Encouraging Mathematical Thinking

Parents, do you want to encourage your young people to think mathematically? Here are some ways to accomplish that.

Preschoolers

Nurturing Mathematically Talented Preschoolers—While it can be difficult to find programs for three- to five-year-old mathematically precocious children, there are things that you can do at home to encourage and feed their talents. Click on the link above and find suggestions that include

• Specific building materials, including LEGOs, Tinker Toys, Lincoln Logs, K’nex, Magna-Tiles, tangrams, and blocks of all shapes and sizes. Ideas are also provided for using these building sets.
• Ways to use mathematical logic in everyday conversations
• Ideas for working with fractions

There is no need for formal lessons. All of the suggestions provided are applied through play activities.

Elementary School Students

10 Practically Fun Math Games and Activities for Your Preteen—While the title of this article suggests that young people be close in age to teenagers, many of these activities are appropriate for much younger children. Author JC Ryan lists eight indoor activities and two outdoor activities that parents may not automatically think of as building math skills.

Kindergarten through High School

Have You Seen These 8 High Quality, Free Maths Websites?—Activities here cater to an enormous range of abilities and offer math related subjects from basic counting through calculus, current economic theory, and puzzles.

Alternatives for Gifted High School Students

Some high school students are ready to move on academically long before their peers. As stated in High School Alternatives for Gifted Teens, “It’s easy to find stories of 13-year-olds going off to college, but many gifted kids just aren’t ready to leave the nest early.” At the same time, they may have already finished or tested out of the regular high school curriculum. Author Suki Wessling suggests that students in this situation investigate

• Alternative schools
• Community college classes
• Private schools, if they can be flexible with your student
• The book, Serving Gifted Learners Beyond the Traditional Classroom: A Guide to Alternative Programs and Services 
• Online high school courses
• Homeschool 

In addition to the suggestions above, check out the OpenCourseware Consortium, which is a collaboration of higher education institutions and associated organizations from around the world creating open educational content that is free to the public.

A student who finishes high school early might also take a year or two to pursue her passions in a very focused manner, furthering her studies in music, theatre, art, dance, language, cultures, science, etc.

The best solution for finding answers to any education dilemma is often a combination of possibilities.

Free Guidebooks to Help Exceptionally Bright Children

The Davidson Institute serves profoundly gifted young people under the age of 18. As part of its mission, Davidson Institute professionals have written a series of guidebooks designed to assist families in finding the most appropriate educational settings for their exceptionally bright children. The guidebooks are excellent resources and can be downloaded at no cost. While the guidebooks are written for parents and students, teachers should also become familiar with them so that they can effectively advise families.

• Advocating for Exceptionally Gifted Young People—What should you know about your child? What should you know about gifted education? How should you formulate a plan? How should you approach your child’s school? How can you monitor your child’s education?
• Investigating Early College Entrance: A Guidebook for Parents and a Guidebook for Students—How does one assess whether a student is ready for early college entrance? How might early entrance impact the family? What about scholarships and other financial aid?
• Investigating Gap Year Opportunities—A gap year is a “break from formal education to become more immersed in another culture, to volunteer domestically or abroad, to gain experience and maturity…” It is becoming more common in the U.S., especially for students who graduate early from high school. This guidebook discusses possible options for a gap year, the pros and cons of taking a gap year, and what colleges think of students who pursue this option.
• Volunteerism and Community Service—This guidebook provides resources, strategies, and valuable information to think about when considering the who, what, where, when, how, and why questions associated with volunteering.
• Considering Homeschooling—Readers will find information on homeschool curriculum, applying to college, cost considerations, networking with other families, homeschool laws and more.
• Mentorships—How does one search for a mentor? What types of mentoring relationships are available? What characteristics should a great mentor have?

Exercising Minds through Questioning

Bright students often come to class thinking they must know all the right answers. What they (and many adults) may not realize is that thinking is not driven by answers, but by questions. It is the sense of wonder and curiosity that drives understanding. As the old saying goes…The more you know, the more you realize you don’t know. The more you learn about a subject, the more you realize there is to know. Perhaps having students list thoughtful questions at the conclusion of a unit would be a better determiner of knowledge gained than taking a test.

Young people learn to develop inquiring minds when they hear their parents and teachers ask thoughtful questions of themselves and others. One way to do this is to use Socratic Questioning. Socratic questions help to

• Clarify issues
• Question assumptions
• Justify statements
• Understand the ideas of others
• Imagine consequences
• Relate different issues 

Divergent questions are also useful. They usually begin with words or phrases such as

• Imagine…
• Suppose…
• Predict…
• If…, then…
• How might…
• Can you create…
• What are some possible consequences…

Here is one example of questioning for young children in kindergarten or first grade after reading and discussing Jack and the Beanstalk.

Q. What did Jack do when he got to the giant's castle?"

A. Jack hid from the giant, found the goose that lays the golden eggs, was discovered by the giant, fled, reached the bottom of the vine, and then chopped it down. The giant, of course, tumbles down, breaks his neck, and Jack lives happily ever after with his mother and his newly found wealth.

Q. Did Jack trespass illegally? (In kindergarten terms, "Did Jack go into someone's house where he did not belong?")

A. Yes!

Q. Did Jack steal the goose that lays golden eggs?"

A. Yes!

Q. Did Jack, then, refuse to give back what did not belong to him?

A. Yes!

Q. Then did Jack escape down the bean vine and cause the giant to be killed?"

A. Yes!

Q. If Jack trespassed, stole, and murdered the giant, why is the giant the villain of this story?