Aspects of biological science range from the study of molecular mechanisms in cells, to the classification and behaviour of organisms, how species evolve and interaction between ecosystems.

The study of biology can be divided into different disciplines –

• Ethology

• Evolutionary Biology

• Physiology

• Genetics

• Molecular Biology

• Morphology

• Systematics

• Ecology

1. That branch of science which treats of the composition of substances, and of the changes which they undergo in consequence of alterations in the constitution of the molecules, which depend upon variations of the number, kind, or mode of arrangement, of the constituent atoms. These atoms are not assumed to be indivisible, but merely the finest grade of subdivision hitherto attained. Chemistry deals with the changes in the composition and constitution of molecules. See Atom, Molecule.
2. An application of chemical theory and method to the consideration of some particular subject; as, the chemistry of iron; the chemistry of indigo.
3. A treatise on chemistry.

Mathematics as a Discipline

A discipline (a organized, formal field of study) such as mathematics tends to be defined by the types of problems it addresses, the methods it uses to address these problems, and the results it has achieved. One way to organize this set of information is to divide it into the following three categories (of course, they overlap each other):

1. Mathematics as a human endeavor. For example, consider the math of measurement of time such as years, seasons, months, weeks, days, and so on. Or, consider the measurement of distance, and the different systems of distance measurement that developed throughout the world. Or, think about math in art, dance, and music. There is a rich history of human development of mathematics and mathematical uses in our modern society.
2. Mathematics as a discipline. You are familiar with lots of academic disciplines such as archeology, biology, chemistry, economics, history, psychology, sociology, and so on. Mathematics is a broad and deep discipline that is continuing to grow in breadth and depth. Nowadays, a Ph.D. research dissertation in mathematics is typically narrowly focused on definitions, theorems, and proofs related to a single problem in a narrow subfield in mathematics.
3. Mathematics as an interdisciplinary language and tool. Like reading and writing, math is an important component of learning and "doing" (using one's knowledge) in each academic discipline. Mathematics is such a useful language and tool that it is considered one of the "basics" in our formal educational system.

To a large extent, students and many of their teachers tend to define mathematics in terms of what they learn in math courses, and these courses tend to focus on #3. The instructional and assessment focus tends to be on basic skills and on solving relatively simple problems using these basic skills. As the three-component discussion given above indicates, this is only part of mathematics.

Even within the third component, it is not clear what should be emphasized in curriculum, instruction, and assessment. The issue of basic skills versus higher-order skills is particularly important in math education. How much of the math education time should be spent in helping students gain a high level of accuracy and automaticity in basic computational and procedural skills? How much time should be spent on higher-order skills such as problem posing, problem representation, solving complex problems, and transferring math knowledge and skills to problems in non-math disciplines?