| Hello educators, I’m Mark Wahl the owner/director of Mark Wahl Learning
Services and Books. You’ve come here because Here's your first motivational idea: our phone number (360) 221-8842 occurs in this order at position 13,733,742 in the digits of Pi! On our links page is a site that will find your or a student's phone number occurs in Pi's digits! (Use any favorite number or year, e.g., 2008 starts at the 11,651st place!) Using resources shown on this site you can:
You've probably discovered that successful math learning (useful, conceptually grounded, transferable to new situations, real-world relevant) is pretty rare – to be treasured when it happens. But how to make that happen more often -- that's the question Math learning is an obstacle-course for most. Obstacles to quality math learning are plentiful. In my many years of experience I’ve probably seen them all, including:
How students leap to math success Youths can leap over any of these obstacles to math success. I’ve seen it more times than I can count! Having been in the business of waking kids up to math for thirty years, I know that the right approach can make up for a multitude of assumed impossibilities and disabilities–poor self-image, hating math, "spacing out," constant forgetting, blowing tests even with a high homework grade, some ADD, some ADHD, "dyscalculea," etc., etc. Classes, groups and individuals, exposed to my different approaches experience dramatic results. Dynamic teacher workshops and my three books help teachers stimulate students’ natural learning abilities, bringing kids out of the math doldrums into math power. (Click the "Professional Development" and/or "Books to Buy" tabs above if you want to look at them.) Young people, or even adults, just need to get the real scoop behind the methods in a clear and fun way. They are thirsty for the concepts, the number sense, the "gut feeling," the internal knowing that what they are doing is right. Yes, even if they just say "I’m bored," or "This sucks!" they would love to be truly turned on to math. They just don’t think it’s possible. Let’s face it, math boredom, anxiety, and hatred are legitimate, --even healthy-- reactions to material that is meaningless, monotone, black-and-white and repetitive. How would you react with a daily portion of sawdust for your meals? How students regain contact with their Here’s a simple, basic example touching on the bodily-kinesthetic and visual-spatial intelligences of a child (there are numerous others that could show you more in-depth use of these and other intelligences). How much is 30 ¸ 1/2 + 10? Answer fairly quickly! "Twenty-five," say even some teachers if asked to answer quickly, and so do most kids. This comes from a misunderstanding of the nature of all division questions. Even if you get it right by doing the little flip trick you learned in school, does the answer you got really make sense to you? Let’s bring in a little bodily, physical, "gut" sense to this abstract question. What does 20 ¸ 5 mean? Not what’s the answer, but what does it mean? It means one of two things: "How many 5s can be packed into 20?" (the packing question), or "If 20 is cut into 5 same-sized parts, how much is in each part?" (the cutting question). Let’s consider 30 ¸ 1/2 as a packing question. It’s asking how many 1/2 units (or dollars) will pack into 30 units (or dollars). The answer is of course, 60 and no one could persuade you otherwise. Then add 10 to get the correct answer to the question: 70. And you have it with conviction. Our math friend the Bodily-Kinesthetic Intelligence The above discussion is a very simple example of switching the intelligence "channel" for input of information. In this case it was switched from the usual linguistic/symbolic and logical/mathematical channels often used (poorly) to communicate math to a quick touch on the bodily-kinesthetic channel in which the physical notions of packing and cutting were employed (either verbally or, better, with dramatic body motions in both teacher and learner) for "gut" understanding. You can do it with the Visual/Spatial Intelligence too. You can also switch to the visual/spatial/diagramatic channel and leap to clarity in division. Just draw 30 circles and cut each in half with a line Æ Æ Æ Æ Æ Æ Æ Æ Æ Æ Æ Æ Æ Æ Æ Æ Æ Æ Æ . Count, or reason to, how many halves are in the 30 circles. So 30 ¸ 1/2 = 60. Gardner’s Multiple Intelligence Theory There are eight intelligences highlighted by researcher Howard Gardner. Each has been painstakingly proved by him to be equivalent to any other by any scientific criterion you can think of. When we speak of someone being "intelligent," instead of meaning they are verbally sharp or they are powerfully logical, we can actually accurately mean they are intelligent in any of six other ways: interpersonally, kinesthetically, spatially, intrapersonally, musically or naturalistically. If that’s so, it stands to reason that if you teach math through all the intelligence channels you have a vastly increased chance of reaching every brain you are working with. Now, a Manual on how to teach or explain I’ve gone into this and many other teaching strategies in great detail in my book just reprinted in 2008 with key revisions and updates: Math for Humans: Teaching Math through 8 Intelligences, geared primarily for grades 3-9. As author, I'm offering this 256-page book, with extensively illustrated 8 1/2 x 11 pages, chock full of teaching ideas and many ready-to-go activities to you for $35.95 (take a 10% web discount) cost to you lower than any other source) that thousands of teachers and parents have gladly paid. Don't delay, get this help for your teaching now! Click here to view the book and some other choices. And check out my classic A Mathematical Mystery Tour now just $39.95-- a book that can give your students goosebumps and metaphysical insights as they learn math skills using the naturalist, visual-spatial and interpersonal intelligences among others! The free accompanying Mystery Tour Guide adds depth, practice, and entertainment to the book. The fascinating Millennial Supplement is meant to accompany this book (extra $7.95 cost) and raise its challenge to high school algebra level while also updating and adding to content of the Mystery Tour for 5th grade and up. For all Click Here. 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