Generally speaking, most schools do Algebra I in 9th grade, Geometry in 10th grade, Algebra 2 in 11th grade, then Pre-Calculus in 12th or maybe Business Math. Some try to accelerate that by a year and start Algebra I in 8th grade and have students taking Calculus in 12th in order to be prepared for STEM courses in college.
But a podcast I recently listened to challenged my thinking as a math teacher. Is this really the best preparation we should be giving teens in high school? Here are some of the points I took away to “chew on” — still thinking. . . (See my initial conclusions at the end of this article.)
What’s the “norm” for math education?
In the 1960’s when the Russians sent their Sputnik space craft into orbit before the United States, we as a nation began putting more of an emphasis on math and science in the typical high school curriculum. Around that time is when the “Algebra-Geometry-Algebra 2 Sandwich” became the norm in schools, where the learning of Algebra was interrupted by a year of intensive geometry. Today many schools are pushing teens into algebra sooner and trying to get them through a year or two of calculus before high school graduation so they will be ready for STEM programs in college.
Has this American approach to teaching math been successful? In terms of how U.S. students perform relative to students from other countries, the answer is “no.” On the most recent Program for International Student Assessment (known as PISA), a standardized test administered in 70 countries, the U.S. placed 39th in math, just behind Hungary and Slovakia. American math performance is substantially worse than on either science (25th place) or reading (24th). (quoted from Freakonomics article referenced below)
Should our math curriculum change compared to the 1960s?
Our world has changed since 1960. We have calculators and computers in our hands every day. We are in an information age which means we are collecting data faster than ever before, but we are not producing students able to filter, organize, and interpret the data.
Another skill lacking but needed in today’s marketplace is the ability to use data to create meaningful graphs and tables to support arguments in communicating with others. This skill is needed in almost every profession today.
A third critical skill that needs to be developed is the ability to read and properly interpret tables and number data presented in books, articles, and presentations. You’ve heard the saying, “Numbers don’t lie – but liars know how to use numbers!” Critical thinking skills are needed to look at numbers in presentations and determine if they are being used in a correct way.
What math is used in “real life” jobs?
The staff of the popular Freakonomics Podcast did an informal survey of their listeners and found that only about 2-4% of people in “the real world” actually use calculus and geometry on a regular basis if at all. But over 80% said that they do use Excel or Google spreadsheet programs to create and then manipulate data and present it to others on a regular basis. But how many teens finish high school somewhat proficient in using a spreadsheet program?
Another survey was conducted to find out what math is most widely used and needed for success in real-life occupations. The answers might be a little surprising. Here’s what David Coleman, the C.E.O. of the College Board says:
“The first is the most humble, but it’s powerful, it’s arithmetic. The command of the four operations: subtraction, multiplication, division, and addition — but crucially, fractions.
“The next area of math that’s hugely predictive of your future success is what I would call data analysis and problem-solving, including rates, ratio, proportion, designing quantities that interact with one another in that way, and watching their growth over time in development.
“The third area of math that’s extremely widely used is what I would call the heart of algebra, which is linear equations. That portion of algebra is then very widely used in other disciplines to open up many other problems.”
How is the SAT test driving changes in math curriculum?
David Coleman is leading the College Board to make drastic changes to the SAT test that most high school seniors take. Those changes include having a section of arithmetic skills that students must complete without use of a calculator, including science data and interpretation of charts and graphs as part of the reading sections, as well as in the math sections.
Coleman explains it further this way:
“Do you know how when we grew up, students would call themselves, proudly, verbal kids or math kids, so you could get an 800 on the verbal section even though you didn’t like numbers and you never had to encounter them. And there were a lot of kids like that. And then there were math kids. The new SAT disrupts that picture in what’s called now not verbal, but evidence-based reading and writing. There are five passages, two of them always are a passage from science that includes numbers, data, and a passage from a social science, like economics, that includes data. You can no longer be perfectly verbal without being able to read and analyze data from charts, tables, and graphs. Because what was so silly was that people call themselves highly verbal and wide readers, when in fact they’re illiterate when they reach science or the social sciences if they can’t evaluate numbers.”
A review of the new SAT reveals that twenty percent of the SAT math questions test data fluency; and, amazingly, 10 percent of the questions on what used to be the verbal section are data questions also. A decade ago, those numbers would have been close to zero.
Why is this important? Well, if it is on the SAT, then schools that want their students to perform well will adjust their curriculum to include teaching those concepts and skills more.
What’s the bottom line for parents and teachers of teens in Christian schools?
- We need to make sure students are competent and getting regular practice solving basic arithmetic (adding, subtracting, multiplying, dividing) – especially with fractions and decimals. And without the use of calculators!
- The math units about graphing lines (linear equations) in the math curriculum should be emphasized and reviewed for mastery and understanding
- Students should become fluent at using Excel or Google Spreadsheets – putting in data, using formulas, creating meaningful graphs and charts, and drawing valid conclusions from the data
- Units about statistics should not be skipped or avoided, but carefully covered
- Algebra I and Algebra 2 are probably more important to include at the high school level than Geometry (or use a curriculum like Saxon that integrates geometry into the algebra).
- Find examples of tables of data, charts, survey results, etc in the media and use them for discussion and application with your students.
- Have guest speakers from various occupations and ask them to explain to your students what math skills they find are important in their employees or job (nurse, Chick-Fil-A manager, pastor, etc)
This has gotten me thinking about how to apply it to our school situation, but I am not making any major changes right away. I do have a retired accountant teaching some basic Excel spreadsheeting to my older teens in a mini-class. When we cover graphing of lines in Algebra, I want to supplement with some “real-life” application problems this time around.
I am not currently teaching Excel as a course for credit in our school but wondering how to incorporate that more. Do any of you readers know of a good course, perhaps online, that a teen could work through to learn spreadsheet skills? Put some suggestions in the comments below!
The inspiration for this article came from listening to the podcast here, and then going back to read the transcript. Read it for yourself here: http://freakonomics.com/podcast/math-curriculum/
Please leave your own comments, observations, recommendations, or questions in the comment section below!
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