Martin Gardner’s books (together with hundreds of others) adorned my father’s bookshelves when I was growing up. Filled with mathematical puzzles, many were accessible to me as a child. His clear, simple writing focused on the joy of untangling mysterious knots (sometimes literally). The New York Times profiles Mr. Gardner on the occasion of his 95th birthday, on the eve of the publication of his 70th(!) book.

He is the world’s best-known recreational mathematician, and has probably introduced more people to the joys of math than anyone in history.

Language is a uniquely human ability that evolved at some point in the six million years since humans and chimpanzees diverged. Even without being taught or having adults to copy, children develop sophisticated language systems. In contrast, reading is a skill that does not develop without intensive tuition and practice.

Since most of us learn to read as children, while at the same time building countless other skills, researches have found it nearly impossible to isolate brain structure changes related specifically to reading. In the October 14 edition of Nature, researchers describe a study with former guerrillas in Colombia who learn to read for the first time as adults. The study has helped scientists see firsthand how brain structure changes after learning to read as well as pinpoint the key regions of the brain involved in literacy.

These findings have the potential to further research into the causes reading disorders such as dyslexia. Studies of dyslexics have shown reduced grey and white matter in regions that grow after learning to read. The new study suggests that some of the differences seen in dyslexia may be a consequence of reading difficulties rather than a cause.

Believe it or not, teaching kids it’s ok to fail may actually help them learn. It seems that trying, and failing to retrieve an answer, is actually helpful to learning. If this turns out to be true, then “failing to learn” could take on an entirely new meaning.

In the article Getting It Wrong: Surprising Tips on How to Learn, authors Henry L. Roediger and Bridgid Finn, discuss research that shows, “People remember things better, longer, if they are given very challenging tests on the material, tests at which they are bound to fail.”

The study by researchers Nate Kornell, Matthew Hays and Robert Bjork has turned the idea of errorless learning (the old drill-em-and-kill-em) on its ear. Their findings, Learning, Memory and Cognition in The Journal of Experimental Psychology, demonstrate that students learn better when conditions lead them to make errors. Their results show that, “if students make an unsuccessful attempt to retrieve information before receiving an answer, they remember the information better than in a control condition in which they simply study the information.”

So how can students and teachers use failure to improve the way we learn? One idea is for students to attempt to answer the questions at the end of a chapter before they start reading. If the book doesn’t contain questions, students can follow the SQ3R method. Since 1946, this approach has been successfully adopted by students to formulate their own questions as they preview, or survey, a chapter. Teachers can help create opportunities to fail in the classroom by giving pretests prior to lectures and assigned readings. Both previewing and pre-testing direct the students’ attention toward critical concepts.

If this somehow seems counterintuitive, consider the following two experiments. In the study, The Pretesting Effect: Do Unsuccessful Retrieval Attempts Enhance Learning? [pdf], some students were given a pre-test on an essay they had not read, while others read the essay and either had their attention directed toward critical ideas with italics and bolding or were allowed additional time to study. The students who guessed first performed 10 percent better than those who had their reading directed or who studied extra. In a different experiment by Kornell, Hays and Bjork, students were to be tested on “weak pairs” of words. The first group was given 8 seconds to guess the other word in a given pair (the probability of guessing correctly was between 2 and 3 percent). Regardless of their guess, this group was then given 5 seconds to see the correct combination, such as star-night. The other group was given 13 seconds to memorize each set of paired words. As in the first experiment, the students who were challenged to guess the answers performed about 10 percent better.

I’m starting to think my kids already had this figured out for themselves. For years, my older son has driven us crazy by trying to solve math problems his way before following the steps shown in the textbook. As for my younger son, I cringe to think of the number of times I’ve begged him to study a spelling list or review his notes before asking me to quiz him. Each time, he refuses, saying he “learns it better” when he gets the answer wrong the first time.

Following their experiments, the authors concluded that “unsuccessful tests are helpful, not hurtful,” as long as feedback is provided. Their findings suggest “educators and learners should introduce challenges into learning situations, including using tests as learning events, even if doing so increases initial error rates.”

Dr. Florrie Ng of the University of Illinois built on Dr. Carol Dweck’s praise research (“Brainology: Motivated to Achieve!“) by telling American and Chinese mothers a lie.

During a manufactured break in student testing, Ng informed each mother that her child had performed below average on the first test in a study. Hidden cameras recorded American mothers avoiding negative comments and moving on to discuss other topics with their children. The Chinese mothers, who were just as warm and nurturing toward their children, were recorded making comments along the lines of, “You didn’t concentrate” and “Let’s look over your test.” These mothers spent the majority of the break discussing the test and its importance.

After the break, the Chinese kids’ scores on the second test jumped 33 percent, more than twice the gain of the Americans.

While Dweck and Ng focus primarily on how praise relates to academic performance, their research also demonstrates how various types of parental expectations can positively or negatively impact student persistence and motivation.

Turns out, there’s a circuit in the brain (or as Dr. Robert Cloninger puts it, “a neural network running through the prefrontal cortex and ventral striatum”) that controls how we respond to failure. With the right level of meaningful support, students can learn to use their internal reward center to exert more effort, even during long periods of delayed gratification. Kids with a can-do attitude have learned that perseverance, not external rewards or praise, is the key to overcoming obstacles.

For more on how to avoid raising a “praise junkie,” see the ABC News excerpt from the book Nurture Shock: New Thinking About Children by authors Po Bronson and Ashley Merryman. For parents who aren’t ready to quit the praise habit cold turkey, you can still help build motivation by making your kudos as specific and sincere as possible.

“Systematic phonics instruction produces significant benefits for students in kindergarten through sixth grade and for children who are having difficulty learning to read.”

A study by New Horizons for Learning identifies these common components of effective reading programs:

1. Phonics Instruction

The July 2009 Johns Hopkins study, Effective Programs for Struggling Readers concludes that an emphasis on phonics greatly improves tutoring outcomes, particularly in a one-on-one setting with a professional teacher. The phonics method of reading instruction breaks language down into its simplest components to help readers understand how letters are linked to sounds (phonemes) and spelling patterns.

2. Listening Comprehension

To help students improve comprehension, tutors and parents can intentionally teach listening skills by showing students how to figure out unknown words and stopping to ask questions about a passage (What do you think will happen next?, Why was that boy so excited?). Like reading comprehension, listening comprehension requires background knowledge on the content being presented.

3. Reading Comprehension

Current research shows that readers often struggle with reading comprehension due to lack of familiarity with the content. For example, a child who has never been to an amusement park may not understand a story about a roller coaster ride. On the other hand, cognitive psychologist Daniel Willingham writes, “If you take kids who score poorly on a reading test and ask them to read on a topic they know something about (baseball, say, or dinosaurs), all of a sudden their comprehension is terrific better than kids who score well on reading tests but who don’t know a lot about baseball or dinosaurs.”

4. Tutoring Opportunities

Every one of the programs studied by New Horizons for at-risk readers places a high value on private tutoring, agreeing that concentrated, individualized attention is critical to an effective reading program.

5. Extending Reading into the Home

According to those interviewed, the final critical component for students to acquire successful reading skills is to read at home every day.

Now students of all ages can make professional-looking graphs and charts with ease. The National Center for Education Statistics (NCES), the primary federal entity for collecting and analyzing data related to education, has created a free, easy-to-use graphing tool on its Kids’ Zone web site.

Sometimes, complicated information is difficult to understand and needs an illustration. Graphs or charts can help impress people by getting your point across quickly and visually.

From 3-dimensional bar graphs to pie charts and area graphs, it’s a breeze to input data at Kids’ Zone, and the output is as impressive as any chart ever produced by the father-of-charts himself, Ross Perot.

The most difficult step for students may be figuring out which style or format will best communicate their data. But never fear, the NCES has thought of this as well, offering a brief tutorial that explains when to use:

Line graphs: Line graphs are used to track changes over short and long periods of time. When smaller changes exist, line graphs are better to use than bar graphs. Line graphs can also be sued to compare changes over the same period of time for more than one group.
Pie Charts: Pie charts are best to use when you are trying to compare parts of a whole. They do not show changes over time.
Bar Graphs: Bar graphs are used to compare things between different groups or to track changes over time. However, when trying to measure change over time, bar graphs are best when the changes are larger.
Area Graphs: Area graphs are very similar to line graphs. They can be used to track changes over time for one or more groups. Area graphs are good to use when you are tracking the changes in two or more related groups that make up one whole category (for example public and private groups).
X-Y Plots: X-Y plots are used to determine relationships between the two different things. The x-axis is used to measure one event (or variable) and the y-axis is used to measure the other. If both variables increase at the same time, they have a positive relationship. If one variable decreases while the other increases, they have a negative relationship. Sometimes the variables don’t follow any pattern and have no relationship.

The NCES graphing tool also gives students a chance to control the look of their graph, including labels; font size and style, headers; and font, grid, and background color. A preview tab lets users check their creation prior to printing, downloading, or emailing. Graphs are saved on the site for 30-days from the last time viewed or edited.

Is your child’s teacher confusing poor reading comprehension with a lack of background knowledge?

With so much focus on decoding and fluency, background knowledge is often overlooked when evaluating students for reading comprehension. This entertaining video by cognitive psychologist Daniel Willingham demonstrates just how critical background knowledge is to our comprehension.

“Prior knowledge is vital to comprehension because writers omit information. For example, suppose you read He just got a new puppy. His landlord is angry. You easily understand the logical connection between those sentences because you know things about puppies (they aren’t housebroken), carpets (urine stains them) and landlords (they are protective of their property.)”

Fortunately there are strategies teachers and parents can follow to help students build background knowledge. But first, according to Willingham, “We have to recognize that reading is an interaction between the words on the page and the knowledge in the reader’s head. Without background knowledge, you can’t comprehend a text to a level we would call “understanding.”

A great number of parents who call TeamUP! Tutors are riddled with guilt. “If only I had called you sooner” is their constant refrain. But how is a parent supposed to know when it’s time to call-in the pros?

The education experts at GreatSchools.net encourage parents to catch the problem early. “The most compelling reason to hire a tutor is if your child is having trouble in school. In this case, don’t delay seeking help.” Criteria for families considering a tutor include:

• grades don’t reflect the amount of effort being put in
• homework is incomplete or done incorrectly
• student exhibits a lack of confidence or low motivation
• misbehavior at school becomes an issue
• student is anxious or ill-prepared for tests

The article points out that many high school students would have been better off with earlier one-on-one tutoring intervention. As true as this may be, we say stop the recriminations and focus on the challenges facing your student today.

A professional tutor and well-managed tutoring program can gradually to fill past learning gaps while addressing your child’s immediate learning needs. As your student makes progress, you’ll see that it’s not just tutor time. It’s guilt-free tutor time!

If only SpellingCity.com had been around during my children’s elementary school years. Today’s students can type in their spelling words, click a “test me” button, and have the computer take over quizzing responsibilities previously held by parents, in my case usually while attempting to prepare dinner.

The free tool’s friendly interface is easy to use and allows children to listen to a word, or hear it in a sentence, before typing their answer. For more challenging lists students can choose the “teach” button to have each word spelled and defined prior to taking the practice test. For extra practice, the site can also use spelling lists to generate word searches and scramblers, matching games, alphabetized lists, and crossword puzzles.

“The equation is simple: No matter what their background, students who take challenging math courses in high school get better jobs and earn more money throughout their entire lives.”

Do you have a reluctant math student living under your roof? The Math Works advocacy kit from Achieve.org is written for every student who has uttered the famous words: “I won’t use math in my job, so no sense suffering through more than I need to graduate.”

If this sounds even a little familiar, it’s worth your time to download Math Works, a series of one-page fact sheets written for high school students to explain the lifetime advantages of taking advanced math:

• Advanced Math Equals Career Readiness
• All Students Need Advanced Math
• Advanced Math: Closing the Equity Gap
• Americans Need Advanced Math to Stay Globally Competitive
• The Value of the Fourth Year of Mathematics
• Math’s Double Standard and Exposing the Myth: Advanced Math Does Not Increase Drop Out Rates

If your student is still not convinced that, regardless of post-graduation plans, engaging in rigorous math will lead to greater opportunities, the Mathematics at Work brochures may offer enlightenment. Drawn from leading industries nationwide, these case studies illustrate the advanced math knowledge and abstract thinking skills necessary to advance in today’s workplace.

For more in-depth reading, download The Building Blocks of Success: Higher-Level Math for All Students [pdf], a policy paper which synthesizes current research on why math is so important to all students and how it serves as a foundation for higher-order thinking and improves access and success in college and careers.

Created in 1996 by the nation’s governors and corporate leaders to help raise academic standards, Achieve is an independent, bipartisan, non-profit education reform organization based in Washington, D.C. The intent of the Math Works materials is to help policymakers, advocates, educators, parents, and students understand the connection between higher-level math courses and college access and success, workplace and career readiness, and personal and U.S. competitiveness.