114 TExES Mathematics / Science 4 – 8 Exam

The TExES Mathematics / Science Exam is a certification examination that is designed to determine whether or not an individual has the knowledge necessary to teach mathematics and science at the middle school level in the Texas public school system. This exam assesses the individual’s knowledge of a variety of mathematical and science-related topics and the individual’s understanding of the teaching methods required to effectively teach these subjects. This exam may be required, in addition to or instead of the Generalist 4 – 8 Exam, in order to become a certified middle school teacher in the state of Texas depending on the exact type of teaching position the individual is pursuing. The exam consists of 110 multiple choice questions, 100 of which are scored and 10 that are not scored, that are related to the following areas:
Number Concepts (approximately 8 questions)
Patterns and Algebra (approximately 11 questions)

Geometry and Measurement (approximately 11 questions)
Probability and Statistics (approximately 8 questions)
Mathematical Processes and Perspectives (approximately 5 questions)
Methods of Mathematical Instruction and Assessment (approximately 8 questions)
Scientific Method, Scientific Inquiry, and Scientific Processes (approximately 11 questions)
Physical Science (approximately 11 questions)
Life Science (approximately 11 questions)
Earth and Space Science (approximately 11 questions)
Methods of Science Instruction and Assessment (approximately 6 questions)
The exam-taker will be supplied with a Formula and Definitions Reference Sheet, a scientific calculator, and a copy of the Periodic Table for the exam. The exam-taker will have five hours to complete the exam and the exam will be scored on a scale of 100 – 300 with 240 set as the minimum score considered as passing for the exam. The registration fee for the Mathematics and Science 4 – 8 Exam is $82 and the exam is only administered in a paper-based format. However, there are usually other exams and fees that are required in addition to this exam in order to become certified as an entry-level middle school teacher within the state of Texas.

114 TExES Mathematics / Science 4 – 8 Exam Practice Questions

Sample Study Notes

1. Explain what math is and why the basics are important.

Math explains the logic of and relationship between numbers. It is used everyday in countless ways and in order to minimize potential math phobia, teachers need to make the subject relevant to the students’ lives and use examples with which they are familiar and that make sense to them. In order to do that, learning the basics is critical, because all math concepts are built on addition, division, fractions and shapes; all mathematical relationships flow from these concepts. It is imperative students understand one concept before moving on to the next. If they fail to grasp the basics, students become confused as they progress to higher levels, because they are unable to apply appropriate background knowledge when introduced to geometry, algebra, probability and statistics. Making math fun by injecting a sense of wonder and excitement into learning how to use numbers in everyday life goes a long way in preventing a fear of math from developing. Some fun activities: play cards, checkers or backgammon; build a tower with interlocking blocks; or count the legs on a centipede.

2. Define mathematics, arithmetic, algebra, geometry, probability, statistics, trigonometry, and calculus.

The American Heritage College Dictionary defines mathematics as “the study of the measurement, properties and relationships of quantities using numbers and symbols.” It is a formal science of structure, order and relationship, and is considered the basic language and foundation of all the other sciences. It is critical in the development of technology. It evolved from counting, measuring and describing shapes. Some areas of mathematics and their definitions:

ARITHMETIC: a system to count numbers using addition, subtraction, multiplication and division.
ALGEBRA: an abstract form of arithmetic using symbols to represent numbers.
GEOMETRY: the relationship of points, lines, angles, surfaces and solids.
PROBABILITY: the calculation of the chances that certain events will occur.
STATISTICS: the collection, organization and analysis of data.
TRIGONOMETRY: the relationship of the sides and angles of triangles.
CALCULUS: the limits, differentiation and integration of the functions of variables.
3. Discuss patterns and functions and equivalence and equations and what they represent.

There are some basic concepts students need to understand in order to begin to think algebraically, so they can use what they “see” to make generalizations about “unknowns.” Patterns and functions represent change and relationships. Repeating patterns show the same unit over and over again; in growth patterns, each unit is dependent upon the one before it, as well as its position in the pattern. The function is the relationship between values, e.g. the second depends on the first. Using concrete examples helps students visualize what the function is describing. As students begin to understand functional relationships, symbols can be used as abstract stand-ins for the relationships. Equivalence and balance are critical concepts in understanding algebraic equations. It is important for teachers to explain that the equal sign represents some type of relationship between the numbers and symbols on each side of the sign: if a calculation is performed on one side, the same calculation must be performed on the other side. Each side is equal; the equation must balance.

4. Discuss science in middle school.

Adolescents come to school with background knowledge and a basic understanding of how things work. They have reached conclusions based on their perception of the physical world and what they learned in previous classes. A wise teacher uses students’ knowledge and natural curiosity when introducing and explaining complicated scientific concepts. He builds on ideas already known and corrects any misconceptions. Science has a history. Students need to be familiar with the socio-economic environment in which a theory was introduced in order to truly understand why something did or did not work, why it may have been proven wrong or why a better way was discovered with later experimentation. In a science classroom, safety must always be a priority. Since it is an interactive area, it needs to be ventilated and appropriate safety equipment (e.g. water, fire extinguisher, protective gear, etc.) needs to be available. The students need to understand how to operate the instruments in a safe manner, so instructions should be provided in writing as well as verbally. Questions should be asked and answered before any activity is started.

5. Define the term science.

The American Heritage College Dictionary defines science as “the observation, identification, description, experimental investigation and theoretical explanation of phenomena.” Its Latin root is scientia, which means “knowledge.”

NATURAL SCIENCE is concerned with the natural world; SOCIAL SCIENCE studies human behavior. Both are based on empirical evidence, which is observable data that can be verified by other scientists who are working in similar situations under the same conditions.
FORMAL SCIENCE is the systematic study of a specific area; it is essential to developing the hypotheses, theories and laws used in other scientific disciplines, i.e. describing how things work (natural science), how people think, and why they do what they do individually and as a society (social sciences). It is based on a priori evidence, which proceeds from a theory or assumption rather than from observable phenomena.
APPLIED SCIENCE is using scientific research in any of the natural, social and formal sciences to address human needs.
6. Define scientific method, scientific inquiry, deductive and inductive reasoning.


SCIENTIFIC METHOD: a set of procedures used to study natural phenomena. It provides guidelines with which to pose questions, analyze data and reach conclusions. It is used to investigate an event, gain knowledge or correct earlier conclusions about the occurrence and integrate the new information with previously learned data. Researchers pose hypotheses, and design experiments and studies to test them. The process must be objective, documented and shared with other researchers so the results can be verified by replicating the study in similar situations under the same conditions.
SCIENTIFIC INQUIRY: used to explore theories and develop explanations for natural phenomena. It has two functions: to provide a description of how something happens and to explain why the process succeeds or fails.
DEDUCTIVE REASONING: a process in which a specific conclusion logically follows from a general premise. If the premise is true, the conclusion is true. Deductive reasoning is used in mathematics.
INDUCTIVE REASONING: a process in which a universal conclusion is formed from considering an individual example. Inductive reasoning is the methodology of the natural and social sciences.
7. Describe the steps used in the scientific method.

The steps of the scientific method described here are not necessarily used in exactly the same way in all sciences. Sometimes they happen at the same time or in a different order and may be repeated during the course of the study. Whatever order researchers use, the steps should be applied with intelligence, imagination and creativity. The following sequence is the one used most of the time.
1. A question is asked about a natural phenomenon. It should be stated in specific language to focus the inquiry.
2. The subject is thoroughly researched. Previous test results are studied. It is important to understand what the earlier experiment(s) proved or disproved.
3. With information gleaned from researching the topic, a hypothesis is formed about a cause or effect of the event, or its relationship to other occurrences.
4. An experiment is designed and conducted to test the hypothesis and gather information.
5. The resulting data is analyzed to determine if they support or refute the hypothesis.
It is common for test results to lead to more questions about the subject or a related phenomenon.

8. Discuss life science.

Life science (or biology) is the study of living organisms: their structure, function, growth, origin, evolution and distribution. The word biology is Greek: bio means “life”; logos means “speech”; biology literally means, “discussion about life.” It became a separate science in the late nineteenth century, when researchers discovered that all organisms shared basic traits. Biology studies how living things began, divides them into species, and describes what they do and how they relate to each other and the rest of the natural world. There are four unifying principles in biology: cell theory, evolution, genetics, and homeostasis. The disciplines in the life sciences are grouped by the organisms they study: botany studies plants; zoology studies animals; and microbiology studies microorganisms. These groups are further divided into smaller, specialized categories based on the level at which they are studied and the methods used to study them; for example, biochemistry studies the chemistry of life while ecology studies how organisms interrelate in the natural world. Applied fields of the life sciences, such as medicine and genetic research, combine multiple specialized categories.

9. Define the unifying principles of biology: cell theory, evolution, gene theory, and homeostasis.


CELL THEORY: the cell is the basic building block of all living things; it is the smallest unit of life able to function on its own, e.g. bacteria and protozoa. In higher organisms, groups of cells form the organs and tissues. There are two kinds of cells: prokaryotic, which are present only in bacteria; and eukaryotic, which are found in all other life forms. New cells form by dividing from existing cells.
EVOLUTION: as a result of natural selection and changes in the gene pool (genetic drift), inherited traits morph from one generation to the next.
GENE THEORY: the traits of all living organisms are encoded in their DNA, the chromosome component that carries genetic information. These traits are passed from generation to generation. The physical or biochemical characteristics are capable of adapting to changes in the environment, but the only way these adaptations can be transferred to the genes is through evolution (see above).
HOMEOSTASIS: a self-regulating, physiological process that keeps biological systems stable and in proper balance internally, no matter what is happening in the external environment.
10. Discuss the National Assessment of Educational Progress requirements for assessments in math and science.

The U.S. Department of Education established criteria for testing comprehension of math and science concepts using recommendations from the National Assessment of Educational Progress. Students in both disciplines are required to not only know facts but also need to be able to integrate those facts into previously acquired information by using critical thinking skills developed through studying these subjects. In other words, students need to be able to use the facts in practical applications found in the real world. The assessments developed by educators, curriculum specialists and the business community emphasize the importance of assessing students’ ability to reason, understand concepts, solve problems, evaluate results and communicate knowledge of the subject matter. The tests attempt to measure whether students can take cognitive skills learned in math and science, apply them in other disciplines and use them outside of school in meaningful ways. The study of science is divided into three major areas: earth, physical and life sciences. Math requires the study of: number sense, properties, operations, measurement, data analysis, statistics, probability, algebra and functions.