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Peter Liljedahl describes a Building Thinking Classrooms (BTC) framework that shows teachers how to set up a classroom that promotes thinking. BTC is divided into 4 toolkits. The first toolkit consists of thinking tasks, vertical non-permanent surfaces, and visibly random groups. The second pertains to defronting the classroom, giving thinking tasks verbally and early while standing, voluntary homework, and mobilizing knowledge. The third consists of using hints and extensions to maintain flow, consolidating, and students writing meaningful notes. The fourth toolkit involves assessment. Though Liljedahl's research pertains to K-12 classrooms, the framework sounded promising for higher education as well. To test this, the framework was tried in a college-level calculus I course, taught at a small liberal arts college. There were 15 math and computer science students enrolled. The class met twice a week for 2 hours each day over a 13-week semester. There was one professor and two teaching assistants. They applied most of the aspects of the toolkits to see if the framework was upheld in a higher education setting.

The two most popular decision-making processes are tossing a coin and playing rock, paper, scissors. In the activity described in this article, students find the theoretical probabilities of winning a coin toss and a round of the rock, paper, scissors game. They next devise strategies to win and test them out. Students then compare the theoretical probabilities they found with the experimental probabilities. The mathematical topics covered in this activity include calculating basic probability; understanding that for independent events A and B, P(A and B) = P(A) × P(B); recognizing a geometric series and applying the appropriate formula to find what it converges to; and understanding the meaning of descriptive statistics. Students were able to prove that although theoretically both games are fair in that they both give each of the two players a 50 percent chance of winning, several strategies can be employed to make each game unfair.

Two sections of a college discrete mathematics class were taught using cooperative learning techniques throughout the semester. The 33 students attending these sections were randomly assigned into groups of three. Their final examination consisted of an individual and group blended examination where students worked in their groups and discussed questions, but each student had a different version of the examination and their own questions to answer. Afterwards, students were given a questionnaire and one group from each section was interviewed to see how they rated blended assessment. The majority of students preferred the blended examination over an individual examination, however not every student felt this way. One benefit of the blended examination was being able to verbalize test questions, which led to a better understanding of them. Concerns about the blended examination such as time, fairness, and difficulty concentrating were raised.

In this brief article Elana Reiser describes her favorite lesson that combines popular culture with mathematics in a way that motivates student thinking and participation. Exploring open-ended problems, students may feel uneasy at first, but working in small groups often leads them to experiment with a variety of solutions. Reiser explains that under these circumstances, students always seem to generate creative mathematical ideas. This lesson focuses on an episode of "The Big Bang Theory" (season 2, episode 9) in which Raj, Howard, and Sheldon discuss Leonard's dating history as a geometric progression.

The article explores on contemporary movies and television shows, containing one or more mathematical elements, of which teachers use in boosting motivation among students. It examines on several examples of mathematics in movies and television based on the National Council of Teachers of Mathematics (NCTM) suggested Content Standards. Suggestions to teachers for them to initiate a discussion with students based on the selected movie or television show are provided.