On the Way to Observe How Future Primary School Teachers Reason About Fractions

Abstract

In our contribution we focus on the possibility to use an educational tool called Concept Cartoons in future primary school teachers' education, as an instrument for observing how future primary school teachers reason about fractions. In the introduction section we present Concept Cartoons, and also the primary school level of the fractions topic. In the first part of the research we analyse data obtained when future primary school teachers were solving a problem in the Concept Cartoon form. The task which we adapted to this form belongs to primary school mathematics, it focuses on the concept of a fraction per se (on the parts-and-whole decision and on comparison of two pre-partitioned models with diverse wholes). Using Concept Cartoons, we can observe which statements about the issue our respondents consider as correct, and which kinds of reasoning they use in their justifications. In the second part of the research we analyse problems that the respondents themselves posed in the Concept Cartoon form, with particular focus on tasks devoted to fractions.

Assessing Future Teachres' Knowledge on Fractions: Written Tests vs Concept Cartoons

“…Such asymmetry is also reported by Lamon (1999) in so called shrinking and enlarging within the topic of percentages: here the statement "A is 25 % more than B" does not correspond to the statement "B is 25 % less than A". For more about linguistic issues related to fractional changes and different structure and difficulty levels of tasks on fractions at primary school level in the Czech Republic see (Samková and Tichá, 2017b).…”

“…all interpretations of fractions including ratios and percentages, and operations on Printed ISSN: 2336-2375 fractions) during their teacher preparation content courses. And, like elsewhere in the world, they tend to provide misconceptions on the topics, especially on issues related to the part-whole interpretation (Hošpesová and Tichá, 2015;Samková and Tichá, 2017b;Pavlovičová and Švecová, 2017).…”

“…has a similar structure and a similar difficulty as the task T3, see the attributes of the two tasks given in Table 1. The method of how to use Concept Cartoons for diagnosing knowledge of future teachers and the particular Concept Cartoon from Figure 1 had been already tested previously (Samková and Tichá, 2017b;Samková, 2018a). This particular Concept Cartoon combines three bubbles containing procedures and results (Pavla, Karel, Radek), and a bubble introducing a result with a reference to a missing drawing that leads to the result (Tonda).…”

“…In my recent work, I have studied an educational tool called Concept Cartoons and its opportunities in assessing various aspects of future teachers' knowledge, e.g. their way of grasping situations related to word problems (Samková and Tichá, 2015), the openness of their approach to mathematics (Samková and Tichá, 2016b), their reasoning (Samková and Tichá, 2017b), problem posing skills Tichá, 2016b, 2017b), informal foundations of pedagogical content knowledge (Samková, 2018a). One of the first studies (Samková and Tichá, 2015) showed how problems assigned in the Concept Cartoon form might become a valuable alternative to standardly assigned word problems.…”

Uplatnění otevřeného přístupu k matematice v přípravě budoucích učitelů 1. stupně ZŠ – empirická studie v kontextu badatelsky orientovaného kurzu

“…Ve svých předchozích studiích jsem ji uplatnila např. při zkoumání didaktických znalostí obsahu (Samková, 2016b) a při zkoumání, jak budoucí učitelé 1. stupně ZŠ uvažují o matematických tématech (Samková & Tichá, 2017). Využití Concept Cartoons pro diagnostické účely je inovativním přístupem k tomuto nástroji, neexistuje tedy žádné srovnání s jiným výzkumem.…”