How can we make sense of what we learned today?" This is a question the author commonly poses to her algebra students in an effort to have them think about the connections between the new concept they are learning and concepts they have previously learned. For students who have a strong, expansive understanding of previously learned topics,…

In this article, a mathematics teacher educator presents an activity designed to pique the interest of prospective secondary mathematics teachers who may doubt the value of learning abstract algebra for their chosen profession. Herein, he contemplates: what "is" intended by the widespread requirement that high school mathematics teachers…

The simple process of iteration can produce complex and beautiful figures. In this article, Robin O'Dell presents a set of tasks requiring students to use the geometric interpretation of complex number multiplication to construct linear iteration rules. When the outputs are plotted in the complex plane, the graphs trace pleasing designs…

Today, the Common Core State Standards for Mathematics (CCSSI 2010) expect students in as early as eighth grade to be knowledgeable about irrational numbers. Yet a common tendency in classrooms and on standardized tests is to avoid rational and irrational solutions to problems in favor of integer solutions, which are easier for students to…

KenKen® is the new Sudoku. Like Sudoku, KenKen requires extensive use of logical reasoning. Unlike Sudoku, KenKen requires significant reasoning with numbers and operations and helps develop number sense. The creator of KenKen puzzles, Tetsuya Miyamoto, believed that "if you give children good learning materials, they will think and learn and…

The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. When absolute value problems become more complex, students often do not have sufficient conceptual understanding to make any sense of what is happening mathematically. The authors suggest that the…

Proof is a central component of mathematicians' work, used for verification, explanation, discovery, and communication. Unfortunately, high school students' experiences with proof are often limited to verifying mathematical statements or relationships that are already known to be true. As a result, students often fail to grasp the true nature of…

Authors use combinatorical analysis to prove some interesting facts about the Fibonacci sequence.

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…

Using license plates and telephone numbers for teaching probability ideas involving counting rules is suggested. How each is useful is illustrated in some detail. (MNS)

Understanding rational numbers is often an elusive goal in mathematics. Presented is an approach for teaching rational numbers that has been used with many preservice and elementary school teachers. With some adaptation, the approach could be used with secondary school students. (RH)

Explores trapezoidal numbers, which are the result of subtracting two triangular numbers. Includes classroom activities involving trapezoidal numbers to help students develop their problem-solving skills. Includes reproducible student worksheets. (MKR)

In a course on proofs, a number of problems deal with identities for Fibonacci numbers. Some general strategies with examples are used to help discover, prove, and generalize these identities.

A method for making divergent series converge is described. Proofs of the procedure are presented. (MNS)