For every individual child, kindergarten is meant to consolidate early academic, learning and intellectual skills in order to benefit subsequent, more challenging learning experiences from first grade onwards (Zuckerman & Halfon 2003). Children show different strengths and weaknesses at school entry. Some are strong on intellectual skills while others are less able (Duncan et al. 2007). Similarly, some have a more dedicated work ethic and others are less engaged towards task completion and academic activities in the classroom (High & the Committee on Early Childhood, Adoption, and Dependent Care and Council on School Health 2008). Helping instructors identify which children are at risk of experiencing academic difficulty can help prevent later academic adjustment problems. The purpose of the present study is therefore to describe different student profiles of readiness and to examine how these profiles forecast later achievement.

What kinds of skills are desirable in young learners? General intelligence is a very good predictor of academic achievement, successful and gainful employment, career potential and higher lifestyle quality (Colom & Flores-Mendoza 2007; Deary et al. 2007; Der, Batty & Deary 2009; Duncan et al. 2007; Kuncel, Hezlett & Ones 2004; Romano et al. 2010). Recent evidence also suggests that intellectual skills may be more important than non-cognitive skills, such as motivation, for academic achievement (Lu et al. 2011). There is empirical evidence to suggest that intelligence begins to crystallise around the time of school entry and then remains relatively stable through late adulthood (Deary et al. 2012). Furthermore, standardised assessments of intellectual ability remain common for screening and identifying kindergarten students with potential learning problems or exceptional ability.

In addition to general intelligence, children also need knowledge-based intellectual skills in mathematics and language to help them acquire increasingly complex lessons (Westerveld et al. 2015). Several large-scale studies have shown that receptive vocabulary and number knowledge are highly predictive of subsequent achievement (Duncan et al. 2007; Pagani et al. 2010; Romano et al. 2010). Furthermore, these skills appear to predict achievement regardless of gender, the types of homes children come from or family income.

Finally, researchers are increasingly aware that learning draws upon a number of competencies in addition to intellectual skills typically measured by standardised tests (Duckworth et al. 2007; Duckworth & Seligman 2005; McClelland, Acock & Morrison 2006). School entry is the first time children encounter expectations regarding time limits for accomplishing tasks and adhering to an agenda. Furthermore, as early as kindergarten, children must learn to focus their energies on teacher-directed activities, delay gratification and follow formal and informal rules in the classroom setting (McDermott, Mordell & Stoltzfus 2001; Mischel, Shoda & Rodriguez 1989). When asked about which characteristics they favoured in young students, elementary school teachers tend to indicate child ability to self-regulate, pay attention and effectively manage behaviours (Rimm-Kaufman et al. 2002). Consequently, how teachable young children are in the classroom is likely to play an important role in early academic adjustment. For this reason, a person-environment-fit perspective predicts that productive behaviour and the capacity to adapt to classroom demands is likely to support successful child transitions into formal schooling regardless of intellectual ability and knowledge-based skills (Alexander, Entwisle & Dauber 1993; Bowles, Gintis & Osborne 2001; Fantuzzo et al. 2007; Li-Grining et al. 2010; McWayne, Fantuzzo & McDermott 2004; Skinner, Kindermann & Furrer 2009).

Classroom engagement represents a reflection of productive behaviour and of person-environment-fit in the school context. A child that is engaged in the classroom is attentive to teacher directions, displays cooperation and completes work independently and on time. When actively applied by students, such behaviours set the stage for short- and long-term academic and personal success (Cunha et al. 2005; DiPrete & Eirich 2006; Fitzpatrick & Pagani 2013). Classroom engagement also falls under the broader category of learning-related behaviours which are likely to be partially driven by self-regulatory skills (Rimm-Kaufman et al. 2009; Sasser, Bierman & Heinrichs 2015). Self-regulation comprises a combination of cognitive and emotional strategies individuals use to influence their own internal states, thoughts and behaviours. As such, self-regulation is likely to support classroom engagement behaviour by facilitating effortful control, delay of gratification and self-control.

There is evidence that early language, mathematical and intellectual and classroom engagement skills represent important components of kindergarten readiness. However, little research to date has examined whether it is possible to describe different types of learners based on these dimensions. The majority of school readiness studies have employed variable-based analytic approaches, which estimate the relative contributions of individual school readiness indicators to academic outcomes. This approach is useful for identifying significant predictors of achievement. However, such variable-based approaches assume that children are a homogenous group, or that relationships between variables are the same for all children. Variable-centred approaches also preclude the existence of subgroups of children that may differ in their profiles of school readiness. One exception is a study by Sabol and Pianta (2012) who used a person-centred approach to detect five preschool profiles on the basis of child emotional and cognitive control. The authors then examined how profile membership predicted achievement in the fifth grade. Although research using variable-centred approaches have generally concluded that socioemotional skills are non-significant predictors of later achievement (Duncan et al. 2007), a recent study using a person-centred approach has found that socioemotional skills predict academic success when they are present in students with poor cognitive control (Denham et al. 2012). This finding highlights the potential usefulness of applying person-centred approaches which are better suited for taking into account multiple and correlated characteristics of children.

The present study draws upon a population-based longitudinal sample of French-Canadian children. A first objective is to employ a person-centred approach to examine whether student risk profiles can be identified in kindergarten on the basis of child school readiness characteristics. A second objective is to estimate whether kindergarten student profiles differentially predict achievement outcomes by the end of the fourth grade. We expect that kindergarten students showing higher levels of risk in terms of their intellectual, academic and engagement skills will perform worse academically four years later.

Several child and family demographic factors may influence both child school entry competence and later academic outcomes. Children who are chronologically older at school entry may be better prepared and maintain an advantage relative to younger classmates. Girls also tend to be better prepared at school entry than boys and tend to show less disruptive classroom behaviour (Duncan et al. 2007). Children who grow up in poverty also face a constellation of family and environmental risk factors that undermine school readiness (Duncan & Brooks-Gunn 1997; Noble, Norman & Farah 2005). Finally, problematic behavioural characteristics such as presenting high levels of hyperactivity, physical aggression or emotional distress can interfere with learning behaviour in the classroom and thus undermine child academic achievement (Chen et al. 2010; Pagani et al. 2001). Inversely, prosocial skills predict improvements in academic performance (Ladd, Birch & Buhs 1999). As such, the present study includes measures of child sex and age, socioeconomic status and family background characteristics and behavioural adjustment as control variables.

The first goal of this study was to examine whether children show different profiles of school readiness. We found three types of kindergarten students that differed on the basis of their academic, intellectual and classroom engagement skills. The majority of children in our population-based sample (57%) showed an adaptive pattern of school readiness, characterised by high scores on all of the kindergarten skills. Nevertheless, a substantial proportion of children (43%) appeared less than optimally prepared to learn and demonstrated less than optimal levels of school readiness. Although both of these groups showed low levels of receptive vocabulary and fluid intelligence, the moderate risk group scored higher on kindergarten number knowledge and classroom engagement. To our knowledge, this study is the first to identify two at-risk profiles of kindergarten children based on knowledge-based, intellectual and classroom engagement skills.

Children showing moderate and low levels of readiness differed in measurable ways on classroom engagement and mathematics skills. The relationship between kindergarten number knowledge and classroom engagement observed in our study is consistent with previous research linking both skills to effective cognitive control (Blair & Razza 2007; Fitzpatrick & Pagani 2013). In the classroom, children with poor levels of cognitive control have a harder time sitting still, following sequential instructions, managing time and keeping their desks neat (Fitzpatrick & Pagani 2012). Furthermore, cognitive control also partially explains early mathematical ability and child reasoning skills through attention, working memory and inhibitory control mechanisms (Blair & Razza 2007).

Kindergarten receptive vocabulary and fluid intelligence appeared to be less closely related to mathematical ability and classroom engagement in our profiles. This may have been the case because receptive vocabulary and fluid intelligence are distinct from cognitive control and may be more highly related to general intelligence or socioeconomic status. Although important for academic achievement, general intelligence may be more resistant to intervention. Consequently, it may be especially efficient to target cognitive control as a means of promoting both classroom engagement and math achievement in at-risk kindergarten students.

The second aim of our study was to examine whether school readiness profiles are prospectively associated with subsequent academic achievement. We compared children with the most adaptive pattern of school readiness to two groups of children showing lower levels of school readiness. Compared to children showing the most adaptive school readiness profile, children in the low and moderate readiness groups had poorer outcomes in the fourth grade. Belonging to the moderate readiness group, characterised by better mathematical and classroom engagement skills, also predicted a significant long-term advantage when compared to children showing the lowest levels of school readiness. Both the moderate and low readiness classes of children had lower levels of intellectual and language skills. Consequently, our findings provide some evidence that in the absence of these skills, adequate classroom engagement and mathematical skills may represent a protective factor in the classroom. These findings provide a more detailed understanding of school readiness and expand on previous research which has mainly used variable-centred approaches to explain the relative importance of school readiness characteristics (Duncan et al. 2007; Pagani et al. 2010).

The findings from this study advance our knowledge of school readiness by suggesting that a combination of productive classroom behaviours reflecting conscious effort and task-orientation, in addition to academic and intellectual skills, may give young students the strongest foundation for later achievement. Children belonging to the lowest readiness group showed the greatest difficulty in both teacher and directly assessed mathematics. This is not surprising as these children also showed the lowest level of early mathematics knowledge. Interestingly, children in this group, which did not differ significantly from the moderate risk group in terms of early language and intellectual skills, also experienced the most difficulty in reading and writing by the fourth grade. Consequently, these results suggest a role for early mathematical and classroom engagement in predicting later verbal performance. Fourth-grade achievement in reading involves highly automatic letter and phoneme identification processes which are knowledge based and are reinforced by opportunities for literacy found outside the formal schooling environment (Hart & Risley 1995). Nevertheless, reading achievement also requires effective reasoning skills, learning strategies and cognitive control (Altemeier, Abbott & Berninger 2008). Inhibitory control, which is a main component of cognitive control strategies, has been found to play a significant role in the acquisition of letter identification automaticity and phonemic awareness (Blair & Razza 2007). Furthermore, writing and its components in terms of composition, spelling and punctuation represent a problem-solving process driven by planning, translating and reviewing material being produced for communication purposes (Altemeier et al. 2006). Finally, learning in other academic realms such as science also depends on similar sets of skills because it requires similar memorisation and reasoning strategies.

Our findings suggest the potential benefit of targeting classroom engagement and number knowledge with children showing low levels of kindergarten readiness. Classroom engagement skills, in particular, can be routinely and cost-effectively monitored and assessed by elementary school teachers during instructional activities (Lee & Reeve 2012). More importantly, classroom engagement skills represent malleable behaviours that can be targeted through preschool intervention or shaped, reinforced, and modelled by classroom teachers (Fredricks, Blumenfeld & Paris 2004). Finally, the identification of different profiles of child readiness in our large population-based sample may benefit the development of more tailored and refined kindergarten interventions.

A promising avenue for increasing both number knowledge and classroom engagement involves strengthening child cognitive control. The development of interventions that strategically combine computerised training, classroom instruction and curriculum, aerobic exercise, mindfulness training, and martial arts, tailored to suit the needs of different learners, are likely to be especially effective in promoting classroom engagement and mathematical skills (Bierman et al. 2008; Diamond et al. 2007; Flook et al. 2010; Kamijo et al. 2011; Klingberg et al. 2005; Klingberg, Forssberg & Westerberg 2002; Lakes & Hoyt 2004; Lillard & Else-Quest 2006). Children showing initially higher levels of academic risk, such as children from disadvantaged families, boys and children with ADHD, have also been found to benefit the most from cognitive control training (Diamond & Lee 2011). Targeting these skills therefore appears to be a promising strategy for equalising inequalities in achievement.

Our findings should be interpreted in the context of certain limitations. First, although prospective, our results are based on a correlational study of development occurring in a natural context. As a result, despite our attempt to methodologically reduce the competing influence of several child and family confounding variables, it is not possible to infer a causal relationship between our independent and dependent variables. In this study, we preferred to adopt a person-centred approach to observe how features of school readiness co-occur in a population. As a result, this method prevents us from identifying precisely which features of school readiness make a stronger overall contribution to later achievement. Nevertheless, the results of other longitudinal studies of school readiness with the same sample provide evidence that both classroom engagement and intellectual skills measured in kindergarten represent robust and independent predictors of later achievement (Fitzpatrick & Pagani 2013; Pagani et al. 2010).

The possibility of early detection and intervention with children at risk of learning difficulties represents our most promising strategy for circumventing a number of expensive social problems which are associated with high school dropout, such as unemployment, substance abuse and involvement in crime (Cunha et al. 2005; Shonkoff 2011). Although it is common to screen for intellectual skills and early academic skills at school entry, classroom engagement skills are not routinely assessed. These behaviours can be easily recorded and monitored by regular classroom teachers as an alternative to more expensive screening often conducted by professionals using universal, inexpensive and ecological assessments. Policies concerned with school readiness could be ameliorated by incorporating strategies aimed at helping teachers assess and reinforce engagement behaviour and mathematical skills in the kindergarten classroom. The prospective associations found in this longitudinal study speak directly to preventive practices in contexts concerned with learning and instruction. They also support the need for preschool interventions and early screening procedures which involve knowledge-based, intellectual and learning-related skills.