EXAMINING SECONDARY MATHEMATICS TEACHER CANDIDATES’ LEARNING AND ENACTMENT OF MATHEMATICS TEACHING PRACTICES: A MULTIPLE CASE STUDY

This qualitative case study explored three teacher candidates’ learning and enactment of discourse-focused mathematics teaching practices. Using audio and video recordings of their teaching practice this study aimed to identify the shifts in the way in which the teacher candidates enacted the following discourse practices: elicited and used evidence of student thinking, posed purposeful questions, and facilitated meaningful mathematical discourse. The teacher candidates’ written reflections from their practice-based coursework as well as interviews were examined to see how two mathematics methods courses influenced their learning and enactment of the three discourse focused mathematics teaching practices. These data sources were also used to identify tensions the teacher candidates encountered. All three candidates in the study were able to successfully enact and reflect on these discourse-focused mathematics teaching practices at various time points in their preparation programs. Consistency of use and areas of improvement differed, however, depending on various tensions experienced by each candidate. Access to quality curriculum materials as well as time to formulate and enact thoughtful lesson plans that supported classroom discourse were tensions for these teacher candidates. This study shows that teacher candidates are capable of enacting discourse-focused teaching practices early in their field placements and with the support of practice-based coursework they can analyze and reflect on their practice for improvement. This study also reveals the importance of assisting teacher candidates in accessing rich mathematical tasks and collaborating during lesson planning. More research needs to be explored to identify how specific aspects of the learning cycle impact individual teachers and how this can be used to improve practice-based teacher education courses.

Action and perception: Neural indices of learning in infants

Early human development offers a unique perspective in investigating the potential cognitive and social implications of action and perception. Specifically, during infancy, action production and action perception undergo foundational developments. One essential component to examine developments in action processing is the analysis of others’ actions as meaningful and goal-directed. Little research, however, has examined the underlying neural systems that may be associated with emerging action and perception abilities, and infants’ learning of goal-directed actions. The current study examines the mu rhythm—a brain oscillation found in the electroencephalogram (EEG)—that has been associated with action and perception. Specifically, the present work investigates whether the mu signal is related to 9-month-olds’ learning of a novel goal-directed means-end task. The findings of this study demonstrate a relation between variations in mu rhythm activity and infants’ ability to learn a novel goal-directed means-end action task (compared to a visual pattern learning task used as a comparison task). Additionally, we examined the relations between standardized assessments of early motor competence, infants’ ability to learn a novel goal-directed task, and mu rhythm activity. We found that: 1a) mu rhythm activity during observation of a grasp uniquely predicted infants’ learning on the cane training task, 1b) mu rhythm activity during observation and execution of a grasp did not uniquely predict infants’ learning on the visual pattern learning task (comparison learning task), 2) infants’ motor competence did not predict infants’ learning on the cane training task, 3) mu rhythm activity during observation and execution was not related to infants’ measure of motor competence, and 4) mu rhythm activity did not predict infants’ learning on the cane task above and beyond infants’ motor competence. The results from this study demonstrate that mu rhythm activity is a sensitive measure to detect individual differences in infants’ action and perception abilities, specifically their learning of a novel goal-directed action.

THE ROLE OF RULES, EXAMPLES AND INDIVIDUAL DIFFERENCES IN THE ACQUISITION OF DECLARATIVE AND PROCEDURAL SECOND LANGUAGE KNOWLEDGE

The relevance of explicit instruction has been well documented in SLA research. Despite numerous positive findings, however, the issue continues to engage scholars worldwide. One issue that was largely neglected in previous empirical studies - and one that may be crucial for the effectiveness of explicit instruction - is the timing and integration of rules and practice. The present study investigated the extent to which grammar explanation (GE) before practice, grammar explanation during practice, and individual differences impact the acquisition of L2 declarative and procedural knowledge of two grammatical structures in Spanish. In this experiment, 128 English-speaking learners of Spanish were randomly assigned to four experimental treatments and completed comprehension-based task-essential practice for interpreting object-verb (OV) and ser/estar (SER) sentences in Spanish. Results confirmed the predicted importance of timing of GE: participants who received GE during practice were more likely to develop and retain their knowledge successfully. Results further revealed that the various combinations of rules and practice posed differential task demands on the learners and consequently drew on language aptitude and WM to a different extent. Since these correlations between individual differences and learning outcomes were the least observed in the conditions that received GE during practice, we argue that the suitable integration of rules and practice ameliorated task demands, reducing the burden on the learner, and accordingly mitigated the role of participants’ individual differences. Finally, some evidence also showed that the comprehension practice that participants received for the two structures was not sufficient for the formation of solid productive knowledge, but was more effective for the OV than for the SER construction.