According to Merriam-Webster, percolate means “to pass slowly through something with many small holes in it” “Percolate.” Merriam-Webster.com. Merriam-Webster, n.d. Web. 17 Nov. 2016.. It’s a wonderful analogy to the process of learning math, especially the more difficult concepts of higher math. Time and patience are required for a liquid to percolate through a fine sieve. Our brains are no different. But, we live in a time where expediency seems to be the measure of the facile brain. Kids that learn concepts quickly are viewed as the smartest in the class to the detriment of the slower learners who are left behind or marginalized.
My students work hard (for the most part) to master new concepts in math, and as they progress through a unit that builds upon itself they should be ready for the test. That’s not always the case. Often they get to the test, and the concepts are still a swirl of formulas and processes that haven’t settled into their appropriate home in their brains. They must work very hard to apply a particular concept or concepts to more difficult questions – the types of questions put at the end of a test that count for many more points than the easier rote questions testing skills mastery. For example, a student learning the concepts of factoring quadratic equations such as y=6x²-5x-4 into its factors (3x-4)(2x+1) is attempting to master a difficult new skill that uses math facts and integer mastery. There are processes I can teach them to make the task easier, but when this concept is placed into the framework of a word problem the task gets much harder. The typical word problems for quadratics are area problems and projectile problems. Both will require the student to use skills from other areas of math. The area problem will require the use of geometry formulas. In addition, they will have to recruit skills for building math expressions from word phrases, a very hard concept for some learners. If they fail at any one of these skills, then they will miss the entire problem.
Many of my students complain that they don’t get enough difficult questions for practice, so they can master blending concepts before the test. I agree with them. Skills work is not enough practice to help them harden concepts in their minds. They must play with the concepts and use them in a variety of situations, so the necessary connections are made across different areas of the brain. It takes time and patience for this type of learning to happen. And for some students, it will take longer than the rest of the class.
The US is lagging behind other countries in STEM scores, not because we aren’t capable of mastering these subjects, but because we don’t let kids play and explore with math. They have to see the applications for math, so the rote work will have a point.
My students ask me all the time, “when will I ever need to use the concepts of special right triangles or the unit circle?” I’ll respond by asking them what careers interest them – programming, engineering, business, doctor, or art (to name a few). I can see applications of math to all of these careers, even if they don’t. Jobs in the future will depend on students who have a passion for STEM, STEM jobs article. I am always trying to pass my love of math and science to my students. I think it is the most important part of my job, so I am patient. I wait for the ideas to percolate into their very capable brains (even the slower ones) because I want them to have every opportunity possible when they are adults. Learning shouldn’t always be about speed, some of our best and most creative minds take their time, letting ideas percolate before charging ahead with the first idea to pop into their mind.
This post is in response to the daily prompt, Percolate. Daily Prompt: Percolate