1. Introduction

Learning engagement is a key indicator for evaluating the learning process and predicting learning outcomes, and its relationship with second language acquisition has become a research hotspot. Existing research has explored the definition and dimensions of learning engagement, as well as its relationship with learning outcomes. However, there has been insufficient attention paid to the effects of learning engagement in second language acquisition, and empirical research conclusions are controversial. Learning engagement has a positive predictive effect on language skill acquisition and foreign language performance, but its role as a multidimensional construct (including cognitive, emotional, behavioral, and other dimensions) in second language acquisition is complex. This study is based on the theory of complex dynamic systems and adopts an individual centered research approach to examine the interaction patterns of three sub dimensions of learning engagement and their impact on second language proficiency (including language and thinking), in order to reveal the interaction relationship between the sub dimensions of learning engagement, clarify the comprehensive role of learning engagement in second language acquisition, and provide reference for teaching interventions.

2. Literature review

Learning engagement is a key factor in second language acquisition, covering three sub dimensions: cognition, emotion, and behavior. Cognitive engagement involves learning strategies and self-regulation, emotional engagement focuses on learners' emotional experiences, and behavioral engagement refers to learners' behavioral performance and level of participation. Empirical research shows that learning engagement has a positive impact on second language proficiency, but there is controversy over its mechanism of action. The theory of complex dynamic systems provides a new perspective for the study of learning engagement, emphasizing the comprehensive connection and collaborative effects of various dimensions of learning engagement. The individual centered research method focuses on the heterogeneity of learners, identifies the interdependence between different dimensions of learning engagement, and their comprehensive effects on second language acquisition. The aim of this study is to explore learning engagement patterns from the perspective of task microenvironment based on the task of reading and writing continuation, and systematically analyze the multiple impacts of learning engagement on second language writing ability and critical thinking ability.

3. Research methods

Introduced research methods, including research subjects, data collection, and data analysis. The research subjects are 119 second year English major students from a certain university in China, with no overseas experience, aged 19-21, currently studying the course "Intermediate English Writing (2)". Data collection includes tasks such as continuation writing after reading argumentative essays and a learning engagement scale. The task of continuation after reading requires students to complete a 500 word argumentative essay within 60 minutes. The writing and critical thinking abilities will be evaluated and scored by two English major teachers. The Learning Engagement Scale consists of 11 items and uses the Likert 7-level scale, which has good reliability. Data analysis was conducted using R software for cluster analysis, including two steps of discrimination and clustering. Finally, based on the clustering results, one-way ANOVA and post hoc testing were performed to examine the differences in writing and critical thinking abilities among learners with different learning engagement patterns.

4. Results

Through discriminant analysis, 119 participants were clustered into four categories of learners, each exhibiting a unique learning engagement pattern. There are significant differences in emotional, cognitive, and behavioral engagement among learners with different modes of engagement. In terms of writing ability, learners with different engagement modes show significant differences in essay length and language expression, among which learners with the "high high engagement mode" have significantly better writing ability than learners with other engagement modes. In terms of critical thinking ability, learners with different engagement modes show significant differences in the total score, correlation, accuracy, and logicality of critical thinking ability. Among them, learners with the "high high high engagement mode" have significantly better critical thinking ability than those with other engagement modes.

5. Discussion

This chapter is based on the theory of complex dynamic systems and adopts an individual centered research path to explore the interaction patterns of learning engagement sub dimensions (emotion, cognition, behavior) through cluster analysis. The study found that there are four modes of learning engagement, in which learners exhibit unique cognitive thinking, emotional experiences, and behavioral performance. The cognitive thinking, emotional experience, and behavioral performance behind the learning engagement model show a convergence, indicating that learners have a high degree of correlation and positive synergy among the dimensions of learning engagement when completing reading and writing tasks. Emotional investment exhibits complexity in the task microenvironment, which is consistent with cognitive and behavioral investment, but also exhibits uniqueness in certain situations. The learning engagement mode has a differentiated impact on second language writing and critical thinking abilities, with learners in the high high engagement mode scoring significantly higher in writing and critical thinking abilities than those in the medium medium medium low low engagement mode. Different learning engagement modes have significant differential effects on the length and language expression of second language writing compositions, but their impact on content and structure is not significant. Different modes of learning engagement have differentiated effects on the relevance, accuracy, and logicality of critical thinking abilities, but have little impact on clarity and depth.

6. Conclusion

This chapter summarizes the contribution of the individual centered research pathway in the field of second language acquisition learning engagement research, including the identification of four learning engagement patterns through cluster analysis and their differentiated effects on second language writing and critical thinking abilities. The study confirms the effectiveness of the individual centered research pathway and provides useful references for foreign language teaching practice. At the same time, it is pointed out that future research can further explore the interactive relationship between learning engagement and other individual differences, as well as their comprehensive impact on second language acquisition.