The One Thing You’re Doing That Could Hold Your Child Back in Math

Have you ever had math anxiety?  If so, you’re not alone.  Many people claim to suffer from math anxiety – and expressing it can actually affect their kids.

Parents’ beliefs are contagious

Studies have shown that parents who express anxiety while helping their children with math reduce their children’s performance in first and second grades.  When mothers informed their daughters that they were not good at math, the daughters’ work in the subject declined.  

It’s not just the parents

Female teachers’ math anxiety has been shown to negatively affects girls’ math achievement.  In one study, the more anxious the female elementary school teachers were, the more likely the girls in their classes became infected with the stereotype that girls were not good at math – and the girls’ math performance was impacted in a measurable way.   The boys in their classes were unaffected. 

Why is math anxiety a problem?

Math anxiety affects math performance.  Math anxiety can have a disruptive effect on working memory, which is needed to attack math problems.  When a child is preoccupied with fearful and apprehensive thoughts, their brain is not fully focused on the challenging task at hand, putting them at a distinct disadvantage that affects their learning.  This is particularly common when children are given timed tests.

Higher level math will be a lot more important to the next generation.  American students, at a minimum, generally have to take 10 years of math classes to achieve a high school diploma – the least amount of education needed to get even an unskilled job in today’s job market.  Lack of confidence in math leads students to avoid certain careers because completion of high level math is needed for entry.  This doesn’t only apply to the obvious scientific occupations, many college business programs actually require two semesters of calculus.  

As time goes on, STEM careers will become a much larger part of the economy.  The working world will be transformed in radical ways in short periods of time.  For example, driverless cars could make taxi drivers and truck drivers obsolete within ten years.  Uber and similar companies are already making full time taxi driving a thing of the past.  Today’s kids will need a solid foundation in the STEM subjects to prepare them for a job market we can’t even imagine today.

So how can parents help their children learn math more easily?

If you struggled with math or have had anxiety, refrain from expressing it to your child.  Talk positively about how math (even simple computations) help you in your daily life today.  Praise all efforts and perseverance with their homework, even when they don’t arrive at the right answer at times.  If you’re a mother who has a daughter, let her know you are confident in her ability to achieve in math.

Parents can foster positive attitudes about math by stressing that math is a just a subject learned by practice and persistence.  There is no such thing as a “math person” and anyone can learn math.  Making mistakes is just a healthy part of that process – not proof of any lack of ability or intelligence.  In fact, making mistakes in math has been shown on MRI scans to make a person’s brain grow.  There is no race or gender that has any special advantage when doing math, those stereotypes are totally wrong.

Parents can help their kids learn math by encouraging them to play math enrichment games and do puzzles to develop number sense.  Visuals like board games are especially helpful for developing a child’s understanding of math concepts.  Spatial skills -  the comprehension and recall of the spatial relations between objects - are closely related to math skills.  Studies have shown that kids benefitted immediately after playing a number line game similar to Snakes and Ladders and a visual model of the positive and negative number line helped kids intuitively understand how negative numbers work.  The more kids play games and have fun with numbers, the less math anxiety and the more confidence they will have exploring math.

Click here to see: 9 Great PictureBooks to Help Your Kid Learn Math

Click here to see: 6 Simple Ways toImprove Your Child’s Math & Spatial Skills

What do so many girls hate math class?

Many of us women grew up hating math and believing we were no good at it.  Today girls echo these sentiments even though they are brought up to understand that girls have the same ability to understand math as the boys.  So, why is it that even today in America, girls still more consistently dislike math compared to boys?

According to Jo Boaler, Stanford University Professor and author of What’s Math Got To Do With It?  , girls tend want a deeper understanding of what they’re studying - they want to know why a formula works, why we use a particular formula, and where it comes from.   Girls aren’t satisfied with mechanically plugging in the numbers and giving the teacher the right answer without knowing why they are doing it.  Many boys share this desire as well, but the girls tend to reject math as a subject when they aren’t happy with the traditional way math is taught.

How math is taught is important because it is needed for many 21^st century STEM jobs.  If we are to have more women entering the science and technology occupations we need to retain women in the higher level math classes those fields require.  Women are just as capable at learning math as men – this is proven in the many countries where women achieve at the same levels as men.  We need to stop seeing math as an inborn ability rather than a skill that is learned through practice and persistence.

“In mathematics education we suffer from the widespread, distinctly American idea that only some people can be ‘math people.’ This idea has been disproved by scientific research showing the incredible potential of the brain to grow and adapt. But the idea that math is hard, uninteresting, and accessible only to ‘nerds’ persists.  This idea is made even more damaging by harsh stereotypical thinking—mathematics is for select racial groups and men. This thinking, as well as the teaching practices that go with it, have provided the perfect conditions for the creation of a math underclass. Narrow mathematics teaching combined with low and stereotypical expectations for students are the two main reasons that the U.S. is in dire mathematical straights.” Jo Boaler, The Stereotypes That Distort How Americans Teach and Learn Math

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What Does Your Education Level Says About Your Life Expectancy?

Did you know that how long you went to school can actually affect how long you live?  At every level of education, there is a difference in life expectancy.  This has been shown time and again in studies controlling for other factors such as income, race, and gender.  Getting a high school diploma is the first step in increasing one’s statistical longevity, and the advantages above the high school level continue to increase for each year incrementally.  There is a strong link between each year of post-secondary education and:

·        Seat belt use

·        Being a Non Smoker

·        Avoiding excessive alcohol (defined as more than 5 drinks in a sitting)

·        Having working smoke detectors in the home

·        Having a Body Mass Index (BMI) under 30   

·        Getting regular colorectal screening

·        Getting regular mammograms

·        Access to healthcare

Even when a 4 year degree isn’t completed, there are still measurable statistical improvements from the additional schooling.  For example, smoking is associated with a 6 year loss in life expectancy across the board, and for each year of education after the 12th grade, the number of smokers continues to drop.  This effect is paralleled with that of overeating and heavy drinking: each year of additional education reduces their odds by a quantifiable amount.  The education effect even extends to spouses:  for married people, their health is affected by how educated their spouse is – the higher the spouse’s education level, the better their health.

What is particularly interesting is that the cost of the unhealthy behavior doesn’t predict the connection.  For example, health insurance can be expensive even with employer assistance, and there are almost always co-pays.  So it is not surprising that more educated people have health insurance – after all, their income tends to be higher and they are more likely to work for employers that assist with the cost.  Lack of health insurance is a known barrier to getting adequate medical care.   People who have health insurance are more likely to use preventative care that has a measurable effect on their life expectancy - but the likelihood of screenings such as mammograms is still stratified by educational level.  And, there are sharp differences in people reporting being unable to see a doctor due to cost:  27% of high school dropouts, 18% of high school graduates, but only 8% of college graduates.

It’s understandable that there would be a connection between education level and access to health care.  But what about practices and habits that aren’t expensive?  Smoke detectors have a small cost but their implementation doesn’t follow income levels, rather, their use is predicted by educational attainment.  Similarly, it’s common knowledge that wearing a seat belt saves lives, it cost nothing to buckle up, and it takes almost no time.  In spite of those facts seat belt use isn’t universal, rather, it’s likelihood increases with education.  Each year of formal education adds 3% to the rate of seat belt usage.  And when it comes to harmful habits that clearly cost money to engage in - smoking, drinking, and overeating - they tend to be more prevalent the less formal education one has.

The association between life expectancy and educational attainment was not always so pronounced.  Back in 1960, studies showed very little correlation.  But perhaps it began with the 1964 Surgeon General’s Report on Smoking and Health, which resulted in a clear decline in the number of educated people smoking.  Since then, the amount and availability of health information to the average person has exploded.  During the last 25 years, the longevity disparity based on education has increasingly expanded.  In fact, the difference is widest in the youngest segment of the population and appears to be growing wider.  In the 21st century, higher educational attainment is becoming more and more of an asset in increasing an individual’s life expectancy.

If Your Child Doesn’t Develop This, Some High Paying Career Options Will Be Denied

“[I]t has been well demonstrated that children who do not acquire number sense early in their mathematics education struggle throughout their entire subsequent school and college years, and generally find themselves cut off from any career that requires some mathematical ability”. 

                               -- Keith Devlin, Stanford Mathematician

With technology changing, tomorrow’s job market will be dramatically different than today’s.  High tech careers, which demand excellent STEM skills, will grow exponentially and many jobs that don’t require a college education will be exported to lower wage countries – or replaced by new inventions.  Already college graduates enjoy a lower rate of unemployment and higher wage growth than those with a high school diploma according to a recent Georgetown University report. 

So, how do parents make sure their child is primed for success in the STEM-oriented job market they will ultimately face after graduation?

Part of developing a strong background in STEM will involve a good foundation in math.  Studies show that children who fall behind in the early grades tend to stay behind in high school.   A good grounding in math requires excellent number sense.  In fact, current US Common Core standards for math emphasize number sense as a fundamental goal. 

Number sense means:

• A basic understanding of what numbers mean (including fractions, decimals, negative numbers)
• Being able to use different ways to express the same number, for example, 50% or ½ or 0.5
• Estimating skills
• Rounding skills
• Determining the degree of precision needed in a situation
• Choosing measurement units to make sense for a particular task
• Comparing physical measurements between various systems of measurement (such as the English system and the metric system)

People with number sense are those who can use numbers flexibly.  Research with low and high achieving math students between the ages of 7 and 12 has demonstrated that the high achieving students use number sense.  The researchers concluded that low achievers are often struggling not because they have fewer memorized math facts at their disposal, but because they don’t use numbers flexibly.   A 3 minute video demonstrates this flexibility associated with number sense as applied to multiplication.

Without number sense, there is no foundation for advanced math understanding – just as without a knowledge of phonics and word meanings there is no advanced reading.  Mere memorization of math facts and regurgitation under timed test pressure is no substitute for understanding.  Today’s kids will need to build a strong base in number sense for tomorrow’s economy.  

6 Simple Ways to Improve Your Child’s Math / Spatial Skills

Spatial ability is the comprehension and recall of the spatial relations between objects.  Spatial skills and math skills are related to each other (see previous blog entry below).  When you improve your child’s spatial skills, you generally improve their math skills as well.  You don’t have to use high tech or expensive methods to help your kids’ spatial skills.  Here are some easy ways to give your kids an edge:

Board Games 

Board Games give children a great visual in the form of the board itself, and there are many that exercise spatial skills.  In clinical research, a game similar to Chutes & Ladders with consecutively numbered, linearly arranged, equal-size squares was shown to improve kids’ understanding of the number line.  Skippity is an easy visual strategy game that anyone who knows how to “jump” in checkers can learn within 1 minute, and requires kids to visualize each move they are contemplating before acting.   Robot Turtles helps kids understand the basics of programming displayed visually on a board.  Escape Medusa's Rage allows kids to visualize and understand the number line – including negative numbers – in a large, colorful graphic.

Jigsaw Puzzles

Children who play with puzzles develop better spatial skills.  A recent study by the University of Chicago found puzzle play to be an important predictor of spatial skills even after controlling for differences in the parents’ education, and household income.  When doing a jigsaw puzzle, children visualize where and how a particular piece will fit before they try it.  The trial and error aspect reinforces their correct guesses and helps teach them why some of their guesses are wrong.  Children are stimulated to learn by self-correction, and learn that persistence pays off.  Some puzzles even combine logical thinking with art appreciation, for example, puzzles of famous paintings such as Luncheon of the Boating Party by Renoir.

Building Blocks & Construction Toys 

Essential skills and ideas are practiced and built up through block play, including measurement, estimation, comparison, balance, and symmetry.  Blocks and construction toys come in such a wide variety of types – from traditional wood square cubes to plastic bendable toys like Reptangles, Squigz Benders or Joinks to variety boxes like Craft - Struction.  Many Lego sets come with plans that are given in pictures, not words, so that children can create regardless of their reading or language skills.  Kids sharpen their spatial skills by comparing what they’ve built with the diagram and correcting any inconsistencies.

Innovative STEM Toys

More complex than building blocks are new toys that are designed to address the growing interest in STEM (Science, Technology, Engineering, & Math).  Kids can learn by doing in the physical world, offline.  Thames and Kosmos

Kids First Aircraft Engineer gives kids the kit and instructions to build 10 simple airplane models including a helicopter. Snap Circuits allows kids to create their own electronic games and gadgets.  Goldiblox sets seek to inspire girls in particular with toys like their create your own Zipline Action Figure (including a doll that rides on the zipline). 

Mazes

Mazes are purely visual and teach kids to look before they leap.  They can choose from strategies like starting at both ends and meeting in the middle.  Printable mazes and toys that allow kids to create their own mazes are great ways for kids to practice spatial skills while having fun.

Coloring

Geometric pattern coloring books help kids create their own patterns using color and careful attention to detail.  Patterns of the Universe demonstrates 17 mathematical themes such as - Prime Numbers, Venn Diagrams, and Fractals.   

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9 Great Picture Books That Help Your Kid Learn Math

When asked, many kids will say that math is their least favorite subject.  Traditional methods involve formulas, drills, and no explaining why we are learning something.  But math doesn’t have to be this way.  Here are some great illustrated picture books for kids that explain math concepts – how they work in pictures, and most importantly, WHY these ideas are important and useful.

A Very Improbable Story

by Edward Einhorn

A boy wakes up with a cat on his head that won’t get off until the boy wins a game of probability using objects around his house

One Grain of Rice

by Demi

The power of compounding interest is said to be the Eighth Wonder of the World and is illustrated for kids by the story of a young girl who feeds her village by doubling a grain of rice every day for 30 days

Anno’s Mysterious Multpilying Jar

by Masaichiro and Mitsumasa Anno

Factorials, or multiplying 1 x 2 x 3 x 4….etc is demonstrated in a way kids can visualize

You Can Count on Monsters

by Richard Even Schwartz

The numbers 1 to 100 are illustrated as monsters in order to demonstrate what the difference is between prime and composite numbers

G is for Googol:  A Math Alphabet Book

by David M. Schwartz

Each page illustrates a concept in math such as binary code, exponents, and probability, along with where we see it in the world

Sir Cumference series

by Cindy Neuschwander

Sir Cumference, Lady Di of Ameter, and their son Radius are characters that simplify math concepts while telling entertaining stories set in medieval times.  Each book takes one topic such as the base 10 number system or measuring the area of a circle. 

How Much is a Million?

by David M. Schwartz

A wizard shows a group of kids what the number one million means in whimsical illustration

What's Your Angle Pythagoras 

by Julie Ellis

Pythagoras helps his father by discovering the secret of the right triangle and a practical use for it

Pythagorus and the Ratios

by Julie Ellis

Pythagoras and his cousins want to win a music contest, but can’t understand why their instruments sound so bad and so different from one another.  Comparing their instruments to his, Pythagoras discovers that notes that sound melodious together have certain mathematical ratios.

Why Developing Your Child’s Spatial Skills Could Help Your Child Learn Math

American universities report that a startling 60 % of incoming students need remedial math help.  It is a shocking fact that American students are paying additional college tuition to learn high school level math, in order to continue with their education.  After 12 years in school, why are so many not fully prepared for college?

Studies find that kids who are behind in math in the early grades tend to stay behind.  Math classes build on prior learning, so if a student doesn’t have a strong foundation in numeracy, they will continue to struggle in math.  And, many American children cite math class as their most hated.  So, can parents keep kids from falling behind and inspire an interest in exploring math?

Does your child like to play with blocks, puzzles, and board games?  If so, they are developing their spatial ability – and at the same time, improving their math skills.

Spatial ability is the comprehension and recall of the spatial relations between objects.  This ability is seen as a specific type of intelligence along with logical reasoning, verbal aptitude, and memory skills.  This type of intelligence itself is broken down into subtypes, such as the ability to rotate objects in one’s mind.

We use spatial skills in our everyday life, for example, when we parallel park, navigate with a map, catch a ball, or rearrange furniture.  Spatial ability is also used in math class, for example, understanding a number line, finding geometric patterns, or determining whether an object is vertically or horizontally symmetrical.

Spatial reasoning strongly correlates with math skills.  For example, children’s quality of block play at age four has been found to predict their math achievement in high school.  Also, when researchers directed fourth graders’ attention to the symmetry between positive and negative numbers (that -3  is the same distance from zero on a number line as + 3, for example), the students got better at solving problems in that area – and in higher level math they hadn’t seen before.

Spatial skills have been found to explain at least part of the difference in math grades between girls and boys.   Traditionally, boys have played more with toys like blocks and construction sets than girls.

Both math and spatial skills are not inborn abilities – they are learned through practice.  Math knowledge in the early grades lays the foundation and builds confidence for kids in the upper grades and beyond.  Parents who play math games with their kids help them improve their math performance.

Math board games often have a spatial element – for example, Chutes & Ladders arranges the number line into groups of ten, helping kids understand our base 10 number system, along with aiding them with addition and subtraction skills.   Playing games and doing puzzles are great ways to stimulate a child’s spatial and math skills while having fun. 

There is no such thing as a “math person”

The best way to learn is to play.

Pay Gap Between High School & College Educated Americans is at Widest Ever

College graduates earned 56% more on average than high school grads in 2015, according to recent reports by the Economic Policy Institute. This is an increase of 51% in 1999 and is the largest increase since the EPI began tracking this data in 1973.  College graduates were also employed at a higher rate to begin with (83%) than high school grads (66%). 

It used to be that a person could drop out of high school and get honest work that paid enough to start a family with.   Things changed slowly, and businesses operated using landline telephones and the mail.  People expected to be in their line of work for a lifetime.  Society had a need for people to do work that doesn’t exist as an occupation in today’s high tech, self-serve environment. 

For example, there was a time when even an elevator required a trained professional operator (see Why Elevator Operators Went Extinct) But improved technology eliminated that job, and the elevator operators had to look for other work.  Most parents today know what steno was – but our kids don’t because dictation is dead thanks to word processing.  Kids also don’t plan to be travel agents anymore – there are still a few, but they mostly operate at the luxury end of the market.  Will cab drivers be next thanks to driverless cars?  Or is Uber already making full time driving as a profession obsolete?

But the wage disparity didn’t start with the iphone or the internet.  According to the EPI, a large gap in wages goes back to 1979.  The average of the bottom 90% of American workers by income was $28,559.  By 2015, it only averaged $34,481 (about 22% higher, 36 years later).  The top 5% of wage earners averaged $142,817 in 1979 and by 2015 were earning, on average, $287,983 – more than doubling during the same time period.  As more of the simplest jobs become automated and technology changes, there will be more need for educated workers such as computer programmers and healthcare specialists.

All signs point to the importance ofa college education in the 21st century.  To be sure, there will always be some jobs that don’t require one.   But as the simplest jobs become automated, there will be fewer to be had.  The only thing that seems certain is that today’s kids will need a solid foundation in STEM (Science, Technology, Engineering, & Math) along with a college education, to achieve the American Dream. 

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How Can Using Symmetry Help Teach My Child How Negative Numbers Work?

What Does Symmetry Have to Do With Teaching Kids About Negative Numbers?

Negative numbers are closely related to the idea of symmetry. Students use their perception of visual symmetry to help them understand the abstract symmetry of integers along the number line.

Using symmetry appears to help not just in teaching children negative numbers, but in improving their ability to solve higher-level math problems they haven’t seen before.  In studies, participants were likely to incorporate symmetry as an almost automatic part of their thinking. That’s important because many skills – such as decoding words in reading – are more effective when they become instantaneous and reflexive.

The biggest surprise was on what educational researchers call “generativity” – the tendency of kids to apply the ideas of symmetry on their own to problems they haven’t encountered before.   They did surprisingly well with word problems using spatial positions, negative fractions, and introductory algebra.

So as it turned out, students who learned to rely on symmetry didn’t simply do better than other students on the material they had just been taught. They also did better on math topics that they hadn’t yet studied.   

Research has also shown that the more parents of kindergarteners do math related activities with their children – such as board and card games – the better their math performance in 1st and 2nd grade. The good news is that math skills are learned through practice, and math knowledge is gained through experience. Playing a game makes that process fun and easy.   

The best way for kids to learn anything is through play

Creature Quest is the math board game that teaches kids how positive & negative numbers work

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