This past Saturday marked the tenth meeting of the Bay Area Mathematical Artists Seminars. You might recall (see the post about Bay Area Mathematical Artists Seminars, VI) that at a recent meeting, we had a very stimulating dinner conversation about the future of mathematics education, with Scott Kim helping to guide the conversation.
Everyone was so engaged, it was unfortunate that the conversation had to come to an end. So I invited Scott to lead a more formal discussion at a later meeting of the BAMAS. We met at BAMAS member Stacy Speyer’s place — thanks for hosting, Stacy!
The discussion was quite animated. Scott prepared a handout based on a lengthy blog post he wrote about various issues revolving around mathematics and mathematics education. He graciously gave me permission to reblog his ideas. The post is rather lengthy, so I’ll share it in installments. You can go to Scott’s blog yourself if you can’t wait to read more. So without further ado, I’ll let guest blogger Scott Kim take the wheel. His original post was dated July 6, 2014.
Navigating Math Education
Imagine that you are a sailor on a leaky boat that is on fire, sailing in the wrong direction, with a quarreling crew. Which problem would you fix first?
Well, that depends. If the leak is slow and the fire is raging, then you would put out the fire first. If the leak is gushing and the fire is small and contained, you would fix the leak first. It makes sense to fix the most urgent problem first.
What you would NOT do is fix one problem and declare victory. If your goal is to get to your destination safely, then you must fix ALL the problems, no matter how difficult. Anything less will not get you where you want to go.
Such is the situation with math education. The problems are so difficult and so numerous that it is tempting to fix one problem, and give up on the rest. And certainly we have to prioritize if we are to make progress. But if we are to get the ship of math education back on course, then we, collectively, must fix ALL the problems of math education. Nothing less will get us where we want to go.
Fixing all of math education may sound impossible or impractical. And indeed it is a formidable challenge. Well-meaning entrepreneurs who have launched successful businesses frequently grind to a halt when they try to start their own innovative schools. Resistance comes from all sides — standardized testing, textbook publishers, parents, administrators, government officials, and the students themselves trying to get into college.
But change is in the wind. America is losing its competitive edge, colleges are becoming impractically expensive, and the internet makes us dream of free education right now for everyone. I say we face the problem with eyes wide open, assess the full range of challenges we face, and look for the smartest moves that get us where we want to go.
With that in mind, here is my survey of the problems plaguing math education, and steps we can take to fix them. I’ve grouped the challenges into four levels that range from the tactical to the strategic: Mechanics, Meaning, Math, and Society.
Level 1. Faulty MECHANICS (fire)
The most obvious and urgent problem is that the mechanics of math are taught as a series of blink and you’ll miss it lessons, with little opportunity to catch up.
This one-size-fits-all conveyor belt approach to education guarantees that virtually everyone gradually accumulates holes in their knowledge — what Khan Academy founder Sal Khan calls Swiss cheese knowledge. And little holes in math knowledge cause big problems later on — problems in calculus are often caused by problems in algebra, which in turn are caused by even earlier problems with concepts like fractions and place value.
Here are three ways to fight the fire of poor pacing.
1a. Self-paced learning. The Khan Academy addresses the urgent problem of pacing by providing short video lectures that cover all of K-12 math. While the lectures themselves are fairly traditional, the online delivery mechanism allows students to work at their own pace — to view lectures when and where they want, and to pause and rewatch sections as much as they need. All lectures are freely available at all times, so kids can review earlier concepts, or zoom ahead to more advanced concepts. Short online quizzes make sure that kids understand what they are watching. And with an online dashboard that shows exactly how far each child has progressed, teachers can assign lectures as homework, and use class time to tutor kids one on one on exactly what they need.
Solution: the “flipped classroom.”
1b. Visual learning. I love the Khan Academy. My son hated it, because he, like many students, is a visual learner, and Sal Kahn’s lecture stick largely to traditional symbolic math notation. He would have done better with a visual experiential curriculum. Some kids are primarily audio or kinesthetic learners, some learn best socially. The bottom line is that different kids learn in different ways, and no one way is right for everyone. Education needs to address all learners, not just kids who learn in words.
Solution: teach every lesson three different ways.
1c. Testing for understanding. Nothing can change in education unless testing changes. Traditional standardized tests born of the No Child Left Behind era use multiple choice tests that assess only rote memorization of routine math facts and procedures. The new Common Core State Standards for mathematics, now entering schools across the nation, replaces standardized multiple choice tests with richer tests that include essay questions graded by human beings — a better way to assess mathematical understanding.
Solution: better assessment.
If we douse the fire of poor pacing in math education, we will increase test scores and student confidence. But there is more to mathematics than teaching the mechanics well.
I hope your interested is piqued! Scott will continue next week….