Guest Blogger: Scott Kim, II

Today, I’ll continue with reblogging Scott Kim’s in-depth post about transforming mathematics education.  You might want to read last week’s post to get caught up.

I will say that the discussion generated quite a bit of interest.  Participants have been actively responding to each other in a very lively email thread.  The comments and discussions are still ongoing — I am having a hard time keeping up with them!  But in a later post, I’ll summarize some key ideas and observations made by members of the group.

But for now, I’d like to turn it over to Scott Kim.  Again, if you’re anxious to read the entire post, please feel free to go to his blog.  Or just be patient….  But you can see by looking at the heading that Scott is addressing a very important issue next.  I can still recall — when teaching gifted high school mathematics and science students — really understanding where the question “When am I going to ever use this?” comes from.

The answer is pretty simple.  Bright students want to know.  When I first started teaching at university, I thought it was the students’ job to find motivation for doing mathematics — after all, they were paying a lot of money for their education.

But I eventually realized that there are only about three months between the end of high school and the beginning of college.  Nothing magical happens to students to transform them into self-motivated human beings, hungering for knowledge for its own sake.

Actually, one of my goals is never to hear the question “When am I ever going to use this?” again.  If I do a good job teaching and motivation concepts, students will already be able to answer that question, and won’t need to ask it any more.

Yes, it’s a more challenging way to teach.  But I can tell you, for me, it has been worth it.

Now I’ll let Scott take over.  Enjoy!  We’ll look at the third level next week.

Level 2. Lack of MEANING (leaks)

The most common complaint in math class is “when are we ever going to use this?” And no wonder; the closest most kids get to using math meaningfully is word problems, which are typically dull mechanical problems, dressed up in dull mechanical narratives.

Traditional mathematics education focuses on teaching rote computational procedures — adding, dividing, solving quadratic equations, graphing formulas, and so on — without tying procedures to meaningful situations. Unfortunately most adults, including many teachers and administrators, think this is how it must be. But teaching only the rote procedures of math is like teaching only the grammar and spelling of English, without explaining what words mean, or letting kids read books. Mechanics without meaning is not just deathly boring, it is much harder to learn.

Here are three ways to plug the leaks of meaningless math.

2a. Use math. In our increasingly digital society, kids spend less and less time playing with actual physical stuff. All the more reason to get students out of their desks and into the world, where they can encounter math in its natural habitat, preferably integrated with other subject areas. My friend Warren Robinett told me “a middle-school teacher I knew would, after teaching the Pythagorean Theorem, take the kids out to the gym, and measure the length and width of the basketball  court with a tape measure. Then they would go back to the classroom and predict the length of the diagonal. Then they would go back to the gym, and measure the actual diagonal length. She said some of the kids would look at her, open-mouthed, like she was a sorceress.”

Solution: use problems that kids care about, and excite student interest.

2b. Read about math. Before we learn to speak, we listen to people speak. Before we learn to write, we read books. Before we play sports, we see athletes play sports. The same should apply to math. Before we do math ourselves, we should watch and read about other people doing math, so we can put math in a personal emotional context, and know what the experience of doing math is like. But wouldn’t reading about people doing math be deadly boring? Not if you are a good story teller. After all, mathematics has a mythic power that weaves itself into ancient tales like Theseus and the Minotaur. My favorite recent math movie is a retelling of the classic math fable Flatland, which appeals as much to my 7-year-old daughter as to my adult friends. Here’s a list of good children’s books that involve math.

Solution: read good stories about math in use.

2c. Ask your own questions. In math class (and much of school) we answer questions that someone else made up. In real life questions aren’t handed to us. We often need to spend much time identifying the right question. One way to have students ask their own questions is to have them make up their own test questions for each other. Students invariably invent much harder questions than the teacher would dare pose, and are far more motivated to answer questions invented by classmates than questions written by anonymous textbook committees. Mathfair.com goes further to propose that kids build and present their own physical puzzles in a science-fair-like setting. Kids can apply whatever level of creativity they want. Some focus on art. Some on story. Others add new variations to the puzzles or invent their own.

Solution: Give kids freedom to ask their own mathematical questions, and pursue their natural curiosity.

If we plug the leaks of meaningless math, we will grow a generation of resourceful mathematicians who understand how to solve problems. But are we teaching the right mathematics?  (To be continued….)

Transforming Mathematics Education: BAMAS, X

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

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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….