math Archives - Pearl Lewis

The Joy of Mathematics

2 June 2012 by Dr Lewis

That the mysteries of mathematics can put a smile on your face may seem far-fetched to some. It is not, however, a strange idea to Professor Arthur T. Benjamin of Harvey Mudd College. He loves mathematics and is certainly the most enthusiastic mathematics teacher I have ever seen in action. I purchased “The Joy of Mathematics” for a family member, but ended up sitting down to watch the lectures with the gift recipient. I don’t recall ever seeing a maths teacher with so much energy and eagerness to share what he knows. If you are not terrified by numbers (and even if they do scare you a little), you are ready for the magic of mathematics presented in a way only a passionate and down-to-earth mathematician can do it.

“The Joy of Mathematics” consists of 24 half-hour lectures that celebrate the sheer joy of mathematics. The lectures are taught by a mathematician who is also a magician, with numbers and the odd rabbit in the hat. Professor Benjamin is renowned for his feats of mental calculation performed before audiences at schools, theaters, museums, and conferences. Yes, you will be in awe of him as you watch him process numbers at speeds that will make you dizzy. But unlike many other magicians, the professor isn’t selfish with his mathematical magic tricks. In this course, Professor Benjamin lets you in on some of the secrets of his wizardry. You may be astounded to learn how easy it is to perform some calculations you once thought would need more than your pocket calculator. By the end of the course, you may decide your new bag of tricks has turned you into something of a minor maths wizard yourself.

Who can benefit from this course? This course is a great refresher course for those who have lost touch with their high school mathematics training and want to feel more comfortable around numbers. It’s also a great warm-up to college entry-level mathematics, and precursor to advanced algebra and basic calculus. For those high school students who feel threatened by mathematics, time spent working through the examples given during the lectures will deepen understanding and boost confidence. Even if you have a degree in mathematics, this course is sure to work out your mental muscles in a way that is both enjoyable and enlightening.

While the complexity of the material presented is not beyond the abilities of average high school students in beginner algebra courses, be warned that at times Professor Benjamin’s enthusiasm causes him to accelerate. If he starts presenting new concepts too quickly, don’t be afraid to reach for the remote and rewind… over and over again, until you feel comfortable enough to move on. In fact, Professor Benjamin is well aware that his audience is not a university class and will remind you to use your remote from time to time. Take his advice to get the most out of these lectures. Take each lecture at your own pace. Repeat each lecture a few times to let the explanations sink in. I also recommend keeping a pen and the notes that accompany the DVDs handy. Add your own personal notes to those provided with the lectures. You will learn a lot during each short lecture, and personal notes will help you reflect better on what you have learned before you start a new topic. Don’t move on to a new lecture until you feel like you “got it”, or at least got most of it. If you progress too quickly without understanding and internalizing the material, the more advanced lectures may be lost on you.

“The Joy of Mathematics” is currently available from The Great Courses, a company that strives to make high quality teaching and the skills of university professors accessible to the general public. (Photo credit: Richard Faverty)

Learning Math the Natural Way

16 February 2012 by Dr Lewis

Let’s be honest. Not every child is a natural mathematician. Encouragement and praise is great, but the help it provides can never substitute for real, hands-on, practical help that makes the mathematics learning experience effective. Many children try their best, yet their efforts leave them caught in a constant struggle to grasp the mathematical concepts. Their frustration is evident as they become tongue-tied with the heavy math jargon. How can a parent or teacher reach those children who are not natural logical or mathematical learners? How does one bring the best out of the kids who don’t naturally thrive on numbers and logic problems? In her book, “Memory Tips for Math, Memorization and Learning Styles: The Successful Way to Teach K-5 Math” Donnalyn Yates proposes a practical and creative solution that will take a lot of the “ouch” out of math class.

“Memory Tips for Math, Memorization and Learning Styles” recognizes that the three most common perceptual learning styles are visual, auditory and tactile/kinesthetic. Learning activities in the book focus on providing these categories of learners with stimulation that leads to effective learning. Acronyms, pictures, rhymes, and stories help students to develop vocabulary and retain mathematical procedures. For example, think about how you learned the relationship between the gallon, quart, pint and cup. Now imagine if you had discovered this relationship through a story of fantasy. Imagine the Kingdom of Gallon in which lived three queens of the family of Quart. Each Queen Quart lived in a castle with a young prince and princess – they’re the Pints. Prince and Princess Pint don’t have children but each of the Pints has 2 cats – the cats are the Cups. Imagine how much fun you might have had in Math class if you learned using the tools provided in “Memory Tips for Math, Memorization and Learning Styles: The Successful Way to Teach K-5 Math”. As you read the creative examples, don’t be surprised to find yourself conjuring up a few inspired examples of your own to help your child or student learn more effectively.

This book can be purchased at a discount of 30% for a limited period. Use coupon code FEBRUARYCART305USD at check out. The coupon expires on 19 February 2012.

Questions and answers are simply mathematics

4 February 2012 by Dr Lewis

If you find the study of mathematics dreadfully boring, it is time to play a little. In “Amusements in Mathematics” by Henry Ernest Dudeney (published by David Gaddy, Nov 2011), plenty of mathematical fun is crammed into 640 pages. According to the author, this collection of puzzles and mathematical problems was created so that the user of the book could tap into the pleasure of “doing math”.

Henry Ernest Dudeney (1857-1930), an English mathematician, is best known as a master of logic puzzles. The author views mathematical puzzles as perplexing questions begging our answers. The reader is drawn into the hunt for solutions and answers to these questions. Asking and answering questions is a part of human life, and comes naturally to us all. When mathematics is viewed as the process of asking and answering questions, we allow ourselves to bypass any existing “number” prejudices and start to enjoy what comes naturally.

“Amusements in Mathematics” also includes a discussion on the psychology of puzzles and the application of math in our daily lives. It is an excellent resource for mathematics teachers seeking a readily accessible collection of “questions” that will spice up a lesson. However, this puzzle book is just as useful to anyone seeking a little mental stimulation – after all, we can all answer questions and should not shy away from the challenge of doing so often. This extensive collection of puzzles and problem-solving exercises is now available from Lulu.com. The book can be purchased at a saving of 20% until the end of February 2012 using the following coupon code: 20% off books – Enter code FEBBOOKS12 – Save up to $25 – Offer ends 2/29/12

Parents are the reason that students cannot hack the Math in Physics?

3 March 20115 June 2010 by Dr Lewis

$High school kids cannot use fractions.$ “Another physics teacher told me that students cannot hack the math in physics,” says Stewart Brekke in his article entitled, “Urgent Math Crisis in our Nation: Basic Math Deficits Affect Student Performance in High School Physics and Chemistry“. Is this an unusual observation for a Physics teacher? Brekke estimates that the USA “may now have over 100,000 high-school students who do not know fractions and decimals well enough to do high-school physics and chemistry successfully, let alone go on to college and pass a physics or chemistry course.”

There is clearly a problem on our hands – many teens cannot do basic mathematics. Where do we find the source of this problem?

Stewart Brekke speculates that part of the problem may be attributed to the elementary schools placing too much emphasis on reading skills and not nearly enough on basic arithmetic skills. Japanese elementary school students typically spend two to three times as much time on developing mathematical skills as their American counterparts. The result of this shift in priorities is evident. Stewart also believes that the “lack of a proper foundation at home” is also a significant contributor to the poor arithmetic skills observed in high school students. Sadly, many children enter first grade without being able to count to ten, and their progress in arithmetic skill development is severely hampered.

“It is not that parents do not care, for, on the whole, I have seen them show deep concern about their children’s education, but that many of these parents do not take the time to teach their children number facts nor reading skills. These parents must be informed early that their child’s success in school means that they must start educating their children before they enter kindergarten,” says Brekke.

Education systems all over the world invest vast sums of money into remediation of high school students struggling with poor basic skills. Yet high school Physics and Chemistry classes continue to shrink in size as teenagers avoid confronting the issues that stand in their way of understanding these subjects. Are we trying to solve a problem instead of preventing it? What would happen if more of the national or state education investment was used for programs aimed at educating the PARENTS of pre-school children, thus effectively equipping them to help their children develop the basic skills needed for future success at school?

Can parents make a difference at home? All indications are that if parents do not participate in the education process BEFORE their child enters the school system, they may in fact be contributing to their child’s future scholastic failure.

Mathematics as a Family Activity

3 March 20111 April 2010 by Dr Lewis

Mathematics doesn’t belong exclusively in the maths classroom. Parents can, and should, integrate it in a number of enjoyable family activities. In most cases, when they are enjoying themselves, children will not even be aware that they are developing their mathematical skills as they play. Do parents require special skills or need to take some course to encourage their children to develop basic mathematical skills early? Fortunately not. In fact, you don’t even need to be “good at Mathematics” to have fun with your kids. And that is the key: fun. Children need to learn that addition, subtraction, multiplication, and division (and later calculus and trigonometry) are not just useless, intimidating procedures weighing down their homework. The best way for children to learn this, is to learn it without directly associating the learning with formal Mathematics.

As part of this blog, I will share some of the mathematics-oriented family activities that I enjoy, and which don’t require special training. Some of these ideas will be so obvious and “everyday” that you will wonder why you haven’t been “playing” all along. Join me as we explore these ideas and develop them into games for the whole family.

Where it all begins…

3 March 201124 March 2010 by Dr Lewis

Welcome to my blog. You are invited to journey with me as we explore learning. Before you decide that this topic has no relevance to you, let me present evidence to the contrary. You are, after all, able to read this paragraph right now because you learned to read at some earlier time. You can also tell me how many letters are in the first word of this paragraph, because once upon a time you learned to count. Just like me, you are an experienced learner. Learning is something we all do, and have done since we were infants. As both a scientist and an educator, I derive great pleasure from seeking truth, acquiring knowledge, experimenting with it, and then sharing that knowledge and experience with others. This blog is my way to share what I have learned, and am still learning, with you. Join me as we ask questions, seek answers, digest old angles to the learning debate, explore new ideas that make learning exciting for children and adults alike, and take down the intimidating monsters that have guarded the gates to learning for too long.