Math is Not Linear

Math is often taught in a linear way, and each new year, students revisit topics and build upon them with the ultimate goal at the end of high-school being calculus. Geometry plays a big part, and I remember all kinds of min/max calculus problems involving solid shapes. But what strikes me, is how little the topic of statistics is taught in the K-12 setting. Many who graduate from college are not going to use much of the higher-leveled math in their careers, but they will be exposed to a lot of data – and they should be able to recognize when this data gets misrepresented in the news. When someone reads something that begins, “research says…,” do they understand those numbers and what they mean? Can they recognize a graph when it’s skewed to favor the author’s point of view? Infographics are some of the best visual ways of trying to convey data, but some of them are simply just beautiful art and actually quite misleading. Some, of course, are brilliant.

This week, the New York Times had an article titled Teacher’s Colleges Upset by Plan to Rate Them. The U.S. News and World Report has told many colleges to comply or they may simply get an F rating. Even though many of the colleges (including Columbia, Harvard, and Michigan State) have all stated that the measuring systems are flawed.

This week’s New Yorker, has a piece by Malcolm Gladwell also criticizing the U.S. News and World Report for its general ranking of schools. Honestly, how can you compare apples to oranges? And yet they do. When you factor many of the measurements: endowment, scholarship, tuition, graduation rate, and so on, how do you give each of the measurements equal weighting?

And yet, for some reason, people would rather not think about all the different numbers. They want a nice little number that they can use to order the schools. The U.S. News and World Report admittedly says that the way they weigh its metrics aren’t scientific in any way. Obviously, not a reliable source, yet their publication sales continue to rise.

When measuring teacher effectiveness, the same kinds of things must be considered. How much do you weigh experience, achievement in test scores, degrees earned, anecdotal reputation, etc.? The test scores are a tricky one too. If you’re not comparing the same group of kids, you’re comparing apples to oranges. Furthermore, if you’re comparing one school to other schools, can you aggregate data such as financial aid, diversity, ratio of teachers to students, test scores, and so on. Again, we’re comparing watermelons to tomatoes. Local magazines love to compare schools in the city using data that’s usually dated and not very useful. They also like to come up with an aggregate score and rank schools.

I think some of the metrics measured are legitimate and should be looked at closely, but to give each of those an arbitrary weighting so as to come up with a single number for a ranking is not good math.

These past two weeks in second grade math, the children have been making paper quilts. While not a lot of statistics were involved, the children were employing their knowledge of measurement, area, perimeter, addition, multiplication, fractions, estimation, and problem solving. Not to mention that the quilts also lent themselves nicely to social studies themes like the Underground Railroad as well as integrated nicely with story telling.

So many math text books present fractions in a chapter midway through the year. In reality, fractions are everywhere. They’re in music, quilts, baking, Lego, and so on. Why wait to introduce the concept of ‘half’ midway through the year, when you can use it all year long? I guess I want my students to see the connections between fractions, and measurement, and the operations they need to use to solve problems involving those connections. Fractions aren’t something that exist in a vacuum. They’re part of these children’s world. It’s everywhere – and to wait until chapter 8 (or whatever it is in the book you’re using) is just wrong.

I know I meandered from the topic of statistics using fractions in second grade, but as adults, statistics are all around us. The data is often analyzed by ‘experts’, but we need to be able to do better than take someone else’s word for it or buy into the simplicity of an arbitrary ranking system. Malcolm Gladwell’s article in the New Yorker may seem obvious to many, but many are reading U.S. Weekly News!

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3 thoughts on “Math is Not Linear

  1. It is funny that you brought this up. My middle son is great with math but with fractions he stumbles a bit for him. What I mean is that he actually gets one or two wrong on the questions. My daughter is in grade 2 and we will be starting fractions in math soon. But with other things she has been learning it. Sounds silly but a good way to get a young child to understand the concept of fractions have them sort laundry and put the clothes away. It is amazing how such a mundane task gets the brain clicking. That being said I just ordered a boat load of fraction math manipulates. I noticed with their base ten blocks if they can touch the numbers the concept comes easy. Often on their own they begin to see the equations in their life. Even while play they will stop and let me know. However, when I teach them this way it is very hard to prove to the VSB that I am teaching those concepts only because there is no physical proof. ( I have thought about taking video’s as proof) BTW…I am sooo going to steal that paper quilt idea! Thanks!

  2. Have you seen the book You Can Count on Monsters by Richard Evan Schwartz? He is a math professor at Brown who developed this clever way of teaching kids about prime numbers and factoring. Factoring is all about breaking a number down into its prime number components, so each factor tree for 1-100 is accompanied with an illustration of a “monster” that is a graphical integration of the component prime “monsters” of that number – you see each number in terms of groups of dots, the factor tree and the monster. This book is yet another example of how an unusual presentation of a fundamental math concept might just make sense to a kid who doesn’t otherwise “get it.” Have a wonderful and restful break!

    • I haven’t see it yet, so thank you for the recommendation. I’ve just put it on hold at the public library and can’t wait. It sounds like it’s just my kind of thing. Have a great break too!

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