Page 180 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

178
Chapter 6
experiences with math in the past and thus more stable than math self- efficacy, which is - by definition - more future oriented and therefore malleable (Wolff et al., 2018). Furthermore, fourth grade children have accumulated greater experience with arithmetic fluency than advanced mathematical problem-solving and the strong association between math self-concept and arithmetic fluency thereby accounted for as well (Marsh et al., 2005; Weidinger et al., 2018). Math self-efficacy predicted neither arithmetic fluency nor mathematical problem-solving, which was unexpected. It is possible that math self-efficacy only becomes a significant predictor of math abilities later in development (i.e., after grade 4). Young children are less able than older children to judge their math performance and thus have less well-formed expectations for their performance and beliefs about whether they will succeed or not (Pajares & Miller, 1994). Also, an unexpected finding in the present research was that math anxiety did not predict any aspect of the children’s fourth grade math performance. The explanation for this may lie in that children in Dutch elementary schools generally experience encouraging environments and therefore math anxiety did not play a predictive role in this research. Dutch elementary school children have generally been found to have sufficient self-confidence for the learning of mathematics (Hickendorff et al., 2017; Inspectie van het Onderwijs, 2021; Mullis et al., 2020).
To summarize, children’s prior math knowledge and skill, defined as the level of arithmetic fluency and mathematical problem-solving ability at the start of grade 4, was found to be an important predictor of their mathematical abilities in the present research both during and at the end of grade 4. Both visuospatial and verbal updating were significant predictors for their mathematical problem-solving at the end of grade 4, while inhibition and shifting related indirectly to the development of their mathematical problem-solving ability during the course of grade 4 (via arithmetic fluency and after control for their mathematical problem-solving at the start of grade 4). With regard to the predictive roles of the children’s math-related beliefs and emotions, only math self-concept played a predictive role but then for only the development of arithmetic fluency over the course of grade 4