Problem Solving in Mathematics Education

Invited Lectures from the 13th International Congress on Mathematical Education

“…3. Generally speaking, a solver's pathway of the shifts of attention is stipulated by choices the solver is empowered to make and by enacting the following types of resources: See also Koichu et al (2007a) and Liljedahl et al (2016) for detailed discussions of approaches to conceptualizing heuristics.…”

Embedding problem-solving in a primary mathematics programme

“…Problems are tasks that are solved not just by direct effort but also by play or some creative insight (Holton, 2009;Liljedahl, SantosTrigo, Malaspina, & Bruder, 2016). Problem-solving has been regarded as an important aspect of mathematics, and the teaching and learning of mathematics for a long time (Liljedahl et al, 2016;Schoenfeld, 2007). The 1992 New Zealand mathematics curriculum document (Ministry of Education, 1992) refers to problem-solving as involving the use of interesting and realistic contexts that are personally meaningful to the learners; open-ended problems that do not necessarily have one solution; problems that yield solutions that require the use of more than one mathematical skill; problems that require searching for information; thinking; and "the systematic collection of data or evidence, experimentation (trial and error followed by improvement), flexibility and creativity, and reflection" (Ministry of Education, 1992, p. 11).…”

Formation of Schoolchildren’s Creative Activity on the Final Stage of Solving a Mathematical Problem

“…Another approach is based on systematic use of heuristic methods in teaching mathematics. Its authors are Artemov (1973), Balk (1969), Semenov (1995), Trinchero & Sala (2016), Liljedahl, Santos-Trigo, Malaspina, Bruder (2016) and others. Liashchenko (1988), Schwarzburd (1964) and others consider students' independent work as priority educational activity to be the basis for the formation of creative activity.…”