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.

The Do-It-Yourself Movement

The Atlantic carried an article titled School for Hackers: The Do-It-Yourself Movement Revives Learning by Doing. The article is consistent with the project-based learning concept where students explore real-world problems and challenges.

Because we have become so used to providing young people with ready-made toys and technology, we often miss opportunities for them to use their own ingenuity to problem solve and create. In addition, we are not passing down what used to be common knowledge about folk crafts, creative cooking, model building, woodworking, gardening, collecting, etc. There is a movement now to revive the do-it-yourself (DIY) philosophy and get kids involved in building and creating.

Through the do-it-yourself movement, students learn research skills, understand subject matter at a deeper level, and are more deeply engaged in their work.

When a young person builds a model rocket, or a kite, or a birdhouse, she not only picks up math, physics, and chemistry along the way, she also develops her creativity, resourcefulness, planning abilities, curiosity, and engagement with the world around her.

There are many resources that will help you introduce kids to the DIY movement.

• Hobby shops—both store fronts and online varieties have all kinds of materials and kits.
• Knitting, sewing, and quilting stores have not only supplies, but often offer free or low cost instruction.
• Home Depot often has building classes specifically for children.
• Local summer camps, workshops, and clubs such as Tinkering School.  
• Fifty Dangerous Things (you should let your children do)—plenty of exciting ways for your children to explore the world around them.
• Magazines such as Make where you will find an archive of fun projects for kids of all ages.

Self-Directed Learning for Gifted Students

Taking the initiative to design one’s own learning may be the ultimate educational experience and can be used with homeschoolers, in the classroom, or independent of any school environment.

Directing one’s own curriculum as a child becomes the basis for lifelong learning as an adult. It opens the door to pursuing subjects and activities that are personally interesting. Passions develop because one is able to choose the content and the timeline. The topic may or may not be a traditional academic subject: both are valuable.

In a typical school situation, students are told what to study and they are given timelines for accomplishing specific tasks. While this traditional method builds many skills and can produce a lot of knowledge, young person may only learn to do what she is told and not learn to love learning for learning’s sake. Parents and teachers can encourage young people to walk down the path of passion.

Resources for self-directed learning include:

• Self-Directed Learning—This site provides ideas for teaching self-directed learning and for becoming a self-directed learner. It also includes articles, archived newsletters, and links to other helpful websites.
• Self-Directed Learning—This article includes an explanation of self-directed learning, lists its benefits, and discusses what teachers can do to help the process.
• The International Society for Self-Directed Learning —For those who really want to study the concept of self-directed learning. Here you will find back issues of this organization's journal.

Fostering Focused Interests

Decades ago, I used to edit an antiques and collectibles tabloid. The publication contained many interviews with people who studied and collected specialty items. I was amazed at the items that wound up in these collections, the numbers of people who became passionate about their areas of interest, and the amount of information that could be learned from trivia that may have seemed meaningless to the rest of society.

One man’s house was filled with bells of all sizes. Another person’s basement contained display cases of pencils. Still others collected vintage buttons. Each of these people could cite all kinds of historical facts about his collection.

A visit to eBay will also reveal the number of people who collect and sell special interest items. These are not hoarders. These are people who genuinely get excited about their area of interest and learn everything they can about it.

Young people also may find niches that allow them to focus their learning through collections. Really being able to “get into” a subject builds traits that may transfer to more traditional areas of learning and also guide students to future work. Some of these traits include:

• tenacity
• networking with others of like minds
• creativity
• stress reduction
• pride in one’s accomplishments
• setting and working toward goals 

While there are many hobbies, collections, and special interests from which a child may choose, I will use trains as an example to illustrate my point. As parents and educators, we want to encourage young people to pursue their passions. Here are some possible ways to do that with trains.

• Museums: When you’re traveling, take time to visit railroad museums. For a list of railroad museums across the nation and throughout the world, visit RailMuseums.com.
• Train Stations: Click here for a list of train stations around the world. Some have historic architectural significance and some are very modern.
• Build a Model Railroad: Building one’s own model railroad is a fantastic way to enhance creativity, work on fine motor skills, manage money, learn to read and understand detailed instructions, and plan. Such hobbies often begin in childhood and continue long into adulthood. For learning all about building a model railroad, check out Building Your Model Railroad.
• Books: Want to learn about the history of trains and railroads and the people who were most influential in creating them? This information will help a student to understand the development of transportation and help put general history in perspective. One also can learn about today’s high-speed trains and commuter systems, the future direction of rail travel, and how that might influence societal trends. For a list of railroad books, go to sites such as Railroad Bookstore or Golden West Books.
• Train Clubs and Organizations: Clubs and organizations are great places to not only learn about your hobby, but also to meet other people with the same interest. Adult members may act as mentors to young people, providing encouragement and expertise. For a list of model railroad clubs, go to Rails USA and search by your state.
• Take a Ride: Consider a vacation by rail or just a ride downtown on a commuter train. See listings at Train Traveling. Search local transportation systems such as light rail, subways, and elevated trains at local public transportation sites. 

You can take any subject in which your child shows an interest and brainstorm all of the possible ways to support that interest. You never know where it may ultimately lead.