Tag Archives: math

Help Kids With Tricky Homework

by Bob Cunningham at Understood.org

[O-G reading tutor in Columbus OH: Adrienne Edwards 614-579-6021]

At a Glance

  • It’s common for parents to have trouble helping kids with math homework.
  • Math is a process. It helps to walk through the process with your child.
  • Having examples of a similar math problem can help your child complete tough math homework.

Your child needs help with math homework, but you’re not sure how to do the math problems yourself. Does this sound familiar? You’re not alone. This happens a lot to parents.

Keep in mind that showing kids with learning or attention issues that it’s OK not to know the answers can be a good lesson. Here are some suggestions for approaching math homework with your child.

The Most Important Tip for Math Homework

It’s important not to spend more than 10 to 20 minutes working through math homework that neither you nor your child knows how to do. Spending more time than this will probably just be frustrating for you and your child without providing much benefit.

Try the steps outlined below. If they don’t work, it may be better for your child to get more instruction from a teacher in order to complete the homework.

5 Things to Do When Helping With Math Homework

Here are things to keep in mind when helping your child with tricky math homework.

  1. Start by acknowledging that not understanding what to do can be stressful.You can also say something positive to acknowledge that your child is trying. For example: “I’m proud that you know what the homework is and brought home the proper materials.”
  2. Ask your child to show you an example. This could include a math problem he did in class or a sample math problem from a textbook that includes the answer.
  3. If your child can’t find an example problem, try typing one of the homework problems into an internet search. Your child’s worksheet, textbook or notebook might have a title or math term to search for online. Your search will bring up a list of websites designed to help with math. Try a few sites if the first one doesn’t help.
  4. Once you’ve found a sample problem either from your child or online, ask how the teacher said to do the problems. Having a completed example in front of him can help your child recall any instructions and class discussions.
  5. Use the sample problem to figure out the process to follow to solve the problem. Make notes of each step your child remembers as you work your way through the first problem together. This reminds your child that math is a process. The list you create also gives your child something to take to the teacher to show his efforts, even if he doesn’t come up with the right answer. The teacher can use the list to correct the process so that your child can solve the problem in the future.

3 Things to Avoid When Helping With Math Homework

Here are three things to avoid doing when your child asks for math homework help.

  1. Try not to begin by asking your child what the teacher said to do. If your child remembered that, he likely wouldn’t be asking for your help.
  2. Try not to contact the teacher right away. Kids with learning and attention issues might give up easily or get angry if they’re not sure what to do. But it’s important for them to try to think of ways to approach the situation before going to the teacher.
  3. Try not to write a note that just says your child didn’t understand the assignment. Give the teacher information about what your child has trouble with, such as adding fractions. This can help find the “missing piece” to solve math problems.

For more help with sticky homework situations, here are tips on how to win homework battles. And visit Parenting Coach for ways to work with kids who give up too easily.

Key Takeaways

  • Try not to spend more than 10 to 20 minutes working through math homework that you and your child don’t know how to do.
  • It’s good to take notes while you’re trying to help solve a math problem.
  • If the process helps your child solve the math problem, great! If not, he can show these notes to his teacher for more instruction.

About the Author

Bob Cunningham

 

Orton-Gillingham reading tutor in Columbus OH: Adrienne Edwards, 614-579-6021. Or email aedwardstutor@columbus.rr.com

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+ Dr. Cheesman: Some Games to Boost Math Skills

From the IDA Newsletter: By Elaine Cheesman, Ph.D.

There are times when we want kids to put down the iPad or tablet and to play traditional games (e.g., dominoes, board games, card games) with humans, particularly when the whole family is on vacation and it has been raining for days.

Playing traditional games is beneficial on many social and academic levels and can provide real-time practice for children in both reading and math skills. Research by Ramani and Siegler (2008) suggests that playing board games strengthens proficiency in foundational math tasks—counting, estimating, subitizing (i.e., the ability to perceive at a glance the number of items presented, such as on dice), recognizing written numerals, adding and subtracting, and comparing numerical sizes.

Many children with reading difficulties also struggle with math skills. Even though they may not have been formally diagnosed with dyscalculia, a learning disability related to math calculation, these individuals may display one or more of the following characteristics:

  • Use of inefficient calculation strategies
  • Difficulty memorizing basic arithmetic facts
  • Early difficulty with subtraction
  • Lack of “number sense” (e.g., comparing the relative size of two numbers—Which is greater? 3 or 9)
  • Subitizing
  • Dysfluent processing of written numbers or mathematical symbols
  • Linking written or spoken numbers to the idea of quantity
  • Difficulty understanding place value
  • Trouble learning or understanding multi-step calculation procedures (e.g., multi-digit multiplication and long division)
    This App chat reviews math websites and mobile apps that can strengthen basic math skills needed to play traditional family games as well as higher-level calculation skills. It avoids programs/apps that require extensive reading, include in-app purchases, or contain distracting images and/or audio that may disrupt the primary task.

Subitize Tree

Developer: Doodle Smith Ink
Website: www.doodlesmithink.com
This app provides subitizing practice using a variety of representations (e.g., dominoes, dice, fingers on hands, and playing cards). Players can choose a specific representation to practice, change the amount of time the images are displayed, and select the range of numbers used. Settings are intuitive and easy to use. The goal is for players to correctly subitize in order to free captive animals. One animal is freed for every four correct responses. Incorrect responses signal display of the correct response. 2

ModMath

Developer: Division of Labor
Website: www.modmath.com
This free app provides virtual graph paper and a keyboard with numbers and math operation symbols for laying out equations and problems in all four operations with whole numbers and fractions. Intuitive settings enable contrasting rows and/or columns. After solving the problems, the user can save, print, and email completed worksheets.

Dexteria Dots—Get in Touch with Math

Website: www.dexteria.net
This is an intuitive math game that teaches the concepts of number sense, addition, subtraction, greater-than (>), and less-than (<). The user separates or combines dots to produce a value. For beginners, larger dots represent greater values, and smaller dots represent smaller values. There are three main options for gameplay, and each includes four levels. All levels have time limits. In addition, bonus dots are awarded, and most challenges have multiple solutions.

Ten Frame Fill

Developers: Mike Egan and Randy Hengst
Website: www.classroomfocusedsoftware.com
This app is designed to improve addition and subtraction skills in the family of 10. In this app, a ten frame is shown with tokens. The player is shown an addition problem and a complementary subtraction problem and asked, “How many more are needed to make 10?” The players can drag tokens of another color or touch the number for the correct response.

Word Problems

Developers: Mike Egan and Randy Hengst
Website: www.classroomfocusedsoftware.com
This app provides practice in simple math word problems requiring addition and subtraction with answers of 10 or less. The user can solve one of three types of equations. The user has the option to use virtual manipulatives to solve the problem and the option to show the number sentence.

X-tra Math.com

Website: www.xtramath.com
This free website helps users automatize computation skills in the four operations for problems related to decimals and fractions. Timed activities challenge the user to respond in at least ten seconds, but optimally in three seconds or less, with immediate feedback for slow or incorrect responses. Progress-monitoring graphs show responses of ten seconds, three seconds, and areas that require more practice.

CoolMath4Kids.co

Website: www.coolmath4kids.com
This free website calls itself an “amusement park” for math. It features kid-friendly information and engaging games using the four basic operations plus geometry art. The instructions require reading skills, and the visual layout may be distracting for some students. Tabs for both parents and teachers provide guidance, instructions, and options to select targeted activities. A related website for practicing pre-algebra and higher-level math is CoolMath (described below)

CoolMath

Website: www.coolmath.com
This free website is an extension of CoolMath4Kids (described above) that provides engaging games and information related to advanced math (e.g., pre-algebra, algebra, trigonometry, calculus), geometry art, and science. Tabs for both parents and teachers provide guidance, instructions, and options to select targeted activities.

References

Ramani, G. B. & Siegler, R. S. (2008). Promoting Broad and Stable Improvements in Low-Income Children’s Numerical Knowledge through Playing Number Board Games. Child Development, 79(2), 375-394.

www.aboutdyscalculia.org

Other Dr. Cheesman’s App Chats available:
Dr. Cheesman’s App Chat: Literacy Instruction
Dr. Cheesman’s App Chat: Spelling
Dr. Cheesman’s App Chat: Interactive Books for Kids, Teens, Adults
Dr. Cheesman’s App Chat: Holiday Gifts! (Word Games and Logic Puzzles)
Dr. Cheesman’s App Chat: Vocabulary and Morphology

Dr. Cheesman is an Associate Professor at the University of Colorado Colorado Springs. The courses she developed were among the first nine university programs officially recognized by the International Dyslexia Association for meeting the Knowledge and Practice Standards for Teachers of Reading.

Copyright © 2014 International Dyslexia Association (IDA). Visit the IDA site: http://www.interdys.org

 

Orton Gillingham tutoring in Columbus OH:  Adrienne Edwards 614-579-6021 or email aedwardstutor@columbus.rr.com

+ Khan Academy: Free YouTube Math Tutorials (and More)

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Since I last mentioned Khan Academy and its free online math sessions on YouTube, it has grown by leaps and bounds. 

There are now 1800 + step-by-step tutorials at the site: http://www.khanacademy.org.

The Khan Academy site is a not-for-profit 501(c)(3) with the mission of providing a world-class education to anyone, anywhere.

Find user-paced exercises developed as an open-source project, allowing the Khan Academy to become the free classroom for the world.

Log in for your own user-paced practice and instruction.

You’ll find tutorials in

  • Algebra
  • Arithmetic
  • Banking/Money
  • Biology
  • Brain Teasers
  • CAHSEE Example Problems
  • Calculus
  • California Standards Test: Algebra I, Algebra II, Geometry
  • Chemistry
  • Credit Crisis
  • Current Economics
  • Developmental Math
  • Differential Equations
  • Finance
  • Geithner Plan
  • Geometry
  • History
  • Khan Academy Related Talks + Interviews
  • Linear Algebra
  • MA Tests for Educational Licensure MTEL-Pre-Algebra
  • Organic Chemistry
  • Paulson Bailout
  • Physics
  • Pre-Algebra
  • Pre-Calculus
  • Probability
  • Statistics
  • Trigonometry
  • Valuation + Investing
  • Venture Capital + Capital Markets

We’ve been seeing and hearing this site mentioned in many different places — most recently Fareed Zakaria’s “Global Public Square.”   I thought you ‘d like an update.

This is a very impressive site.

reading tutoring in Columbus OH:  Adrienne Edwards  614-579-6021 or email aedwardstutor@columbus.rr.com

+ Using Gestures to Learn Math

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Gesturing can perhaps help students develop new ways of understanding math.

For a long time scholars have known that movements help retrieve information about an event or physical activity associated with action.

An article by Susan Goldin-Meadow, Susan Wagner Cook and Zachary A Mitchell in Psychological Science is the first to show that gestures not only help recover old ideas, they also help create new ones.

The article, titled “Gesturing Gives Children New Ideas About Math,” provides information that can be useful for teachers, say the experts.

Lead author and psychologist Susan Goldin-Meadow says,

“This study highlights the importance of motor learning even in nonmotor tasks, and suggests that we may be able to lay the foundation for new knowledge just by telling learners how to move their hands.” 

For the study, 128 fourth-grade students were given problems of the type 3+2+8=___+8.

None of the students had been successful in solving that type of problem in a pre-test. 

The students were randomly divided into three instruction groups.

  • One group was taught the words, “I want to make one side equal to the other side.”
  • The second group was taught the same words along with gestures instantiating a grouping problem-solving strategy — the silent demonstrater’s  V-shaped hand indicating 3+2, followed by a fingerpoint at the blank (group and add 3 and 2 and put the sum in the blank).
  • The last group was taught the words along with the gestures instantiating the grouping strategy but focusing attention on the wrong numbers — the silent demonstrater’s V-shaped hand indicating 2+8, followed by a fingerpoint at the blank.  The experimenter demonstrating did not explain the movement or comment about it.

All of the students were given a test in which they solved new problems of this type.  They then explained how they reached their answers. 

Students who repeated the correct gesture during the lesson solved more problems correctly than students who repeated the partially correct gesture; but the latter group of students solved more problems correctly than students who repeated only the words.

The number of problems children solved correctly could be explained by whether they added the grouping strategy to their spoken repertoires after the lesson, Goldin-Meadow said.

Because the experimenter never expressed the grouping strategy in speech during the lesson, and students picked it up on their own as a new idea, the study demonstrates that gesture can help create new concepts in learning, the researchers feel.

“The grouping information students incorporated into their post-lesson speech must have come from their own gestures.  Children were thus able to extract information from their own hand movements.  This process may be the mechanism by which gesturing influences learning.”

More research is of course needed.  But this is an idea worth trying in classrooms and at kitchen tables!

sole source: online article from Science Daily on 2/26/09.  www.sciencedaily.com .  Drawn from an article by Goldin-Meadow, Wagner Cook and Mitchell in Psychological Science, “Gesturing Gives Children New Ideas About Math.” 

+ No Gap for Girls in Math Scores, Study Shows

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This is Tamar Lewin’s article in the NY Times:

Three years after the president of Harvard, Lawrence H. Summers, got into trouble for questioning women’s “intrinsic aptitude” for science and engineering — and 16 years after the talking Barbie doll proclaimed that “math class is tough” — a study paid for by the National Science Foundation has found that girls perform as well as boys on standardized math tests.

Although boys in high school performed better than girls in math 20 years ago, the researchers found, that is no longer the case. The reason, they said, is simple: Girls used to take fewer advanced math courses than boys, but now they are taking just as many.

“Now that enrollment in advanced math courses is equalized, we don’t see gender differences in test performance,” said Marcia C. Linn of the University of California, Berkeley, a co-author of the study. “But people are surprised by these findings, which suggests to me that the stereotypes are still there.”

The findings, reported in the July 25 issue of Science magazine, are based on math scores from seven million students in 10 states, tested in accordance with the federal No Child Left Behind Act.

The researchers looked at the average of the test scores of all students, the performance of the most gifted children and the ability to solve complex math problems. They found, in every category, that girls did as well as boys. (To their dismay, the researchers found that the tests in the 10 states did not include a single question requiring complex problem-solving, forcing them to use a national assessment test for that portion of their research.)

Janet Hyde, a professor at the University of Wisconsin, Madison, who led the study, said the persistent stereotypes about girls and math had taken a toll.

“The stereotype that boys do better at math is still held widely by teachers and parents,” Dr. Hyde said. “And teachers and parents guide girls, giving them advice about what courses to take, what careers to pursue. I still hear anecdotes about guidance counselors steering girls away from engineering, telling them they won’t be able to do the math.”

Girls are still underrepresented in high school physics classes and, as noted by Dr. Summers, who resigned in 2006, in the highest levels of physics, chemistry and engineering, which require advanced math skills.

The study also analyzed the gender gap on the math section of the SAT. Rather than proving boys’ superior talent for math, the study found, the difference is probably attributable to a skewed pool of test takers. The SAT is taken primarily by seniors bound for college, and since more girls than boys go to college, about 100,000 more girls than boys take the test, including lower-achieving girls who bring down the girls’ average score.

On the ACT, another college entrance test, the study said, the gender gap in math scores disappeared in Colorado and Illinois after the states began requiring all students to take the test.

 

 
source: This is Tamar Lewin’s article in the NY Times on 7/25/08.  www.nytimes.com

tutoring in Columbus OH:   Adrienne Edwards   614-579-6021   or email   aedwardstutor@columbus.rr.com

+ Breezy New Book on Math by Oxford Mathematician

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This is Jordan Ellenberg’s review of Andrew Hodges’s book “One to Nine: the Inner Life of Numbers” in the NY Times:

My cousin, bound for a top liberal arts college in the fall, was amused when I told her I was reviewing a book about big ideas in mathematics, from the classical to the contemporary. “Don’t they already know everything about math?” she asked. “You know, there’s algebra … and then calculus … and that’s it, right?”

Andrew Hodges, a fellow at Oxford and the author of the lively new book “One to Nine,” would have been horrified, but not surprised. My cousin, in his view, is a victim of the pedagogical tradition that presents math as an eternally fixed array of computations, to be memorized and repeatedly executed without motivation or explanation. The result, he writes, is a “legacy of fear and anxiety generated by schools, which leaves most of their victims with a lifetime of mumbling apologetically about ‘my worst subject.’”

“One to Nine” offers a different model for teaching math — discursive rather than linear, topical rather than abstract and remote, and, above all, manically energetic rather than repetitive and plodding. The book is composed of nine chapters, each focused — very, very softly focused — on one of the first nine natural numbers. Chapter Four, for instance, starts out with the observation that four is a perfect square, and from there skips along to the construction of Latin squares, the irrationality of the square root of two, the definition of the logarithm (whose relation to “four” never comes entirely clear), complex numbers, and the even more exotic quaternions (a number system in which “numbers” are actually strings of four integers, and the product of two numbers depends on the order in which you multiply them!), the theory of four-dimensional spacetime and Einstein’s equation E=mc2 (squares again) before finishing with a short and speculative account of the theory of twistors, one of many competing candidates for the universe’s underlying geometry.

Catch all that? Hodges’ lightning pace allows him to cover in one little book the greatest hits of the last 3,000 years of math and physics, leaving plenty of room for jabs at the Bush administration and quotes from the Pet Shop Boys (these so frequent as to be tabulated in the index).

The overall effect is like that of a lecture by the type of professor who paces back and forth in front of the blackboard, with insistent voice and waving arms, and has trouble adhering to the ostensible syllabus for any extended period. Being this type of professor myself, I can attest that the style is popular with students. But it requires discipline to convey real information as well as enthusiasm.

Hodges often manages that trick. He ably explains the subtly distinct shadings of the word “probability” in statements like “There’s a 90 percent probability I’ll get a six in the next 12 rolls of this die,” “There’s a 90 percent probability of a catastrophic climate change in the next 50 years” and “There’s a 90 percent probability that the current warming of the earth is a result of human activity.” This is the kind of tacit knowledge about mathematical practice that’s unrelated to computations and hard to test, so it doesn’t show up in school math classes. But it’s crucial for arguing sensibly about the planet’s uncertain future. Hodges is also excellent at describing the ways in which mathematical thinking winds its way into every aspect of human life, from fashion to politics to finance, whether we’re aware of it or not. Like Molière’s Monsieur Jourdain, most people have been speaking math their whole lives.

The hyperactive style of “One to Nine” is less well suited to more conventional mathematical material. Georg Cantor’s notoriously mind-boggling hierarchy of infinities is covered in just three pages; the proof of the irrationality of the square root of two, a theorem so profound and startling in its time that its discoverer is traditionally held to have been drowned in the sea by his scandalized Pythagorean colleagues, gets just one. And it’s hard to imagine a novice reader getting much from exposition this compressed:

“Latin squares can be used for devising a duty roster for n dirty jobs in a houseshare of n people. Or, for comparing the effect of n drugs on n animals in some doubtless vital trial. Who said mathematics wasn’t useful? Similar ideas lead to the error-correcting codes which make it possible for computers to communicate reliably. Or, for that matter, to football leagues, speed-dating nights and the plot lines for ‘Desperate Housewives.’”

Too much of the book is like this passage, which is not exactly math, but what Stephen Colbert might call “mathiness”: a series of fervent gestures that gives the impression that mathematical ideas are being expressed, but doesn’t actually deliver the goods. Readers will enjoy sprinting through “One to Nine,” and they’ll certainly learn that there’s much more to the subject than the algebra and calculus taught in high school. But they might not be able to explain exactly what.

Source: This is Jordan Ellenberg’ s review in the NY Times on 7/6/08.  Ellenberg is an associate professor of mathematics at the University of Wisconsin-Madison and the author of “The Grasshopper King,” a novel.  “One to Nine: The Inner Life of Numbers,” by Andrew Hodges is published by WW Norton & Co. at 330 pages, and costs $23.95.

tutoring in Columbus OH:   Adrienne Edwards   614-579-6021   or email  aedwardstutor@columbus.rr.com

+ Singapore Math: Intensive Teacher Trainings

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Intensive Five-day Summer Institutes in teaching “Singapore Math” are scheduled in Orlando (June 23-27), San Francisco (July 14-18), and Boston (July 28-August 1). 

These three will focus on the fundamentals, and are geared to teachers of grades 1-6 who have little or no experience in Singapore Math, “especially those who intend to supplement a non-Singapore Math program or adopt a Singapore Math program.”

A fourth Institute titled “Advanced” will be held in Boston from August 4-8.  The advanced seminar will be directed at grade 1-6 educators with in-depth training experience in teaching Singapore Math who are either supplementing their current program or adopting the Singapore Math curriculum.

Call toll free 1-800-462-1478 or www.SDE.com/revolutionary.

Conference registration is $1395.  It includes a tool kit containing $500 worth of customizable materials: Singapore Math for US Handout Book; an 8-step Model Drawing Book;  the Teaching Elementary Mathematics book; a voucher to redeem one “sample set” from the Primary Mathematics book series (includes one copy of both A & B versions of a Teacher’s guide, student textbook and student workbook — your choice of grade level).

Trainees receive 26.5 total contact hours plus 2 additional hours upon completion of the on-demand electronic follow-up training.  For futher information about graduate credit through Antioch University Seattle and Chapman University College, visit www.SDE.com/revolutionary and follow the “credit” link.

WHAT IS “SINGAPORE MATH?” 

When the US Department of Education commissioned a study in 2005 to find out why Singapore, a country with a population half the size of New York City, ALWAYS scores No. 1 in a widely accepted comparison of global math skills, it concluded, “Singapore’s textbooks build deep understanding of mathematical concepts through multi-step problems and concrete illustrations that demonstrate how abstract mathematical concepts are used to solve problems from different perspectives.”

By contrast, the study said, “traditional US textbooks rarely get beyond definitions and formulas, developing only students’ mechanical ability to apply mathematical concepts.”

Many eminent mathematicians agree.  In fact, according to an LA Times article on March 9 2008, it is hard to find a mathematician who likes the standard American texts, or dislikes Singapore’s.

An article by Barry Garelick from Stanford’s Hoover Institution shows a US textbook side by side with the Singapore Math book.  “Singapore Math’s textbook is thin, and contains only mathematics — no games.  Students are given brief explanations, then confronted with problems which become more complex as the unit progresses.”

By contrast, the US text, “typical of many math textbooks in the US is thick, multicolored, and full of games, puzzles and activities to help teachers pass the time” but which rarely challenge students.

Singapore’s text contains no graphics other than occasional cartoons pertaining to the lesson at hand, no spreadsheet problems, and no problems asking students to use a calculator to find the “mean number of dogs in a US household”.

With SM, students are required to show their mathematical work, not explain in essays how they did the problems or how they felt about them.

According to the Hopkins article, “While a single lesson in a US textbook might span two pages and take one class period to go through, a lesson in a Singapore textbook might use five to ten pages and take several days to complete.  The Singapore texts contain no narrative explanation of how a procedure or concept works; instead there are problems and questions accompanied by pictures that provide hints about what is going on.  According to the AIR (American Institutes for Research, a government group) report, the Singapore program ‘provides rich problem sets that give students many and varied opportunities to apply the concepts they have learned.’ ”

Another key difference: the number of topics covered for a single grade: the AIR study frequently criticizes American math texts for being an inch deep and a mile wide, covering a great range of topics with little time spent on developing the material, including mastery of math facts.

The Singapore texts also present material in a logical sequence throughout the grades, and expect mastery of the material before the move to the next level.  “In contrast,” writes Garelick in the Hoover article, “mainstream American math texts and curricula frequently rely on a ‘spiral’ approach, in which topics are revisited and reviewed.  The expectation is that not all students achieve mastery the first time around.”

An Ohio schoolteacher summed up the “spiral” approach on an Internet math forum by writing that students “can’t remember how to do it when they do return — or if they do remember it, it’s now being taught in a different way.”

But the most important feature of Singapore’s texts, according to Garelick, is an ingenious problem-solving strategy built into the curriculum.  Word problems are for most students the most difficult part of any mathematics course.

Singapore’s texts help solve the problem.  A key step in problem-solving is model-drawing.

Typically, in US texts, students are taught to use a method called “Guess and Check” — trying combinations of numbers until the right numbers are found that satify the conditions of the problem (a method that many mathematicians consider inefficient). 

The Singapore bar-modelling technique not only provides a powerful method for solving problems, but also serves as a link to algebra.  Symbolic representation of problems, the mainstay of algebra, emerges as a logical extension of the bar-modeling technique.

On Your Mark — Get Set — Think!

The LA Times article describes the classroom of Arpie Liparian, a first grade teacher.  She stands in front of her class with a stopwatch.  The only sound is of pencils scratching paper, as the students race through the daily “sprint,” a 60-second drill that is a key part of the Singpore system.  The idea, once commonplace in math classrooms, is to practice problems until they become second nature.

Critics call this “drill and kill,” but one math coach calls it “drill and thrill.”  Liparian’s students don’t all finish all the problems in 60 seconds; only one girl gets all the answers right.  But they are all bubbling with excitement, and Liparian praises every effort.  “Give yourselve a hand, boys and girls,” she says when all the drills have been corrected.  “You did a wonderful job.”

That math coach, Robin Ramos, says that what isn’t obvious to the casual observer is that this drill is carefully thought out to reinforce patterns of mathematical thinking that carry through the curriculum.

“These are ‘procedures with connections,’ ”  Ramos says, arranged to convey sometimes subtle points.  This thoughfulness — some say brilliance — is the true hallmark of the Singapore books, according to advocates.

Yoram Sagher, a math professor at the University of Illinois, says that after 10 years of studying the Singapore curriculum, he still has “very pleasant surprises and realizations” while reading the books.  He is constantly amazed, he says, by the “gentle, clever ways that the mathematics is brought to the intuition of the students.”

It is true that the Singapore texts are not as teacher friendly as most American texts.  “They don’t come with teahers’ editions, or two-page foldouts with comments, or step-by-step instructions about how to give the lessons.  And in our math-phobic society, many teachers lack a strong math foundation to begin with.

Key to implementing the Singapore Math curriculum —  and achieving the spectacular results seen in a few select schools — will be intensive training of teachers.

sources: Barry Garelick’s Hoover Institution journal article  on “Miracle Math”from fall 2006; also Mitchell Landsberg’s article in the LA times on 3/9/08 (www.latimes.com ); and SDE flyers promoting the Singapore Math Intensive Institutes.