By highlighting Nature of Science, Scientific Inquiry, and Science and Social Ethics, the Texas Essential Knowledge and Skills (TEKS) affords a variety of opportunities to integrate HPS into STEM. The Mathematical Process standards specify that students apply mathematics to problems arising in society (including the past), the development of mathematical concepts, and communicate mathematical ideas orally and through writing. Scientific Process skills include an expectation that students research and describe the history of science and contributions of scientists, and Scientific Concept sklls highlight the historical development of a variety of concepts.
Scroll down for excerpts from the High School and Middle School TEKS that explicitly address the history, social context, or nature of math and science.
In addition, the Texas State Board for Educator (TEA) Certification also includes standards recognizing the history and nature of science (NOS) and the historical development of math:
High School TEKS
§111.34. Geometry
(b.1.B) recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes; and
(b.1.C) compare and contrast the structures and implications of Euclidean and non-Euclidean geometries.
§111.39. Algebra I, §111.40. Algebra II, §111.41. Geometry, §111.42. Precalculus, §111.43. Mathematical Models with Applications, and §111.44. Advanced Quantitative Reasoning
(c.1.A) apply mathematics to problems arising in everyday life, society, and the workplace
(c.1.D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
(c.1.G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
§111.45. Independent Study in Mathematics
(c.1.A) apply mathematics to problems arising in everyday life, society, and the workplace
(c.1.D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
(c.1.G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
(b.1.3) ...students will extend their mathematical understanding beyond the Algebra II level in a specific area or areas of mathematics such as theory of equations, number theory, non-Euclidean geometry, linear algebra, advanced survey of mathematics, or history of mathematics.
§112.32. Aquatic Science
(b.2) Nature of science. Science, as defined by the National Academy of Sciences, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.
(b.3) Scientific inquiry. Scientific inquiry is the planned and deliberate investigation of the natural world. Scientific methods of investigation can be experimental, descriptive, or comparative. The method chosen should be appropriate to the question being asked.
(b.4) Science and social ethics. Scientific decision making is a way of answering questions about the natural world. Students should be able to distinguish between scientific decision-making methods and ethical and social decisions that involve the application of scientific information.
(c.3.F) research and describe the history of aquatic science and contributions of scientists.
§112.33. Astronomy
(b.2) Nature of science. Science, as defined by the National Academy of Sciences, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.
(b.3) Scientific inquiry. Scientific inquiry is the planned and deliberate investigation of the natural world. Scientific methods of investigation can be experimental, descriptive, or comparative. The method chosen should be appropriate to the question being asked.
(b.4) Science and social ethics. Scientific decision making is a way of answering questions about the natural world. Students should be able to distinguish between scientific decision-making methods and ethical and social decisions that involve the application of scientific information.
(c.4) Science concepts. The student recognizes the importance and uses of astronomy in civilization.
(c.4.A) research and describe the use of astronomy in ancient civilizations such as the Egyptians, Mayans, Aztecs, Europeans, and the native Americans;
(c.4.B) research and describe the contributions of scientists to our changing understanding of astronomy, including Ptolemy, Copernicus, Tycho Brahe, Kepler, Galileo, Newton, Einstein, and Hubble, and the contribution of women astronomers, including Maria Mitchell and Henrietta Swan Leavitt;
(c.4.C) describe and explain the historical origins of the perceived patterns of constellations and the role of constellations in ancient and modern navigation
(c.13.A) research and describe the historical development of the Big Bang Theory, including red shift, cosmic microwave background radiation, and other supporting evidence;
§112.34. Biology
(b.2) Nature of science. Science, as defined by the National Academy of Sciences, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.
(b.3) Scientific inquiry. Scientific inquiry is the planned and deliberate investigation of the natural world. Scientific methods of investigation can be experimental, descriptive, or comparative. The method chosen should be appropriate to the question being asked.
(b.4) Science and social ethics. Scientific decision making is a way of answering questions about the natural world. Students should be able to distinguish between scientific decision-making methods and ethical and social decisions that involve the application of scientific information.
(c.3.F) research and describe the history of biology and contributions of scientists.
§112.35. Chemistry
(b.2) Nature of science. Science, as defined by the National Academy of Sciences, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.
(b.3) Scientific inquiry. Scientific inquiry is the planned and deliberate investigation of the natural world. Scientific methods of investigation can be experimental, descriptive, or comparative. The method chosen should be appropriate to the question being asked.
(b.4) Science and social ethics. Scientific decision making is a way of answering questions about the natural world. Students should be able to distinguish between scientific decision-making methods and ethical and social decisions that involve the application of scientific information.
(c.3.F) research and describe the history of chemistry and contributions of scientists.
(c.5) Science concepts. The student understands the historical development of the Periodic Table and can apply its predictive power.
(c.6) Science concepts. The student knows and understands the historical development of atomic theory. The student is expected to:
(c.6.A) understand the experimental design and conclusions used in the development of modern atomic theory, including Dalton's Postulates, Thomson's discovery of electron properties, Rutherford's nuclear atom, and Bohr's nuclear atom
§112.36. Earth and Space Science
(b.2) Nature of science. Science, as defined by the National Academy of Sciences, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.
(b.3) Scientific inquiry. Scientific inquiry is the planned and deliberate investigation of the natural world. Scientific methods of investigation can be experimental, descriptive, or comparative. The method chosen should be appropriate to the question being asked.
(b.4) Science and social ethics. Scientific decision making is a way of answering questions about the natural world. Students should be able to distinguish between scientific decision-making methods and ethical and social decisions that involve the application of scientific information.
(c.3.F) learn and understand the contributions of scientists to the historical development of Earth and space sciences.
(c.5.D) explore the historical and current hypotheses for the origin of the Moon, including the collision of Earth with a Mars-sized planetesimal
§112.37. Environmental Systems
(b.2) Nature of science. Science, as defined by the National Academy of Sciences, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.
(b.3) Scientific inquiry. Scientific inquiry is the planned and deliberate investigation of the natural world. Scientific methods of investigation can be experimental, descriptive, or comparative. The method chosen should be appropriate to the question being asked.
(b.4) Science and social ethics. Scientific decision making is a way of answering questions about the natural world. Students should be able to distinguish between scientific decision-making methods and ethical and social decisions that involve the application of scientific information.
(c.3.F) research and describe the history of environmental science and contributions of scientists.
§112.38. Integrated Physics and Chemistry
(b.2) Nature of science. Science, as defined by the National Academy of Sciences, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.
(b.3) Scientific inquiry. Scientific inquiry is the planned and deliberate investigation of the natural world. Scientific methods of investigation can be experimental, descriptive, or comparative. The method chosen should be appropriate to the question being asked.
(b.4) Science and social ethics. Scientific decision making is a way of answering questions about the natural world. Students should be able to distinguish between scientific decision-making methods and ethical and social decisions that involve the application of scientific information.
(c.3.F) research and describe the history of physics and chemistry and contributions of scientists.
§112.39. Physics
(b.2) Nature of science. Science, as defined by the National Academy of Sciences, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.
(b.3) Scientific inquiry. Scientific inquiry is the planned and deliberate investigation of the natural world. Scientific methods of investigation can be experimental, descriptive, or comparative. The method chosen should be appropriate to the question being asked.
(b.4) Science and social ethics. Scientific decision making is a way of answering questions about the natural world. Students should be able to distinguish between scientific decision-making methods and ethical and social decisions that involve the application of scientific information.
(c.3.D) explain the impacts of the scientific contributions of a variety of historical and contemporary scientists on scientific thought and society;
(c.5.A) research and describe the historical development of the concepts of gravitational, electromagnetic, weak nuclear, and strong nuclear forces;
§112.49. Geology, Meteorology, and Oceanography
(c.3.E) research and describe the history of geology, meteorology, oceanography, and contributions of scientists.
(c.5.A) research and describe the historical development of scientific theories of the Earth's formation
(c.6.A) research and describe the historical development of the theories of plate tectonics including continental drift and sea-floor spreading
§112.71. Principles of Technology
(c.3.D) explain the impacts of the scientific contributions of a variety of historical and contemporary scientists on scientific thought and society
§113.41. United States History Studies Since 1877
(27) Science, technology, and society. The student understands the impact of science, technology, and the free enterprise system on the economic development of the United States.
§113.42. World History Studies
(1)...Students analyze the connections between major developments in science and technology and the growth of industrial economies,
(27) Science, technology, and society. The student understands how major scientific and mathematical discoveries and technological innovations affected societies prior to 1750. The student is expected to:
(A) identify the origin and diffusion of major ideas in mathematics, science, and technology that occurred in river valley civilizations, classical Greece and Rome, classical India, and the Islamic caliphates between 700 and 1200 and in China from the Tang to Ming dynasties;
(B) summarize the major ideas in astronomy, mathematics, and architectural engineering that developed in the Maya, Inca, and Aztec civilizations;
(C) explain the impact of the printing press on the Renaissance and the Reformation in Europe;
(D) describe the origins of the Scientific Revolution in 16th century Europe and explain its impact on scientific thinking worldwide; and
(E) identify the contributions of significant scientists such as Archimedes, Copernicus, Eratosthenes, Galileo, Pythagoras, Isaac Newton, and Robert Boyle.
(28) Science, technology, and society. The student understands how major scientific and mathematical discoveries and technological innovations have affected societies from 1750 to the present. The student is expected to:
(A) explain the role of textile manufacturing and steam technology in initiating the Industrial Revolution and the role of the factory system and transportation technology in advancing the Industrial Revolution;
(B) explain the roles of military technology, transportation technology, communication technology, and medical advancements in initiating and advancing 19th century imperialism;
(C) explain the effects of major new military technologies on World War I, World War II, and the Cold War;
(D) explain the role of telecommunication technology, computer technology, transportation technology, and medical advancements in developing the modern global economy and society; and
(E) identify the contributions of significant scientists and inventors such as Marie Curie, Thomas Edison, Albert Einstein, Louis Pasteur, and James Watt.
Middle School TEKS
§111.26. Mathematics, Grade 6; §111.27. Mathematics, Grade 7
(b.1.A) apply mathematics to problems arising in everyday life, society, and the workplace;
(b.1.D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
(b.1.G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
§111.28. Mathematics, Grade 8
(b.1.A) apply mathematics to problems arising in everyday life, society, and the workplace;
(b.1.D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
(b.1.G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
(b.6.C) use models and diagrams to explain the Pythagorean theorem.
(b.7.C) use the Pythagorean Theorem and its converse to solve problems; and
(b.7.D) determine the distance between two points on a coordinate plane using the Pythagorean Theorem.
§112.18. Science, Grade 6
(a)(1) Science, as defined by the National Academy of Science, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.
(a)(2) Scientific hypotheses are tentative and testable statements that must be capable of being supported or not supported by observational evidence. Hypotheses of durable explanatory power that have been tested over a wide variety of conditions become theories. Scientific theories are based on natural and physical phenomena and are capable of being tested by multiple, independent researchers. Students should know that scientific theories, unlike hypotheses, are well-established and highly reliable, but they may still be subject to change as new information and technologies are developed. Students should be able to distinguish between scientific decision-making methods and ethical/social decisions that involve the application of scientific information.
(a)(3) ...Recurring themes are pervasive in sciences, mathematics, and technology. These ideas transcend disciplinary boundaries and include change and constancy, patterns, cycles, systems, models, and scale.
(a)(4)(A)(i) To develop a rich knowledge of science and the natural world, students must become familiar with different modes of scientific inquiry, rules of evidence, ways of formulating questions, ways of proposing explanations, and the diverse ways scientists study the natural world and propose explanations based on evidence derived from their work.
(a)(4)(A)(ii) Scientific investigations are conducted for different reasons. All investigations require a research question, careful observations, data gathering, and analysis of the data to identify the patterns that will explain the findings. Descriptive investigations are used to explore new phenomena such as conducting surveys of organisms or measuring the abiotic components in a given habitat. Descriptive statistics include frequency, range, mean, median, and mode. A hypothesis is not required in a descriptive investigation. On the other hand, when conditions can be controlled in order to focus on a single variable, experimental research design is used to determine causation. Students should experience both types of investigations and understand that different scientific research questions require different research designs.
(a)(4)(A)(iii) Scientific investigations are used to learn about the natural world. Students should understand that certain types of questions can be answered by investigations, and the methods, models, and conclusions built from these investigations change as new observations are made. Models of objects and events are tools for understanding the natural world and can show how systems work. Models have limitations and based on new discoveries are constantly being modified to more closely reflect the natural world.
(a)(4)(B)(iii) Energy resources are available on a renewable, nonrenewable, or indefinite basis. Understanding the origins and uses of these resources enables informed decision making. Students should consider the ethical/social issues surrounding Earth's natural energy resources, while looking at the advantages and disadvantages of their long-term uses.
(b)(3)(D) relate the impact of research on scientific thought and society, including the history of science and contributions of scientists as related to the content.
§112.19. Science, Grade 7
(a)(1) Science, as defined by the National Academy of Science, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.
(a)(2) Scientific hypotheses are tentative and testable statements that must be capable of being supported or not supported by observational evidence. Hypotheses of durable explanatory power that have been tested over a wide variety of conditions become theories. Scientific theories are based on natural and physical phenomena and are capable of being tested by multiple, independent researchers. Students should know that scientific theories, unlike hypotheses, are well-established and highly reliable, but they may still be subject to change as new information and technologies are developed. Students should be able to distinguish between scientific decision-making methods and ethical/social decisions that involve the application of scientific information.
(a)(3) ...Recurring themes are pervasive in sciences, mathematics, and technology. These ideas transcend disciplinary boundaries and include change and constancy, patterns, cycles, systems, models, and scale.
(a)(4)(A)(i) To develop a rich knowledge of science and the natural world, students must become familiar with different modes of scientific inquiry, rules of evidence, ways of formulating questions, ways of proposing explanations, and the diverse ways scientists study the natural world and propose explanations based on evidence derived from their work.
(a)(4)(A)(ii) Scientific investigations are conducted for different reasons. All investigations require a research question, careful observations, data gathering, and analysis of the data to identify the patterns that will explain the findings. Descriptive investigations are used to explore new phenomena such as conducting surveys of organisms or measuring the abiotic components in a given habitat. Descriptive statistics include frequency, range, mean, median, and mode. A hypothesis is not required in a descriptive investigation. On the other hand, when conditions can be controlled in order to focus on a single variable, experimental research design is used to determine causation. Students should experience both types of investigations and understand that different scientific research questions require different research designs.
(a)(4)(A)(iii) Scientific investigations are used to learn about the natural world. Students should understand that certain types of questions can be answered by investigations, and the methods, models, and conclusions built from these investigations change as new observations are made. Models of objects and events are tools for understanding the natural world and can show how systems work. Models have limitations and based on new discoveries are constantly being modified to more closely reflect the natural world.
(b)(3)(D) relate the impact of research on scientific thought and society, including the history of science and contributions of scientists as related to the content.
(b)(11)(A) describe the physical properties, locations, and movements of the Sun, planets, Galilean moons, meteors, asteroids, and comets;
(b)(11)(C) describe the history and future of space exploration, including the types of equipment and transportation needed for space travel.
§112.20. Science, Grade 8
(a)(1) Science, as defined by the National Academy of Science, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.
(a)(2) Scientific hypotheses are tentative and testable statements that must be capable of being supported or not supported by observational evidence. Hypotheses of durable explanatory power that have been tested over a wide variety of conditions become theories. Scientific theories are based on natural and physical phenomena and are capable of being tested by multiple, independent researchers. Students should know that scientific theories, unlike hypotheses, are well-established and highly reliable, but they may still be subject to change as new information and technologies are developed. Students should be able to distinguish between scientific decision-making methods and ethical/social decisions that involve the application of scientific information.
(a)(3) ...Recurring themes are pervasive in sciences, mathematics, and technology. These ideas transcend disciplinary boundaries and include change and constancy, patterns, cycles, systems, models, and scale.
(a)(4)(A)(i) To develop a rich knowledge of science and the natural world, students must become familiar with different modes of scientific inquiry, rules of evidence, ways of formulating questions, ways of proposing explanations, and the diverse ways scientists study the natural world and propose explanations based on evidence derived from their work.
(a)(4)(A)(ii) Scientific investigations are conducted for different reasons. All investigations require a research question, careful observations, data gathering, and analysis of the data to identify the patterns that will explain the findings. Descriptive investigations are used to explore new phenomena such as conducting surveys of organisms or measuring the abiotic components in a given habitat. Descriptive statistics include frequency, range, mean, median, and mode. A hypothesis is not required in a descriptive investigation. On the other hand, when conditions can be controlled in order to focus on a single variable, experimental research design is used to determine causation. Students should experience both types of investigations and understand that different scientific research questions require different research designs.
(a)(4)(C) Force, motion, and energy. Students experiment with the relationship between forces and motion through the study of Newton's three laws. Students learn how these forces relate to geologic processes and astronomical phenomena. In addition, students recognize that these laws are evident in everyday objects and activities. Mathematics is used to calculate speed using distance and time measurements.
(a)(4)(A)(iii) Scientific investigations are used to learn about the natural world. Students should understand that certain types of questions can be answered by investigations, and the methods, models, and conclusions built from these investigations change as new observations are made. Models of objects and events are tools for understanding the natural world and can show how systems work. Models have limitations and based on new discoveries are constantly being modified to more closely reflect the natural world.
(b)(3)(D) relate the impact of research on scientific thought and society, including the history of science and contributions of scientists as related to the content.
(b)(6)(C) investigate and describe applications of Newton's law of inertia, law of force and acceleration, and law of action-reaction such as in vehicle restraints, sports activities, amusement park rides, Earth's tectonic activities, and rocket launches.
