When I first founded Vertical Learning Labs, I wrote a chemistry textbook called Chemistry from the Ground Up, and released it online and as an interactive multitouch textbook for the iPad. I really wrote this textbook for myself and had no intention of publishing it. I basically asked myself: “What would a vertical middle school chemistry curriculum look like?”
The textbook starts by laying the foundation for the particle theory of matter:
- All matter is made up of particles.
- Those particles are in perpetual motion.
- Some of the particles are attracted to one another.
Building on this foundation, the reader is then able to construct an intuitive and functional understanding of the states of matter and the processes of evaporation and condensation. In the construction phase, the reader is deepening existing concepts while building new ones on top of them. In the diagram above, this is reflected by the transition from yellow to green to blue blocks. Notice that when the concept of solubility is introduced, it is already blue. That is because solubility builds directly on top of the same foundation that the reader developed and strengthened earlier in the study of states of matter and phase transitions.
Later, the reader drills down to discover what causes particles to be attracted to one another. By drilling down, the reader gains a deeper understanding of atoms and molecules. This deeper understanding enables the reader to recognize when and why certain properties are characteristic properties of a pure substance, and to build new understandings about cell chemistry on top of the existing foundation instead of off to the side in isolation.
For the reader, the particle theory of matter represents the ground truth. The ground truth must be intuitive enough so that everything built on top of it just makes sense, and it must be functional enough so that the reader can reason through problems with it. Building on top of the ground truth strengthens and reinforces it. Drilling down and deepening the ground truth enables you to build higher and wider above it. I think that it is worth noting that two components of my ground truth, molecular attraction and dynamic equilibrium are barely mentioned in the standard middle school science curriculum.
Consider the conservation of matter. In Chemistry from the Ground Up, this is the first concept introduced, and it is introduced abstractly and in isolation. But later, as the reader applies the particle theory of matter and visualizes the motion of particles, particles are never created nor destroyed. This is reinforced when particles move among the gas, liquid, and solid states, and reinforced again as systems of particles proceed toward dynamic equilibrium. The conservation of matter becomes integral to the reader’s understanding of matter, and the reader applies it intuitively to solve increasingly complex problems. By the time the reader is balancing equations of chemical reactions by counting and conserving the number of atoms on both sides, it has developed into a powerful analytical tool.
If learning has been vertical, then the reader should have no trouble extending this foundation to understanding the carbon, nitrogen, and oxygen cycles. In fact, it should be blindingly obvious at this point that there is a fixed number of carbon atoms on Earth, and that these carbon atoms are “stored” in various molecules that are constantly undergoing physical and chemical changes. So imagine the shock when the reader learns that, 400,000 years after the Big Bang, the universe is made up of hydrogen and helium atoms, and that virtually no carbon, nitrogen, or oxygen atoms exist at all. This cognitive dissonance should lead to the reader to drill down to nuclear reactions and nucleosynthesis, supplanting the conservation of matter with the conservation of mass-energy.
Beyond enabling us to construct a more intuitive and functional understanding of chemistry, building up and drilling down in one domain also fosters the development of skills and habits of mind that encourage us to build up and drill down in all domains. This includes an ability and willingness to actively test and revise mental models.