The Graduation Rate Myth

Robert Weissburg, professor of Political Science at Cornell, gives a stunning indictment of student irresponsibility in this John W. Pope foundation article, and some of the reasons faculty put up with it.

What he doesn't analyze are the psychological effects of their previous twelve years of schooling. The flaws in lower education are rife; I can't go into them all. But I'd like to examine two which have devastating effects and are directly related to the kind of behavior Weissburg laments:

• False self-esteem-building practices
• Test-driven instruction

First, the mis-directed ideas of phony self-esteem dominant in the last 20-30 years has encouraged teachers and parents to praise children regardless of accomplishments or effort. This practice seems to be motivated by at least two beliefs:

1. Children's egos are so delicate they cannot withstand any negative feedback from others.
2. Children cannot develop self-esteem without continuous praise from others.

In fact, a large portion of solid self-esteem results from achieved competency as a result of hard work, and from the regular experience of failure.

Why?

Because failure will always be a normal part of life and if a child does not learn how to overcome failures and continue to strive for his or her goals, that child will have a very difficult time in adulthood.

A child who has a false sense of self-worth and efficacy, and little experience with overcoming failure, is extremely vulnerable to depression, drugs, and suicide when faced with the actual problems of life because he or she is, in fact, incompetent. No amount of praise will overshadow those facts.

Optimally, parents and teachers encourage students to work hard at their learning, while modeling and expecting serious achievement, and giving praise for actual accomplishments. Negative feedback should be factual and task-oriented - "Here's where the equation has an error" - not directed at the child - "You should know better than to write the equation like that; here, this is how it should be."

In a Montessori classroom, self-development and self-esteem are achieved by mastering the work. The materials through which learning is accomplished are designed to be just hard enough to be challenging, but not so hard as to be impossible to master. At the same time, they are just the kinds of things children find fascinating to do, given their level of development. All this results in flow experiences for children, making them highly motivated to work.

Here is a video that illustrates how young children (3-6 years old) develop their sense, motor, and observational skills through the materials:




 And here's a video illustrating the mathematics curriculum:


The older a child gets, the more advanced and complicated the materials, until he or she is competently working abstractly, but with a rock-solid foundation in reality through previous work with concrete materials. Here's a video about the elementary level: http://www.youtube.com/watch?v=cBs73rff0n0&feature=share&list=PLFB81B46845AB1919 (embedding wasn't allowed).

and one about the arithmetic of fractions, usually the hardest and least-understood arithmetical operation: http://youtu.be/GKHM5unkza4

This kind of work develops happy, competent, self-directed individuals who want to learn.

And one of the other elements that makes this possible is the competency-driven curriculum that does NOT center on standardized testing.

Which leads back to Weissburg's complaints: the second major element motivating poor student behavior has been the inordinate emphasis on standardized tests these past 20 years.

Schools, teachers, and students have been rewarded on test scores alone - not actual learning or competent teaching. Students are talked at, not engaged in the learning. Teachers feed information (not understanding) and students learn that all they need to know is what's necessary to score well on tests.

So are we surprised that's all they're interested in? That they just want to "get through" the class and will find any way to do that efficiently and economically? That they don't respect their teachers - that they're not oriented to understanding the material? They have not been encouraged to be invested in learning or in achieving the actual competency of understanding.

I lament the situation with Weissburg, because of the enormous wasted time and potential - and worry whether they will be able to learn enough as adults to overcome these handicaps.

Lecture Fail

A debate is raging in The Chronicles of Higher Education regarding lectures. There are many laudable points on both sides.

However, I'm chagrined at the faculty members who aren't asking: do we know the optimal way for students to learn? What are the principles? What do we know about human development, and how is that relevant to our problem? What skills do these students need to benefit from the way we're teaching?

What's most unrealistic to me is the faculty member's belief that what students need to do is concentrate for 90 minutes on her lecture, i.e. apply their will. That's the solution?

It seems as if faculty favor lectures for a variety of reasons. I won't visit the non-productive ones, such as the fact that it may be a lot less work for a professor. Let's just look at positive reasons. A lecture can skillfully condense the essentials the student needs to learn about a subject, and faculty are often concerned that students learn what's fundamental and essential.

It's also personally satisfying to many faculty members to demonstrate their superior knowledge. And faculty are often the kind of people who really enjoy sharing knowledge with others. But most students aren't necessarily motivated to do so, or to be the recipient of knowledge summarized and shared, rather than acquired by first-hand experience. In the latter types of experience the student can enjoy the feeling of gaining competence - "look what I did myself!"

What the Flow research highlights is the limits of attention. It takes huge amounts of mental energy to concentrate, i.e. to pay attention, to information that arrives in a form which is difficult to mentally ingest. Here are some of the reasons:

1. Abstract ideas generally take more energy to attend to because they don't engage the senses or body or, often, the listener's deepest motivation. Instead, on their own the listener has to come up with imaginary objects or instances to embody what the lecturer is saying. That's why aids such as visuals or demonstrations are good to use. And, unless the listener is naturally interested in the subject, he has to cheerlead himself into continuing to pay attention. In the case of most students and most lectures, I'm betting they must cheerlead with a stick ("I'll fail!") rather than a carrot ("This stuff is cool to know!").
   
2. Listening while sitting still in a seat is extremely difficult because it doesn't engage the senses or the body.
   
3. If the listener gets confused, or stops paying attention for a bit of time, he or she has no opportunity to ask questions or re-start the lecture; the rest of the presentation may be worthless or, at the least, less than optimal as a learning experience because it can't be followed well.
   
4. Optimal human attention span is about 20 minutes (in other words, the length of TED talks) - 90 is almost impossible unless it's a full-body-and-mind engaging activity, like a sport or watching a movie, in which the emotions are engaged. OR unless it's a Flow activity for that person. Lecturing can easily be a Flow activity, especially if the lecturer finds the material interesting.
   
5. A good listener has an internal dialogue with the lecturer, pondering the truth of comments, asking questions about what is said, and trying to find the data in memory to answer them. Some people do this naturally, but the vast majority have no natural skill: they need to be taught how to "actively listen." And they're not getting that in the lower grades - so no wonder they're abyssmal at it in college.
   
6. Neither are most students in lower education given the activities, materials, or opportunities to learn how to concentrate. And then they're expected to figure out how to do it on their own when they arrive at college? (Developing the ability to concentrate is something Montessori classroom do well, because the materials are designed to trigger Flow for students. )

See the summary, student comments, and faculty responses and videos here.

New Evidence on Math Gap Between Genders

Read the new study available at the Notices of the American Mathematical Society on the mathematical ability gap between boys and girls. Researchers Kane and Mertz find it's much smaller than imagined, and examine various theories about it.

In Montessori we've found that girls can do just as well as boys at mathematics, using our hundreds of mathematics materials, but most girls seem to need to use the materials longer than the boys. We start all children out using materials as three year olds and introduce them to more and more advanced mathematics materials up through middle school.

Rediscovery of What We Already Knew in Montessori

Apparently the Erikson Institute's new program "The Early Mathematics Education Project," recently instituted at 300 Chicago public schools, incorporates real objects and events to teach young children the fundamentals of mathematics. This was reported today in the Wall Street Journal in an article titled "New Calculation: Math in Preschool."

According to the article, "Evidence is mounting about the importance of teaching math in preschool and kindergarten."

I'm glad they've just discovered this! But it's not a new calculation: Montessori schools have been teaching fundamental mathematical concepts in preschool (Children's House to us) for over 100 years, because Maria Montessori discovered the importance of doing so that long ago.

We use fabulous, beautiful materials, such as the Trinomial Cube. Here's the equation it represents:





And the Golden Bead materials teach the basics of addition and subtraction so that even 4 year olds can do equations to the millions.

The Montessori Method has dozens of carefully designed and tested mathematical materials to work with.

One of the first graduates from my school, Council Oak Montessori, is now a parent of a three year old there. He came to a parent meeting and described how the mathematics materials helped him in all his later school career (and even to today), by teaching him how to concretize and visualize mathematical operations. And he didn't start at our school until 2nd grade.

Ah well, it's great that the students at CPS are getting SOME mathematical concretization.

"To really learn, quit studying and take a test"

A new study from Purdue, discussed in this New York Times article, finds that students who take a test about material they've learned have 50% more recall of the material than those who either repeatedly study the material, or those who study and draw diagrams of it.

I can see immediately two important learning principles operative in these results: 

1. The test focuses attention and motivation, which always makes someone remember better and, as the writer mentioned, shows the person what they don't know, possibly interesting them in correcting their ignorance.

But do most students care about what they don't know? My observation is that many just want to get done with what they're studying to go on to the next requirement.

2. The article's analysis claims that testing requires active reconstruction of material, which helps recall. They used a free-form essay as the test in which the student reconstructed the material learned.

Actively reconstructing knowledge requires a person to not only recall what they've learned, but conceptually organize it and this does help with learning and retention.

But whether testing always helps is not clear to me. Multiple choice tests, so often used, require recognition of material rather than active recall and reconstruction. So the inference from this study, that testing results in better learning, is flawed. 

In Montessori, students study through learning materials, such as these. They are designed to illustrate concepts through real objects - a better way to fix knowledge in memory than mere paper and pen, as it engages the senses and the students' activity. 

And we use a three-period lesson to teach the student how to use each learning material:

1. Teacher names objects in material and demonstrates its use, with as few words as possible.

2. Student practices material, with teacher asking "show me this" etc.

3. Student demonstrates use of material/meaning to teacher, with the teacher asking "what's this" etc.

This last step requires the student to reconstruct his own knowledge in order to present it correctly - giving him an opportunity to see the gaps, like a test. When a child thinks he has mastered the material, he can ask the teacher to "test out" of it by demonstrating how much he knows about using it.

The Hand as the Instrument of the Mind

"Using advanced tools such as magnetic resonance imaging, researchers are finding that writing by hand is more than just a way to communicate. The practice helps with learning letters and shapes, can improve idea composition and expression, and may aid fine motor-skill development."

"How Handwriting Trains the Brain," in the Wall Street Journal, you can read about a "new" discovery we've known in the Montessori world for 100 years.

“The hands are the instruments of man’s intelligence.” 
“The human hand allows the minds to reveal itself.”
“The mind and the hand are prepared separately for written language and follow different roads to the same goal.”  Maria Montessori 

Hence, the thousands of "hands-on" Montessori materials in a Montessori school. 

The Neurology of the Montessori Method

In the Montessori Method, we attempt to convey learning through as many senses and physical motions as possible, for more effective learning. Montessori captured this idea in her saying "The hand is the instrument of the mind." It's the basic reason we have so many materials for the children to work on.

I just discovered this blog with lots of information on the Montessori Method - and this informative post on neurological research which explains the basis of these principles.

And this article from the Dana Foundation "What dance can teach us about learning" summarizes research that's also relevant to this issue.

(Hat tip to Cynthia Gillis)

A Method Rooted in Independence

Encouraging a child's independence is deeply rooted in the Montessori Method - one of the reasons I love it.

Beginning with the very young children (3-6 year olds), students work individually on materials which develop their senses and motor abilities and their independent powers of observation, analysis, and integration - the essence of reasoning. Group work is not encouraged for the very young, who are just forming their minds, as it is in Progressive schools. However, children can work together if they want to.

Furthermore, well-trained Montessori directresses are very respectful of individuals, their styles of learning and living, their interests, and their ideas.

(We call Montessori teachers "directresses" or "directors" because they more guide the children than instruct them, the materials do the instruction).

Group work become a bigger component of the curriculum as the children get close to adolescence; as students develop, they need to learn how to work with other people to prepare them for adult life.

However, the children are encouraged to work at their individual best: not compete with each other. Human beings are naturally competitive, but it is very distracting to develop self-motivated learning habits when competition is emphasized, especially for the very young.

The ugly head of social pressure rears up to tear the young mind and heart away from the inherent joy of learning.

All these elements serve to encourage even the most timid child to be independent in their thoughts and actions, a welcome respite from the kind of social pressure I talked about in my previous post.

That's not to say that Montessori schools are immune to social pressure - I've seen plenty of teachers promoting their scientifically unsubstantiated or unexamined views on the environment and nutrition, among other topics, through special projects and lessons.

Fortunately, the many aspects of Montessori which encourage factual observation and reasoning mitigate against this.