Upper secondary school remedial courses: Creative and demanding tasks or drills

Abstract

This study explores the views of teachers in upper secondary schools on creative and demanding mathematical tasks and whether they find that students in remedial courses have the grounds to improve their mathematical competency with such tasks. In the national curriculum for upper secondary school increased emphasis is placed on students acquiring the skills in mathematical, critical and creative thinking (Mennta- og menningarmálaráðuneytið, 2012) necessary to face the challenges of the 21st century where jobs will require resourcefulness and creativity rather than knowing how to follow directions mechanically. Therefore, it is important for students to work on tasks in their education where those skills can be honed. In mathematics teaching emphasis can be placed on either relational understanding or instrumental understanding (Skemp, 1976; Hiebert & Carpenter, 1992). A framework for analyzing whether solving mathematical tasks requires relating mathematical concepts to one another or not was used (Stein et al., 2009). Research suggests that teacher competency is critical in implementing tasks in which a solution requires higher order thinking so that teachers do not do too much of the thinking for students (Henningsen & Stein, 1997; Stigler & Hiebert, 1999; Kilpatrick et al., 2001; Niss & Jensen, 2002). Five participants teaching remedial courses in mathematics from three upper secondary schools were interviewed, both before and after they assigned tasks to their students where the search for a solution required both critical and creative thinking. Solving the mathematical tasks created for the research required an understanding of the equality sign and students’ own generalizations about inverses and identities in both addition and multiplication from results of simple calculations. Course syllabuses were also analyzed. The research question is: What are the views of Icelandic mathematics teachers of tasks in which a solution requires critical and creative thinking of students in remedial courses? The key findings were that the teachers generally considered students in remedial courses to have the necessary skills to be able to learn from working on such tasks. Many mentioned the importance of task diversity. Demand was apparent for a collaborative moderated platform on the web where teachers can share materials with one another. Only one teacher thought such cognitively demanding tasks were unsuitable for low-achieving students. Suggestions were made about how learning materials of this nature could be weaved together with less demanding tasks but more research is needed concerning the most suitable order of different types of tasks (Rittle-Johnson et al., 2015; Pesek & Kirshner, 2000). Differing viewpoints emerged about the use of solutions and example tasks that show procedures without connections to other mathematical ideas. Evidence suggests that there is a shortage of tasks in Icelandic upper secondary school learning materials in which a solution requires mathematical thinking and reasoning (Anna Helga Jónsdóttir et al., 2014). The nature of mathematics as a discipline and as a school subject has changed with the rapid evolution of computers and information technology. Traditional drill exercises can easily be solved with apps that even show all the steps to the correct answer. A student’s correct answer is meaningless if an opportunity to demonstrate understanding is not given. 21st century society requires citizens rich in creativity and resourcefulness, as opposed to ability to handle mechanical procedures. Schooling should increasingly prepare future citizens with tasks in which a solution requires creative and critical thinking. Perhaps the art of being a mathematics teacher lies in drawing the line between when to define a concept in a traditional way and when to encourage students to explore and discover it themselves. The results of this study highlight changes that have taken place in the kinds of tasks upper secondary school teachers want to see in Icelandic mathematics learning materials. Current textbooks are old and were published when a different curriculum was in force and designed for teaching methods that were in line with norms at that time. Creativity has been increasingly emphasised in the national curriculum and needs to become a significant part of mathematics learning, especially for students who need additional assistance to acquire the expected mathematics learning outcomes of the lower secondary school. Increased development of learning materials in Icelandic should be encouraged; these should build on the needs of students and teachers, be line with the times we live in and give students an opportunity to acquire the necessary skills for participating in the society of tomorrow.