Teaching with Tasks for Effective Mathematics Learning

The Necessity for Well-Founded Teacher Education in Economics – Findings from Curriculum Analyses

“…Various studies provide evidence that CK and PCK correlate (r = .81 for mathematics and physics see Krauss et al 2008;Blömeke et al 2008;Riese & Reinhold 2012; r = .4 for German and r = .6 for English see Blömeke et al 2011;r = .4 for Economics see Kuhn et al 2014; see also Bouley et al 2015). Further confirming this connection, teachers who have deficits in CK have been found to have difficulties when it comes to identifying students' misconceptions, providing descriptions or explanations, and implementing appropriate assignments (Halim & Meerah 2002;Thanheiser 2009;Sullivan et al 2010Sullivan et al , 2013. The following section focuses on how teachers acquire CK during their university education.…”

Fostering Middle School Students Number Sense Through Contextualized Tasks

“…This question is relevant, since number sense is the most important mathematical concept in the 21st Century for K-12 education (Devlin, 2017) and is a valuable way of thinking in daily life (Reys R. E., Reys, Nohda, & Emori, 1995); hence, it "should permeate all aspects of mathematics teaching and learning" (Reys B. J., 1994, p. 114). On the other hand, deficiencies in students' knowledge are largely due to a lack of connection between school knowledge and the informal or intuitive knowledge they possess (Fuson, 1992;Sarama & Clements, 2009); based on this, several researchers and curricular designers propose implementing contextualized tasks as a means to favor students' mathematics understanding (Sullivan, Clarke, & Clarke, 2013).…”

“…One of the main objectives of mathematics education is to provide theoretical and methodological principles to guide the design and implementation of tasks that foster the development of students' mathematical understanding. Tasks design is important, since characteristics and inherent pedagogies of tasks are key aspects that determine the nature and qualities of students' learning (Sarama & Clements, 2009;Sullivan, Clarke, & Clarke, 2013) and, on the other hand, tasks constitute the main instrument that teachers have to help students understand mathematical ideas (Anthony & Walshaw, 2009). On this line of ideas, mathematics education research has obtained evidences that the greatest gains on mathematical understanding are related to tasks that require high levels of mathematical thinking and reasoning, and that engage students in "doing mathematics or using procedures with connection to meaning" (Stein & Lane, 1996, p. 50).…”

Evaluating the suitability of mathematical thinking problems for senior high‐school students by including mathematical sense making and global planning

“…Such problems require more than the mere application of already learned mathematical procedures (Hughes, Monaghan, Shingadia & Vaughan, 2006). Although it can be difficult to select such mathematical thinking problems for the curriculum, internationally, mathematics education researchers have pointed out that it is important that students work with this kind of problem (Anthony & Walshaw, 2009;Sullivan, Clarke & Clarke, 2013;Watson & Mason, 2006).…”