To explain successful subject matter learning with digital tools, the specification of mediating
cognitive processes is crucial for any empirical investigation. We introduce a cognitive …

Instructional design research promotes interactive and adaptive scaffolds as features of
educational technology. Mathematics education research can guide elaborated fractions …

Rational numbers are amongst the most difficult topics in the elementary and secondary
school curriculum and teaching them requires an appropriate knowledge base of teachers to …

When school students compare the numerical values of fractions, they have frequently been
found to be biased by the natural numbers involved (eg, to believe that 1/4> 1/3 because 4> …

Children's ability to place fractions on a number line strongly correlates with math
achievement. But does the number line play a causal role in fraction learning or does it …

Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates
children show surprising intuition when making approximate, nonsymbolic ratio judgments …

Understanding rational numbers is a complex task for primary and secondary school
students. Previous research has shown that a possible reason is students' tendency to apply …

The last decade has seen a rapid growth in our understanding of the cognitive systems that
underlie mathematical learning and performance, and an increased recognition of the …

Rational number knowledge is a crucial feature of primary school mathematics that predicts
students' later mathematics achievement. Many students struggle with the transition from …

Pedagogical content knowledge forms the core of teachers' professional knowledge; it refers
to knowledge about making subject matter accessible to students. Thus, the formation of …