Contents lists available at ScienceDirect Learning and Individual Differences journal homepage: www.elsevier.com/locate/lindif Child-centered and teacher-directed practices in relation to calculation and word problem solving skills Eija Pakarinen a,b, ⁎ , Eve Kikas c a Department of Teacher Education, University of Jyväskylä, P.O. Box 35, 40014 University of Jyväskylä, Finland b Department of Psychology, New York University Abu Dhabi, United Arab Emirates c School of Natural Sciences and Health, Tallinn University, Narva mnt 25, 10120 Tallinn, Estonia ARTICLE INFO Keywords: Math skills Child-centered practices Teacher-directed practices Primary school Cross-lagged associations ABSTRACT This study examined transactional associations between classroom-level math skills and teaching practices. Participants were 523 children from 31 classrooms. Math skills were assessed three times. Teaching practices were observed in Grades 1 and 3. Child-centered practices promoted subsequent calculation skills whereas teacher-directed practices were associated with a lower level of calculation skills. Higher problem-solving skills at Grade 2 predicted more child-centered practices and less teacher-directed practices in third grade. Moreover, calculation skills mediated the effect of child-centered practices on problem-solving skills. The results suggest that teaching practices and math skills are mutually related across the first years of primary school. 1. Introduction The influential role of teachers and teaching practices in fostering children's academic skills in early elementary classrooms is widely ac- knowledged (e.g., Kikas, Silinskas, Jõgi, & Soodla, 2016; Kikas, Pakarinen, Soodla, Peets, & Lerkkanen, 2018; Daniels & Shumow, 2003; Hamre & Pianta, 2005; Perry, Donohue, & Weinstein, 2007). However, previous research has provided less consistent results on the beneficial effect of specific teaching practices on child outcomes. For example, many studies have indicated that child-centered (cf. learner-centered) teaching practices involving individualization of instruction, en- couragement of autonomy, and focus on positive relationships in the classroom are beneficial to children's academic skills (for a review, see Kikas et al., 2016; Kikas et al., 2018; Cornelius-White, 2007; Marcon, 1999; Perry et al., 2007). There are also studies, which have demon- strated the beneficial effect of teacher-directed practices in promoting the development of basic skills (e.g., reading fluency) (see Huffman & Speer, 2000; Stipek et al., 1998). Therefore, there is an evident need to gain further understanding of the role that teaching practices play in development of academic skills depending on the specific nature of the skills, that is, whether they are simple or complex. We extend previous findings by addressing three important issues. First, the role that teaching practices play in the development of math skills has been in- vestigated to a much lesser extent (see Kikas, Peets, & Hodges, 2014; Kikas et al., 2016 and Perry et al., 2007 as exceptions) than that of reading skills. Second, most research to date has focused either on cross-sectional data or investigated child outcomes at two time points but teaching practices only once, and possible transactional effects of teaching practices and academic skills have not been examined. Third, most previous research examined preschool or kindergarten years while elementary school grades have received far less attention in the lit- erature. Thus, the present study makes a unique contribution to the existing literature by examining cross-lagged associations between children's calculation and problem-solving skills and teaching practices across Grades 1 and 3. 1.1. Teaching practices and children's academic skills Children spend a great amount of their waking hours at school and in the classroom. Therefore, in line with ecological systems theory, classrooms provide children with an important developmental context (Bronfenbrenner & Morris, 1998; Hamre & Pianta, 2010; Pianta, 1999), and teachers' instructional and interactional practices can be assumed to be the central drivers of children's academic development (Hamre, Hatfield, Pianta, & Jamil, 2014; Pianta, 1999). Teachers have been shown to differ in terms of the teaching practices (i.e., quality of cli- mate, management, and instruction) they deploy in the classroom (Kikas et al., 2018; Howes, 2000; Mashburn et al., 2008), and these differences are related to children's various developmental outcomes (e.g., Kikas et al., 2014; Kikas et al., 2018). As a result of differing https://doi.org/10.1016/j.lindif.2019.01.008 Received 1 June 2018; Received in revised form 23 January 2019; Accepted 24 January 2019 ⁎ Corresponding author at: Department of Teacher Education, University of Jyväskylä, P.O. Box 35, 40014, Finland. E-mail addresses: eija.k.pakarinen@jyu.fi (E. Pakarinen), eve.kikas@ut.ee (E. Kikas). Learning and Individual Differences 70 (2019) 76–85 1041-6080/ © 2019 Elsevier Inc. All rights reserved. T