It remains a challenge for teachers to integrate modeling tasks in everyday mathematics classes. Many studies have been conducted that show the difficulties faced by teachers. One of the challenging aspects in this regard is that of assessment. In the present study, a connection between structures of learners' solution strategies and cognitive…

The cognitive relationship between intuition and proof is complex and often students struggle when they need to find mathematical justifications to explain what appears as self-evident. In this paper, we address this complexity in the specific case of open geometrical problems that ask for a conjecture and its proof. We analyze four meaningful…

Probabilistic reasoning underpins much of middle school students' future work in data analysis and inferential statistics. Unfortunately for many middle school students, probabilistic reasoning is not intuitive. One specific area in which students seem to struggle is determining the probability of compound events (Moritz and Watson 2000). Research…

Dual-process theories posit two distinct types of cognitive processing: Type 1, which does not use working memory making it fast and automatic, and Type 2, which does use working memory making it slow and effortful. Mathematics often relies on the inhibition of pervasive Type 1 processing to apply new skills or knowledge that require Type 2…

In this paper two studies are reported in which two contrasting claims concerning the intuitiveness of the law of large numbers are investigated. While Sedlmeier and Gigerenzer ("J Behav Decis Mak" 10:33-51, 1997) claim that people have an intuition that conforms to the law of large numbers, but that they can only employ this intuition…