The Power of Myths for Positive Purposes

How do we convince students to believe in their capacity to learn?

In earlier blogs I have argued that inherited talent is not a fixed capacity. All of us have the capacity to achieve high levels of performance in domains of knowledge that we are passionate about. The critical factor is sustained effort and strategically designed efforts. With sustained Deliberate Practice all of us can learn far more than we realize.

But that leaves the question of what are the antecedents of the capacity for sustained effort. I believe that for most of our students one of the answers comes from the insights of social psychology. Group identity has the power to shape behavior and performance. Positive role models, both as personal mentors and in the form of group identify play a large role in telling us what we are capable of doing.

Here is a story, part fiction, part fact.

A seventh grade girl comes home from school furious and upset about her math teacher. She screams to anyone who will listen, “He is such an idiot. No one can understand anything he explains in class. I can’t possibly do my homework.” Fortunately her wise old uncle is visiting. He is a retired math teacher and offers to help her with her homework

“I can’t possibly do the homework. There is nothing you can do. I’m just stupid in math,” she screams as she runs up the stairs to her bedroom and slams the door behind her. The whole house shakes from the slamming door.

The wise old uncle slowly climbs up the stair, knocks on her door, and talks to her from behind the closed door. “You can’t possibly be stupid in math,” he says. “You remember your aunt, (She had died seven years ago.) well she was very smart in
math. In fact she was an engineer.” The wise old uncle was actually stretching the truth. The aunt was good at math, just not quite an accomplished engineer.

From behind the door the uncle hears a faint, “Yes I remember her.”

“Well, you know how much of her personality and intelligence you have inherited from her! If she was good at math, then you cannot be stupid at math,” he persuasively argues. Again faintly from behind the door he hears, “Well o.k., but I still hate math!”

“That is fine,” the wise old uncle says. “ You can hate it if you want, but you know you can do it. Why don’t you come out of your room, and I will help you with your homework.”

The girl comes out, and within fifteen minutes the uncle was able to explain the work and the girl realized she wasn’t so stupid in math.

What do we learn about the capacity for sustained effort from this story? First, who we think we are has a huge impact on what we think we can do. As long as we think we cannot do it, we won’t work at it. When we are convinced that we can do it, and with the guidance of a skillful teacher, we will be able to work at it until it gets done. Both experiences, negative and positive, are self-reinforcing.

Second, who we think we are is “socially constructed.” All of us carry around in our heads ideas of what group we belong to and what we have inherited or learned from our group. These messages can be damaging when they come in the form of stereotypes that undercut our potential, such as “girls are not good at math.” “Russians are good at chess.” We often call these messages, stereotypes, and work to debunk them. However, the human psych is programmed to believe in group membership and characteristics, it is not enough to debunk negative messages. As parents and teachers, me must also consciously, explicitly, strategically, and consistently present to our children messages in the form of stories and role models that embody the capacity for accomplishment.

Because, the wise old uncle was able to socially construct a positive myth that enabled the young adolescent to believe in herself. He freed the girl from her defeatist self-perception and re-constructed a positive self-mage: she inherited a math talent. Should we not create the group identity that all SFDS students, because they are at SFDS, are “good at math” and therefore capable of high levels of accomplishment?

The Myth of Talent – Chapter 2

How do we learn the capacity for sustained effort?

In my last blog, I discussed the role of deliberate practice and sustained effort in achieving high levels of performance and accomplishment. This week I explore the fundamental importance of social inclusion and psychological safety in creating an environment where students can learn the capacity for sustained effort.

This blog discusses the rationale behind setting up student affinity groups at SFDS. To read more about student affinity groups click here.

Here is a story from my personal experience that helped me understand how the social context of a learning environment can dramatically influence one’s capacity for sustained effort. This is a true story.

The well-known author of Reviving Ophelia, Mary Phiper, was coming to town to give a lecture at the local college. As Head of School and advocate of empowering female students, I invited several female students to attend the lecture. They needed a ride, so I volunteered to do car pool.

As I entered the voluminous lecture hall, the girls saw some friends and scurried off. I was alone. I looked around for someone to sit with, noticing that I was one of only about a dozen males among hundreds of females. Everyone was talking excitedly in small groups about the upcoming lecture, eagerly anticipating bonding around a common purpose and commitment. I was feeling quite proud of myself, as an evolved, progressive male, for supporting female empowerment. Of course, I was anticipating all the praise I would receive for being supportive of women. (The male ego is a fragile construct.)

I approached a group of women to join the excitement about the event and receive some of that praise. The group simply ignored me. They turned away and didn’t even acknowledge my presence. I turned away, a little put off, and approached another group. The same thing happened. Then I tried making eye contact with some women colleagues I recognized. Again there was no eye contact and no acknowledgement of my presence. Clearly no one was going to talk to me, and certainly I was not going to receive that praise that I thought I deserved.

I was starting to feel anxious. My stomach got tight and my palms a little sweaty. No one was being mean to me. No one said anything insulting. I was just invisible. I got the message. I was not really welcome. They would tolerate my presence at the lecture, but I was not going to be included in any of the animated conversations. So I quietly sat down and accepted my appropriate place in this setting.

I listened attentively to the lecture, found the students at the end, and drove home. As I was pulling into my driveway, I realized I had no memory of anything Mary Phipher had said. I couldn’t recall a single idea or theme. My social isolation had impacted my short-term memory, and therefore prevented me from learning. Even as a highly accomplished middle-aged white male, known and respected in the community, my social isolation in this specific situation inhibited my capacity for short-term memory, which is obviously connected to sustained effort.

This brief encounter taught me a valuable lesson about the importance of psychological safety. If this could happen to me, what is the impact of a similar situation for a six-year old or twelve-year old in our school? Do our students who are a racial minority, family income minority, or in a family structure that is not the norm experience similar isolating messages in our school? Do we unintentionally send others a message that they are not welcome in our school community? If we understand that unintentional social isolation can have a powerful affect on memory, attention, and the capacity for sustained effort, don’t we have an obligation as a school community to make every child feel welcome?

It is the recognition that social isolation, intended or unintended, can impact learning, that forms the basis for organizing affinity groups in our school. This year we invited parents who identify as Asian, Latino, African-American, mixed heritage, or LGBT to have an informal gathering at school with each other and the Head of School. In these gatherings, participants talked about their common experiences as parents and the experiences of their children. While all parents said they and the kids’ experiences were fundamentally very positive, there were many stories of difficulties they faced because of their minority status. The time together and shared stories was affirming and energizing, serving as a sanctuary acknowledging that they were not alone. This affirmation and acknowledgement generates psychological energy and safety that builds the capacity for sustained effort when faced with an uncomfortable learning environment.

Last week we provided an opportunity for Upper School students of color to participate in affinity groups. In Advisory meetings all students were introduced to the idea of affinity groups and provided an opportunity to ask questions. Later in the week in Study Hall, students of color met in an affinity group to be together, to share common experiences, and to feel affirmed for who they are.

Knowing that social isolation and psychological insecurity reduces ones capacity to learn, we are forming affinity groups to help students affirm their identity and know that the School truly welcomes their whole self in this community. The intended result will be an increased capacity to learn at SFDS. For more information on affinity groups both in general and at SFDS please read a letter from Renée Otero, Director of Diversity at SFDS.

Stay tuned for a story about how the myth of inherited math ability can be used to generate sustained effort.

The Myth of Talent

How does a person reach high levels of performance and accomplishment?

The argument and ideas presented in this blog series will explain the role and importance of 1) deliberate practice, 2) sustained effort, 3) psychological safety and confidence, 4) relationship with an admired teacher, 5) group identity, and 6) social isolation or inclusion in achieving high levels of performance and accomplishment. These ideas were presented to the faculty of SFDS in my inaugural address in September 2007 and to a speech to the Upper School student body last winter. I believe these ideas have powerful implications for both the design of instruction and the social culture of a school environment.

How does a person reach high levels of performance and accomplishment? The first answer that comes to mind is likely, “You have got to have talent, and talent is essentially inherited,” Inherited talent is only a small part of the answer. Research on expert performance in a wide variety of professional fields demonstrates that most of us are capable of much higher levels of performance than we think; there are no inherent limits to our accomplishments. The limits we place on ourselves because of our sense of our talent have been proven to be artificial and often a self (not)-fulfilling prophecy.

I first encountered these ideas in an article in the New York Times titled "A Star Is Made" by Stephen J. Dubner and Steven D. Levitt. (New York Times, May 2006, Freakonomics) The authors analyze the puzzling phenomenon that most of the professional soccer stars in Europe were born in the first three months of the year. They discovered that in youth leagues throughout Europe, coaches routinely selected slightly older kids for their teams, mistaking physical maturity for ability. Hence, early in their lives these kids were selected to play on competitive teams, benefiting from years of practice and excellent coaching. The random factor of their birth dates (not inherent talent) gives them the opportunity to be groomed for elite performance and made into stars.

What does excellent coaching provide that leads to expert performance? Sustained deliberate practice. Deliberate practice means more than simply repeating a task over and over. Rather it means 1) setting appropriate specific goals, 2) obtaining immediate feedback, 3) correcting the performance based on the feedback, and 4) concentrating as much on technique as outcome. Research done by Anders Ericsson at University of Florida has demonstrated that many people can become experts in tasks such as short term memory, playing a violin, chess, software design, golf, and even surgery with years devoted to deliberate practice.

How might these concepts of sustained deliberate practice play out in a classroom environment? An instructor who is interested in helping students become excellent writers of compelling nature non-fiction, might first focus on opening sentences that grab the reader’s attention. Students would practice writing sentences and then get feedback from the instructor. That feedback would enable them to revise and revise again. Once they develop this expertise, the instructor would move on to another specific goal, such as “placing accurate detail in the context of ecological dynamics.” Again the path to excellent performance requires getting feedback, revising, and correcting. Over time the accumulated series of specific skills gets combined into an integrated performance. Of course, the requirement is devoting lots of time to practice and correction under the watchful eye and honest evaluation of an admired coach, mentor, or instructor.

The authors do acknowledge that devoting concentrated effort over extended periods of time is not that easy to do. They suggest that in order to devote the time, you must love what you doing. You can’t reach expert performance levels unless you are passionate about what it is you are practicing. However, our own experiences tell us that it takes more than passion. We know we can love to do something, but not always have the discipline to engage in deliberate practice. Have the authors just replaced the myth of talent with the myth of passion? Indeed, it seems they are suggesting that either you have the capacity for sustained effort or you don’t, once again implying that raw inherited talent (this time a talent for passion) determines the capacity for sustained effort.

I believe the capacity for sustained level can be learned. Next week I will tell some stories that illustrate how a relationship with a teacher, your psychological confidence, group identify, and sense of social isolation and/or inclusion powerfully affect your capacity for sustained effort.

Stay tuned.

Financing Independent Schools – An Introduction

During every one of my discussions with parents in the Community Meetings this fall the issue of rising tuition came up. Parents asked with genuine worry what should they expect, and is there any alternative to steadily rising tuitions? These questions were consistent with the comments made in the surveys conducted by the Strategic Review Task Force last year. The Board of Trustees has been asking these very same questions as it reviewed the findings of the Financial Task Force in 2007 and again at the January 2008 meeting.

This blog entry explains why tuition increases every year, and addresses how our school can mitigate these increases in order to maintain our commitment to the core value of socio-economic diversity.

Following is a summary of the financial issues:

1. Salaries and benefits make up 69% of all expenses.
2. Salaries and benefits rise every year by 5-7%.
3. There are three sources of revenue: tuition, annual fund, and endowment income.
4. The more we have in annual fund & endowment income, the less we need in tuition
5. With tuition rising at 5% per year, more and more families will qualify for tuition assistance.
6. This additional revenue to fund expanded tuition assistance will come from increases in endowment and annual fund income
7. Because socio-economic diversity is a fundamental core value of the School, the Board of Trustees has an institutional imperative to raise these additional funds

The Necessity of Cost Increases
The financing of an independent school education requires tuition increases of 5% - 7% annually. The revenue is needed to meet rising annual costs such as salaries, benefits (health insurance), utilities, and liability insurance. Salaries and benefits make up 69% of all expenses. Unlike many other professions, teacher salaries are structured like an apprentice model. They start at a low level, Step 1 is $50,000, and increase annually in small increments. There are no large increases when they achieve a mastery level. At SFDS a teacher with 15 years experience earns $70,000. These annual increases should meet or exceed the rate of inflation so that eventually teachers have a wage that enables them to live in San Francisco. It is these annual increments plus escalating insurance costs that increase total annual expenses and necessitate revenue increases.

The Financial Structure of Independent Schools
The components in this simple chart are the three main sources of revenue that SFDS, and every other independent school in the nation, must manage.

lllllllllllRevenue Sourcelllllllllllllllll% of Total Revenue
lllllllllllTuitionlllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll79%
lllllllllllAnnual Fund Raisingllllllllllllllllllllllllllllllllllllllll14%
lllllllllllEndowment & Investment Incomelllllllllllllllllllll6%

The Importance of Non-Tuition Revenue Sources
The only way to mitigate annual tuition increases is to increase the revenue from non-tuition sources: fundraising and endowment. From FY 2006 through FY 2009, thanks to the generosity of our community, both annual fund and endowment income will have increased significantly.

lllRevenue Source lll% Cum. 4 year Inc. llDollar Inc.
lllAnnual Fund lllllllllllllllllllllll48% llllllllllllllllllll$394,000
lllEndowment Incomelllllllllllll66% llllllllllllllllllll$288,000
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll________
lllTotal Non-Tuition Revenue lllllllllllllllllllllllllllll$682,000

As you can see in the chart above, by FY 2009 the annual fund will have increased by 48% and our endowment income will have increased by 66%. During the same time period, the cumulative tuition increase will be 21%. Clearly non-tuition revenue is increasing at a rate much higher than tuition revenue. This additional non-tuition revenue has effectively lowered the magnitude of current and future tuition increases.

Full Per Pupil Costs and “The Gap”
Tuition for the next school year will be $22,310. However tuition income does not reflect the full cost per pupil. The total budget for 2008-09, not including funds for tuition assistance, is $9,861,000, making the full per pupil cost of an SFDS education $24,650 per student. This difference or “gap” between the full per pupil cost and tuition ($24,650 vs $22,310) is $2,340. Non-tuition funds, primarily the School’s annual fund and endowment income, make up this difference. In a purely financial sense, each student and family receives a discount on the full cost of the educational program at SFDS through the allocation of non-tuition revenues.

A Strong Commitment to Socio-Economic Diversity
SFDS is fundamentally and intentionally committed to socio-economic diversity. We must provide access to our school to families from a wide range of family incomes and adult work careers. We understand that diversity of background and experience is a pre-condition for creating a dynamic academic culture that teaches critical thinking. When students are analyzing texts, probing critical questions, and listening to opinions from diverse frames of reference, that is when they learn to think.

Access to and participation in our community by this broad spectrum of families is a cornerstone value of SFDS. Therefore, it presents us with a financial imperative. As tuition continues to increase, more families will qualify for tuition discount. We are committed to providing that opportunity. Funds to support this discount will come from increases in the annual fund and endowment.

The Board fully understands and is committed to pro-active efforts to increase non-tuition revenue even more than the recent past. We understand that in order to be successful, we will have to create a clear and compelling case and present it to potential donors in personal conversations. Personally, I am very optimistic that our community has both the spirit and resources to make this crucial aspiration a reality in the near future.

What Is an Academic Kindergarten?

http://www.sfds.net/extras/Academic_Kindergarten.pdf

I wrote the above articles during my tenure as Head of School at Park School in Baltimore. They were also the starting points for the talk and discussion at last week’s kindergarten coffee. What follows is a summary of the presentation to our kindergarten parents.

In an age of standardized testing, many parents are rightfully concerned about what constitutes an academic kindergarten. In contrast to some of the media and government pressures, it is my view that skill lessons in letter identification and phonics are not age-appropriate for early childhood and can hinder rather than support cognitive development. At four and five years old children can, of course, be taught to write down their names or repeat the names of letters. However, these learned behaviors do not represent meaningful skills to young children; they do not use them to further their curiosity and knowledge. And, adults must force young children into unnatural conditions in order for them to mimic the intended behaviors. In order to develop the capacity for conceptual thinking, young children need to engage in activities that fire their curiosity and encourage them to build connections between themselves and the world around them. First-hand observations of the natural and social world that lead to conversations and questions enable children to follow their curiosity. Imagination and creativity are actually the keys to academic accomplishment.

Consider the following two stories:

Story 1
Three young pre-school students are asked to sit at their desks with worksheets. One teacher stands at the blackboard drawing a series of letters and shapes. A second teacher stands with the students, helping them circle the corresponding letter or shape. One young boy struggles with the assignment. He sinks down in his seat, looking back and forth from blackboard to desk, trying his best to fill out his worksheet correctly. At times he rubs his eyes, frantically trying to clear his mind and focus on what was obviously a very difficult task for him. The teacher spends most of her time managing the behavior of this boy. She tries her best to help him focus and finish the lesson correctly. He wants desperately to do what the adults are asking, even though the specific letters he is learning are just empty symbols unrelated to any content and interesting information. He does make some marks that the adults seem to accept, and he is then permitted to hurry off to the block corner where he builds a castle.

Story 2
A young girl accompanies her mother on various errands one night. She notices the moon is up. At each stop she mentions to her mother that she sees the moon again. In the middle of the drive, she announces that the moon is following them. The girl is
acting just like a young physicist. She knows that usually when she moves from place to place her environment changes; the same objects are not in two different places. On this night, however, the moon remained in view throughout the drive. Puzzled by the discrepancy between what she saw and what she expected, she created a theory to explain the phenomenon. Her theory to explain the unusual observations: the moon is following her. Not knowing how to explain to her daughter that the moon is not really following them, the mother instead seeks to engage her daughter in a letter-recognition activity. She points to a nearby pharmacy sign and asks the child to identify the letters of the store’s acronym. Unwittingly, the mother has directed her child away from her natural interest and observation in the moon.

Rather than asking children to participate in activities that are disconnected from their experience, let us choose another way. Let us choose to support our children as they explore their unique internal understandings of the world through language and imaginative play. To do this, we can always return to the method of asking questions. We promote cognitive development by asking, “Why do you think that?” and “What else do you notice?” These questions encourage young children to come up with their own theories and narratives about the world – a practice that builds children’s imagination and cognitive reasoning.

It can be difficult to find the time in our hectic schedules to delve into the long, circuitous conversations that result from listening to our children about their interests and observations. It does require tremendous patience and perseverance to participate in children’s thinking. However this empathy with children is exactly what activates cognitive growth and intellectual development.

Leaning Into Conflict

Often in life, the most interesting conflicts are not between right and wrong. They are conflicts between competing “good things to do.” When resolving a conflict between right and wrong, you debate the issues, decide what is right, and then try and dredge up courage to do the right thing. When a conflict arises between two valuable things to do, it is much more difficult to decide what should be done.

Last August we became aware that the first night of the Grade 5 Outdoor Ed program and the first night of Hanukkah were falling on the same night. Forces beyond SF Day School’s control scheduled both events. The Marin Headlands Institute provides SFDS with a date for our annual event. We cannot reschedule. And the date of Hanukkah, well … that was decided many years ago.

This conflict put families in an impossible situation: Should they require their kids to stay home and participate in an important family religious celebration and miss Outdoor Ed, or let their kids go to Outdoor Ed and miss the family celebration? How could the School put families in such a difficult situation? How could the School resolve this conflict between two genuinely and equally valuable experiences?

A group of parents, teachers, and administrators met to discuss the situation. We did not retreat to our respective pre-determined positions and argue for the rightness of our own values. Instead, we leaned into the conflict. We listened and affirmed the values of the other. We agreed we had a big mess, and promised to avoid it, if we could, in the future. We brainstormed a long list of alternatives. We evaluated the list to see what changes in both the School program and family celebrations each idea would require. Finally we agreed to invite the Jewish families, including siblings, to come to Marin Headlands and celebrate on site. But that idea didn’t quite seem right, and the parents suggested inviting all the families. That is what we did!

The celebration took place this past Tuesday, December 4. It was a dark and stormy night. Huge waves were crashing over the 100 foot Bird Rock. Families brought latkes, applesauce, sour cream, and personal family menorahs. I told the story of Hanukkah, emphasizing the historical fight for religious freedom against an autocrat with an overwhelming and exorbitantly technologically armed force. It was a bloody story; the students were mesmerized. We ended with lighting all the menorahs.

I concluded with a discussion with the students about why we would celebrate together and get to know one another’s deep traditions. Why is it that in every tradition grandfathers tell stories to their grandchildren? What is it the elders wish their grandchildren to remember? Of course, it is the values these stories teach, and vivid personal story-telling, year after year, secures the memory deep in our consciousness. We all hope our children will live out these values in their adult lives.

By leaning into a conflict of competing “goods” we were able to enhance the family traditions of all the families in the SFDS fifth grade.

Deep and profound thanks to everyone who made it happen!.

Blowing Up The Principal: Pneumatic Bags

DAY 1 - THE EXPERIMENT

As I entered Mr. Bool’s seventh grade science classroom, each student was holding and manipulating a plastic bag with a straw sticking out one side. I asked one student what the class doing, and she explained they were making “pneumatic bags.” She showed me that they had taken a flimsy supermarket plastic bag, taped all the edges closed, and inserted a plastic straw halfway into one of the sides. They were now blowing on the straw to inflate the bags and then slowly deflating them being careful not to break the bag or cause a leak in any of the sides. She explained they were going to use the air pressure in the bags to push up some weight.

I was struck by how each student was intently crafting his/her bag, sealing the sides, and alternatively showing the success to their classmates or asking for guidance from Mr. Bool or a fellow student. These were scientists at work preparing their apparatus for the experiment soon to be enacted.

Mr. Bool asked several students to help him balance one of the tables on a floor scale. He then asked one of the students to read and record the weight on the white board in front of the science lab. The students then prepped a second table that had been placed in the middle of the room. They placed their bags along the side length of the table, three on each end, with the straws facing out. Once this was done, they helped Mr. Bool lift the other table upside down, with the legs pointing to the ceiling, and placed it on top of the plastic bags.

Impulsively I signaled to the teacher if I might climb onto the table. The students had all crouched down poised by their bags with the straws extending outward, ready to blow. He nodded and up I climbed. He asked me one last question before giving the instruction to blow. “How much do you weigh?” “One eighty-five,” I answered and the number was written on the white board under the weight of the table.

As the students began to blow, the bags inflated, and both the table and I began to rise! One student was ready with a cm ruler and called out the rise of the table, “Five, nine, twelve, fourteen centimeters.” “POP!” One bag’s seal suddenly gave way. “Oh no!” moaned another as her bag slipped off the edge, pushed out by the pressure. I remained floating on air, slightly tilted to my left, for a few more minutes until the students stopped blowing and the table and I settled back down.

Mr. Bool asked several questions about what had happened, focusing on the terms “force, weight, mass, and pressure.” All the data was recorded for next day’s discussion.


DAY 2 – THE LECTURE

When I returned the next day, an outline of a lab report and the data from the previous day were written on the white board. A standard lecture / discussion unfolded, with Mr. Bool discussing how the force of the air pressure contained in the plastic bags had lifted the mass of the table and me. He explained how the invisible molecules of oxygen and hydrogen in the bags, moving incessantly at high rates of speed, were bouncing off the plastic walls and thereby creating the pressure to push up the table.

It was, of course, the real experience of seeing and feeling the table rise as the bags inflated that made it possible for the students to understand the physical reality of invisible, tiny air molecules. The scientific words and abstract concepts became a physical reality for the students.
Mr. Bool then asked the students to calculate the area of the tabletop in square inches. He then showed them how to calculate the mathematical measurement of pressure by dividing the weight of the table by the area to get the pounds per square inch.


DAY 3 – THE LAB REPORTS

When I returned the third day, the students were scattered around the room writing their formal report. Herb provided the classic structure: Procedure, Results, and Discussion/Explanation. The students were filling in the chart with numbers, calculating the pounds per square inch, and composing narrative sentences to explain the results.

Here is one student’s explanation of air pressure from her lab report. I know I could not have explained what happened to me with this degree of detail. Could you?

After doing this experiment, I can easily see that air can exert a force or pressure against the wall of its container. This can be seen because all that air was able to lift 285 pounds. This was only possible with the Kinetic Molecular Theory, which states that air molecules are always moving, and since they are always moving, the air molecules are colliding.

There are far too many air molecules in our atmosphere to count, which is why collisions between those molecules are so frequent. There are 4 sextillion molecules of air in every cubic inch of normal air (air that is not in a container). One air molecule experiences about ten billion collisions per second while traveling at 1,000 miles per hour. Since these molecules are always colliding, when air is compressed in a container (in this example, a bag) they collide against the wall of the container. When they collide against the wall they create a force (because the molecules of air have mass), and since that force is spread out all along the walls of the container, it is called pressure.

As we blew into the pneumatic bags, more and more air molecules were in the bag, and they collided more creating more pressure on the wall of the bag. As the bag inflated, it applied pressure against the underside of the table and lifted it. To be able to lift the table the air molecules need to be compressed. This means that the molecules are being squeezed together as tightly as possible so that more molecules can enter the bag. Since the room between air molecules is larger than the molecules themselves, they can be compressed and expanded easily. The more molecules there are in the bag, the more pressure is applied.

Pressure is measured in psi (pounds per square inch). To find out the psi in this example, you find the force (285 lbs.) and find the area of the table, (2160 sq. in.). Then divide the force by area, and you get the pressure (Force divided by area=pressure). In this instance, the psi equals .13194. This means that for every square inch on the table there’s .13194 pounds pressing on it. That pressure raises the table, so this is how air creates a force.

This series of learning activities is a model of thoughtful instructional design. Note the variety of activities,

1. Crafting of scientific equipment by each and every student, requiring precision and care,


2. Enacting, demonstrating, measuring, and recording a surprising result - Lifting a Table – requiring the participation of all students,


3. Listening and note taking to learn specific scientific terms and abstract concepts, and understanding HOW they described the physical events,


4. Applying a mathematical calculation to more precisely describe physical events,


5. Composing on a blank page a coherent and integrated written document that shows the connections between physical event, abstract concepts, and mathematical symbols, in your own words

In-depth learning can only occur when all of these different modalities are offered to students in a purposefully designed sequence with sufficient time devoted to each activity. Too often in schools time is not allowed for the students to conduct the experiment, AND to discuss the concepts in words, AND to apply mathematical symbols to the words and events, AND to put in all together in a coherent report. Teachers are often pressured in many ways to compact the process. They might demonstrate the event instead of having every student do it, combine the lecture/discussion and writing, or give a short answer test. That would result in superficial learning. Without time for each phase the students won’t integrate in their minds the events, the concepts and the symbols.

Understanding how abstract concepts and mathematical symbols represent and describe physical phenomena is the fundamental process of human intelligence. By structuring a sequence of learning activities, we can enable students to develop their capacity for conceptual thinking and problem solving.