Materials

Non-verbal cognitive ability was assessed with the Matrices test adopted from the Cognitive Assessment System-Version 2 (CAS-2; Naglieri et al., 2014). Children were asked to choose one piece among six alternatives to complete accurately the missing part of a graphic image that was composed of a pattern of shapes. The test was terminated when four consecutive mistakes were made. The total number of correct trials were recorded as the score of this task (maximum score = 44). Cronbach’s alpha reliability coefficient in the reliability in the CAS-S manual was 0.91 and 0.88, in grades 2 and 4, respectively (CAS-2; Naglieri et al., 2014).

Attention was assessed with the Expressive Attention test adopted from the CAS-2 (Naglieri et al., 2014). Children were presented with a pattern of words in a mixed variety of colors; second-graders were presented with only three colors (red, blue, and yellow) and fourth-graders were presented with four colors (red, green, blue, and yellow). They were asked to state the color of the ink of those words but not reading of the words as fast and accurate as possible. For example, the correct answer of a Chinese word “yellow” printed in red color is red. There were eight items for demonstration, eight items for practice, followed by a total of 40 words on one page for testing. Recording of time use started when children said the first color. The total number of correct answers and the time taken to state all of the words were recorded. The score of each child was calculated using the formula: . Split-half reliability coefficient in our sample was 0.95 and 0.91, in grades 2 and 4, respectively. Split-half reliability was calculated by first dividing the data into two groups using the parity grouping method and then correlating the two groups (Johnson and Penny, 2005).

The N-back working memory task was adopted from the work of Kirchner (1958) and was implemented using E-prime 2.0, Psychology Software Tools, on a desktop computer. Stimuli included three solid black geometrical shapes ●(circle), ■(square) and ▲(triangle) that were randomly shown inside one of the squares of a 3 × 3 matrix. Children were asked to perform 1-back, where n = 1, as 2-back would be difficult for young children and reduce the test reliability (Pelegrina et al., 2015). To perform the task, children had to decide whether the geometric shape and position currently shown was the same as the one previously shown. If the shape and position of the target stimulus were both consistent with the one shown before, children were instructed to press button “A” on a laptop computer within a 3500 ms time limit, or they were instructed to press button “L.” The geometrical shapes were shown 1000 ms, and the inter-stimulus interval was 3500 ms. Children should press the button within 4500 ms, or a miss response would be recorded. Each child was given eight practice trials to familiarize the task. There were a total of 24 items in the task. The total score was the proportion of correct answers, converted from percentages (i.e., maximum score = 1). Split-half reliability in our sample was 0.85 and 0.87, in grades 2 and 4, respectively.

The number line estimation task was adopted from Siegler and Opfer (2003) and was implemented on a rectangular (21.8 cm × 13.5 cm) pad. The materials included a 15-cm line with one end marked with 0 and the other end marked with 100 (i.e., min = 0, max = 100) and 28 numbers: 3, 4, 6, 8, 12, 14, 17, 18, 20, 21, 24, 25, 29, 33, 39, 42, 48, 50, 52, 57, 61, 64, 72, 79, 81, 84, 90, and 96. The number 20 and 50 were used for practice. Each child was given 26 trials to do number line estimation. In the number-to-position (NP) version of the task, which was performed in this study, children were asked to make numerical estimations by putting a single mark on each line (from 1 to 100) to indicate the location of a number presented on the number line. For example, they were given a number, say 20, and had to put a single mark on the line to indicate the location of 20. We calculated each child’s percent absolute error using the formula: . For example, if a child was asked to estimate the location of 20 on a 0–100 number line and placed the mark at the location that corresponded to 25, the percent absolute error would be 5% [(25 – 20)/100], i.e., a score of 0.05 for reflecting number line estimation errors. The lower the score, the better the number line estimation ability. Cronbach’s alpha reliability coefficient in our sample was 0.81 and 0.70, in grades 2 and 4, respectively.

Two measures of mathematical skills were administered: calculation fluency and math problem-solving. Calculation fluency was adopted from WIAT-III (Wechsler Individual Achievement Test-Third Edition; Wechsler, 2009) and included two subtests: addition fluency (e.g., 2 + 1) and subtraction fluency (e.g., 7 – 1). Each subtest has 48 items, and children were asked to solve as many items as possible within a 60-s time limit. The total score was the total number of correct additions, subtractions and multiplication (max = 144). In our sample, split-half reliability coefficient was 0.88 in grade 2, and 0.93 in grade 4. Math problem-solving was also adopted from WIAT-III (Wechsler, 2009), and children were asked to solve one-on-one mathematical problems. The test was terminated when four consecutive errors were made. The total score was the total number of problems correctly solved (max = 72). Cronbach’s alpha reliability coefficient in our sample was 0.82 and 0.85, in grades 2 and 4, respectively. Split-half reliability was calculated by first dividing the data into two groups using the parity grouping method and then correlating the two groups (Johnson and Penny, 2005).