Learn to Identify - and Make the Most of - Six Opportunities in Mistakes

The ShillerMath philosophy says that every mistake is a learning opportunity because it encourages discussion and improves understanding of concepts and process.

Are you getting excited about your child's next mistake?

Parents with children that reach their full potential have a clear strategy for dealing with mistakes because they will occur early and often. The language a parent uses in identifying and correcting mistakes has a huge impact on how well or poorly the child will learn and enjoy math.

Education expert Larry Shiller suggests the following approach when a mistake is made:

    1. Focus on the process, not the person. When they mess up, children, like adults, don't like to hear that they are a lesser person (because they're not); blaming a child for a mistake discourages interest. Try using phrases like, "Does that seem right?" "I might've come up with a different answer. Let's take a look at the steps we are using to solve this problem." "I would've got that answer wrong too! Let's see how we can get to the correct answer and understand why it's correct." Or: "Maybe there's a different approach; let's start from the beginning to get it right."

    2. Keep a sense of humor. When a child associates math with laughter and warm feelings, it's bound to be a good and lasting one.

    3. Use the other senses (touch and movement, hearing, sight, smell). Math is best learned when it is concrete before it is abstract. Put the audio CD on and sing and dance along. Use the manipulative index to find an activity that uses a favorite manipulative.

    4. Be creative. Feel free to extend the activity or game in the lesson - or make up games as you go along should the urge strike. The ShillerMath.com customer downloads page opens a whole new world of arts and crafts that make math fun.

    5. Mistakes are opportunities to identify holes in the child's knowledge or approach. ShillerMath recommends employing the Socratic Method of questioning to help the child discover his or her own error. Once the hole is known it is usually easy to "fill." Be sure the reasons for the mistake are well understood before moving on: "This card says three thousands and you have two thousands. How many more thousands do you need to have three thousands? That's right: one more thousand. You may get another thousand."

    6. Go back to basics. Revisit the Montessori Three Period Lesson of "This is, Show me, What is," which is explained fully in the ShillerMath Parent Guide and lesson books.

All this talk on mistakes; what about when the child does something correctly? One word: PRAISE. We will explore praise more in a future blog post. In the meantime, don't miss out on treating a mistake as an opportunity. Keep in mind that these tips work for all areas of learning, not just math.

Who was Maria Montessori?

Born 1870 in Chiaravalle, Italy, Dr. Maria Montessori, Italy's first female physican, developed a unique educational approach that for nearly 100 years has been successfully applied to millions of children worldwide, starting with children with learning difficulties and extending today to children of all intellectual and socio-economic levels.

The Montessori method considers children to be intelligent and highly capable of learning when placed in an environment and with materials that provide them with respect and privacy. It includes three key elements:

  • Motor education
  • Sensory education
  • Language

The Montessori - ShillerMath combination helps children to learn math and language arts and to become productive members of society throughout their lives.

For more information on the Montessori approach, you may visit these informative sites:

An excellent book on the Montessori method is Teaching Montessori in the Home: The Pre-School Years by Elizabeth G. Hainstock. This is one of many books written for parents about Montessori that are available online or at your local library or book store.

The US Math Crisis

We have a math crisis in the U.S.

Maybe that's the least of our problems. But maybe not. Consider this:

  • 80% of US 8th graders cannot calculate fractions, decimals and percentages
  • 40% of US 4th graders cannot tell NE from SW on a map

It's really just us. The world does better:

  • In Germany 35% of teens take and pass advanced placement exams; in the US it's 4%
  • In Japan kids start algebra two years ahead of those in the US

What are the repercussions?

  • In the California State University system 60% of Freshman are required to take remedial math and science classes
  • One in five adult Americans cannot:
    • Calculate the total of a purchase w/tax & tip
    • Locate an intersection on a road map
    • Enter background information correctly on a form
  • MIT economist Lester Thurow says that only 20% of Americans have the work skills and education to be competitive in the global marketplace

And no one believes it! In a recent study 71% of high school parents say that they are satisfied with the math education their children are getting. Ouch.

The US has a math crisis. And the repercussions are serious. Join ShillerMath in creating better outcomes for our children and country.

The MultiSensory Approach

Your child completes a lesson correctly - say it was a visual / writing lesson that requires looking at a picture and doing a simple calculation. And then the child successfully completed several drill questions on the same material. Does that mean your child has mastery and a full foundational understanding of the topic covered?

The problem is that this lesson and drill only reached 30% of the child's brain. The other 70%? Not getting this concept.

The 30% that was reached was the visual part of the brain: the neurons from the retina. What about other neurons? Consider for example, if the student was given the opportunity to approach the problem in another lesson with his or her hands ("tactile"). The neurons in the fingertips that sense pressure and temperature reach a completely different part of the brain. Imagine that a second lesson imparts the same concept to the student from a tactile perspective. Now 50% of the brain is in use - and connections between the visual and tactile parts of the brain are made, creating a foundation or web of knowledge that lasts much longer and better supports future learning.

Imagine four lessons on the same concept - one each for Visual, Tactile, Kinesthetic, and Auditory neurons. Now the child's brain is being engaged 100% - to its fullest potential - and connections are rampant. Only then will a child truly have mastery.

A building constructed on only 30% of its foundation won't get very tall until it topples over. That's why the USA 3rd graders score well on international tests but 15 year olds don't: Because they're being taught to use only 30% of their brain.

The four main senses:

  1. Visual. Neurons from the retina.
  2. Tactile. Neurons from the fingers and skin.
  3. Kinesthetic. Neurons from muscles. The thighs, abs, and shoulders are the largest muscle groups. By using these muscles (throwing a ball or otherwise physically moving the body) a completely different part of the brain is involved - one that is nearly always missing from math and language arts curricula.
  4. Auditory. Neurons from the ears. Different materials make different sounds. And songs cause the brain to be involved in unique ways.

Without a complete multi-sensorial experience children lose the richness that comes from absorbing the same material from all the senses: Visual, Auditory, Tactile, and Kinesthetic. Only then will a student form a rock solid web and foundation of knowledge and ability.

Whether your child is gifted, ASD or normal, is a current or former Montessori student, or not, is a pre-K student or in junior high, make sure that the math and language arts programs for your child includes a multi-sensorial approach like the one used by ShillerMath.

Welcome to ShillerMath!

Hi, I'm Larry Shiller, and I'd like to personally welcome you to ShillerMath - and the ShillerMath blog.

From time to time I'll share customer stories, latest thinking, upcoming sales, math learning tips, new product plans, math in the news, and random thoughts.

I'd love to hear from you - it's our customers and prospects and their children that keep us growing and learning.



Larry Shiller