Setting Hands-On Math Apart 

Some Definitions from the Web

Science (from the Latin scientia, meaning "knowledge") refers to any systematic knowledge base or prescriptive practice that is capable of resulting in a prediction or predictable type of outcome. In this sense, science may refer to a highly skilled technique or practice.

Physics  (Greek:physis – φύσις meaning "nature") is a natural science it is the study of matter and its motion through space-time and all that derives from these, such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the world and the universe behave.

Mechanics (Greek Μηχανική) is the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effect of the bodies on their environment. The discipline has its roots in several ancient civilizations. During the early modern period, scientists such as Galileo, Kepler, and especially Newton, laid the foundation for what is now known as classical mechanics.

Mathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.

Albert Einstein, on the other hand, stated," as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Applied Mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains.

Engineering is the science, discipline, art and profession of acquiring and applying technical, scientific and mathematical knowledge to design and implement materials, structures, machines, devices, systems and processes that safely realize a desired objective or inventions.

A Laboratory (informally, lab) is a facility that provides controlled conditions in which scientific research; experiments and measurement may be performed.

A Common Teaching Method

Commonly, the topics and of mathematics, physics and engineering are taught separately. Within a topic there will be history, concepts, logic-based derivations, examples worked by the teacher and exercises to be worked by the student and graded by the teacher. Additionally, a topic may have an associated laboratory in which the students are required to experiment, measure and report.

Setting HOM Apart

HOM is a scientific approach to conveying an understanding of physics and mathematics that employs "do it yourself" observations on models that are based on the contributions to physics of such as Galileo, Kepler, Newton and Lord Rayleigh, the contributions to applied mathematics by such as Pythagoras and Gauss and the contributions of engineers such as Bush. 

HOM's primary emphasis is on the use of applied mathematics in a computer-laboratory environment to construct models of the physical relationships of force, matter and motion in an atmosphere that provides both buoyancy and resistance to motion. The use of a model atmosphere provides computer modeling that closely emulates the physics of our real world.  An even better model would include the effects of Lift.

Deep understanding is acquired by constructing a model of a physical process, by confirming that the model behaves in accord with its design objectives, by employing the model to explore the laws and relationships that have been modeled and by using the model to provide answers to new questions.  Each of the foregoing factors, constructing, confirming, exploring, and responses to "what if", makes a contribution to a student's understanding of the behaviour of the world and universe in which he lives.