Eye-tracking data and mathematical tasks with focus on mathematical reasoning

This data article contains eye-tracking data (i.e., dwell time and fixations), Z-transformed cognitive data (i.e., Raven's Advanced Progressive Matrices and Operation span), and practice and test scores from a study in mathematics education. This data is provided in a supplementary file. The method section describes the mathematics tasks used in the study. These mathematics tasks are of two kinds, with and without solution templates, to induce different types of mathematical reasoning.


Data
While the participants worked with mathematics tasks described in section 2 (see Tables 1e3 and  Figs. 1 and 2), eye-fixations and dwell time were recorded. Mean values of these variables as presented in the supplementary Excel file. Participant scores on Raven's Advanced Progressive Matrices and Operation Span are also included, as well as mathematical practice and test scores. The data file comprises two pages: the first contains the gathered data, as indicated above, and the second contains explanations of the abbreviated variables.

Experimental design, materials, and methods
The supplementary data set includes data from 48 upper secondary and university students. The students were matched into two similar groups based on cognitive scores, gender, and mathematics grade. Cognitive scores include Raven's Advanced Progressive Matrices [2] and Operation Span [3]. Raven's matrices is a standardized test of abstract non-verbal problem-solving while operation Span is a complex working-memory task which measures executive functions involved in coordinating the processing and storage of information (see Refs. [2,3] for detailed information). The participants practiced on mathematics tasks while their eye-movements were recorded by an EyeLink 1000, videobased eye tracker with which was set to a sampling frequency of 500 Hz, a sampling duration above 50 ms and a gaze resolution of approximately one degree across participants (see Ref. [1] for more details). One week after the practice session, the students took a mathematics test to evaluate what they remembered from the practice session. For a detailed description of the method, see Ref. [1]. The data analysis was based on Block distance and Ward's method [4] which through an iterative process merged data into clusters of increasing dissimilarities (see supplementary data file and [4] for detailed information).
Two types of mathematics tasks are presented (Tables 1e3). The general task design is indicated by Fig. 1, where the five areas of interest are marked. Examples can be seen in Fig. 2. The tasks in Table 1 contains a solution template, similar to textbooks, and were given to the first experiment group. The tasks in Table 2 do not include a solution template, and were given to the second experiment group. Table 3 contains the illustrations included the tasks. The difference between the two task types is the information given in the areas marked as 'formula' and 'example'. The purpose of the tasks was to Specifications Value of the Data Eye-tracking is an objective method to observe student's task solving process, and can therefore be used to observe which information students utilize when solving tasks. This is crucial for understanding how task design can influence student's mathematical reasoning. Eye-tracking data can be used to: make additional analyses of students' eye movements. Mathematics tasks can be used: as a template to construct new tasks with the same reasoning requirements to conduct replication studies.
induce either imitative or creative mathematical reasoning [5]. Previous studies have shown that similar task designs fulfill this purpose [6,7]. Within each task set additional tasks were given with different numbers in the question (e.g., How many matches are needed for 20 squares?). If x is the number of squares then the number of matches y can be calculated by Example: 4 squares can be made by How many matches are needed for 6 squares?
2 Double-squares are constructed with matches If x is the number of double-squares then the number of matches y can be calculated by Example: 4 squares can be made by y ¼ 5x How many matches are needed for 7 squares?
3 Stone tiles are placed around flowers.
If x is the number of flowers, the number of stone tiles y can be calculated by y ¼ 5x þ 3.
Example: Around 4 flowers in a row y ¼ 5x How many tiles are needed around 7 flowers in a row? 4 Stone tiles are placed around flower-triplets.
If x is the number of flower-triplets, the number of stone tiles y can be calculated by y ¼ 11x þ 7.
How many stone tiles are needed around 6 flowertriplets in a row?

5
Grey and yellow square tiles with a side length of 1 dm are mounted on a wall.
If the wall is a dm long and b dm high, the number of tiles K along the edges of the wall can be calculated by Example: If the wall is 8 dm long and 6 dm high,

Acknowledgments
This study was funded by the Marcus and Amalia Wallenberg Foundation and Umeå University, Sweden. We direct a special thanks to Tony Qwillbard and Linus Holm for their help.