Logic and Proofs is an introduction to modern symbolic logic. It provides a rigorous presentation of the syntax and semantics of sentential and predicate logic. However, the distinctive emphasis is on strategic argumentation. Students learn effective strategies for constructing natural deduction proofs. This learning is supported by the Carnegie Proof Lab: it provides a sophisticated interface, in which students can give arguments by strategically guided forward and backward steps.
Statics is a sophomore level engineering course, offered in all mechanical and civil engineering programs. Statics forms the essential pre-requisite to a number of follow-on courses, such as dynamics and mechanics of materials, and lays the foundation for design of mechanical systems. In most institutions, Statics is taught in a traditional way with an emphasis on the mathematical operations that are useful in its implementation, but without enough emphasis on modeling the interactions between r
Empirical Research Methods
Regression analysis is an enormously popular and powerful tool, used ubiquitously in the social and behavioral sciences. Most courses on the subject immediately dive into the mathematical aspects of the subject and illustrate the technique on problems that are already highly structured. As a result, most students come away with little idea of the wide range of problems to which regression analysis can be applied and how to represent those problems in a way that cleverly utilizes readily availabl
The Introductory Economics course is a collection of online experiments and related on-line workbooks which can be used by individual learners or to supplement an instructor lead course. In each experiment a student is an active participant attempting to make deals with other traders in a market. After each experiment, the data the students generated is stored and the student will use this data to complete an online workbook. The workbook guides the student through the analysis and much of the e
Does excessive exposure to violent video games cause violent behavior? Does increased gun availability cause more crime or less? Causal claims permeate everyday life and are constantly the subject of "studies" reported in the newspaper. The material in Causal and Statistical Reasoning examines the nature of causal claims and the statistical sorts of evidence used to support them. The material is contained in: approximately 20 content modules, a repository of over 100 short case studies, and a "C
Highlight the meaning of a function, and see how it can be seen as something changing over time, with this tool that links a motion model to a graph.
Piecewise Linear Grapher
Highlight the language of domain and range, and the ideas of continuity and discontinuity, with this tool that links symbolic and graphic representations of each interval of a piecewise linear function.
Highlight the meaning of each component of a linear function's symbolic expression with this tool that links symbolic and graphic representations of translating (dragging) a line vertically or horizontally, rotating it around a fixed point, or reflecting it around the x- or y-axis.
Highlight the rationale behind symbolic operations used to solve a linear equation with this tool that displays changes in the graphic and area models of functions as you change the value of each symbolic element.
Highlight how changing a data set affects the mean, median, and mode with this tool (created by The Shodor Education Foundation and modified by The Concord Consortium) that allows you to add and delete data graphically.
Highlight the meaning of each component of a quadratic function's symbolic expression with this tool that links symbolic and graphic representations of translating (dragging) a parabola vertically or horizontally, dilating it, or reflecting it around the x- or y-axis.
Highlight how symbolic operations on a system of linear equations do (or do not) change the graphic or tabular representations of the system. Note that the System Solver is a tool intended to illustrate the rationale behind the symbolic operations used to solve systems of linear equations, and not a way to learn what procedures to follow.
The Proportioner was developed to support your learning and your students’ learning of proportion. It allows you to manipulate images and compare their dimensions to the dimensions of other images. Using the Proportioner, you can: •Specify image dimensions graphically, numerically or using a scale factor •Duplicate images and modify copies for comparisons •Use one image to "paint" another
Concord.org Five Lessons: A Taste of the Future, Today
This issue of @Concord features five ready-to-use “Lessons” that illustrate how interactive models and tools can fit into real classrooms today. Each of these lessons addresses important content that can be found in all the standards and frameworks, and does it by giving students tools with which to explore and interact. The lessons illustrate how sophisticated math and science content can be taught earlier and how generative the resulting understanding can be.
CK-12 Geometry (CA Textbook)
CK-12's Geometry delivers a full course of study in the mathematics of shape and space for the high school student, relating the ancient logic and modern applications of measurement and description to its essential elements, processes of reasoning and proof, parallel and perpendicular lines, congruence and similarity, relationships within triangles and among quadrilaterals, trigonometry of right triangles, circles, perimeter, area, surface area, volume, and geometric transformations. This digi
Advanced Algebra II (CA Textbook)
Advanced Algebra II provides three complementary resources for teachers and students that combine to provide a friendly, easy-to-understand explanation of Algebra II concepts. The main text, "Activities and Homework", consists of a series of worksheets for both in-class group work as well as homework assignments. The concepts behind those activities are described in detail in the "Conceptual Explanations" text. The third book, the "Teacher's Guide", provides instructors with guides and suggestio
CK-12 Trigonometry (CA Textbook)
This textbook covers topics such as Trigonometry and Right Angles, Circular Functions, Trigonometric Identities, Inverse Functions, Trigonometric Equations, Triangles and Vectors, as well as Polar Equations and Complex Numbers. It can also be used in conjunction with other directed courses in Mathematical Analysis or Linear Algebra as a full course in Precalculus. This digital textbook was reviewed for its alignment with California content standards.
Linear Systems and Optimization: The Fourier Transform and its Applications
The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used. Together with a great variety, the subject also has a great coherence, and the hope is students come to appreciate both.