The effect of the hypothetical learning trajectories and the contribution of the eye-tracking technology in understanding the young children’s mathematical patterning recognition and generalization

Thesis Type: Doctorate

Institution Of The Thesis: Middle East Technical University, Faculty of Education, Department of Elementary and Early Childhood Education, Turkey

Approval Date: 2019

Student: Nursel. Yılmaz

Supervisor: VOLKAN ŞAHİN


The primary aim of this study is to evaluate whether patterning instruction based on a hypothetical learning trajectory (HLT) is more efficacious than the same instruction presented in an integrated manner or business as usual. The HLT-based and integrated instruction were developed using Design-Based Research (DBR) involving three phases and two iteration cycles. The patterning HLT and accompanying instructional activities proposed by Clements and Sarama (2009) was the starting point for the HLT-based instruction and a modified HLT version of this HLT was evaluated in the present study. A randomized control trial involved [n=48] 4- and 5-year-olds assigned to an experimental condition (HLT-based v instruction), an active control (integrated instruction), and a passive control (business as usual). Both concrete and computer-supported activities were utilized during the training. Eye-tracking technology data were collected to better understand the cognitive processes underlying patterning learning. Quantitative and qualitative analyses were used to analyze the collected data. While descriptive statistics and inferential statistics such as ANOVA and ANCOVA were used for quantitative analyses, the heat maps and gaze plots were benefited for qualitative analyses. A significant and substantial difference was found between the treatment and the passive control condition (on the overall score at the delayed posttest. The active control condition likewise significantly outperformed and business-as-usual condition. When each patterning skill (i.e., extension, translation, and core identification) was separately investigated, resuts showed a s ignificant and substantial difference between the groups. Eye-tracking methodology and qualitative analyses revealed a number of interesting findings. Different cognitive behaviors were observed during the extension, translation, and the core-identification of the AB, ABB, ABC patterns. The possible reasons and extensive discussions were followed to lead the implementations and recommendations.