Mathematics is a central tool in developing scientific ideas, in testing scientific claims, and in communicating scientific results. Science, in turn, is a major source of inspiration for the development of new mathematics. Engineering and technology are the application of these two realms of learning to the solution of real world challenges. The Mathematics, Science, and Technology (MST) curriculum integrates these areas with the goal that students be able to apply their learning to new situations, be able to identify new problems and pose original questions, and have the understandings necessary to carry out investigations in pure and applied mathematics and science to answer those questions.

As children grow, they seek to know why things happen, how they happen, and what will happen when they change the parameters of a situation. Our classes enhance this natural curiosity that students all start out with about our natural and man-made worlds, the origins of our universe, and of human history. Students learn factual information and master technical skills in mathematics and science through a combination of traditional approaches and laboratory investigations that require and reinforce those facts and skills and make it possible for them to find answers to questions themselves.

DIVISION ONE (grades 6 and 7)

Course 1 - Engineering

Students work on their design for a snail-paced vehicle in Engineering.

Mathematics is a central tool in developing scientific ideas, in testing scientific claims, and in communicating scientific results. Science, in turn, is a major source of inspiration for the development of new mathematics. Technology is the application of these two realms of learning to the solution of real-world problems. The interplay between all three disciplines and historical and social issues is extensive. The MST curriculum interweaves all three with the goal that students be able to apply their learning to new situations, be able to identify new problems and pose original questions, and have the understandings necessary to carry out investigations in pure and applied mathematics and science to answer those questions.

The engineering course introduces students to engineering problem-solving methods. Students use Lego and Robolab software to design and build first machines and then robots to solve a range of problems. These problems require students to learn and apply ideas from physics (simple machines and mechanical advantage, force, energy, motion), geometry (measurement, similarity), and algebra (proportion and linear behavior) to succeed in their challenges. As they learn about robotics, students learn fundamental programming concepts and ideas from computer science.

Students explore connections between engineering and art including the work of Alexander Calder and Arthur Ganson. The class studies Computer-Aided Design (CAD) which teaches a range of core geometric concepts and then visits a Computer-Aided Manufacturing (CAM) facility to see how robots can carve out real versions of their virtual illustrations.

The course culminates with comparisons of societies with different levels of technology and how engineering to solve third world problems requires creativity and the ability to use different materials and energy sources. For their final project, students design an original invention carried out for a client in their family, the school, or the broader community.

Course 2 - Doing Research in Mathematics and Science

There are many similarities and differences in the way new knowledge is derived in mathematics and science. In this course, students explore a range of scientific and mathematical settings as they practice asking questions, posing problems, and developing theories about the settings. They grapple with how a conjecture differs from a theorem and a hypothesis differs from a theory as they learn how to be junior mathematicians and scientists carrying out original research. Topics include: Experimental design and the statistical analysis of data, number theory, algebra, geometry, statistics and probability. This integrated biology and mathematics research curriculum includes an ecological research project at the Arnold Arboretum.

DIVISION TWO (grade 8)

Course 3 - Marine Science

Marine Science develops and applies biological, chemical, physical, algebraic, and geometric ideas to the study of the environment. During the first term, students develop an understanding of biomes and how climate and other forces create specific ecosystems. They explore how the water, carbon, and nitrogen cycles operate in different biomes. Students gain an appreciation for the interconnected nature of our world and the behavior of humans by exploring the effects of man-made pollution on the environment. The class focuses on marine environments, the properties of water, and water quality. During these studies, functions (linear, exponential, logistic, etc.) are used to model processes such as population growth and light penetration in a lake.

During the second half of the year, the physics of water is studied using concepts of force, pressure, density, concentration, center of mass, and buoyancy. To facilitate their research of a lake or ocean setting, students build a Sea Perch – a remotely operated submersible vehicle designed at MIT, the construction and operation of which involves the above concepts. For their final exhibition, students use their Sea Perch to research a freshwater or saltwater environment. Students present their findings in a report that provides quantitative analysis to support their claims and raise additional questions.

DIVISION THREE (grades 9 & 10)

Course 4 - Revolutions in Mathematics and Science

This course compares and contrasts the relatively recent historical evolution of a truly scientific understanding of chemistry with the ancient development of a rigorous approach to mathematics and the blossoming of geometry that were reflected in Euclid's Elements. Within mathematics and science, what are our standards for asserting the truth of a statement? What types of evidence do we accept? How do the mathematical and scientific communities work to reach agreement on what knowledge is valid? Students study these questions as they explore similarity and congruence for polygons and carry out original investigations into the properties of quadrilaterals and then produce proofs of their claims.

The angle bisectors of a parallelogram form congruent shapes.

In their chemistry studies, students learn the needed supporting mathematical skills (e.g., logarithms for acids and bases and exponential decay for Newton's Law of Cooling). The class learns how the geometry of electron orbitals affects bonds and the shape of molecules, how to balance chemical reactions, how redox reactions occur within biological systems and everyday life, and the laboratory techniques needed to explore these topics experimentally. In the final trimester, students see how one intellectual revolution begets another with the surprising discovery of non-Euclidean geometries supporting Einstein's Theories of Relativity.

Course 5 - Human Biology and Decision-making

This course compares the biology of different organisms, with an emphasis on human biology, through the lens of molecular, developmental, and genetic and evolutionary concepts. Students study functions in two, three, and higher dimensions and their application to rating and ranking everything from the quality of a college to whether or not a patient is a suitable organ transfer recipient. Trigonometry is used to understand forces involved in skeletal and muscle systems. Game theory and behavioral economics are explored as tools for understanding our brains, the evolution of cooperative behavior, and for making informed decisions that avoid destructive long-term personal and societal consequences. Inferential statistics are used to produce experiments that generate testable conclusions.

DIVISION FOUR (grades 11 & 12)

Course 6 - Calculus, The Sciences, and their Intertwined Histories

Students study the development of the Calculus, its interplay with questions from physics and biology, and the history of these connections. Students develop and test calculus representations of physical settings involving motion and of biological settings involving predator-prey relationships and the spread of a disease and compare their predictions with actual data.

Course 7 - Mathematical Modeling in Science and the Humanities

Mathematics provides one window through which we can study our world. It is invaluable as a tool for supporting active and questioning citizenship. Mathematical modeling will teach the modeling process and skills necessary to creating abstract representations of real world settings. The curriculum's culminating modeling experience is a project that has student groups create an original model and analysis for a question that they generate. These problems, like all real ones, do not come with instructions attached regarding which mathematics ideas or skills need to be applied. Students learn to identify which of their many skills will help them solve a problem and learn how to teach themselves new mathematics when necessary.
Students in past versions of this course have applied their skills to questions from economics, physics, biology, sociology, urban planning, and religion.

Electives

MST electives vary from year to year according to student interest. Past offerings included a course on genomics and biology research.

Computer Science - Object-oriented Programming in Java

Students study how to represent data, design algorithms, and connect the two in programs. Object-oriented methodologies are at the heart of this programming experience. Students build a number of applications both individually and through group projects which require the class to coordinate their programming specifications. Projects include a database, a simplified version of the game Battleship, code-making and code-breaking tools, computer graphics, and many other applications. This course is a prerequisite for AP Computer Science.

Advanced Placement Computer Science

This course follows the curriculum detailed for the Advanced Placement Computer Science Exam. Building on foundations established in the introductory computer science elective, students carry out longer and more complicated projects, develop greater sophistication with class hierarchies, master a greater variety of algorithms, and propose and carry out their own programming ideas. Students are expected to put a lot of independent time into their programming efforts outside of class time.

Technology Elective

For students who joined Meridian after Division 1, this class provides the opportunity to study Computer-aided Design (CAD) and Manufacturing (CAM) and three-dimensional geometry and to carry out the related projects from the Engineering course.