- Paperback: 164 pages
- Publisher: Math Solutions; 58044th edition (February 1, 1998)
- Language: English
- ISBN-10: 0941355195
- ISBN-13: 978-0941355193
- Product Dimensions: 5.2 x 0.5 x 8.2 inches
- Shipping Weight: 12.6 ounces
- Average Customer Review: 12 customer reviews
- Amazon Best Sellers Rank: #459,513 in Books (See Top 100 in Books)
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Math: Facing an American Phobia 58044th Edition
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From Library Journal
An award-winning educator and author of many math storybooks for children grades two to eight, Burns explains her teaching approach by example, presenting her ideas as classroom scenarios and conversations. She believes that children learn math concepts best by trying to apply them to ambiguous, real-life situations. She also argues that "anything known about how children learn was ignored once our school math learning began." Her book is like a role-playing game for math teachers. Rather than presenting specific lesson plans or educational games, Burns illustrates a style of teaching that encourages children to discover mathematical concepts by themselves. For instance, the chapter on fractions describes the lesson and the classroom give-and-take as a group of fifth graders works out solutions, with reproductions of the students' written papers to show how individual children followed different methods to think out a solution. Though aimed at teachers, this book has an easy style that makes it accessible to parents as well.AAmy Brunvand, Univ. of Utah Lib., Salt Lake City
Copyright 1998 Reed Business Information, Inc.
Math has gotten a bad reputation with the American public, and this book for parents and teachers provides possible reasons why this is so. The book also discusses what math can and should mean to people and explains how adults can avoid passing their math phobias on to their children.
Author Marilyn Burns traces the underlying conflict between the public s assumption that mathematics means arithmetic and the belief of math educators that the mathematics taught in schools must foster reasoning, thinking, and problem-solving skills. The book begins by outlining the mathematics involved in preparing a holiday dinner: determining the size of the turkey, the amount of stuffing required, and the cooking time. Burns then compares this practical mathematics to what is taught in schools, explaining that there is a divide between the classroom emphasis on paper-and-pencil activities and the real-world application of mathematics. As an example, a chapter on pizza problems explores the meaning of doubling an object size, the relationship between diameter and area, and processes of mathematical thinking and investigation. Other topics discussed are the value of timed math tests, the use of expanded student answers in student-teacher communication, and the appropriate use of the calculator. The final chapters contain practical suggestions to help children avoid math phobias. Burns recommends actively engaging children in mathematics outside the classroom and supporting and encouraging children throughout their math education. An answer key contains the solution to the seven problems found in the book. Detailed explanations and illustrations of the reasoning behind the solutions are designed to help readers think mathematically. --Reviewed by Judy Spicer, Mathematics Abstractor. Reprinted with permission from ENC Focus: A Magazine for Classroom Innovators, 9 (3), 69 (2002).
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In a nutshell, Burns argues that Americans have a math phobia and do poorly in math because they were brought up to believe math was a series of repetitive exercises with no real world applications. Rules for manipulating fractions with various mathematics operations seem almost random to students who, in a desparate attempt to pass classes, try to memorize these rules and then reproduce them in the correct places. But of course, there are only so many "rules" one can memorize and after a while, as all upper grade, high school and college math teachers know, students begin using the "rules" at inappropriate times and then "fail." They conclude that math is just "too hard" for them and, worse yet, they pass their fears and frustrations off on their children.
Burns' solution for this problem is teach math with a genuine real world context. We don't multiply and divide fractions for the sake of solving problems on a worksheet. We do it so we can double 3/4 cups of flour (or water, etc) when baking. And she offers a lot of lessons and ideas for showing children practical math applications for what they are learning. These are at the heart of her book and I would venture to guess that every teacher would find some benefit from chapters 9-11 of this book.
But the book is also fundamentally flawed in several respects. In the first instance, Ms. Burns de-emphasizes the rote learning exercises involving addition and subtraction, multiplication and division, in favor of "higher level" math applications and reasoning. She is hardly alone in this. In my district, the head of elementary math instruction recently told sixth grade teachers to give their students calculators so their lack of computational skills would not hinder their understanding of higher level math concepts. This policy is an absolute disaster for children. Recent research show that "math fluency," the ability to quickly recall such information without having to think (and without having to use a calculator) is an absolute prerequisite to understanding higher level math concepts. [...]
[...]. Using calculators while "thinking" about "real world" math problems undermines this fluency and actually hinders children in their ability to make a real world connection. Worse yet, Burns discourages the use of pencil and paper in such basic facts exercises as she includes. Her rationale is that math is a thinking exercise, not a writing one, and that using pencil and paper is "like expecting children to write before they can tell their own stories."(p.10) Again, sheer nonsense. Writing and thinking are not separate acts, and doing one actually helps the other. In particular, writing helps one to commit key concepts and math facts to memory and can help expand our understanding of more advanced concepts.
But there is a far broader problem with this book and indeed much of the educational "research" that I have seen. This is that none of the book involves "research" at all. At no point does Ms. Burns actually do the sort of study that is commonplace for academic publications in other fields. She never takes two groups of children, teaches them by the same methods, but gives (for example) one group a calculator and denies it to the other to see what outcomes, if any, are observed. She doesn't even use published resources to defend fundamental points made in her book. Her central claim is that the old style of math alienated people and made them phobic of math. Her evidence? A conversation with an unnamed engineer on an airplane. (She later disparages this very source since he disagrees with her about calculator usage.) Now, in my opinion, she is correct (as is the engineer) but the fact of the matter is that this sort of thing could not be published in any other academic setting. Private conversations with unnamed sources are not evidence. Nor is a written correspondence with a novelist and third person accounts of what some unnamed parents might think. Burns might have done better by citing SAT scores over time. As of 1998, when this book was published, these scores would not have defended her ideas (from chapter 8, "School Math Then, School Math Now") because student scores in 1998 were lower than in 1967. By 2005, however, they were higher. Is this evidence that Burns is right? Perhaps. Many of her ideas are even more common-place now than they were in 1998. But then again, the new test scores could also reflect the influence of test preparation courses, unheard of in 1967 but common place now. Part of the demand for these courses is that they teach math in the traditional way to make up for the deficits caused by the lack of basic skills our students have after 12 years of modern math education. The new emphasis on math fluency could also be a cause of higher test scores. How do we know? A good start would be to do some actual research into what really works in math using the scientific method and carefully constructed study and control groups. Large scale surveys of teachers at all levels (including college and community college) could also be helpful too.
In the final analysis, I give the book 3 stars because it raises a lot of issues for the thoughtful reader. Many teachers (some of whom share the phobia Burns describes) will applaud it. Even teachers who are critical, like myself, will find something of value in it. But this book is most important because it shows the state of where math research is. For math education to become a serious field of study, we need to move beyond this. We need to apply the same rigorous standards to the study of math education that are typical of other fields of research.
This is an easy reading book that should help parents understand the trends in mathematics education and give ideas how to help their children to enjoy mathematics rather than the situation where children hate mathematics.
That would surely be a "hard" class, with lots of dropouts. But even with its rigor, I nevertheless, still wouldn't expect it to produce a Shaq or an Iverson. For that matter I'm not sure it would actually produce basketball players at all. Neither does Marilyn Burns, in this wonderful book, as she cites this example of a "ridiculous" way to learn basketball and matches it to the way that so many of us were taught mathematics. We can chuckle at the example - but for many it is a nervous chuckle, indeed.
Most of us grew up to be neither basketball stars nor mathematicians - nor even adequate users of mathematics in our lives - and to be desperately resistant to revisiting any part of our mathematical upbringing.. As a 6th grade math teacher, I know this too well. At a party I can find as little company as the proctologists once conversation has turned to professions. On "Parents' Night" the easiest way to clear the room is to hint that we might all "try some examples" of what the students will be doing in the year.
This "phobia" seems also to be the basis for the immense friction that efforts to reform mathematics have faced in the past decade. Approaches that favor students actively engaging in math, talking to each other, (talking to parents!), responding to open-ended problems and creating algorithms are just so alien that they have faced fierce resistance. Many Americans are as eager to "just get through" their children's school mathematics experience as they were to survive their own. Any attempt to elaborate or reposition the subject (especially to engage them in new approaches) is, for them, just delaying early parole from their child's sentence to "serve" 8-12 years. Like any neurosis, this phobia has enervated some and produced mathematical cripples; but it has also energized others whose sense of overcoming math as an obstacle informs their own sense of the nature of "success."
Burns knows this from more than a decade of working, through her "Math Solutions" project, training tens-of-thousands of pre-service and active teachers in new approaches to their classrooms. She is well known in math education circles for her "Math By All Means" series: which included books with refreshingly new models for teaching `core' topics such as division in grades 3 and 4 as well as unheard of topics such as probability in elementary classrooms. She has since branched into a growing collection of books aimed to directly engage and intrigue kids, as well as more books aimed at bolstering the uncertainty of many teachers who face new challenges but sense the roots of the math phobia in their own lives.
I believe this book is her book for parents. Burns commences with a warm chapter discussing the central national mathematics ritual of the year - the production of the perfect Thanksgiving Turkey. Who knew it to include so much math? Or, as Burns dryly wonders, to have driven the market to produce the "pop-up" turkey to let the math phobics off the hook! From there she moves to discuss everything from the role of calculators and testing to specific `topics' (teaching fractions and percents), to a general retrospective on "Math then and now" and a prospective look at solving the phobia problem.
Burns seems well aware of the difficult fact that the math phobia will, itself, deter many adults from even a glance at this book. It is surely by design that it is a slender and un-intimidating volume, sprinkled with clear illustrations and quite a few examples of student's work. Along the way, it scatters seven less-than-traditional math problems through the chapters and ends with a chapter entitled "Not your everyday answer key."
Its odd that in a culture swamped with self-help books, where folks will line up, unflinchingly, to purchase books about surviving depression or abusive relationships. I find it hard to imagine many math "phobics" marching to the cash register with this book in hand (perhaps, thus, more saleable through an online venue). Burns is not one to proffer deep analysis for such troubled folks. Instead she offers a chuckle and a hand for a short walk through a place where math is engaging enough to almost be... fun; a place where our children are exploring every day; a place where the challenges of the 21st century won't be faced with the intellectual tools of the 19th.
Buy this book for yourself. Buy a pass-around copy for friends who can't seem to get past grousing about the "new, new" math. Buy one for the members of your school board and the principal in your child's elementary school. Buy a sympathy copy to anyone you see worrying the pages of one of E.D. Hirsch's "What your nth=Grader Needs to Know" tomes. What they, and we, really need to know is how to think. This book is a good starting point.