Tag Archives: math

“It is foolish to answer a question that you do not understand. It is sad to work for an end that you do not desire. Such foolish and sad things often happen, in and out of school…” Into every life, it is said, a little rain must fall. Farmers and firefighters may take comfort in the inevitability of precipitation, but most others see an unanticipated deluge for what it is: a problem. Everywhere you look–on tests, in school, throughout life–you find problems. Problems, by their very nature, require solving. Unfortunately, many of us don’t really have a strategy to solve problems apart from painful trial and error. Those who study heuristics, however, have a distinct advantage. A heuristic can be any practical approach to problem solving, learning, or discovery. George Pólya, the Hungarian master of heuristics, systematized problem solving with unparalleled lucidity. His influential work, How to Solve It: A…

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Albert Einstein, genius that he was, reportedly commented that, if he only had one hour to solve a problem, he would spend 55 minutes defining the problem and the remaining 5 minutes solving it. No matter that this quote is most likely apocryphal; the brilliance and truthfulness of it transcends its false origins. Any great mind can recognize how much work goes into understanding a problem before actually solving it. George Pólya certainly understood the reality of problem solving. This highly influential Hungarian mathematician is well-known for his contributions to complex analysis, mathematical physics, probability theory, geometry, and combinatorics. However, he most distinguished himself to the masses through his work on heuristics, which is to say problem solving. In 1945, Pólya wrote How to Solve It: A New Aspect of Mathematical Method, a small book with a large impact. This volume describes his four principles of problem solving, steps so…

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Math on exams like the SAT and ACT has always been tough and seems to be getting tougher. Every year, we’re seeing more advanced concepts from Algebra 2, trigonometry, and statistics added to the tests with very little of the core arithmetic, algebra, and geometry being removed. Plus, both tests continue to emphasize math conceptual understanding and problem solving. What is a college-bound high schooler to do? Obviously, careful attention during math class over the extent of a student’s academic career will build the foundation for strong test scores. Furthermore, exceptional test preparation will close faulty gaps in knowledge and understanding. But test takers looking for every advantage on test day need to embrace any strategy that can help manufacture points under pressure. We don’t just want accuracy… we want speed. How can you save precious seconds on every question to ensure a decent shot at every point on the…

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Many students become convinced somewhere along the line that they are “bad at math,” or that their brain isn’t wired for math. In some cases it is just a matter of finding the subject uninteresting. But, at its worst, this self-definition can have deep impacts on a student’s ability to achieve. Certainly, skills in all areas differ from person to person—-very few of us are going to win a Fields Medal—-but how much truth is there to the idea that otherwise talented students are inherently “bad at math?” Well, it turns out that the typical student is about as bad at math as they are willing to be. Of course, students vary widely in their math aptitude, including grades in their math courses and scores on their standardized tests. Surely, that implies something about math ability, but research is showing math aptitude may have a lot more to do with…

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Once known as the college entrance exam of choice for strong math students, the ACT has always demanded both broad and deep mastery of math concepts learned from grade school to high school. The SAT may currently hold the crown for the test best suited for math whizzes, but ACT Math is tough and getting tougher. Understanding the new ACT Mathematics Reporting Category provides useful insights into the test maker’s assessment goals for this part of the test. Preparing for Higher Math Of the 60 questions on the ACT Math test, roughly 36 (57-60%) of them evaluate what is considered high school math, spanning the point where students learn to use algebra as a general way of expressing and solving equations to advanced topics in Algebra 2 and Trigonometry: Number & Quantity (7–10%) Students must demonstrate knowledge of real and complex number systems, integers and rational exponents, and vectors and…

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Just about every battery of standardized tests, with the notable exception of the LSAT, includes some math sections. This means that you will either have to deal with math on your big tests or become a lawyer to avoid it! For the non-attorneys out there, math on standardized tests can not only be managed, but mastered. Obviously, you’re not likely to perform well on questions testing math you’ve never learned. In some cases, you may encounter concepts you haven’t yet covered in school, such as when teens taking the SAT or ACT early in junior year see Algebra 2 topics they’ll learn later in the year. But much more common are those instances where you have forgotten math you learned long ago. The SAT & ACT math sections cover basic arithmetic, algebra, and geometry along with increasingly more complex concepts. Even advanced math students struggle to recall the definition of…

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