How Practice Helped Me Learn the Pythagorean Theorem and Can Help You Too!

When I was a kid, I learned that “the shortest distance between two points is a straight line.” I read that in a math book and memorized it, but it meant very little to me. The factoid stayed with me, though.

My path to school

My path to school

I grew up on a military base, and family housing was large apartment buildings set at right corners to one another with a wooded area in the center.

Every day I left my apartment in the far-left corner of one building, walked along the front of the building, turned left, walked along the front of the next building, and then arrived at school. It was a boring, repetitive walk, so one week, I decided to test out that “shortest distance” idea to see if the straight line through the wooded area in the middle of the apartment buildings would indeed be shorter. I did my experiment over two days. Day one, I took my normal route and counted my steps. The next day, I took the straight path through the woods and counted my steps. Lo and behold, the shortest distance to school was indeed a straight line! (I then worked a little Pythagorean Theorem on my right triangle path to school and solidified that knowledge as well!)

I share this little story about my youthful nerdiness to talk about something training often overlooks or improperly applies: the necessity of practice. Practice is critical to the development of new skills. It allows learners to apply new skills and receive feedback on the results. The process of practicing increases learning in a way that simply reading about a skill will never do. If I hadn’t done my little path-to-school experiment, these math concepts would have remained facts to memorize rather than becoming truths understood by experience.

Once you acknowledge the importance of practice, how do you ensure the practice is effective? To increase practice’s effectiveness:

Space it out. Practicing activities with a few days between sessions helps put the learning in long-term memory. The work we do to remember what we learned a few days ago strengthens our memories! In my example, I learned that geometrical tidbit about straight lines in 7th grade and tested it in 8th grade when learning about the Pythagorean Theorem jogged my memory. Clearly, I still remember both some 30 years later!

Weave it together. When you weave together concepts or skills within the same lesson, as opposed to the traditional learning structure of focusing on one concept or skill at a time, the contextualization makes the concepts truer to life.. Think of how you communicate: you ask questions, listen, and reply all in one conversation, so learning listening, questioning, and other conversational skills together gives them greater context and meaning. When you mingle old concepts with new concepts, you’ve added spaced practice too, which increases the training’s efficacy.

Mix it up. Varying the types of practice activities and the way skills are practiced increases learners’ abilities to transfer learning from one situation to another. Plus, because different types of practice activities engage different parts of the brain, memory is strengthened. We probably used worksheets when we learned geometry (though I can’t remember them), which is one kind of practice. Pairing that with some hands-on activities (like my path-to-school experiment) truly drives home the learning.

Practice is an important part of any training program. Practice that is spaced, with concepts woven together, and that includes a variety of activities is statistically more effective than practice that excludes these three aspects. Effective practice equals improved learning.