A Math Paradox: The Widening Gap Between High School and College Math

An article by by Joseph Ganem expressing ideas that were recently expressed by professors at the University of Manitoba, and concerns I myself have seen in my classes. Two articles in the Winnipeg Free Press here and here discuss the challenges of teaching math in Manitoba and raise questions like the article below on whether or not we (the education system) are doing a sufficient job. The math teachers I know are working hard to do the best job possible, but maybe we ought to be doing more (did I just derive an “ought” from an “is” – David Hume rolls over in his grave) – Read more in the article below…

We are in the midst of paradox in math education. As more states strive to improve math curricula and raise standardized test scores, more students show up to college unprepared for college-level math. The failure of pre-college math education has profound implications for the future of physics programs in the United States. A recent article in my local paper, the Baltimore Sun: “A Failing Grade for Maryland Math,” highlighted this problem that I believe is not unique to Maryland. It prompted me to reflect on the causes. The newspaper article explained that the math taught in Maryland high schools is deemed insufficient by many colleges. According to the article 49% of high school graduates in Maryland take non-credit remedial math courses in college before they can take math courses for credit. In many cases incoming college students cannot do basic arithmetic even after passing all the high school math tests. The problem appears to be worsening and students are unaware of their lack of math understanding. The article reported that students are actually shocked when they are placed into remedial math.The article did not shock me. It described my observations exactly. In recent years I’ve witnessed first hand the disconnect between the high school and college math curricula. As a parent of three children with current ages 14, 17, and 20, I’ve done my share of tutoring for middle school and high school math and I know how little understanding is conveyed in those math classes. Ironically much of the problem arises from a blind focus on raising math standards (see more at The Back Page)

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Einstein’s Secret to Amazing Problem Solving (and 10 Specific Ways You Can Use It)

Einstein is quoted as having said that if he had one hour to save the world he would spend fifty-five minutes defining the problem and only five minutes finding the solution. This quote does illustrate an important point: before jumping right into solving a problem, we should step back and invest time and effort to improve our understanding of it. Here are 10 strategies you can use to see problems from many different perspectives and master what is the most important step in problem solving: clearly defining the problem in the first place! The Problem Is To Know What the Problem Is – The definition of the problem will be the focal point of all your problem-solving efforts. As such, it makes sense to devote as much attention and dedication to problem definition as possible. What usually happens is that as soon as we have a problem to work on we’re so eager to get to solutions that we neglect spending any time refining it. What most of us don’t realize — and what supposedly Einstein might have been alluding to — is that the quality of the solutions we come up with will be in direct proportion to the quality of the description of the problem we’re trying to solve. Not only will your solutions be more abundant and of higher quality, but they’ll be achieved much, much more easily. Most importantly, you’ll have the confidence to be tackling a worthwhile problem. Continue reading at: Einstein’s Secret to Amazing Problem Solving (and 10 Specific Ways You Can Use It).