Khan Academy and the mythical math cure

My recent post about the differences between Salman Khan and Conrad Wolfram’s TED Talks (Compare and contrast: using computers to improve math education) brought a lot of traffic to the blog, some great comments, and more than a few Twitter conversations about how to teach math.

So I’d like to get more specific about what I think is wrong about the Khan Academy approach by writing about things I see as wrong with the way we teach math in the US.

No matter if we agree or not about Khan Academy, I’m fairly certain we can agree math learning is not going as well as we’d like (to say the least.) Too many people are convinced by the system that they “hate math”, and even students who do well (meaning, can get decent test scores) are often just regurgitating stuff for the test, knowing they can safely forget it shortly afterward.

There is plenty of blame to go around… locked-in mile-wide inch-deep curriculum, focus on paper and pencil skills, lack of real world connections, assessments that are the tail that wag the dog of instruction, a culture that accepts “bad at math” as normal, teacher education programs that have don’t have enough content area specialization, … you can probably add to this list.

I can’t tackle all of these. But if you are interested, I’d like to share my thoughts about Khan Academy and a few epic math myths that are relevant to a discussion of the Khan Academy. In America, these myths are so pervasive that even people who were damaged by the way they were taught themselves accept them and insist that their children be taught using exactly the same methods.

I think these myths explain both the widespread acceptance of Khan Academy as a “revolution” and also why in reality it’s not going to change anything.

Myth: Learning math is about acquiring a sequential set of skills (and we know the sequence)
I think people have a mental image of math that looks something like a ladder. You learn how to add single digit numbers – rung one. You learn 2 digit addition – rung 2. You learn 3 digit addition – rung 3. In this model, you get to rung 3 by throughly learning rung 1 and then rung 2.

The myth continues with the idea that the march up the ladder goes faster if we tell children exactly how to do the problems step-by-step. In the language of math instruction, these step-by-step processes are called algorithms. Some kids “get it”, some don’t, but we accept that as a normal way that learning happens, and “help” the ones who don’t get it by drilling them harder in the step-by-step process, or devising additional tricks and supports to help them “remember” how to solve the problem.

If they don’t learn (meaning pass tests), we take this as evidence that they haven’t practiced the steps well enough, and prescribe more of the same.

Khan Academy plays perfectly into this myth. Here are a convenient set of videos – you just find the one you need, push play and the missing rung in your mental math ladder is filled in.

A corollary to this myth is that we can test students for these discrete math skills, see which “rungs” are missing, and then fix that problem with more instruction and practice on that specific skill.

Let’s diagnose how we think about learning a simple math skill
When we teach 2-digit addition, we immediately introduce the algorithm of “carrying”. You should know, though, that the U.S. form of carrying is just one of many addition shortcuts, not handed down on stone tablets. It’s not used world-wide, nor is it something that people naturally do when adding numbers. But it’s cast in concrete here, so we teach it, then we practice that “skill”. With our ladder model in mind, if a child can’t answer the 2-digit problems correctly you do two things: 1) Do more practice on the rung under it, and 2) do more practice in the algorithm, in this case, carrying.

The problem is that if a student has simply memorized the right answers to rung 1 without real numeracy, reviewing carrying will not increase that understanding. In fact, it will reinforce the memorization – because at least they are getting SOMETHING right. They are like the broken watch that’s right twice a day. This issue gets worse as the math gets more complex – the memorization will not be generalizable enough to solve more complex problems.

A different vision of learning

“Some of the most crucial steps in mental growth are based not simply on acquiring new skills, but on acquiring new administrative ways to use what one already knows”. Papert’s principle” described in Marvin Minsky’s Society of the Mind.

If this is true, and since these administrative skills are not sequential, it makes it less likely that we really learn math in a sequential way. I think we’ve all had similar experiences, where a whole bunch of stuff suddenly makes sense.

This different vision of how people learn is called “constructivism“. It’s a theory of learning that says that people actively construct new knowledge by combining their experiences with what they already know. The “rungs” are completely different for each learner, and not in a specific order. In fact, rungs aren’t a very good metaphor at all.

“…constructivism focuses our attention on how people learn. It suggests that math knowledge results from people forming models in response to the questions and challenges that come from actively engaging math problems and environments – not from simply taking in information, nor as merely the blossoming of an innate gift. The challenge in teaching is to create experiences that engage the student and support his or her own explanation, evaluation, communication, and application of the mathematical models needed to make sense of these experiences.”Math Forum

Learning theory? What’s the point?
We need to talk about learning theory because there are different ones at play here. And to be complete, we are also going to need to talk about teaching theory, or pedagogy, along the way. Constructivism doesn’t mandate a specific method of teaching, but is most often associated with open-ended teaching, constructionism, project-based learning, inquiry learning, and many other models. Most of these teaching models have at the heart an active, social view of learning, with the teacher’s main role as that of a facilitator.

However, the teaching theory underlying most of American math education is instructionism, or direct instruction – the idea that math is best taught by explicitly showing students how to solve math problems, then having students practice similar problems. Direct instruction follows when you believe that math is made up of sequential skills. Most American textbooks use this model, and most American teachers follow a textbook.

This is important distinction when talking about Khan Academy. Khan Academy supports teaching by direct instruction with clear (and free!) videos. If that’s your goal, you’ve found the answer…. but wait…

Is clarity enough?
Well, maybe not. Even if you believe in the power of direct instruction, watch this video from Derek Muller, who wrote his PhD thesis on designing effective multimedia for physics education. Really, if you are pondering the Khan Academy question, you must watch this video.


“It is a common view that “if only someone could break this down and explain it clearly enough, more students would understand.” Khan Academy is a great example of this approach with its clear, concise videos on science. However it is debatable whether they really work. Research has shown that these types of videos may be positively received by students. They feel like they are learning and become more confident in their answers, but tests reveal they haven’t learned anything. The apparent reason for the discrepancy is misconceptions. Students have existing ideas about scientific phenomena before viewing a video. If the video presents scientific concepts in a clear, well illustrated way, students believe they are learning but they do not engage with the media on a deep enough level to realize that what was is presented differs from their prior knowledge. There is hope, however. Presenting students’ common misconceptions in a video alongside the scientific concepts has been shown to increase learning by increasing the amount of mental effort students expend while watching it.” – Derek Muller, Khan Academy and the Effectiveness of Science Videos

Derek makes an interesting point – clarity may actually work against student understanding. Videos that slide too smoothly into an explanation do not give a student a way to process their misconceptions and integrate prior knowledge. The very thing that makes the videos so appealing – Khan’s charisma, sureness, and clarity may lull the viewer into comfortable agreement with the presentation without really absorbing anything (Research references and Dr. Muller’s PhD thesis on this subject)

Hooks, not ladders
This goes back to my original point. People learn by reorganizing what they already have in their head and adding new information that makes sense to them. If they don’t have a “hook” for new knowledge, it won’t stick. The tricky part is, though, that these hooks have to be constructed by the learner themselves.

Wishful thinking about downloading new information to kids is just that – wishful thinking.

There is no doubt that Khan Academy fills a perceived need that something needs to be fixed about math instruction. But at some point, when you talk about learning math, you have to define your terms. If you are a strict instructionist – you are going to love Khan Academy. If you are a constructivist, you are going to find fault with a solution that is all about instruction. So any discussion of Khan Academy in the classroom has to start with the question, how do YOU believe people learn?

I have more to say about Khan Academy and math education in the US — this post turned into 4 parts!

Part 1 – Khan Academy and the mythical math cure (this post)
Part 2 – Khan Academy – algorithms and autonomy
Part 3 – Don’t we need balance? and other questions
Part 4 – Monday… Someday

My context for these posts: I fully admit I’m not an expert in math or math teaching, just an interested observer of K-12 education in the U.S. In my work, I have unique opportunities to see lots of classrooms in action and talk to lots of teachers. It means I get to see patterns and similarities in classrooms all over the country. I don’t intend to do a literature review or extensive research summary in these posts. This comes from my personal experience, my master’s degree in educational technology and draws from a subjective selection of research and sources that have had a deep impact on my thinking about learning. Finally, I am NOT trying to tell teachers what to do. I’m not in your classroom — that would be silly.

New – Technology literacy whitepaper

Download PDFToday we are happy to announce the release of a new whitepaper written by Jonathan D. Becker, J.D., Ph.D. Associate Professor of Educational Leadership at Virginia Commonwealth University, with Cherise A. Hodge, M.Ed. and Mary W. Sepelyak, M.Ed. Dr. Becker is an expert researcher in achievement and equity effects of educational technology and curriculum development.

Assessing Technology Literacy: The Case for an Authentic, Project-Based Learning Approach (PDF)

This whitepaper takes a comprehensive look at the research, policies, and practices of technology literacy in K-12 settings in the United States. It builds a research-based case for the central importance of “doing” as part of technology literacy, meaning more than just being able to answer canned questions on a test. It also explores the current approaches to develop meaningful assessment of student technology literacy at a national, state, and local level.

Where “doing” is central to students gaining technological literacy, traditional assessments will not work; technological literacy must be assessed in ways that are more authentic.

Building on this definition, the whitepaper connects project-based learning and constructivism, which both hold “doing” as central to learning, as the only authentic way to assess technology literacy.

True project-based assessment is the only way to properly assess technological literacy.

Finally, it examines our TechYES Student Technology Literacy Certification program in this light.

A review of existing technology literacy models and assessment shows that the TechYES technology certification program, developed and implemented by the Generation YES Corporation using research-based practices, is designed to provide educators a way to allow students to participate in authentic, project-based learning activities that reflect essential digital literacies. The TechYES program includes an excellent, authentic, project-based method for assessing student technology literacy and helps state and local education agencies satisfy the Title II, Part D expectations for technology literacy by the eighth grade.

This whitepaper can be linked to from our Generation YES Free Resources page, or downloaded as a PDF from this link.

Sylvia

PS – Share this important research with your PLN!

Thinking about summer professional development?

If you are thinking about summer professional development, think about Constructing Modern Knowledge!

The 3rd annual Constructing Modern Knowledge summer institute will be July 12-15, 2009 in Manchester, NH USA (near Boston).

In addition to master educators and edtech pioneers, the Constructing Modern Knowledge 2010 faculty includes history educator James Loewen and bestselling author of Lies My Teacher Told Me; popular provocateur and author, Alfie Kohn; MacArthur Genius and incomparable school reformer, Deborah Meier; and children’s author, illustrator and animator, Peter Reynolds. Cynthia Solomon, Brian Silverman, Sylvia Martinez (that’s me!), Gary Stager and John Stetson round out the amazing faculty.

Constructing Modern Knowledge is a minds-on institute for educators committed to creativity, collaboration and computing. Participants have the opportunity to engage in intensive computer-rich project development with peers and a world-class faculty. Inspirational guest speakers, pre-conference expedition and social events round out the fantastic event.

Constructing Modern Knowledge is about action, not listening to speakers. It’s where we learn together how to make project-based learning happen in real classrooms with real software and real computers.

CMK 2010 info

Spend four cool summer days in New England making puppets roar, robots dance, animations delight, movies move, simulations stimulate, photos sing and leave with memories to last a lifetime! See you there 😉

Early bird registration deadline is May 1 –  Register online now!

Sylvia

Constructivist Celebration @ ISTE 2010

New announcement! Here we go again – the 4th annual Constructivist Celebration @ ISTE is open for registration. If you are going to ISTE (formerly known as NECC) this June in Denver, consider coming a day early for this very special event. It sells out every year, so don’t delay!

Constructivist Celebration @ ISTE – Sunday, June 27, 2010 8:30 – 3:30

The Constructivist Celebration is an opportunity for you to let your creativity run free with the world’s best open-ended software tools in a great setting with enthusiastic colleagues who share your commitment to children, computing, creativity and constructivism. You might think of this stimulating event as a spa day for your mind and soul!

Best of all, the Constructivist Celebration @ ISTE is being held within a few minute walk of the Denver Convention Center, home of the ISTE Conference.

Then you will enjoy five hours of creativity on your own laptop using open-ended creativity software provided by consortium members FableVision, Inspiration, LCSI, and Tech4Learning. Participants will also receive a TechYES Student Technology Certification Mini-kit from Generation YES and SchookIT folks will assist with project development.

Creative computer-using educators deserve to eat like an Italian prince. That’s why this year’s Constructivist Celebration includes continental breakfast, mid-morning refreshment, a three-course Italian lunch and afternoon snacks. This is in addition to the free creativity software and Imagine it2 DVD each participant will receive.

At $60 for the whole package, the Constructivist Celebration is an incredibly affordable event!

Sign up today for the Constructivist Celebration @ ISTE 2010.

I’m excited about this event, it’s always a fun, fabulous day with a creative community. Every year it’s different, and every year I learn something new. I can’t wait to see some of you there!

Sylvia

Constructivist Celebration at MACUL

The Constructivist Consortium in partnership with SIGTELE is bringing the popular Constructivist Celebration to Michigan! Plan to join in this MACUL pre-conference learning experience on Wednesday, March 10, 2010 in Grand Rapids. Participants will receive the day’s educational program, a hearty lunch and free software from Constructivist Consortium members, including five free tools from Tech4Learning: Pixie, Frames, WebBlender, Twist, and ImageBlender.

This hugely popular workshop, also offered as a pre-conference event at the National Education Computing Conference (NECC/ISTE) sells out quickly each year. Don’t miss your chance to learn with the best at this full-day, hands-on workshop led by Constructivist Consortium co-directors Melinda Kolk and Gary Stager.

More information and registration here.

If you aren’t convinced, read this article (PDF) by Mary Saffron,
SIG TeleLearning Communications Officer about her experience at the NECC Constructivist Celebration in the latest MACUL Journal.

If you are in the Grand Rapids area or are attending MACUL, be sure to add this event to your conference registration!

Sylvia

Constructing Modern Knowledge 2010

It’s back!!!

Plans are shaping up for an amazing 3rd Annual Constructing Modern Knowledge summer institute, July 12-15, 2009 in Manchester, NH USA (near Boston).

In addition to master educators and edtech pioneers, the Constructing Modern Knowledge 2010 faculty includes history educator James Loewen and bestselling author of Lies My Teacher Told Me; popular provocateur and author, Alfie Kohn; MacArthur Genius and incomparable school reformer, Deborah Meier; and children’s author, illustrator and animator, Peter Reynolds. Cynthia Solomon, Brian Silverman, Sylvia Martinez (that’s me!), Gary Stager and John Stetson round out the amazing faculty.

Constructing Modern Knowledge is a minds-on institute for educators committed to creativity, collaboration and computing. Participants have the opportunity to engage in intensive computer-rich project development with peers and a world-class faculty. Inspirational guest speakers, pre-conference expedition and social events round out the fantastic event.

Constructing Modern Knowledge is about action, not listening to speakers. Attendees work and interact with educational experts committed to maximizing the potential of every learner. The rich learning environment is filled with books, computers, robotics materials, art supplies, toys and other objects to think with.

The real power of Constructing Modern Knowledge emerges from the collaborative project development of participants. Each day’s program consists of a discussion of powerful ideas, on-demand mini tutorials, immersive learning adventures designed to challenge one’s thinking, substantial time for project work and reflection.

CMK 2010 info

21st Century educators need to develop their own technological fluency and understand learning in order to meet the changing needs and expectations of their students. Constructing Modern Knowledge will help participants enhance their tech skills, expand their vision of how computers may enhance the learning environment and leave with practical classroom ideas.

Spend four cool summer days in New England making puppets roar, robots dance, animations delight, movies move, simulations stimulate, photos sing and leave with memories to last a lifetime!

Each participant receives a suite of open-ended creativity software from Tech4Learning, LCSI, Inspiration Software, FableVision and other members of The Constructivist Consortium free-of-charge for use at Constructing Modern Knowledge and beyond. The software alone is worth the registration fee!

There is also a July 11th preconference Science and History Tour of Boston available for a nominal fee. Explore the future at the MIT Museum and visit the past during a private guided tour of the Boston Freedom Trail.

The institute is less than an hour’s drive from Boston in picturesque Manchester, New Hampshire. Free transportation is available from the convenient and affordable Manchester Airport. Discount hotel accommodation has been arranged at the institute venue.

Constructing Modern Knowledge is sensitive to the budgets of schools and educators by keeping registration costs affordable and by offering school/district team discounts. The institute is appropriate for all K-12 educators, administrators and teacher educators – private or public. CEUs are available for an additional fee.

Save $75 on early bird registrations! Register online now!

Sylvia

Reflections from previous years:

‘Teach Naked’ and complacency natives

‘Teach Naked’ Effort Strips Computers From Classrooms – Technology – The Chronicle of Higher Education.

This is one of the stories where you have to actually read the whole thing. At first you think, “Terrific, another educator who hates technology and refuses to join the 21st century.”

College leaders usually brag about their tech-filled “smart” classrooms, but a dean at Southern Methodist University is proudly removing computers from lecture halls. José A. Bowen, dean of the Meadows School of the Arts, has challenged his colleagues to “teach naked”—by which he means, sans machines.

But you would be wrong – read a bit more. He’s not really against technology, he’s against being boring, especially being boring with PowerPoint. He thinks when students come together, the best thing to do is have a conversation. Let the students read the material, or listen to a podcast ahead of time. Use class time to talk, ask questions, and interact with the teacher and other students.

Even though he is taking computers out of classrooms, he’s not anti-technology. He just thinks they should be used differently—upending the traditional lecture model in the process.

Aha! He’s talking about pedagogy, not tools. He’s against lecturing, with or without slideshow accompaniment. And guess who he has to convince about this — yes, those digital natives, the students. Because what they really are is complacency natives. They are used to waiting passively to be told what to learn, how to learn, and then repeating it back.

But he’s taking computers out of the classrooms! Oh no! Evil! But wait, keep reading. He’s removing the fixed computers hooked to projectors. And buying laptops instead. And unbolting the desks and replacing them with movable chairs and tables so the teachers and students can adapt their classroom to suit their learning needs. Oh, hmm… not so crazy.

It’s a great lesson in the sloppy vocabulary of the ed tech world. All “technology” is not created equal. It’s not a technology = good, removing it = bad. We have to be more precise about this. What’s the learning environment? What do you believe about learning? How is technology supporting those goals?

Teach naked? Ok, got to give the guy credit for coming up with something catchy. Getting attention for advocating doing away with lecture is OK in my book. A worthy goal for K-12 would be to produce students who aren’t complacency natives, who arrive at college ready for deep discussion, real learning, and meaningful interactions with other human beings.

Sylvia

Can lectures be interactive?

How do you create interactive computing lectures? « Computing Education Blog.

Nice example from Mark Guzdial about interactive lectures.

A real, authentic problem, with a teacher who doesn’t know the answer, can be energizing for students.  When I make a mistake in live coding, it’s always unscripted, so I don’t immediately know what the bug is.  Most of the time, some student will yell out what I did wrong before I figure it out for myself.  I think that’s a great position to be in, though it does require a heaping helping of humility before starting the lecture.

This doesn’t have to be about coding…

Sylvia

Celebrate creativity and innovation at NYSCATE

The New York state educational technology conference, NYSCATE (Nov. 22-24) always has a top lineup of speakers and keynotes. This year is no exception. The featured keynote is Sir Ken Robinson, a world-renowned advocate for creativity and innovation in learning.

I’ll be there as well, participating in the Constructivist Celebration, two sessions, and a panel. My Monday session is on teacher professional development in a “technology ecology,“ and on Tuesday the topic is games in education. The panel will tackle an intriguing question – What does it mean to be literate in the 21st century (and what does Web 2.0 have to do with it?)

In a special Sunday session, we will explore the second year outcomes of the NYSSTL program (New York State Student Technology Leaders). In more than 30 middle schools in New York, this innovative model for student-centered technology is showing that students can be 21st century leaders. The session will showcase video by two teachers who are working side by side with these student leaders.

Continuing in the creativity theme, if you are anywhere near Rochester on Sunday, Nov. 22 — don’t miss the Constructivist Celebration @ NYSCATE — it’s back and better than ever! Gary Stager and award-winning children’s book author Peter Reynolds will host a full-day workshop at the Strong National Museum of Play. This is the perfect place to explore creative, playful, constructivist learning with computers. The $100 registration fee includes lunch, creativity software from your favorite companies, and new this year, a free TechYES Mini-kit. TechYES is our middle school project-based technology literacy certification program. This is hundreds of dollars worth of the best creativity software and tools PLUS a great day of tinkering with technology.

And a note for you Stager fans, this will be your only opportunity to hear the always entertaining and thought-provoking Gary at this year’s NYSCATE.

The theme of creativity resonates strongly throughout NYSCATE, and the best way to encourage creativity is to allow (and teach) children to be creative problem-solvers in their own lives, both personal and academic. At Generation YES, we are sure there is no better way than to invite students to become leaders and allies in the effort to improve education with new technology.

As you can tell, I’m excited! NYSCATE is one of my favorite education technology conferences of the year and I can’t wait. If you’d like to hear more about what’s going on there, or meet me at NYSCATE, I’ll be there Sunday –Tuesday (Nov. 22 – 24).

Sylvia

Constructivism in practice – making lectures work

Posted with permission from The Institute for Learning Centered Education – Don Mesibov

If you must lecture, please don’t do it early in the lesson.
Most teachers begin a lesson with a launcher, anticipatory set, ice breaker, bell ringer or an exploratory activity (which we recommend). Each of these often motivates students to think something good might happen during class; some of the students actually begin to look forward to what might come next.

Unfortunately, just as students are beginning to think they might not mind being in class, the teacher too often launches into a lecture and all momentum is lost. It’s like the dead scene in a play that interrupts the flow of excitement generated earlier.

Why do teachers lecture early in a lesson? It’s because we have new information we want our students to learn and we want to start by telling them what we want them to know. But it isn’t effective. If the content is completely new to students it is hard to follow the words of a speaker. It is like trying to learn the rules and procedures of baseball when you’ve had no previous knowledge that such a game existed. If you want to teach someone baseball, hand them a glove and have a catch. Put a bat in their hands and pitch to them. Then you can start to explain how the game is played – after, not before, you have actively engaged them.

I’ve sat in the back of the room as teachers have tried to explain to students what they want them to learn. I’ve noticed the faces of the disinterested students. They have no hooks to hang their thoughts on – no context for understanding what the teacher is saying. Sometimes what the teacher says early in the lesson would be more effective if said near the end when the students have been engaged with the new information. The lecture might be more effective as a summary. Once you’ve tried hitting a ball with a bat for fifteen minutes, a mini-lecture on how to stand and how to hold the bat has much more meaning.

Here are some examples of how to engage students with new information BEFORE beginning your explanations.

  • BILL OF RIGHTS: Don’t explain or describe them. Distribute a one page summary of the Bill of Rights, pair the students and ask each pair to prioritize them in order of importance. Then ask each pair to justify its prioritization. There is no right or wrong and it doesn’t matter how each pair prioritizes. What is important is that the students have been challenged to think about each article and what it means.
  • TOO, TO, AND TWO: Pair or group students and ask them to design an ad for their favorite TV show or DVD, or food using each of these words correctly at least once.
  • MIXTURES AND SOLUTIONS: Give students different substances to mix and ask them to share conclusions they reach based on the results.
  • PERCENTAGES: Ask students, in pairs or groups, to share their perceptions of what’s good and what’s bad about buying with credit cards. This can lead to a lesson on percentages that students perceive as relevant when you ask them to assess whether the purchase of a sale item, using a credit card, will actually save money when the interest payments are taken into account.

You can probably come up with more and better examples. My only point is that after you grab the students’ attention with a good opening, don’t blow it by losing the momentum with a lecture that the students probably won’t understand anyway.

Please know that your work in the field of education is as meaningful to our society as anything anyone can possibly do. Thank you for caring about the future of our children!!!!

Don Mesibov October 2009
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Copyright (c) 2009, Institute for Learning Centered Education. All rights reserved.

The Institute is currently registering teams for the 2010 summer constructivist conference, July 19-23, at St. Lawrence University, Canton, New York. Don’t miss the opportunity for this unique conference that models the constructivist behaviors that teachers are using increasingly in the classroom. More information at The Institute for Learning Centered Education.