Differences in success in solving second-degree equations due to differences in classroom instruction

Abstract

The point of departure in this study is that differences in solving seconddegree equations result from differences in what is presented to the students in a learning situation. However, the specified aim is to describe what kind of differences seem to be crucial for learning, and what does seem fruitless.The study is carried out in an upper secondary school in Sweden. Data consist of video-recorded lessons and tests. Two teachers and 45 students participated in this study. The analysis has been made with the aid of variation theory. The results show that the teachers focused on different aspects of a second-degree equation, and that this implied different learning outcomes as some of the aspects were not critical to promoting learning while others were.

From Doing to Learning: Changed focus during a pre-school learning study project on organic decomposition

“…It has been demonstrated to be useful in improving student learning and understanding of specific concepts and phenomena (see, e.g. Davies & Dunnill, 2008;Lo, 2012;Olteanu & Holmqvist, 2012;Pang & Marton, 2005;Wernberg, 2009) and in building teachers' knowledge of learning (see, e.g. Gustavsson, 2008;Pang, 2006;Runesson, 1999;Siu, 2008).…”

Performance and Difficulties of Students in Formulating and Solving Quadratic Equations with One Unknown

“…A limited number of research studies focusing on quadratic equations have documented the techniques students engage in while solving quadratic equations (Bossé & Nandakumar, 2005), geometric approaches used by students for solving quadratic equations (Allaire & Bradley, 2001), students' understanding of and difficulties with solving quadratic equations (Kotsopoulos, 2007;Lima, 2008;Tall, Lima, & Healy, 2014;Vaiyavutjamai, Ellerton, & Clements, 2005;Zakaria & Maat, 2010), the teaching and learning of quadratic equations in classrooms (Olteanu & Holmqvist, 2012;Vaiyavutjamai & Clements, 2006), comparing how quadratic equations are handled in mathematics textbooks in different countries (Sağlam & Alacacı, 2012), and the application of the history of quadratic equations in teacher preparation programs to highlight prospective teachers' knowledge (Clark, 2012).…”

Quadratic equations in Swedish textbooks for upper-secondary school

“…Within the area of quadratic equations, students often study algebra concepts and identities, different solution methods, and applications of quadratic equations in problem-solving. Solving a quadratic equation using the pq formula 1 is one of the most common solution methods in Swedish classrooms (Olteanu & Holmqvist, 2012). Demanding prior knowledge of many algebra rules or identities, quadratic equations take up much knowledge space in the curriculum and form a complex teaching area.…”

“…content. Different approaches for students to solve quadratic equations have been studied since 2000; for example, factoring quadratics (e.g., Bossé & Nandakumar, 2005), completing the square with geometry representations (e.g., Allaire & Bradley, 2001;Fachrudin et al, 2014), and using the pq formula (e.g., Olteanu & Holmqvist, 2012). Learning and understanding quadratic equations and their solution methods have also been studied; for example, students' understanding of quadratic equations (e.g., Vaiyavutjamai & Clements, 2006), and students' understanding of factoring quadratic equations and their difficulties (e.g., Didis & Erbas, 2015).…”