By Laurie H. Rogers
Because every time you use the Charged Particles Method to teach negatives, a brain cell commits suicide.
Traditional Math Method Used to Teach Negatives
Reform Math Methods Used to Teach … Uh …
Balloon Model: In real life, subtracting a sandbag lessens weight, while adding a sandbag adds weight. In the model, however, subtracting a sandbag somehow makes a quantity larger, while adding a sandbag makes it smaller. In the Building and Airplane models, nothing is added or subtracted to make a quantity larger or smaller; the movement up and down is mechanically driven. In the Sea Model, you could say that blowing air out of one's lungs (subtracting air) makes a person sink, although the change in weight would be negligible. But how does one add air under water?
Where in these models is infinity? Where are fractions and decimals? Where is zero located? At ground level? If so, are negatives below the ground? Since when have balloons and airplanes flown, elevators descended, and swimmers paddled below the ground?)
If you search the term “negatives” on the TERC Web site, you'll have a difficult time finding actual negatives, but games about thinking about negatives are explored. Actually, take a few minutes and skim through the 1st Edition units for TERC. This is the approach to K-6 math that has helped to kill off math proficiency in the United States.
(Comment: Looking through the TERC Web site, you can see the end of mathematics ... and possibly all of life as we know it. The school district in my city still uses this curriculum, despite my best efforts to change that.)
Without an understanding of the principles behind the number line, students can’t add and subtract negative numbers with proficiency. Without that capability, algebra, geometry and calculus will be beyond them.
I don’t know why so many people in public education seem not to respect the need for efficiency, effectiveness, sufficiency or student proficiency. Math is a tool, used in the "real world" to get a job done. Time is important; efficiency is vital; correct answers are critical. Those who can use math properly will be hired over those who can’t. There is no time in the “real world” to discover methods, struggle with basic math, or constantly ask a “partner” for help. But math reformers seem to think they have all the time in the world. To them, math isn’t about efficiency and correct answers; it’s about struggle, failing, striving and playing games. Many reformers truly believe that if the teaching was efficient, the lesson failed. Thus, they’re motivated to not just prefer the inefficient models, but to actually eliminate efficient models, to mock them and to label them as counterproductive.
Help your children gain a solid grounding in math by teaching them the traditional methods, such as long division, vertical multiplication and the number line. Traditional methods were developed and honed over thousands of years by very clever adults so that they would be efficient. More-efficient models will be developed, no doubt, but the reform models I've described are not better models.
Don’t let anyone convince you that efficiency and effectiveness in math are unnecessary or counterproductive. People who actually use math (outside of a K-12 classroom) don't believe that.
Please note: The information in this post is copyrighted. The proper citation is:
Rogers, L. (October 2012). “In defense of the number line: Reform methods for teaching negatives fail on decimals, fractions ... and negatives." Retrieved (date) from the Betrayed Web site: http://betrayed-whyeducationisfailing.blogspot.com /.
This article was republished October 25, 2012, on Education News: http://www.educationnews.org/k-12-schools/laurie-rogers-in-defense-of-using-the-number-line-to-teach-negatives/#comment-19236