As far as I can tell from listening to education experts the answer we, as educators, are supposed to give to this question is “no.” The term is too fuzzy, cannot be defined, etc. As far as I can tell from listening to teachers in the classroom, by and large we believe that the answer is “yes.” We try to foster understanding as much as possible in the classroom.

I first ran across the dilemma about understanding by attending workshops designed to focus on learning outcomes. Much to my surprise it was taken as a given that “understanding” could not be a learning outcome never mind what teachers might say. But, I think there’s a problem lurking in the outcomes approach that leads to the conclusion that understanding cannot be a learning outcome. The problem is succinctly expressed in a recent New Atlantic article titled “Is Google Making us Stupid?” The presumption of learning outcomes is “a belief that intelligence is the output of a mechanical process, a series of discrete steps that can be isolated, measured, and optimized... There’s little place for the fuzziness of contemplation. Ambiguity is not an opening for insight but a bug to be fixed.”

I worried for some time that I was alone in the belief that education could focus on understanding. After all, education experts are united in their view of assessment and outcomes. Well, maybe not. Consider Howard Gardner; a well respected psychologist and researcher in education. In his book The Disciplined Mind, he actually advocates a curriculum based on the goal of achieving understanding!

He begins by defining understanding. “An individual understands a concept, skill, theory, or domain of knowledge to the extent that he or she can apply it appropriately in a new situation.” I submit that this is what we should all expect from our students. Rather than feeding them the material that’s going to be on the exam and, what’s worse, feeding them the exact format of the exam, we need to be teaching them to apply what they learn in situations they have not yet seen. After all, isn’t this exactly what they will have to do to succeed in the 21st century world of work? What good does it do to train students to answer specific questions about specific concepts in a completely predictable environment when they will rarely see such environments but will need to figure out how to apply what they’ve learned nonetheless?

In their book Sparks of Genius, Robert and Michele Root-Bernstein illustrate the problems that come from ignoring understanding in education. “The problem with divorcing what and how in education is that knowing about things is not the same as understanding them. Richard Feynman made the point when he said, apropos of the French curve, ‘I don’t know what’s the matter with people: they don’t learn by understanding: they learn some other way- by rote or something. Their knowledge is so fragile.’ “ Feynman is correct and, frankly, the advocates of learning outcomes that ignore understanding are going to be responsible for creating more graduates with excellent grades and fragile knowledge. Is that an accomplishment they will look back on with pride?

When it comes to the emphasis on understanding another way of saying the same thing is that we want to teach students how to think in addition to providing them with useful content. But, do “approved” learning outcomes foster this goal? Let’s look at some of the examples of good learning outcomes: describe, identify, sort, compare, and contrast. While these are useful skills they do not go as far as understanding in the sense that Gardner advocates. When presented with several options (which the students most likely knew they would see on the exam) they can compare them, contrast them, identify them, etc. But, when presented with the complicated world of information and competing claims for their attention are they able to figure out which items need comparing? Can they figure out whether a given description of something (a political speech, a crime scene, a project at work) is accurate or complete? Having identified the main point of a speech, essay, or blog online can they critically evaluate it? Can they understand it? I would hope that these are important questions and I would hope that we as educators would want to help our students master these skills.

In a previous post I mentioned two responses I give to students who feel that we should not bother with questions about reality that have no consequence in how we treat others or live our lives.. The first was that there are practical consequences to the answers we give to these questions. The second was that not everything we do has to be practical or have practical consequences. It occurs to me that there is a third answer to provide. Philosophical questions force us to think beyond our everyday life and this is a good thing.

Philosophical questions by their very nature are abstract and transcendent. They do not directly address everyday life in many cases. While it is possible to draw connections between these kinds of questions and everyday life there is a benefit to being forced to look beyond the mundane and the everyday. Isn’t there? Isn’t life about more than wondering about what you will have for dinner, who fed the dog last, when the lawn will get mowed and other such everyday worries? Asking philosophical questions about the nature of reality ought to inspire us to wonder at the world. For many it may even inspire a spiritual experience or awakening. Of course these things themselves have practical benefits such as the reduction of stress. But, even without these benefits there might be good reason to ask such questions.

I think an important reason is to fully participate in the human community and understand what it means to be human. Part of our endowment is the ability to use reason to think abstractly. Aristotle claimed that this was one of the highest virtues and an important part of living a happy life. Sure, nothing insightful may come from our aimless pondering but something valuable just may. A sense of the wonder of the world, an appreciation of our place in the cosmos, the realization that our concerns and problems are not as big as we sometimes think they are. In short, asking philosophical questions gives us perspective. So go ahead and ask these questions difficult as they may be and elusive as the answers may be. You might just enjoy life a little more as a result!

Here's an anecdote that perfectly explains the need for improved math literacy:

In 1940 engineers from Indiana’s Department of Highways asked the state legislators to purchase an electric calculator for their office. One of the legislators challenged the engineers: “Why would you need a calculator? You are not mathematicians.” An engineer responded, “In order to build safe roads it is necessary to make precise calculations of curves and banking angles. We must factor pi into our calculations and pi is an irrational number- a constant with a value of 3.141593...” The legislator was confused by the mathematical riposte. Shaking his head, he walked into his legislative meeting, taking with him the engineer’s explanation for the “justification” for the expenditure. After a while the legislator emerged with an answer: “We don’t have money for your calculator. But, we decided to change the value of pi for you to 4.”

Source: Math and the Mona Lisa, Bulent Atalay

Here are some useful and interesting links:

Evernote
Nudge
StickK
Personal Brain
Encyclopedia of Life
Cassiopeia Project
Worldwide Telescope
Goodreads
Visible Body

The secret begins at home with actively engaged parents. Parents need to interact with their children and demonstrate to them that learning is a part of life and can be fun and rewarding. There are several tangible ways to do this whether your kids are being homeschooled, in private school, or in public school.

1. Read to them and with them. If your children are young, read to them. You can read them children's stories but also read to them from the classics. If they are too young to understand what you're reading at all (because they are still infants) they will still get some benefit from hearing the words and the interaction. At a certain age they will be able to understand more and more and you've built a solid basis for their own reading ability.

2. Play music for them. If you are a musician play live music on your instrument. If you are not, play them recorded music. Make sure you play a variety including classical music. Give children broad exposure to music. If you are not a musician, take the opportunity to make music with your child through improvised means with toy flutes or recorders or other simply instruments. Again, the important component is the interaction and engagement. This can also build a foundation for further musical development as they get older.

3. Show them the world. This does not necessarily have to involve travel though it can. Even a walk in the park can be an opportunity to show children the world of nature and share some fascinating learning experiences. Show them how things work both at home and out in the world. Explain things to them at the grocery store, the bank, wherever you run errands.

4. Learn about science together. There are many good books with fun and educational experiments and projects you can do at home to foster curiosity, learning, and engagement. Think about it. When a child is born they know nothing about the world around them. You have the opportunity to show them and share that with them. Take it!

5. Make everything a learning experience. Cooking the family mean together can be a chance to learn, doing chores around the house, going to the store. The key is to interact with your children.

6. Ask questions. This applies both to the child and the parent. I have a friend who said to his son, "you're not asking me enough questions!" So many parents would rather their children be seen and not heard. But, they need to learn and you are an important resource. They should be asking you questions and you should be eager to help them learn. If they are in school, you should be asking them about what they are learning in school. Test their learning by seeing if they can explain it to you. If you can ask them questions and they can answer them, this is a good sign that they are getting a good education. If not, this is a sign of a problem that needs to be addressed.

The key is to engage with your kids. My wife and I go to restaurants sometimes and see parents with their children and they are not talking with each other. What a horrible situation. You've got to interact with them and share your knowledge with them. Foster their joy of living and curiosity. This will provide them with a good foundation for life long learning.