I have taught for 28 years. I blog about 21st century schools, transforming educational practices and have Prosci/Adpro change management certification.
I give presentations on my experiences with 21st century education in schools and change management.
I found an article by Joseph Ganem in the Daily Riff entitled, "Can America Figure Out Math?" His dilemma is two-fold. The first is that so many college students drop courses requiring math because they score poorly on the math entrance exams and lack the basic skills to do university math (in particular, calculus). The second is that middle school kids are taught math at a college level. He points out the disconnect between the two. He asks:
"How can students who have studied college level math for years need remedial math when they finally arrive at college?"
He gives three answers.
1. Confusing difficulty with rigor.
He claims we are "pushing students to do ever more difficult problems at a younger age. Attempting difficult problems without the proper foundation is actually an impediment to developing rigor. Students need to be challenged but in such a way that they learn independent thinking. Pushing problems that are always beyond their ability to comprehend teaches dependence-the opposite of what is needed to develop rigor".
2. Mistaking process for understanding.
He says "just because a student can perform a technique that solves a difficult problem doesn't mean that he or she understands the problem...learning techniques without understanding them does no good in preparing students for college... at the college level emphasis is on understanding, not memorization and computational prowess".
3. Teaching concepts that are developmentally inappropriate.
He says "teaching advanced algebra in middle school pushes concepts on students that are beyond normal development at that age.... because math involves knowledge and understanding of symbolic representations for abstract concepts it is extremely difficult to short cut development."
He adds that:
"all three of these problems are the result of the adult obsession with testing and the need to show year-to-year improvement in test scores. Age-appropriate development and understanding of mathematical concepts does not advance at a rate fast enough to please test-obsessed lawmakers.But adults using test scores to reward or punish other adults are doing a disservice to the children they claim to be helping."
He goes on to say that:
"It does not matter the exact age that you learned to walk. What matters is that you learned to walk at a developmentally appropriate time"
I love how this fits with what Dan Meyer and others are saying about learning math. For years I have thought that learning an algorhythm and doing endless calculations does not produce math thinkers and problem solvers. Many of my students still do not know their "math facts". I'm guessing that math has had no meaning to them. I am enjoying the challenge of changing our classroom with these ideas in mind.