Straight Line Reasoning

If you haven’t already, please first take a look at Richard Erdmann’s Youtube video on Factfulness below. Then read his expanded thoughts in this blog!

Think of the four computational operations – addition, subtraction, multiplication and division. Which is the easiest? We tend to like addition – it is easy. Now think of two lines on a graph. One is a straight line and one is curved. Which one is likely to be easier to describe with an equation? The straight line. For every fixed increment on the Y axis, you can add a fixed increment on the X axis and plot the line.

For most of our lifetimes population growth has been a straight line on a logarithmic scale. That is a fact. Factfulness shows us a graph with a straight line describing world population growth for the past roughly 50 to 60 years. If we extend the line, we discover that the world will almost double in population by 2100. It will reach 15 billion. That is a fact. But the birth rate in the world is declining. So much so that the straight line moving up the graph will begin a curve that has a leveling effect before 2100 and the population is likely to be only 11 billion and reasonably stable. Factfullness calls this tendency to think linearly the straight line instinct.

So, now you are a teacher and you look at the textbook. You have 180 days to cover 360 pages. You use a straight line approach. You have to cover two pages a day but you have a nagging suspicion that it is not that easy.

But you are not the only one looking at the textbook. So are the principal, the district and the state. They plot the book out on the calendar and hand you a pacing guide more or less built on a straight line – a linear equation. Then they say, “we are going to come into your classroom once in awhile to observe and one thing we will evaluate is whether or not you are on the right page. Are you keeping pace?”

“Wait, wait,” you say. “Learning is complex, it is not linear. The graph is curved. If I want the students to remember what they have learned, I need them to repeat it. As the required repetition accrues, the new learning in terms of pacing slows down. I will catch up at the end of the year because my students will not need test prep – they will remember and for a long time, but by the end of the year you will have marked me down. That is not right.” In addition, you know that even the curve can be misleading because learning takes place in fits and starts. There are plateaus – like in losing weight. You get a strong start, then it diminishes and once in awhile you stagnate or even worse, you can a few pounds back. Learning is like that. The curve will describe an average for your students but individually their learning will consist of peaks and valleys.

Your argument is correct but the mental trap is strong. The straight line is just so easy to predict. The curved line is more difficult. Again, Factfulness suggests that you never assume a straight line and question it when you see it. Straight lines are the easy way out and often incorrect.

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