I meet a lot of teachers in my work. It’s interesting to listen to their stories about who they are and how they became teachers. I’ve noticed that there seems to be a real split in the ranks about the reason they became teachers.
On one side are teachers who themselves had a good experience in school. They generally were successful and their mission is to create those same kinds of experiences and memories for the children they serve. They are replicating their own experience.
On the other side are teachers who feel the school system failed them. Some dropped out, some rebelled, some got horrible grades, but at some point in their lives they decided to dedicate themselves to righting that wrong. They are determined to create different kinds of experiences and memories for the children they serve. They are remediating their own experience.
I don’t know any other profession where there is such a polarization. And yes, of course this is a generalization. You can’t expect to split a large and varied group of people into two neat groups (let’s not get all left brain/right brain here now.)
But there is a point to be made. Replicators and remediators bring two divergent world views to the table. This disparity can become a problem when we try to talk about how to change education, because we hear the same words and think we are being understood, but the underlying experiences are so vastly different that the meaning is muddled.
And yet, I don’t believe either of those stances are sufficient. We must reinvent education in a way that doesn’t depend on childhood experiences. Because childhood experience is too narrow a lens with which to view the world. We have to think about how our own learning experiences color our opinions and allow other’s experiences to carry just as much weight as ours.
To replicate, to remediate, or to reinvent. I choose reinvent.
“In a role reversal, Ms. O’Bryant and other teachers at Brick Avon Academy are getting pointers from their students this year as part of an unusual teacher training program at 19 low-performing Newark schools.
The lesson learned by Ms. O’Bryant? “It makes you think about really hearing the kids,” she said. “You can learn from them. They have their own language.”
The training program, which is supported by a federal grant, is being run by the National Urban Alliance for Effective Education, a nonprofit group based in Syosset, N.Y. During a daylong workshop, teachers were instructed by the group’s trainer, Eyka Stephens, to watch their students teach mock lessons, study their methods and language, and discuss together what works (and what does not).” (Read more…)
Why does this work? It’s not because the kids are delivering the content better – it’s because of the sense of community and collaboration that’s developed as the learner/teacher roles blur.
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.
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!
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.
This survey was conducted by a filtering company and taken by school administrators and teachers at the annual Christa McAuliffe Technology Conference held in Nashua, New Hampshire in Nov. 2009.
66% of the school administrators and teachers surveyed indicated that students know how to bypass their school system’s content-filtering solution
56% sense that their current security solution hampers the teaching process.
89% consider the Internet is generally safe for students.
While I disagree with the filtering company conclusion that these results mean that better filtering is THE answer, the numbers are interesting. What does it mean when we know something doesn’t work and we keep doing it anyway?
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
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.
An oldie (1993) but a goodie from Alfie Kohn. What does it really mean when when students have the power of choice instead of being powerless? Why is it important, and what kinds of things can students really decide?
To be sure, there is nothing new about the idea that students should be able to participate, individually and collectively, in making decisions. This conviction has long played a role in schools designated as progressive, democratic, open, free, experimental, or alternative; in educational philosophies called developmental, constructivist, holistic, or learner-centered; in specific innovations such as whole-language learning, discovery-based science, or authentic assessment; and in the daily practice of teachers whose natural instinct is to treat children with respect.
But if the concept is not exactly novel, neither do we usually take the time to tease this element out of various traditions and examine it in its own right. Why is it so important that children have a chance to make decisions about their learning? How might this opportunity be provided with regard to academic matters as well as other aspects of school life? What limits on students’ right to choose are necessary, and what restrictions compromise the idea too deeply? Finally, what barriers might account for the fact that students so rarely feel a sense of self-determination today? A close inspection of these issues will reveal that the question of choice is both more complex and more compelling than many educators seem to assume.
Passed on from Michael Steinberg of New York City – PhET Physics Education Technology – a terrific website full of fun, interactive simulations of physical phenomena. There are simulations for biology, physics, chemistry, math, electronics and more.
There are lessons and workshops for teachers, research support and lots of support materials.
The simulations can be run online or downloaded and run offline, and there is even an option to easily download all the simulations in one package.
These simulations look terrific and have easy to use controls and help integrated into each one. Unlike some interactive simulations, these have measurement tools built in so they can be used to support real science learning. Many of them have also been translated into many languages, and are open source so they can be modified if you want.