Support Materials

11. Lessons for Life - Learning and Transfer

Script

Linda Darling-Hammond: When our students go out into the world and run into new experiences, rarely will there be a manual telling them what to do. They'll need to draw on what they've learned before to solve new challenges. 

How do we teach them to transfer what they've learned from one situation to another? How do we teach them to use their knowledge in new ways?

Hello, I'm Linda Darling-Hammond, and that's our challenge for this session of The Learning Classroom

The term transfer refers to the ability to extend what you've learned to a new and different context. 

In a way, the whole point of school is to be able to transfer what's learned inside the classroom to a wide variety of situations both in other school subjects and outside of school entirely. 

Lee S. Shulman, Ph.D., President, Carnegie Foundation for the Advancement  of Teaching:  Transfer is what Jerome Bruner once called, going beyond the information given.  Transfer is what you do, when you can take, something very particular that you've learned, and use it for a wider variety of purposes, and in a wider variety of situations then were apparent when you first learned it.  Transfer is like making an investment.  It's taking something particular and having it expand and become richer, through the ways it can be used more broadly.

Linda Darling-Hammond: Although transfer is at the heart of learning, it is not a given.  Quite often, information learned in one context does not carry to another.

For example, students might learn vocabulary words for a quiz but not use them when they talk or write.  They might learn arithmetic facts but not be able to calculate the sales tax in a store. 

Whether knowledge will transfer depends on how deeply it is learned in the first place, and whether students have learned to recognize patterns or circumstances in which certain kinds of knowledge may be applied.

Transfer works in two ways.  First, students must be able to take the skills and knowledge they learn in the classroom and apply them in the real world.  In addition, their experiences outside of school can contribute to their learning in the classroom.

The ways in which teachers present ideas and how they engage students in working on them has a great deal to do with whether transfer of learning will later occur.

Lee S. Shulman: Probably the most obvious way, and a way that teachers often think that they shouldn't do, because they almost think it's cheating, is explicitly, to, point out to students, the variety of situations to which what they're learning today might be useful or transferable in the future and give them a chance to not only talk about, but even take the time, to have them do, some of those transfer kinds of tasks themselves.

Linda Darling-Hammond: Julie Helber, a teacher at Paddock Elementary School, teaches mathematics so that it connects to the real world. She helps students see how they might use the information in future situations.

Julie Helber: Fourth graders are concrete thinkers. Because of that they need to be able to touch materials, talk about materials or ideas and then they're able to remember them.

(classroom scene)
Julie:
Good morning, everyone.
Class:
Good morning, Mrs. Helber.

Julie Helber: The math program that I use teaches students to think on their feet. It teaches them to, it almost changes their way of thinking about math.

I think that the big ideas of teaching math to fourth graders are that we need to, as teachers, make sure that we're applying the math concepts that they're learning in class to their everyday lives.

(classroom scene)

Julie: I have this problem I need some help with.  I have these four bags of M&Ms. I really want to share them with you, but I don't know what to do here.
Girl:
You can divide them up, like, you can hand out two, two M&Ms and then two M&Ms.
Julie: 
Okay, so, like two at a time. Why would you count by twos and not by ones? Because why?
Boy:
Ones would take forever.
Julie:
  You got it.
Boy:
You could do it by fives, too.
Julie:
Exactly, ones are going to take forever.

Julie Helber: The teaching of mathematics is very tricky, I think as a teacher, because it's the easiest thing to do is to teach them how to do a problem, how to do an algorithm by teaching them a sequence of steps to come to a final answer..       

The hard thing is to teach them how these problems will relate to what they're doing, and that's where they learn the deep meaning of a concept that is being taught in mathematics.

If I am teaching the students basic division problems, we talk about situations that they might encounter where they would need to know a particular division problem.

(classroom scene)
Julie:
Listen to this problem situation. There are 36 people who are taking a trip in some small vans. Each van holds eight people. How many vans will they need? They're not going to come out all even. Your job is to figure out what you're going to do in this situation, because this what we encounter in real life, right?

Julie Helber: I think it's important that before we are getting ready to teach a particular lesson that we need to find out what the students already know about that lesson.  Because a lot of times you can find misconceptions that students have, and you can bring them out and talk about them.

(classroom scene)
Girl: You could cram one extra person and make them share a seat belt.
Girl:
We could make these people
Boy:
Get their own van!
Girl: 
We could use five vans but not fill the whole thing.
Julie:
What did you get on the calculator?
Girl:
I got 4.5.
Julie:
Who else got 4.5 on the calculator? Okay, and what's the question? Read it, Elizabeth, what do they want us to tell, what's the question here?
Elizabeth:
Each van holds eight people. How many vans will they need?
Julie:
How many vans will they need…So can we say we need four.five vans? Michael? No?
Michael:
Because if you take the cubes, um 36, take each eight ones out and then put them like in a row, you'll see five.
Julie:
Okay, how many were full vans? Autumn, can you help?
Autumn:
There would be four full vans and one van that only has four people in it.
Julie: 
Now Kayla, you said something really smart when we were talking, you said, "But they didn't say you could only have four vans," right?  And that's exactly the key to that problem.  They didn't say you could only have four vans filled up with eight people, they just said, "How many vans are you gonna need?" Well, in our case here we're gonna need five vans, right?

Julie Helber: In regards to division with something being left over, we need to make sure that the students understand that what is left over is important.  It's not just a remainder or an R-two. What is R-two? Students need to understand that what's left over is very important.

(classroom scene)
Girl:
Oh, there's four left over!

Julie Helber: And that's really my pedagogy of teaching anything. Is that if I can get the students to explore ideas and make meaning of what they're exploring themselves that's gonna stick with them for a lifetime.

Lee S. Shulman: One of the most difficult things about transfer, is, that you have the knowledge you need, and you don't know that you have it, or you don't recognize that it's useful in this new situation.

People know far more then they realize they know, and they'll give up on a more complicated task, and so, teaching the initial material in ways that increase the awareness of  the students of what they know, how they know it, and a variety of ways of trying to represent the idea in their own head, you know, just multiple connections, makes it more likely that when they do encounter a situation in the future where that knowledge is useful, they've got it packaged or organized in ways that will make it more available.

(classroom scene)
Julie:
How many do each of you have?
Students:
17, 17.
Julie:
Okay, how many are left over?
Boy:
Four
Julie:
What could you do with them?
Boy:
Give them to you?
Julie:
Ha, thank you! Great, now are we all happy? Okayay, me too!

Julie Helber: I think the concepts of mathematics are imbedded into all of the subjects that I teach. If we're measuring something in science, we're using mathematical concepts.  When we're talking about social studies, and students are learning about population, or learning about maps, and distances on maps, they need to understand some math concepts.  Mathematics is one discipline that's tie, it ties all of them together, because you can find it in just about everything. By teaching math this way, they're learning how these ideas are applied to their every day lives, and they'll carry those with them.

(classroom scene)
Julie:
Okay, you're going to work with your partner to do these five questions. You may use your calculators, your array cards, cubes or your brain, like Brian said. 

Julie Helber: I think it's important that, for students to behave like mathematicians, that they need all the materials that they might need in order to solve a particular problem.  I offer all different sorts of ways or methods that they might arrive at an answer.

One of the things that I notice is that there are students that may not be considered a real high academic achiever.

And when they do this type of math in my classroom, you see that they aren't a low achiever. They just needed to hear and understand the information in a different way.

(classroom scene)
Julie:
Sean, what was your sentence?
Boy:
My sentence was, "I left a one dollar bill…"

Julie Helber: Teachers need to be reflective decision-makers.

We need to be able to reflect back on that lesson and decide how could, what could we do to make things better or more meaningful for students.

I asses kids in many ways. Some of my assessment involves just the conversation that's taking place between the students, or between myself and the students.  I can easily assess whether they have a grasp on a particular concept or not.  Sometimes I may use what they're writing in a journal about what they've learned for the day.  And that will help me to assess how they're understanding the concepts.

(classroom scene)
Girl:
Seven by two is 14.

Julie Helber: I'm in my ninth year of teaching, and every year I learn something new about the way that I'm going to change my teaching. So this idea about pedagogy is just evolutionary, it evolves over time.

In that sense, I…evolved as a teacher in teaching mathematics, because I needed to change the way that I was teaching to reach all students.

Linda Darling-Hammond: Julie Helber used the real life situations of dividing M&Ms among friends and dividing students among buses to make her lesson more meaningful.  She asked students to share their thinking so that they would hear lots of different ways of approaching a problem.  These strategies increase the likelihood that her students will understand the concept of division with remainders, so they can use it later.

She also kept a careful eye on what was being learned to guide her decisions about what concepts she would re-teach, so that she could be sure her students had a solid base of understanding.

Lee S. Shulman: And basically there are two kinds of transfer that you can think about.  One is the transfer that occurs between learning the parts of a task, and then using those parts to do something much more complicated.  So, for example, when you were in first or second grade, you learned addition and you learned subtraction, and you learned multiplication.  At some point you had to learn long division.  Now that required transfer, because you had to take what you already learned about adding, and subtracting, and multiplying, and apply all three of those processes to learning a new kind of skill called division. And you can call that vertical transfer, it's taking small pieces and putting them together into a larger more complex skill.

A second kind of transfer occurs, when, you have to take what you've learned in one situation, and apply it to a new situation at roughly the same level of complexity.  And so, for example, if I have learned about the notion of a revolution, in studying the history of the United States, and then I study the history of France, can I apply the notion of revolution can I transfer what I know about revolution, from the American context to the French context, and subsequently, to the Russian context, if I then study the Russian revolution?

These are examples of a more horizontal kind of transfer, where I can take an idea from one situation and move it to another.  And, you can do that within a subject matter area, so, for example you can do it from the concept of revolution for the United States and for France. I'm doing that from within history, or you can do it across subject matter areas.

Linda Darling-Hammond: Donald Johnson is a 7th and eightth grade teacher from Christopher Columbus Middle School.  He creates a project that draws on his students' knowledge of math, science, and social studies and applies them to the complex problem of constructing a bridge.

In this lesson they wear many hats from the outside world, becoming business owners, engineers and bankers. We'll watch them integrate many different kinds of knowledge to solve a problem that gives them practice in transferring their learning to the real world.

(classroom scene)
Don:
What I'm going to be asking you to do is design bridges that you are going to make out of nothing more than toothpicks and glue. Now, this is going to be a type of competition. I'm going to be dividing you all up into companies.

Donald Johnson: Of course I have an idea what is going to be taught each day. So as I'm designing my lesson I ask myself four questions: What is it I want the children to learn? What experience am I going to subject them to, so they have an opportunity to learn it. How am I going to assess that they have learned it, and what opportunity am I going to provide them outside of school to practice it further?

(classroom scene)
Don:
Okay. Who's the director here? Okay, Ms. Stewart, tell me who's going to have what job in your company?
Hadley:
The name for it is carpenter, Amina will be it, she is the transportation chief as well as the architect. Terence Moody is the council.
Don:
Okay, that's good.
Don:
Each company is going to have a budget of one $1,fivefive0,000.  Now that may seem like a lot of money, but each company must first purchase a plot of land.  We need to factor all of that in when you're planning your bridge and when you're estimating the number of toothpicks that it's going to take. Each toothpick is going to cost $10,000, so obviously you're limited in your design.
Don: 
Three of the principles that we've learned about design so far are: balance, form and function. So as you are designing your bridges, you want to keep in mind what each of those has to do with what you're going to make.  For example, balance. James, what does balance have to do with what you are going to design?
James:
 The balance… um… helps it from collapsing or holds it in place, so one side won't be bigger than the other.
Don:
Okay, which design did you think was the strongest?
Willy:
Um, the design that was the strongest to me…
Don:
Out of the four…
Willy:
Was the arch, yeah.. the arch.
Hadley:
When we make up the bridge, make sure that it's even on both sides.

Donald Johnson: Even though we have something that we want to teach, all of the children come with some amount of knowledge about something. So before we start to tell them anything, we want to see what it is they already know, so that we can start to make connections.

When teachers want students to understand that some of the very basic skills they're learning now are going to be really important, because at a later date, they're going to have to put those together in some more complex process. One way to do that is actually to give the students first, the complex task, or process, that they're going to need the separate skills for.  That gives them a kind of vision of the more complex whole that they're aiming toward, then, when they learn the individual processes they can anticipate the later transfer.

(classroom scene)
Don:
Because of the events that you are aware of (shhhhhhh!) that have happened recently, you know we're at war, and a lot of planes aren't flying like they were, so due to that, it's harder to get the materials in. Due to inflation I've had to raise the prices on a couple of the items that you use the most.  The lumber, instead of being $10,000 apiece, is now $12,000 apiece.
Class:
(reacts in astonishment) Whoa!  WHAT?
Boy:
How you gonna just raise prices?  What if we won't have enough money to get it done? Then what?
Don:
I'm not giving anybody a loan. However, in the spirit of competition, everybody wants to see a good game, maybe one my companies that has a lot of money left might be willing to work out something with a company that doesn't have any money.
Boy:
Boardwalk needs what?
Girl:
five0,000.
Boy:
That's out of the question. I think we should give them like 10,000. And I think, which team needs 6,000?
Girl:
Um, the Eclipse.
Boy:
The Eclipse company needs 6,000 dollars. Now, you think we can hassle that down to see how much money they really have right now to see if they're asking for too much?
Girl 1:
We could give you $100,000.
Girltwo:
  But you're not giving us money, you're giving them money.
Don:
Okay, hold on.  Hold on.  Hold on.  I thought we were talking about money.  Now I see Essence coming over here with these toothpicks. What is this all about?
Girl:
We agreed to it.  She give us the money, she gave us little bit of extra money, we give her the toothpicks.
Don:
Okay, now I thought I was the person who gave out the toothpicks. What's the difference between getting toothpicks from you and getting toothpicks from me?
Girl:
They haven't got them.
Girl two:
You cost too much.
Girl:
Trying to help them out, but we still get the money.  You see everybody happy.
Don:
Is that right? Should you be able to do that?
Girl:
The only person that's getting cheated is you. 

Donald Johnson: Basically in order to help them see the connection between concepts, I try to teach them a methodical way of looking at everything. For example, the classic scientific method.  I teach them that science is not a body of unconnected facts and figures to memorize, more it's the study of anything.

(classroom scene)
Girl:
Does it have to be 28 centimeters for each side?
Don:
Now, can I ask you a question? Is the string going to be straight or does it swoop?
Girl:
Let's see how much money we need to .. we gotta, we gotta measure in centimeters the cable is.

Donald Johnson: Any student that I've ever had in any class whether our relationship was friendly or not, they will definitely know the importance of proving everything they ever say, by numbers, because when they get in the real world its about "show me." Even when they're trying to get it down in their resume it's about "show me." What can you make me believe you can do? So the whole approach to solving their own problems by their own experimentation that's what I want them to ultimately be – free thinkers.

(classroom scene)
Girl:
We would have had $65,350, but because he's making us pay for the extra day, we're not gonna have enough for the cable.
Don:
Okay, I also need to know what is the span of your bridge, which means how long it is. The span.

Donald Johnson: They can show me that they've learned everything that I've taught by creating something.

For example, in this particular project, everything that I want them to learn I'll know if they learned it, because I'll see a successful bridge that meets the specifications.

It's not even important whether the bridge wins the contest or if it holds more than one gram. Just that visually I see proof that everybody understood. Now, because there is a group of five of them, obviously I won't see a bridge unless there's been some cooperation. So again it's not something that is pencil and paper, and I'm going to mark off when they get 10% and 20%, but it's more of an application in the real world, because in the real world, the proof is that you did it.

Linda Darling-Hammond: Don Johnson brought the rigors of problem solving in the real world to his classroom.  He required his students to integrate and apply their knowledge, learn to use new tools, and think for themselves.

When his students solved their toothpick shortage problem by working together, they demonstrated that not only did they understand the lesson, but they were also able to take their understanding to a new situation. We can bet they'll be much better able to apply these skills when they leave the classroom.   

Lee S. Shulman: We never have enough time to learn everything we will ever need to know in order to live our lives successfully and fruitfully. So it doesn't matter how long you would make medical school, for example. No physician could ever learn enough in medical school to anticipate every possible patient that will ever walk in her door. And therefore, the challenge of education is always to ask, "What's the least amount of material we can teach really well, that will in turn, make it possible for those whom we teach to use that knowledge in the widest possible range of situations, including not only situations that we can anticipate but also situations that no-one can anticipate." And that's abstractly the problem with transfer. How can you learn less, and make much more of it.

Well, it's important for teachers to understand the concept of transfer, because it's absolutely necessary to protect them against what is probably the worst sin of teaching, which is trying to cover all of the material with equal attention across all the things you anticipate a kid might have to know.  First of all that's impossible.  Second, it is deadly boring.  And third, it's bad psychology.  What teachers – the reason teachers have to understand the notion of transfer is whenever they teach, they have to ask themselves, "What is it about what I'm teaching now, that will be of value, of use, a source of understanding, or of pleasure to my students at some point in the future, when they're in a situation that is not identical to the one they're in now?"  And that has got to be a mantra for the teacher, always asking, not just "Where am I?" and "Where are they now?" but "Where might this be going?" and if they can keep on thinking of that question as they teach, which is the question of transfer, then it can transform the kind of teaching they do.

Linda Darling-Hammond: By teaching the thinking skills that support transfer, Julie Helber and Don Johnson are empowering their students to take ownership of their own knowledge. As a result, they can use what they've learned in many ways and flourish as strong, independent thinkers.

When we cultivate these skills in our students, we prepare them not only to  answer questions on a quiz, but also to live productively in the real world.

This is The Learning Classroom, thanks for watching.  

Return to the Support Materials for Session 11.   

Contributors to this Session

Linda Darling-Hammond
Charles E. Ducommon Professor of Education, Stanford University

Lee S. Shulman
President, Carnegie Foundation for the Advancement  of Teaching

Julie Helber
fourth grade teacher, Paddock Elementary School, Milan, Michigan

Don Johnson
eighth grade teacher, Columbus Middle School, Detroit. Michigan