This Handbook is based on the Science Education Initiative (SEI), a transformative initiative aimed at changing STEM teaching practices in university settings. The SEI was successfully implemented in two institutions (University of Colorado Boulder and The University of British Columbia) over a period of 10 years. The SEI centered on department-based Discipline-Based Education Specialists (DBESs), disciplinary experts with training in the science of teaching and learning who serve as catalysts of change within departments. The two SEIs have influenced the teaching of hundreds of faculty and the learning of tens of thousands of students per year by promoting the use of evidence-based teaching practices in STEM. These teaching practices are informed by research on teaching and learning, and often include some element of active learning.

This Handbook shares the accumulated wisdom of practice in how to effectively implement a model of change based on the SEI. It provides advice to the three main stakeholders in such initiatives: the initiative leaders who provide central direction and management, the departmental leaders who help lead the activities and engage faculty, and the Discipline-Based Education Specialists who partner with faculty to transform courses.

This subject exposes students to a variety of visualization techniques so that they learn to understand the work involved in producing them and to critically assess the power and limits of each. Students concentrate on areas where visualizations are crucial for meaning making and data production. Drawing on scholarship in science and technology studies on visualization, critical art theory, and core discussions in science and engineering, students work through a series of case studies in order to become better readers and producers of visualizations.

This lesson unit is intended to help teachers assess how well students are able to solve problems involving area and arc length of a sector of a circle using radians. It assumes familiarity with radians and should not be treated as an introduction to the topic. This lesson is intended to help teachers identify and assist students who have difficulties in: Computing perimeters, areas, and arc lengths of sectors using formulas and finding the relationships between arc lengths, and areas of sectors after scaling.

Seminar for mathematics majors. Students present and discuss the subject matter, taken from current journals or books. Topics vary from year to year. Topic for Fall 2002: Quantum calculus. Instruction and practice in oral communication provided.

This course is a seminar in topology. The main mathematical goal is to learn about the fundamental group, homology and cohomology. The main non-mathematical goal is to obtain experience giving math talks.

This is an advanced topics course in model theory whose main theme is simple theories. We treat simple theories in the framework of compact abstract theories, which is more general than that of first order theories. We cover the basic properties of independence (i.e., non-dividing) in simple theories, the characterisation of simple theories by the existence of a notion of independence, and hyperimaginary canonical bases.

An interactive applet and associated web page that demonstrate the slope (m) of a line. The applet has two points that define a line. As the user drags either point it continuously recalculates the slope. The rise and run are drawn to show the two elements used in the calculation. The grid, axis pointers and coordinates can be turned on and off. The slope calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of slope, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This short video and interactive assessment activity is designed to teach second graders about solving decimal word puzzles.

This lesson unit is intended to help teachers assess how well students are able to identify and use geometrical knowledge to solve a problem. In particular, this unit aims to identify and help students who have difficulty in: making a mathematical model of a geometrical situation; drawing diagrams to help with solving a problem; identifying similar triangles and using their properties to solve problems; and tracking and reviewing strategic decisions when problem-solving.

This short video and interactive assessment activity is designed to teach fourth graders about solving length and distance problems involving time - word problems.

This lesson unit is intended to help teachers assess how well students are able to: interpret a situation and represent the variables mathematically; select appropriate mathematical methods to use; explore the effects of systematically varying the constraints; interpret and evaluate the data generated and identify the break-even point, checking it for confirmation; and communicate their reasoning clearly.

Students will be able to solve a system of equations  using substitution, elimination and graphing techniques. Primary focus is on linear systems with two variables.  Exploration is on systems involving quadratics, linears and circles with graphing.

This Nrich activity can be used to build up children's confidence with the language associated with 2D shape.

This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.

This lab demonstrates Hooke's Law with the use of springs and masses. Students attempt to determine the proportionality constant, or k-value, for a spring. They do this by calculating the change in length of the spring as different masses are added to it. The concept of a spring's elastic limit is also introduced, and the students test to makes sure the spring's elastic limit has not been reached during their lab tests. After compiling their data, they attempt to find an average value of the spring's k-value by measuring the slopes between each of their data points. Then they apply what they've learned about springs to how engineers might use that knowledge in the design of a toy that enables kids to jump 2-3 feet in the air.

This Nrich game offers an excellent opportunity to practice visualizing squares and angles on grids and also encourages students to look at strategies using systematic approaches. Describing strategies to others is always a good way to focus and clarify mathematical thought.

The whole idea of this Nrich problem is to invite children to picture something in their mind and in this instance, pupils will need to be familiar with properties of a cube. Ideally, it would be good to encourage your class to tackle this challenge purely by trying to imagine what is happening. To convince you and each other of their solutions, they will need to explain particularly carefully what they are picturing, which can be quite tricky, and you may find that they gesticulate rather a lot! In order to reach a joint conclusion, you might find it helpful to make a model of the cube from interlocking cubes.

This course discusses the principles and methods of statistical mechanics. Topics covered include classical and quantum statistics, grand ensembles, fluctuations, molecular distribution functions, other concepts in equilibrium statistical mechanics, and topics in thermodynamics and statistical mechanics of irreversible processes.

This lesson unit is intended to help teachers assess how well students are able to: form and solve linear equations involving factorizing and using the distributive law. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using variables to represent quantities in a real-world or mathematical problem and solving word problems leading to equations of the form px + q = r and p(x + q) = r.

This is a video and interactive assessment activity designed to help first graders learn about subtraction word problems up to twenty.