Teaching in the 3rd Dimension

Doug De La Matter

Head of Science (retired)
Madawaska Valley D.H.S.
Barry′s Bay, Ontario

I have taught all sciences (including senior Chemistry and Physics) for the past 30 years in a small rural high school.

As I worked from day-to-day, course-to-course and term-to-term, I found some tricks that worked and discarded many that didn′t. Now that I have been retired for a couple of years, I have had the time to reflect on my experiences and I see things that I wish I had been given the time to think about when I was on the job.
I hope to share some of those insights here.

From the beginning, I should state my view that learning is NOT gender-based. I am convinced that the presence or absence of Y chromosomes makes NO difference in the potential of humans to learn or do anything (with the possible exception of human reproduction).

Many years ago, I had mixed level classes of Grade 11 physics. One of the assigned tasks was to design and assemble a working electric motor from various supplied parts. All of the Academic level students got busy drawing circuit diagrams and analyzing the problem. Then quite a few groups started looking around for an Applied level student who had taken a tech class to actually build it!

And those students were right.
The best motors were built by students who probably had the least grasp of the theory.

Yes, school DOES mirror "real life"; there are PhDs who can′t change light bulbs and potters who make intricately coloured glazes with no knowledge of the chemistry behind their art.
Every time I see a brick building, I am in awe of the brick-layers, most of whom probably had trouble with high school geometry. How do they build the entire building without getting a single brick facing wrong-side-out?

Thinking back over my experiences, I see how schools select for certain types of thinkers and discard others. I believe that we are losing our most valuable science students by not recognizing and rewarding the way they think.

At this point, you may be anticipating yet another reminder to redesign all of your lessons in light of multiple intelligences. Don′t worry, I know you are too busy for that.

But a quick review will allow me to make one or two points.

Multiple Intelligences (H. Gardner)

The theory of multiple intelligences suggests that there are a number of distinct forms of intelligence that each individual possesses in varying degrees. Gardner proposes seven primary forms: linguistic, musical, logical-mathematical, spatial, body-kinesthetic, intrapersonal (e.g., insight, metacognition) and interpersonal (e.g., social skills).

Hmm...SEVEN different ways to focus your lessons. But wait, if we look a little further, we find that J.P. Guilford has also looked further!

Structure of Intellect  (J.P. Guilford)

In Guilford 's Structure of Intellect (SI) theory, intelligence is viewed as comprising operations, contents, and products. There are:

- 5 kinds of operations (cognition, memory, divergent production, convergent production, evaluation),
- 5 kinds of contents (visual, auditory, symbolic, semantic, behavioral), and
- 6 kinds of products (units, classes, relations, systems, transformations, and implications).

Since each of these dimensions is independent, there are theoretically 150 different components of intelligence.

Only 150 boxes to fill??

From my experience, I would say that on Planet Earth there are about 6 BILLION different combinations of the elements that make up human intelligence. (More, if you try to understand the intellectual worlds of elephants or whales.)

If you can design a variety of experiences for your students, by all means Do It !

One of the most creative people I have met, composes Chemistry songs and teaches very complicated biochemistry using rhyme and music. It works!

But don′t drive yourself crazy.

More relevant to the classroom situation, I think, is the older work by Piaget. Here is a thumbnail sketch of a small part of his life′s work.

The concrete operational stage is the third stage in Piaget's theory of cognitive development.

During this stage, the child begins to reason logically, and organize thoughts coherently. However, they can only think about actual physical objects. They cannot handle abstract reasoning. This stage typically occurs "between the ages of 7 and 12". or, in the case of a lot of MY students, somewhere between Grades 10 and 13 (ages 16 -19).

The formal operational stage is the fourth and final stage in Piaget's theory.

 It is supposed to begin at approximately 11 to 12 years of age, and continues to develop throughout adulthood, although Piaget does point out that some people may never reach this stage of cognitive development.The formal operational stage is characterized by the ability to formulate hypotheses and systematically test them to arrive at an answer to a problem.

The individual in the formal stage is also able to think abstractly and to understand the form or structure of a mathematical problem. So those 13 year-olds in Grade 9 should have no problem accurately visualizing molecules and the kids in Grade 10 will just breeze through Motion problems! Right??

SOME of your junior students have reached this stage, but not all. The rest may be very intelligent. They just cannot understand OUR way of thinking … yet.

In 1984 psychologist David Kolb published his "Learning Cycle Model" ( Experiential Learning ).

He claimed that learning styles could be seen as a continuum:
concrete experience: being involved in a new experience
reflective observation: watching others or developing observations about your own experience
abstract conceptualization: creating theories to explain observations
active experimentation: using theories to solve problems, make decisions

Unfortunately, (in my opinion), Virginia Hartman (in 1995) took Kolb's learning styles and gave examples of how one might teach to each them:

-for the concrete experiencer--offer laboratories, field work, observations or trigger films
-for the reflective observer--use logs, journals or brainstorming
-for the abstract conceptualizer--lectures, papers and analogies work well
-for the active experimenter--offer simulations, case studies and homework.

Personally, I believe she missed an important point. Maybe Kolb did as well.

To me, Kolb was just restating the ages-old "Scientific Method"

Which is just a distillation of what kids have been doing all their lives...

We use ALL of these aspects in learning ANYTHING.

So just where are High School students in the Piaget progression? How can we find out?
 I suggest that may be quite easy if you work some activities into your introductory lessons.

1. On the first day of Grade 9 science class, I would always do the following:

Demonstration: Different candles

Hold up a variety of candles and ask "What do you see?"
Don′t correct them when they answer "a candle". The classic activity here gets the kids to state actual observations, and avoid jumping to the conclusion that it is a candle. I handle that after they have fallen into my "trap".

After several students have identified several candles, I state: "You guys are FANTASTIC! You have just shown me that although candles come in any shape, any colour, any size, yet just by looking at it, you can tell it is a candle...HOW do you do that?"

All the concrete operational types would smile, happy that this teacher was so easy to impress. A few kids would frown, their eyes would glaze over as they suddenly found themselves pondering questions that Plato never found the answer to.

I instantly knew which ones were thinking at the Formal Reasoning level.

[By the way, this is a quick, but valuable exercise for a different reason. I always used to end the discussion by reminding them that students are a lot like candles. No matter what size, shape or colour... once fired up, they all give off the same light. ]

2. Note who gets excited by showy demonstrations... which you should always do whenever you can.

Why?    Well, compare these ways of making a point:

″Write in your notebook:

‘Gases are more soluble in cold liquids than in hot liquids.″

DEMONSTRATE The Root Beer Fountain.

(see the demonstration #9 on my web-page

Which statement will a Grade 9 kid remember more clearly?

A startling event is much more effective as a memory trigger than printed words

3. Use lots of discrepant event Demonstrations (which you should do anyway), but try to notice kids who are the most fascinated by the results. To me, those kids are the furthest away from Formal Operational thinking. They see the concrete evidence, but can’t rationalize it away.


Drop a can of Coke & of Diet Coke in a water-filled aquarium…
"why does the Diet can float?"…"because the regular Coke is heavier!"

Drop in a penny. "So a penny is heavier than a can of Diet Coke"??

Well, why does diet coke float? Chemists know that aspartame is about 200 times sweeter than sugar, so they need to put less dense sweetener inside. This lets us show students just how much sugar there is in a can of pop.

DEMONSTRATE: Put a Coke can and a Diet can on opposite pans of a Pan balance. Use sugar cubes to balance the two loads.

Now, we can just tell them that there are about 8 spoonfuls of sugar in a can of pop, but a concrete thinker (or any type of thinker) will remember the sight of the sugar more easily than the sight of a notebook entry about the point.

[An excellent and meaningful first year class investigation is to research the amounts of sugar in a variety of canned and bottled drinks and display the container with the approriate number of sugar cubes beside each in a display for the school lobby.]

I think we can do other, more quantitative tests in the course of our normal science classes.

When teaching kids how to measure mass with balances, we can run a contest.

"Pour exactly half the water out of a full unmarked Erlenmeyer flask.
Check the weight of the water to see how close you came."

Piaget used such "conservation" experiments to test which level a kid was operating at. The concrete thinkers will tend to pour out half the height, not half the volume.

You can ask for the written records of each try by each student and get a quick survey of "who is where"!

When we know even roughly, what level of development each of our students is at, we can tailor questions and assignments to fit. I used to struggle to make the mathematics of "Density calculations" clear to Grade 9 students. Now I see that I should have made much more use of physical models… find the mass of an actual cubic centimeter of different materials, then of the same materials with 2 cm3 of volume, then with 10 cm3 volume. With enough concrete examples of "mass per cubic centimeter" most students would then be able to accept the abstract concepts of weighing and measuring volumes and then using a formula to be able to compare the "density" (the masses of standard size pieces) inside different objects.

This is worth doing even in a senior class. Many adults do not progress beyond the concrete-operational stage, so just because the students are older does not necessarily mean that they can think about abstract things effectively. As I will show soon, because YOU are a successful academic, you have expertise in one type of thinking, but it is not the only type.


Many teachers notice that Girls seem "more mature" than Boys when they enter High School. They generally have neater notebooks; they don′t lose things as often; they are quieter and more co-operative; they do homework and meet deadlines more regularly. Although most people associate these traits with "maturity", I suggest that there is another important principle at work.

In general, most Girls are already better adapted to the "pencil and paper" 2 Dimensional universe of our classrooms.

I think that as kids grow up in "Western" society, very young boys are given more opportunities to "Play" with 3 dimensional objects. They watch their fathers and other men take things apart and "fix" things.

In the years "BC... before computers", they used to be more physically active too. Why do boys like shoot-‘em-up video games? I think it is because those games display perspective and you have to think in three dimensions to play them.

When they reach school age, they enter a two dimensional universe. They sit in ordered rows, read and write on two dimensional surfaces, and they get fidgety.

I wonder why?

[For a very poignant and informative extension of this idea, and its implications for teaching Math, read the article by a Spanish educator Claudi Alsina posted under the link "How Johnny Became a Flatlander" on my web-site.]

Why do skateboarders never GO anywhere on their boards?
(No, I am not asking "Why don′t they ever go Away?")
What is their fascination with jumping over things and flipping through the air?
Why are most of them Boys?

I think that due to different socialization experiences, more girls adapt to the 2-D world more quickly, and become more comfortable in it.
Why do most boys like science, especially in grade 9?
Is it because it is the only academic class where they get to move around and "do" 3-D activities?

Number of Entries in Biology, Chemistry and Physics and the Success Rates of boys and girls
achieving SCE Scottish Standard Grade awards 1-3 (Scotland)
Source:        http://www.set4women/statistics/tables/table_161.htm

This a clear illustration of trends that are found in many countries.

Why do most Grade 9 girls like the biology part of science best?
Is it because it is the science topic that is taught using mostly 2-D techniques?

(Remember, I′m using broad brush averages here!)

As I will try to show later, what I am really saying is that students of whatever gender who prefer 2-D activities will tend to feel more comfortable studying Biology, because it requires the least facility with 3-D thinking.)
An Irish study of year-2000 students showed a general decline in enrollment in science courses, and more female students are now taking science than males.

However, there is a very sharp contrast in the pattern of science studied by girls.
Three out of every four girls who do a science subject are taking Biology.
Among boys Biology is still the leading subject selected, attracting one-third of all students.
However, Physics is also popular with almost a quarter of boys taking science.

I also found a Harvard PhD thesis in education by Holly James that studied Gr. 7 girls who had enrolled in a summer science and engineering camp.
Of the 9 girls interviewed, 5 wanted to pursue Biology, only one wanted to follow engineering.
They ALL liked projects, but the future engineer is quoted:  "Science can be fun if you do it."

I feel that many times, psychologists draw faulty conclusions about certain observations because they don′t have a good understanding of the underlying process involved in solving a science problem. One book (Boys and Girls Learn Differently! by Michael Gurian & Patricia Henley [ISBN 0-7879-5343-I]) states that girls cannot look at a blackboard full of equations and keep up with the boys in the class because, in the opinion of the authors, they couldn’t think as well in 2 dimensions.

Well, I have taught Physics in grade 11 and at the college preparation (AP) level. In grade 11, the girls were usually superior at handling equations. They worked hard at memorizing them all and plugged in numbers, and got the right answers and the high test marks. At the AP level though, the boys seemed to be more able to look at an equation and "see" what the physical situation behind the symbols was like. This was not a gender issue though. I had several brilliant boys who were used to getting near perfect marks… yet had anxiety problems because "they just couldn′t get" the physics problems.

One year, I hit on the requirement that each problem had to have a fully labeled diagram before I would even look at the solution. Some of those guys almost became violent in their opposition to the idea. But when they finally started to draw, they started to think spatially and understood how to apply the equations to the situation.

There is obviously much valid concern around the world for the gender differences in education. In some places, though, I fear that it is becoming its own industry. I think that too many "experts" get distracted by the "gender" issue and they don′t focus on differences in thought patterns and attitudes between people who have experience and facility thinking in three dimensions and people who are more comfortable using paper.
In spite of my many references to gender differences here, I repeat that I don′t believe it is a biologically significant factor in learning or learning potential.

In a fascinating Norwegian study of children in 21 countries, boys and girls were equal in some "science" experiences ONLY in underdeveloped countries.

[See the link to "interesting articles" leading to Svein Sjoberg′s article]

Note that in less developed countries, the gender differences are much smaller.

To be blunt… if you get your water every morning from a well using a rope and pulley, whatever your gender, you will understand ropes and pulleys!

I would argue that, due to different socialization and education experiences, within western societies, more girls adapt to the 2-D world of the classroom more quickly, and become more comfortable in it.

The psychologist Mel Levine′s "Myth of Laziness" theory seems to imply that we should teach each kid in the learning style that they prefer... to the exclusion of other styles. Although it may be a vital approach for special cases, I strongly disagree with the approach in everyday teaching.

I think we must allow kids to benefit from their strengths, but also challenge their weaknesses.

Here′s a suggestion that I will frame in the context of a science lab, but the essence of it can be applied to almost any form of group work.
How many times in Grade 9, have you had this teaching experience?

"We′re going to do an experiment today.
No! Sit! Wait until I tell you what we are going to do!"

In my experience in a class of 25, there would be about 8 or 9 kids who just couldn′t wait to get their hands on equipment. Most, but not all, would be boys.
Some others would sit back and start drawing data tables instead of even looking at the equipment.
THOSE students would record all the observations and end up leaving when the bell rang, carrying the data with them.
Often, the "equipment-oriented" people would cleaning up the equipment before they left… and not have any written work to turn into a lab report that evening.
The "recorders got the good marks… the "engineers" got late penalties!

Thinking about it now, I would :

Design a test for, or just observe each student′s comfort level in using equipment. When allowed to do an experiment, notice who runs to grab the 3-D equipment and who stays at their desk drawing a 2-D data chart and getting ready to record observations.

Label them as 2-Dimensional or 3-Dimensional thinkers.

Divide the class into groups that include both types. Pair them up as lab partners, and ASSIGN the roles of operator and recorder. Have each one sign the lab data sheet according to what they did. Most important, ROTATE the roles. If you must use groups of three, give each student one of 3 colours as labels. On a "Red day", each member of the group will know who is supposed to do what:

-Blue assembles the supplies and is in charge of directing the clean-up

-Red operates the equipment

- Green records the data.

For the next experiment, Green sets up, and is in charge of clean-up, Blue operates the equipment and Red records the data.

In this way we can get better organization in lab classes AND teach 2-D thinkers to handle 3-D equipment while developing important 2-D skills in 3-D thinkers.

Of course, I realize that this isn′t a new idea. I am sure that 30 years ago they taught me this in Teacher′s College. But I used to rotate lab partners early in the term and then would get lazy and just let them work with friends. Now I see that mixing the two types of thinkers was the important thing to do… even if it was a bit inconvenient for me to take the hostility of the kids who just wanted to be comfortable, letting the partner do the uncomfortable parts of the activity.

An Art teacher I know says that "academic" kids who are often good with paint or pen and ink drawing, become much less confident when sculpting in clay. Students in technical classes try to avoid pen and ink drawing, but are enthused about sculpting in clay from Day One.

Would it make sense to start these kids drawing by giving them objects to draw that they can touch and manipulate, like a crushed pop can, or just their own hand and fingers?

Considered at another level though, this is a very disturbing observation.
Remember the Grade 9 experiment?
Who got the highest mark on the lab report?
The 2-D person who wrote down all the data!
Those 3-D thinkers, those who can think comfortably in one more dimension than we academic-types can, do we funnel them into technical courses because they get lower marks on the 2-D activities that we assign and reward?

Are we missing some of the most flexible thinkers because we aren′t looking for the fruits of their talents?

At ChemEd 05, Rhonda Reist reported that she had tried asking her students to draw a diagram of the procedure for each experiment before they were allowed to begin the laboratory activities. She wanted to encourage students to read and understand the procedure handout. The results were amazing. The class went from asking many questions about the method during the lab to asking NONE.

They all understood what was to be done and just went about doing it.

Another teacher I know was at that talk and tried it with her very talkative class.
The same thing happened.
The change in student behavior is so dramatic that there must be something important going on.

To me, the drawing exercise acts as a bridge from 2-D instructions to 3-D objects. Students have more trouble than we imagine when they are asked to put written instructions into action. Remember which one of the pair of students will be trying to operate the equipment… the 3-D "engineer". But (s)he has trouble making sense of written ideas. When they draw a diagram, the words become pictures and the pictures allow them to visualize the actions in 3 dimensions. The 2-D student translates the "easy" written instructions into visual cues that help when looking at the unfamiliar array of lab equipment on the desk.

So this is why drawing diagrams helped solve those Physics problems!


You may wonder why I am so concerned about things that you probably already do in your classroom in some form or other. My concern is that in the wider world, there is a significant movement to phase the laboratory experience out of science instruction. Similar campaigns will limit your ability to teach other subjects effectively using physical experiences.

Many years ago, I rigged up the first "video-camera on a microscope" setup in my county. For some reason, the Director of Education at the time was shown the device on a visit to the school. His first response was "So does this mean we don′t have to buy any more class sets of expensive microscopes?" In a rather risque moment of candor, I replied that I was trying to teach kids how to use microscopes, not how to watch television!

In a recent issue of the Journal of Chemical Education, [Vol. 81 No. 9 September 2004], a hotly-debated article by Stephen J. Hawkes is titled "Chemistry Is Not a Laboratory Science." In it, he questions the value of laboratory classes in college chemistry courses compared to computer simulations. He may have proposed this as a wake-up issue for discussion… It certainly woke ME up.

Safety and liability concerns are increasingly being quoted to cover up the motive of saving money. "Let them do it on a computer… safer, cheaper and easier and just as effective."

But it is NOT.

People learn different skills when using a computer. The machines are more expensive than basic lab equipment, and the lack of experience in 3-D manipulation and analysis of the world around us can lead to tragic consequences as theory is used in place of experience.

Recently, in the USA, an envelope containing white powder was found in a postal station. The material was analyzed by a hazardous materials lab which reported the "All Clear". Nothing to worry about. The material was identified as the common chemical Toluene. Chemists on a discussion list that I belong to were appalled. Apparently, none of the people that signed the report were aware that Toluene is a colourless liquid, NOT a white powder.
Of course, if the computer says it is Toluene, who are WE to argue?

There is a vast difference between "knowing" how something works and being able to "make" something work.
As students progress in their understanding of experimental science, they develop an instinct for quantities; they learn to look for measurements that can be done quickly and those that require precision.

My  marking scheme for senior science students included how they efficiently measured out quantities.

A student who follows the printed directions and tries to weigh out 2.00 g of a powder by adding and taking away small bits of chemical until the screen reads exactly 2.00 is not an effective worker. An experienced student would weigh out (say) 2.13 g , record that weight and then carry on to use THAT number in the calculations.

The amateur student fills the buret very carefully every time to exactly to the 0.0 mark. The experienced student puts in some liquid, takes a careful reading of the level and gets on with the titration. Computer simulations always start the buret at Zero. How do you fill a buret with a corrosive liquid? Just click a mouse!

Does the computer check to see if you are wearing safety goggles?
Is there an empty beaker under the buret to contain any spills?
Is there an air bubble in trapped in the tip?

The first edition of one of two major Grade 11 Chemistry texts used in Ontario explained that the Copper-clad roof on our Parliament buildings is coated with green copper oxide. Unfortunately, copper oxide is a black powder. If you have done an experiment with it and spilled it onto your lab book, you remember things like that.

In the end, there is no substitute for physical experience.
The more variety of experiences you can provide for your students, the more capable they will be.

Far too often, you and I impose our 2 Dimensional academic skill sets on all of our students. We have good reasons... they are important skills; they promote efficient learning; they are less work for us to organize. But remember that, in many ways, this imposes a restricted way of dealing with the world on those students whose skill sets are better adapted to THREE dimensions.

Volkswagen once ran an ad campaign that divided the world into two groups… drivers and passengers.

Too often, the school system divides students into 2 groups…thinkers and doers....academic and technical. ...OOPS …must use "Canadian Newspeak"....Academic and APPLIED.

Science provides opportunities that few other subjects can, to incorporate 3-D activities into our lessons. Science classes are among the very few places where 3-D thinkers can thrive and hold their own in the 2-D world of school.
(Come to think of it, even physically using a pen to write with is a 3-D activity and connects us to different parts of the brain than a keyboard does...another discussion paper there!)
Demonstrations are entertaining and informative… but they are not sufficient.
The more experiments done by students in your course, the better.

It’ is more work for us, that′s true.

Please Do that work.

Not for entertainment or distraction, but to reinforce 3-D skills as well as 2-D skills for every student in your classroom.

We want to produce

Doers who Think
Thinkers who Do.

I want to end this ′rant′ by urging you to avoid the biggest error of omission I made in my teaching career. Ask every student in every class to send you a postcard or a business card once they have their first full-time job. In 10 years, just think of the inspiring display you will have in your classroom! You will be able to take those young, intimidated, Concrete-Operational students to that display and show them physical evidence that people from your school can do anything they set their minds to.

And if my argument has influenced your thinking,

the Carpenters, Mechanics, and Artists
will be displayed as prominently as
the Doctors, the Research Scientists and Teachers.

We need them all !