placement of the decimal point. As advertised, each of the three would cost less than a penny and is 100 times less expensive than it should be. Even though we point out the inaccuracy, not once has the seller given use the advertised price. I just know that someday someone will challenge this false advertising all the way to the Supreme Court!
But seriously, this is not an issue to be taken lightly. According to the National Assessment of Educational Progress (1996) students perform well when carrying out adding and subtracting procedures, but are lagging in performance when it comes to place value sense. For example, 90% of 13-year-olds could add and subtract multi-digit numbers, but only 60% could construct a number when given its place values. So as you can see, students are calculating with numbers they don’t understand.
These common pricing errors in misplacement of the decimal point result from a lack of understanding of the base-ten place value system and numbers. LearnBop performance data shows that students struggle with interpreting and solving base-ten place value problems. When students are asked to solve a Bop (problem) that involves interpreting place value magnitudes only 47% can answer it correctly on the first attempt without any assistance or guidance. Big surprise, given the incorrect examples they in stores every day!
Performance data also shows that students who couldn’t answer the problem correctly struggled with prerequisite skills including reading and writing multi-digit whole numbers using base-ten numerals, number names, and expanded forms.
Understanding the meaning of base-ten numerals and being able to interpret them sets the stage for fact and procedural fluency but also lays the foundation for learning future mathematics and just good number sense that lends to being a wise consumer. There are a variety of resources and materials to support the learning about and interpreting of the place value system including:
- Progressions Documents for the Common Core http://www.illustrativemathematics.org/
- LearnZillion Videos http://learnzillion.com/
- Illuminations Resources for Teaching Math http://illuminations.nctm.org/
- Illustrative Mathematics Problems http://www.illustrativemathematics.org/
I invite you to share your comments and feedback regarding instructional activities and/or interventions you use for helping students learn about and understand place value and number magnitudes. Thanks!