The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed.

Boaler (2016) asserted that problem posing is the "essence of real mathematics", yet many students do not have opportunities to pose and then solve their own mathematical questions. Rather, students spend their time solving tasks someone else posed--often their teacher or textbook. To promote problem posing, the author designed,…

Peter Dunn and Margaret Marshman present the second of their data files articles in which they discuss the statistical investigation cycle which describes the whole process of conducting a statistical research study. [For "The Data Files: A Series of Articles to Support Mathematics Teachers to Teach Statistics," see EJ1259108.]

The group work test is an assessment strategy that promotes higher-order thinking skills for solving context-rich problems. With this format, teachers are able to pose challenging, nuanced questions on a test, while providing the support weaker students need to get started and show their understanding. The test begins with a group discussion…

The traditional method of teaching math--showing students how to do a procedure, then assigning problems that require them to use that exact procedure--leads to adults who don't know how to approach problems that don't look like those in their math book. Seeley describes an alternative teaching method (upside-down teaching) in which teachers give…

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

Prior research suggests that students' understanding of scientific concepts is pre-determined by their reasoning ability. Other efforts suggest that American students' scientific literacy is in decline. One difficulty Bybee (2009) acknowledges is that there are two divergent philosophical models of scientific literacy. The first describes the…

Due to the growing importance of technology and engineering in the educational landscape, and to support America's ability to contribute to and compete in a global economy, the National Assessment Governing Board (NAGB) initiated development of the first NAEP Technology and Engineering Literacy (TEL) Assessment. Relating to national efforts in…

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

Today's K-20 students have been called, among other names, the net generation. As they matriculate through the education system, they are often exposed to materials and manipulatives used for the past 40 years, and not to the digital media to which they are accustomed. As student scores continue to regress from Grade 3 to Grade 12 and technical…

This 21st Century Skills Map is the result of hundreds of hours of research, development and feedback from educators and business leaders across the nation. The Partnership for 21st Century Skills has issued this map for the core subject of English.

Lessons given to a group of mathematically talented eleventh and twelfth graders enrolled in a problem-solving course that provided practice in applying the heuristic strategy of working backward are detailed. Special attention was given to the process of formulating generalizations that represent large problem classes. (MP)

This paper provides a pragmatic view of efficient use of graphics calculators. Efficiency is described in terms of quick and easy calculation, as debated and evidenced in a Year 12 calculus class. Students' methods of calculation are analysed in terms of the algebraic understanding and technical skills that underpinned them. Patterns in students'…

"Bridging the Gap: Intergenerational Appreciation" is an educational partnership between community residents and high school family and consumer sciences (FCS) students in the Cornwall-Lebanon School District in Lebanon, Pennsylvania. The program provides 10th, 11th, and 12th grade students opportunities to be actively involved with the…

Discusses the challenges of teaching high school geography in a way that enables students to develop an informed, spatial view of the world. Discusses the High School Geography Project and its effect on geography instruction. Suggests a map drawing exercise for students to demonstrate the importance of mental maps. (DK)