Learning to respond to a computer program that is not working as intended is often characterized as finding a singular bug causing a singular problem. This framing underemphasizes the wide range of ways that students and teachers could notice discrepancies from their intention, propose causes of those discrepancies, and implement interventions.…

The importance of computational thinking skills in mathematics has been recognized in educational research for a long time. More recently, this recognition has materialized in formal international recommendations (e.g., by PISA's 2022 Mathematics Framework) and in national or provincial curricular reforms (e.g., in France, Sweden, and Canada) that…

Eliciting student thinking is paramount to effective mathematics teaching and learning. Although one can use many strategies and techniques to promote student thinking, technology is one resource that is often underutilized. Whether it is the informed use of calculators or an interactive website, technology can be leveraged to promote mathematical…

Applied early adolescent researchers often sample students (Level 1) from within classrooms (Level 2) that are nested within schools (Level 3), resulting in data that requires multilevel modeling analysis to avoid Type 1 errors. Although several articles have been published to assist researchers with analyzing sample data nested at two levels, few…

Responsive teaching occurs when teachers take up and "respond" to their students' ideas during instruction (J. L. Pierson, 2008). Although responsive teaching is gaining recognition as an effective strategy for encouraging student learning, few methods of analysis are capable of characterizing the different ways in which teachers take up…

Designing opportunities for students to discover core science concepts can be challenging, however, with a good understanding of their interests, proper planning, and the use of technology and the outdoors, students can become engaged in a way that can leave a legacy for future students. Last fall, this author designed a nine-session unit for a…

Acrostic poems make use of a keyword written vertically, where each line of the poem begins with a letter of the keyword. The structure of this formula poem combined with teacher modeling provides a scaffold for students, showing them how to think flexibly and develop ideas and choose interesting words. Moreover, encoding information in poetic…

In May 2008, the first National Assessment Program for Literacy and Numeracy (NAPLAN) test was administered across Australia to determine the standard of literacy and numeracy achievement of Australia's students in Years 3, 5, 7 and 9. Some students did very well on the tests and some did not. This type of test can tell a great deal about…