The high school football team loses 42–7, but the coach tells the newspaper his players showed a 100% improvement on offense as they were shut out last week. Parents are encouraged until somebody points out that going from zero to seven cannot be expressed as a percentage increase. The coach has now lost twice: once on Friday night and again in Monday’s math class.
Nobody needs a calculator, much less artificial intelligence, to determine who won. The scoreboard handles that nicely. The trouble begins when someone explains why the numbers mean something other than what they appear to mean. Students spend years learning to calculate answers. They should also learn to recognize when a number is being used to sell them something.
School announcements, sports reports, advertisements and college brochures provide enough material to keep a class occupied well beyond the bell.
Take basketball, for example. If a team doubles its victories from one season to the next, the coach calls it a turnaround and the athletic director calls it progress. Then a student checks the record: one win last year, two this year. There has been improvement. But whether that means the coach deserves a contract extension is another question.
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“Doubled” tells us the relationship between two numbers, but it can’t tell us whether either number is impressive. Students who understand that
distinction have learned something they can use long after forgetting the quadratic formula.
The principal’s office offers similar opportunities. Suppose a school announces that algebra failures have fallen by half. Wonderful news, unless the number taking algebra also fell by half. If 40 of 200 students failed last year and 20 of 100 failed this year, the failure rate remains 20%. The announcement is accurate, but the banner celebrating academic progress can stay in the supply closet.
A teacher could give students those figures and ask them to write two headlines. One would make the school look successful, while the other would explain what actually happened. That is a lesson in arithmetic, writing and reading tomorrow’s newspaper.
Classroom averages deserve scrutiny, too. Imagine five students scoring 60, 65, 70, 75 and 100. The class average is 74, although four of the five scored below it. The median, the middle score, is 70. One excellent result has lifted the average, but it has not improved anybody else’s understanding of fractions.
Students could experiment with the figures. What happens if the top score falls? What happens if the lowest rises? They would discover why different measures tell different stories. A single average cannot explain everything happening in a classroom.
For younger children, going shopping may work as a better example. A $40 sweatshirt offered at 25% off costs $30, while a different store sells
the same sweatshirt for $28 without a sale sign.
The first store has the more exciting advertisement and the impression that you’re getting a deal, while the second has the lower price. It helps to be able to calculate the discount to compare prices.
School lunch behavior can provide a lesson in surveys. Ask students standing in the pizza line whether pizza should remain on the menu, and the result will probably favor pizza. The children who brought sandwiches from home have somehow escaped this important exercise in democracy. Students could design a better survey, decide whom to ask and examine how wording affects the answers.
“Would you like a longer lunch?” might get enthusiastic support.
“Would you stay fifteen minutes later for a longer lunch?” introduces a complication, particularly among students with rides waiting outside.
One of my favorite sayings is, “Correlation doesn’t mean causation.” In plain English, it means that two things happening together does not prove that one caused the other. If we posit that students who eat breakfast earn better grades, does it mean that one influenced the other? Breakfast may help, but other factors may come into play, including those students may also sleep more, attend school regularly or have steadier routines at home. It’s a finding deserves investigation, but don’t give scrambled eggs a spot on the honor roll just yet.
The same caution applies to college earnings. Graduates of one college may earn more than graduates of another, but that alone does not prove the college made the difference. One may enroll more engineering students, the other more future teachers.
Comparing their salaries without considering their fields could tell a family more about the careers students chose than the education they received.
By high school, students should be able to carry these questions into their college search. Imagine ten graduates, nine earning
$50,000 and one earning $550,000. Their average salary is $100,000. Their median is $50,000. A family evaluating a college's
earnings claim should ask which figure describes the experience of a typical graduate. Schools need not leave this work entirely to
mathematics teachers. History, science and English all offer occasions to examine evidence. The American Statistical Association made that point in September when describing a forthcoming report on preparing teachers to teach statistics and data across subjects.
AI can calculate an average, summarize a survey or produce a graph, but students still need enough knowledge and context to judge whether the result actually answers their question. While a neatly presented answer can conceal a poorly chosen comparison, the goal is to teach children to ask sensible questions before accepting impressive claims.
What was counted? Who was included? What information is missing? When the football coach announces a breakthrough after losing 42-7, perhaps there’s one more question: Who are we playing next week?
Gerald Bradshaw is an international college admissions consultant with Bradshaw College Consulting in Crown Point.