I am generally a fan of IXL.com, but I see the same sorts of pattern-matching issues there as well. Anytime we ask repeated questions about one isolated skill, this is a serious concern IMO.

While I don’t agree with the pedagogical decisions of KA, we can at least take solace in the fact that students are recognizing and utilizing patterns for their benefit. Seems like an important skill to be successful with mathematics.

Reminds me of the story about the tank-recognizing computer. I doubt we’ll have worthwhile computer scoring that isn’t susceptible to pattern-matching until we have genuine artificial intelligence.

And then the computers will want days off, just as teachers do. :)

Concur with Rebecca.

What you call pattern matching could also be called access to long term memory. When we learn the multiplication tables, we’re learning to pattern match. It’s ok to _teach_ multiplication in a way that reveals meaning, but after that we just want students to _know_ it.

How many times have you come across algebra students who can’t multiply and are doing poorly because of that missing pattern matching routine in their heads?

If there’s any valid criticism it’s that students are learning the wrong patterns.

That’s why open problems are so important. Problems, with not the slightest hint how to proceed. Maybe not even the question is clear. This way of teaching has been discussed in that blog before, I believe (Japanese versus American way).

Note, however, that pattern matching is okay for drill stuff, and even necessarily so. Some drills are unavoidable in math too. We need that before we can do useful things.

I find these kinds of errors showing up often on the gray, blurry line between teaching and computing/programming.

Those who teach don’t necessarily understand programming so they tend to not be able to specify what works in a classroom and the processes or habits that the software is meant to address.

Those who program have never taught so they don’t know how to write the code that solves the problem because they fundamentally don’t understand the problem.

Unfortunately, those who have done both to a sufficient level aren’t writing the programs that most of us need.

You see this in grading programs that ignore the ways teachers operate and get in the way instead of making life truly easier, IWB software that doesn’t work or fails in bizarre ways, or tools and software that include limitations and drawbacks unnecessarily (Looking at you, TI-SmartView).

“I observed how some students made progress in exercises without necessarily demonstrating understanding of the underlying concepts.” – yeah.

We’ve come a long way but not nearly far enough to allow the replacement of teachers; like 11 Micheal I see the best use of Khan as taking the rote memorization out of the hands of the teacher-in-class (though Flash Cards is the Number ONE “really cool idea” promoted by the parents I talk to, especially the home-schoolers).

Let them practice outside of class and bring basic skills to automaticity so that we can do some real work together in our limited time together.

My old school last year relied on a teaching model where the students had to try and teach themselves a lot of math by utilizing classroom resources. A lot of the practice was through Khan Academy or by students completing practice problems with accessible answer keys. Ultimately what happened was that the students only looked for patterns and had no conceptual understanding of the math at all. Even worse was that students who had “mastered” the concept were encouraged to teach the other students how to solve problems but they could only do so in the most superficial manner posssible.

Hi Dan,

Thanks for your thoughts.

“One premise of my work with Dave Majors is that the machines should ask rich questions but not assess them, instead sending the responses quickly and neatly over to the teacher who can sequence, select, and assess them.”

We think the work you’re doing with Dave Majors is really exciting and inspiring. Open-ended questions and peer- or coach-graded assignments are incredibly powerful learning tools and my colleagues at KA don’t disagree. We definitely have plans to incorporate them in the future.

Stephanie

Just because I rock at Madden 2012, doesn’t mean anyone is going to draft me to play in the Super Bowl.

Thank you for bringing Benny back!

I’ve had a copy of Erlwanger’s article (http://www.wou.edu/~girodm/library/benny.pdf) on my desk since our district started touting flipped mastery. I’m so glad others are sharing this informative piece of research.

In the past I’ve heard mathematics could be described in its essence as the search for patterns so this entire article is a surreal experience of ‘Students are gaming the system of learning math by doing the essential essence of math.’

In any event is it not obvious that the use of adaptive learning software must require the close attention of a real teacher?

Dan

Attention to those kinds of patterns is counterproductive.

Is anyone asking the question, “Why are students attempting the much more difficult task of looking for patterns in test questions instead of grade level math?”

I get the idea that students don’t understand math, there is a large measure of guesswork, and students have to fall back on something, but why do they feel more comfortable figuring out linguistic patterns on the fly instead of math procedure?

I suppose there are some obvious answers, but perhaps not.

I’m not sure about difficulty being the factor. I suspect that figuring out the puzzle is what we are programmed to prefer, and students prefer to figure out puzzles, which is human work, than to repeat rote work that can be easily done with a calculator.

Michael I don’t think it is more difficult, but I think for many they have very little faith in their math abilities.

Dan,

I’ll stay out of this interesting discussion on pattern-matching for now, but I’d like to set the record straight on Summit SJ. Our math model as described as concisely as possible: students spend two hours per day on math; one hour in breakout rooms and one hour in the big room (seen in your picture) where students are working independently. In the breakout rooms, students work on challenging tasks and projects (many of which we can thank you for) that develop the standards of math practice, often in groups and with varying amounts of teacher structure. Development of cognitive skills via frequent exposure to these types of tasks is paramount to our program. It is also in the breakout rooms where students’ independent work — which is mostly procedural practice — is framed and put in context. Students’ know that their work in the big room supports what they do in the seminar rooms and vice versa.

I have no qualms with resources like Khan Academy or textbooks with answer keys that allow students to work relatively independently (although the big room still has 3 teachers available) and most importantly frees up my time to work with students on math practice and cognitive skill development. Like you, we see huge potential in tech that helps students further develop in these areas, either by giving good, actionable feedback to students and/or by giving data to teachers who can then make appropriate instructional decisions. In other words, please keep up your work with Dave Major so we can stop using Google Forms and various other makeshift tools!

Plugging away with a student this morning through their comprehension check on the computer generated Algebra I lesson. Student picked answer “d.” I inquired how the student came to the answer. It was an interesting method that involved multiplying the coefficient of a term by its exponent. In other words, he was lucky.

I am a 45 year old college student, who recently passed college algebra course using khan academy. I could not have passed without his knowledgeable math videos. I would love to meet Sal in person to extend my gratitude.

I have always struggled in math, but with his wonderfully detailed step by step videos I was able to make a ‘B’ in college algebra, and let me tell you, I had previously took this class twice and dropped both times because I could not understand, and the teachers didn’t have time to show me each step in detail.

I truly believe that Khan academy is one of the best math websites out there for learning.