Some "math in the news" stories that I've read over the weekend.
1. Start with the famous Dr. Edward Frenkel: He laments that the math curriculum we have is boring and fails to show the beauty and utility of mathematics. In this article you have a video and podcast as well. Dr Frenkel connects math with hacking e-mail, changing the CPI calculations to raise taxes and cut benefits, and the financial crash in 2008. In this LA Times OP-ED piece, Dr Frenkel puts the blame on a curriculum of studying mathematics that is more than a thousand years old. The LA Times article says, "For example, the formula for solutions of quadratic equations was in al-Khwarizmi's book published in 830, and Euclid laid the foundations of Euclidean geometry around 300 BC. If the same time warp were true in physics or biology, we wouldn't know about the solar system, the atom and DNA. This creates an extraordinary educational gap for our kids, schools and society.
If we are to give students the right tools to navigate an increasingly math-driven world, we must teach them early on that mathematics is not just about numbers and how to solve equations but about concepts and ideas." and leads to his point, "
Of course, we still need to teach students multiplication tables, fractions and Euclidean geometry. But what if we spent just 20% of class time opening students' eyes to the power and exquisite harmony of modern math? What if we showed them how these fascinating concepts apply to the real world, how the abstract meets the concrete? This would feed their natural curiosity, motivate them to study more and inspire them to engage math beyond the basic requirements — surely a more efficient way to spend class time than mindless memorization in preparation for standardized tests.
In my experience, kids are ready for this. It's the adults that are hesitant. It's not their fault — our math education is broken.". Personal comment: Many students lack the basics (multiplication tables and fractions) needed for the course they're in and many math teachers (thanks to certification requirements that don't care about math qualifications) don't have that knowledge or appreciation of "power and exquisite harmony of modern math". Add on top of that the a curriculum that is stuffed full of too many topics (a "firehose approach" to learning). In my case I have to cover 1100+ pages of text for the accelerated class I teach. Dr Frenkel's approach is the right prescription IF the students in a class have the proper foundation and IF the teacher has the requisite knowledge and IF (a really big if) there was time in the curriculum. As such it wouldn't fly very well in a typical public school. The need for a teacher to cover the material so the students are prepped for the multiple choice state test that measures their knowledge (which then determines whether the teacher has done their job) precludes that.
2. More typical of today's public school is this article where I found a lot of valid points: "The latest educational fad term is "STEM," which stands for a curriculum in the areas of science, technology, engineering and mathematics. GOOGLE reports over 174 million pages on "STEM education" alone. The problem is that adults, including some educators, still haven't figured out how to make peace with the "mathematics" in STEM. Everyone applauds classes in high-tech robotics as the sine qua non of a good STEM program, but ask them to explain how they integrate any mathematics content into the robotic curriculum and you may be surprised that most of these programs do not even work with mathematics teachers to legitimize themselves."...."The NASA brand has become synonymous with inspiring students, making them feel excited about what they know, and enticing them to learn more about STEM careers. The problem is that in our society, mathematics tends not to make people feel they are competent; it does not excite our emotions in a positive way, and often engenders a sense of dread. Any marketing expert will tell you that mathematics is the poison-pill for any brand, and so over the years NASA and other agencies have largely hidden their mathematics expertise from public view. ... There are no down-sides to students building robots out of parts from a box, and watching as these battery-powered critters scurry around the classroom floor. There is also little or no math involved in these curricula."....."But if you think that NASA is alone in some sinister plot to de-emphasize mathematics you are wrong. Virtually every federal agency that offers STEM resources to teachers does so by minimizing the mathematical content. They do this, for example, by creating middle and high school STEM activities that cover math skills far below what the students see in their corresponding math classes. The rush to make activities "hands-on" has seemingly created legions of resources that have students measure and plot and take a few percentages, but never delve into math concepts above grade eight such as linear equations, statistics and mathematical modeling.". Personal comments: The "regular" Algebra 2 and Geometry classes I've taught have students who still haven't mastered their multiplication tables. They've been passed along through the system even though they don't know what they're doing. In one school I was at, the guidance counselors decided the math classes the student would take for the next year---in many cases over-riding the opinions of the math teacher who had just taught them. That meant students who complained enough would be put into honors classes (even though they didn't belong) and since there were too many students like that, the overall quality of the course suffered. Welcome to today's world of education; the emphasis is not on setting standards. It's more about placating parents and students.
3. Canada has problems that sound just like our math problems and they've identified discovery education as a culprit in why there math scores are going down: "Ontario’s curriculum, however, does not require students to memorize multiplication tables or learn basic algorithms such as long division. They are instead encouraged to break problems down into smaller portions to work through them.". Likewise, here you'll find: " “If you look at what’s been happening, predominantly over the last decade, there’s been an unprecedented emphasis on discovery learning,” said Donna Kotsopoulos, an associate professor in Wilfrid Laurier University’s education faculty and former teacher.
Robert Craigen, a University of Manitoba mathematics professor who advocates basic math skills and algorithms, said Canada’s downward progression in the international rankings – slipping from sixth to 13th among participating countries since 2000 – coincides with the adoption of discovery learning....Parents in Alberta, Ontario and British Columbia, for example, launched petitions over the Christmas holidays, calling on their governments to revamp curriculums with a greater emphasis on basic math skills.". Finally, this article summarizes the problem: "The one side says, “drill and kill.” The other says “drill for skill.” Basically, though, just about every mathematician and math education researcher who was interviewed for this story agrees that the perfect math class should have a mix of skills and problem solving. They just can’t agree on the amounts of each, when to add them, and what to skip."...."How does Shanghai do so well? They devote an average of 14 hours a week to homework (versus three for the Canadians) and 70 per cent have parents willing to pay for extracurricular math classes (versus 28 per cent in Canada). And those students who seem to spend so little class time on math also have teachers trained more rigorously and subject to greater supervision."....." top-performing Asian countries typically cover fewer subjects more deeply, especially in the early grades. A 2004 study found that Grade 1 teachers in Canada were expected to cover 18 topics versus just five in Hong Kong, where even textbooks may be hundreds of pages shorter.". Personal comments: Understand that the poor educational results our country has are inflated. They're pulled up by students who are getting extra tutoring outside of class to fill in the deficiencies of the educational system. Most students that I've encountered lack basic skills (multiplication tables and fractions) and then the schools put calculators into their hands to avoid the drudgery of calculations; they never learn their arithmetic or algebra. But no big deal, pass them through the system and onto the college level. Complaints from parents are minimized, students can claim they're taking accelerated classes even when they lack the math skills of an accelerated student. Now the college has to figure out what to do with them.