Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students' errors

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Students' Improper Proportional Reasoning: A result of the epistemological obstacle of “linearity” (2007, background): “( 2002 ) point out, students' former real‐life practices with enlarging and reducing operations do not necessarily make them aware of the different growth rates of lengths, areas, and volumes.”
Teaching and Learning About Whole Numbers in Primary School (2016, background): “However, errors in additive problems can sometimes be due to the overuse of multiplicative reasoning, both among students (De Bock et al. 2002) and prospective teachers (Cramer et al. 1993).”
Just Answering … or Thinking? Contrasting Pupils' Solutions and Classifications of Missing-Value Word Problems (2010, background): “During in-depth interviews ( De Bock, Van Dooren, Janssens, & Verschaffel, 2002 ) in which pupils solved non-proportional geometrical problems, we found that pupils generally did not consciously and deliberately choose a proportional strategy.”
Remedying secondary school students' illusion of linearity: A teaching experiment (2004, background): “We would argue that ‘‘linearity’’ can be considered as such a presupposition: our in-depth study has shown that students are indeed often unaware of the fact that they are using this early acquired concept ( De Bock et al., 2002a ).”