Abstract
The cognitive diagnosis model is an emerging evaluation theory. The mastery of fine-grained knowledge points of students can be obtained via the cognitive diagnostic model (CDM), which can subsequently describe the learning trajectory. The latter is a description of the learning progress of students in a specific area, through which teaching and learning can be linked. This research is based on nine statistical items in the Program for International Student Assessment (PISA) 2012 and an analysis of the response data of 30,092 students from 14 countries from four attributes based on CDM. Then, it obtains the learning trajectory of students in statistical knowledge. The study found that Bulgaria, Costa Rica, Peru, Mexico, and Serbia have the same learning trajectories. The learning trajectories of almost 14 countries are as follows: (1) uncertainty, (2) data handling, (3) statistical chart, and (4) average.
Highlights
The need for statistical knowledge has grown; an increasing number of statistics knowledge has been presented to K-12 classrooms (Schaeffer and Jacobbe, 2014)
This research gathered a total of 30,092 datasets from 14 countries [e.g., United Arab Emirates (AE), Argentina (AR), Bulgaria (BG), Chile (CL), Colombia (CO), Costa Rica (CR), Jordan (JO), Kazakhstan (KZ), Mexico (MX), Peru (PE), Romania (RO), Serbia (RS), Tunisia (TN), and Uruguay (UY)]
This study defines attributes based on the content area which is given by Program for International Student Assessment (PISA) and specific statistical attribute indicators as four different statistical knowledge points: uncertainty, average, statistical chart, and data handling
Summary
The need for statistical knowledge has grown; an increasing number of statistics knowledge has been presented to K-12 classrooms (Schaeffer and Jacobbe, 2014). In the United States, the Common Core State Standards for Mathematics (CCSSM, National Governors Association Center for Best Practices and Council of Chief State School Officers, 2010) call for students to create and interpret data displays beginning in grade 1. These changes put forward demands on statistical education. Statistics education research has emphasized the need for reform in the teaching method, educational concept, and teaching tools to improve the teaching and learning effect of statistics (Tishkovskaya and Lancaster, 2012). The researcher can obtain information about how to teach through learning trajectories
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