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2 comments about Math for Civil Service Workers.

1. This book was very informative and explained things in a clear and concise manner. I would highly recommend it.



2. This is a great book if you need to review math for any city or state exam. This book provide lots of examples and explains how to do the problems.

4 comments about Out of the Labyrinth: Setting Mathematics Free.

1. As a lover of mathematics I would very much like to believe what the authors say. They talk about a method of teaching mathematics in a problem oriented, non-competitive, low pressure collaborative atmoshphere that turns ordinary students into fellow lovers of mathematics. The authors have been teaching using their method, which they call the Math Circle, since 1994. The book, however, is long on self-promotion and short on details. A visit to the author's Web site uncovers a similar lack of specifics. What you will find is an offer to have the authors set up a program for $1,000 a day plus expenses.
   
   If, as the authors claim, their method can be taught to future teachers and results in higher scores on standardized tests then it will eventually catch on. To me it sounds way too good to be true. I hope that I am wrong.



2. WARNING: This book does not provide cookie-cutter curricula, problem sets and answers. Rather, this book presents a philosophy and approach to unleash curiosity and self-exploration of complex math in students from ages 4 through adult. Full of wit and wisdom and a joy to read, even for interested parents outside of the teaching field.
   
   Written by two highly acclaimed opinion leaders in mathematics education, the book presents a convincing argument for incorporating the art of guided explorations and self-discovery into math curricula. Along the way, they also describe the classroom, organizational and practical issues they faced in founding their non-profit Math Circle in the Harvard University environs.
   
   Mathematics is our lost native language, state the authors. Math talent is a myth, but the drudgery of most early math education fails to instill the confidence and sense of play which invites further exploration. The subtle Art of teaching is woven throughout the book as the lifelong teachers lend examples for creating an intimate model for guiding young students in their own discovery of complex math. Their approach consists of posing foundational questions to group of students -- Are there numbers between numbers? What is Area? -- then guiding a discussion down many paths "propelled by the fun of the chase."
   
   This approach may sound straightforward, but the art requires a spirit of exploration and familiarity with mathematics on the part of the teachers, highlighting some of the challenges. The authors describe after-school and in-school models for incorporating the approach, as well as observations and class notes to lend color.
   
   UPDATE: Recently the Kaplans lectured to leading teachers and educators at conferences by the American Mathematical Society and Mathematical Association of America. Let's hope this momentum continues among the important institutions laying the educational infrastructure.
   
   FULL DISCLOSURE: I have two boys, aged 8 and 6, who have attended the Kaplans' Math Circle classes for the last two years. My wife and I were careful to make sure that our boys were excited enough about the classes to trade off among other activities they love like soccer, art and gladiator battles. The boys re-register each semester and we are continually impressed with the Math Circle's ability to create an environment where the children explore more complex math than I ever thought possible. Math as Play. I'm a convert.



3. It began with the sort of grouse session that all teachers of mathematics from Euclid on would recognize. "Why is mathematics so poorly taught? *We* know how rich and mind-expanding mathematics can be--why don't our students?" But then, instead of the typical sniffs and harrumphs, the conversation took an unusual turn: Robert and Ellen Kaplan resolved to found The Math Circle, an after-school program that, in their words, "teaches the enjoyment of mathematics."
   
   The Math Circle's starting premises are that mathematics is accessible to all, not the preserve of a talented few; that mathematics thrives in a setting of collegiality, engrossment, brio, and good will; and that the best way to learn mathematics is to create it oneself, by experimentation and the free play of ideas. What can follow from these simple but audacious axioms astounds the imagination. Students not only master but discover (invent?) pieces of sophisticated mathematical reasoning, with only minimal guidance from the group leader, who functions as neither authority nor drillmaster, but as moderator and scribe. Having visited The Math Circle, I can testify that the Kaplans' approach works splendidly. In one demonstration, I saw first graders unlock the summation formula for arithmetic series in forty-five minutes. (They hit on Gauss's pairing trick, as well as several more idiosyncratic strategies.) These were ordinary students, many of whom were shaky at the outset on addition, to say nothing of multiplication--yet the problem so drew them in, the development made so much sense to them, that by the end of the session, they all were calculating with ease. What an improvement on sum charts and times tables!
   
   How do the Kaplans do it? *Out of the Labyrinth* is their eloquent meditation on The Math Circle, and more generally on mathematics pedagogy. Bringing nearly 100 years of combined teaching experience to their task, they anatomize the traits and skills that make for success in mathematics and mount a passionate case that anyone can acquire them. They survey the roadblocks--notational, cultural, and psychological--to mathematical understanding. They review the mostly woeful history of mathematics teaching. And finally, they take us inside The Math Circle, sharing tricks and tips and topics, and chronicling in a series of diary entries the surprises, challenges, digressions, and triumphs that spiraled out of a representative course.
   
   All this is accomplished with the conversational warmth and gentle grace that one has come to expect from the Kaplans' writing (*The Nothing That Is*, *The Art of the Infinite*, *Chances Are*). As delightful as it is important, *Out of the Labyrinth* is essential reading for anyone interested in learning or teaching mathematics.



4. The Kaplans teach the enjoyment of mathematics to anyone willing to explore it with them. That is what their Math Circle, which they describe in this book, seems to be all about.
   
   They set out here to explain an approach they have developed to passing on their love of mathematics. They hope and expect more teachers will be interested to offer a similar service and that they will find their approach helpful. The book is entertaining, even inspiring, certainly plausible, and full of the humorous and serious observations of these two evidently very experienced mathematical scholars and educators. For any mathematician who is ready to pick up an invitation to pass on the enjoyment of the subject, I suppose the test of the Kaplan approach will be in the doing. In extremely brief summary, a Math Circle leader carries no kit but rather a good knowledge of mathematics, a suitable collection of teasing openers, and an ability to moderate a seminar of budding mathematicians, usually but not always young. ("You know what?", said one adult student. "I'm going to die a genius!")
   
   The Kaplans point out that not every potential student will necessarily feel interested in turning into a mathematician for a few magical hours every week. Anyone, they believe, can do what mathematicians do, but they are wary of taking students merely on the basis of parental desire or enthusiasm. They describe what they are offering as, in an important respect, a kind of communal and collegial play of the intellect. It sounds pretty friendly. I have a pleasant picture of wizards from the local Math Circle offering to escort the willing by paths of puzzlement to gardens of mathematical delight.
   
   The Math Circle appears to have been evolving for well over a decade. I hope this book makes a thousand teachers and professors, including retired ones, enthusiastic to try out the Kaplan adventure locally - and report to the world. It sounds to me as if there may be a service here that every civilised country should be offering.

5 comments about Math for Humans : Teaching Math Through 8 Intelligences.

1. This valuable collection of Math {teaching and learning strategies}for humans definitely lives up to its name. Superheros like Math Mole, who touts "the best of what moles have to offer" professes that "the real secret of his success in problem solving is his ability to "get his paws dirty,go after subtle leads (always keeping his sense of purpose and direction), then chomp into real results at the end." Like Math mole, Mark Wahl can "sniff a solution from a distance;" what's more, Mr. Wahl can help younsters sniff out solutions and math know-how by appealing to the best children have to offer: their eight basic intelligences! From merely scanning this book, one might pick up tips to use in the classroom immediately. For example,I used a mind map, or graphic organizer,from this book to show my students how to mulitply fractions times whole numbers. It took less than one minute, and my fourth grade math students were enchanted! I can hardly wait to try the other activities Mr. Wahl has developed for students!



2. After our state testing this spring, I decided to have "fun" with math using Mark Wahl's Math for Humans. Little did I know that I would open up an entirely new way of teaching and learning math. I have never seen my 4th graders so engaged and excited by math. Every day they are making new connections and discovering the amazing world of numbers. I've even heard some of my students talking about math outside of the classroom! Each project matches many of the grade-level expectations for Washington State across the five math strands. My students can't wait for the next project and I can't wait to teach math next year beginning with Math for Humans!



3. well written, researched and laid out. concepts and ideas very useful for the classroom. hoping they will help some of my less able math students. activities listed are fun to try.



4. Mark Wahl is brilliant. He provides inspiration, explanation, and techniques (with plenty of examples) for using Gardner's Multiple Intelligences to teach Math to students who may excel in one kind of intelligence over another. The 1997 edition of the book I have was written when Gardner's theory included 7 intelligences. The theory now includes 8 intelligences and Wahl's book has been updated to reflect that.
   
   Wahl leads in his introduction with a great story of a second grader he met who was a budding artist, possessing very high spatial intelligence. She couldn't, however, learn (i.e. memorize) her addition tables. Judgment aside about the value of her teacher and parents forcing that she learn the tables in the timetable and not hers, Wahl undertook the challenge to teach her the arithmetic table. He had her make pictures of the symbols in "8 + 7 = 15 on a large index card and then had her make cards for other Math facts. This student was able to learn Math facts by making her own artistic flash cards. She got to learn by using her high spatial intelligence.
   
   The book provides examples of how to "season", as Wahl likes to say, Math lessons with the multiple intelligences (MI). He gives examples for:
   
   * Linguistic Intelligence (writing about what you learned or experienced)
   * Spatial Intelligence (diagrams with symbols, flow charts for procedures, visual mnemonics, charts, mind maps, graphs, Venn diagrams, branching trees)
   * Musical-Rhythmic Intelligence (clapping, singing, humming, rhythmic movement, rhythmic words, jingles)
   * Bodily-Kinesthetic Intelligence (cubes, blocks, Cuisenaire Rods, calculators, and other manipulatives)
   * Intrapersonal Intelligence (sharing of thoughts, feelings, and ideas with others)
   * Interpersonal Intelligence (discussing of cross-cultural and historical aspects of Math topics)
   * Logical-Mathematical Intelligence (deepening the analysis of concepts, posing questions, making connections, furthering exploration)
   
   Wahl discusses brain hemisphericity, how to use left and right brain skills together to do Math. He discusses learning styles, how to use an understanding of a student's temperament to create an environment for succeeding in Math. He explains the value of students working cooperatively toward solving problems. And, Wahl presents a chapter on dealing with Math anxiety.
   
   While the first half of the book presents and illustrates quite a bit of theory, the second half grounds us with concrete examples, quite a number of activities, that apply what we've learned earlier to real-world classroom and tutoring experiences.
   
   All in all, Math for Humans is a fabulous book, chock full of very inspiring information and ideas with tremendous power to help teachers, tutors, coaches, and parents to teach Math in ways that students can really get and enjoy.



5. I found this book very helpful in learning about the 8 multiple intelligences. The best part was that it was easy to understand. The book was not "dry." It has useful ideas that can be applied in the classroom.

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1 comments about Family Math : The Middle School Years, Algebraic Reasoning and Number Sense.

1. My family really enjoyed playing the math games and doing the activities in this book. We had to put on our thinking caps and discover different math strategies. My kids loved the art in this book. There was also a lot of useful information on how much math my kids need to get into college.