Validation of the Item-Attribute Matrix in TIMSS-Mathematics Using Multiple Regression and the LSDM

The purposes of this study were (1) to validate of the item-attribute matrix using two levels of attributes (Level 1 attributes and Level 2 sub-attributes), and (2) through retrofitting the diagnostic models to the mathematics test of the Trends in International Mathematics and Science Study (TIMSS), to evaluate the construct validity of TIMSS mathematics assessment by comparing the results of two assessment booklets. Item data were extracted from Booklets 2 and 3 for the 8th grade in TIMSS 2007, which included a total of 49 mathematics items and every student's response to every item. The study developed three categories of attributes at two levels: content, cognitive process (TIMSS or new), and comprehensive cognitive process (or IT) based on the TIMSS assessment framework, cognitive procedures, and item type. At level one, there were 4 content attributes (number, algebra, geometry, and data and chance), 3 TIMSS process attributes (knowing, applying, and reasoning), and 4 new process attributes (identifying, computing, judging, and reasoning). At level two, the level 1 attributes were further divided into 32 sub-attributes. There was only one level of IT attributes (multiple steps/responses, complexity, and constructed-response). Twelve Q-matrices (4 originally specified, 4 random, and 4 revised) were investigated with eleven Q-matrix models (QM1 ~ QM11) using multiple regression and the least squares distance method (LSDM). Comprehensive analyses indicated that the proposed Q-matrices explained most of the variance in item difficulty (i.e., 64% to 81%). The cognitive process attributes contributed to the item difficulties more than the content attributes, and the IT attributes contributed much more than both the content and process attributes. The new retrofitted process attributes explained the items better than the TIMSS process attributes. Results generated from the level 1 attributes and the level 2 attributes were consistent. Most attributes could be used to recover students' performance, but some attributes' probabilities showed unreasonable patterns. The analysis approaches could not demonstrate if the same construct validity was supported across booklets. The proposed attributes and Q-matrices explained the items of Booklet 2 better than the items of Booklet 3. The specified Q-matrices explained the items better than the random Q-matrices.

Expert Approaches to Mental Toughness Development in the High Risk Sport of Diving

Research focusing on mental toughness development and high risk sport is limited to one examination of elite gymnasts' perceptions. Coaches have acknowledged that mental toughness is important to performance success, while admitting they do not know effective development strategies. The aim of the current research is to address both these concerns by employing a grounded theory approach to ascertain elite diving coaches perceptions of mental toughness development and what mental toughness is. Seven diving coaches volunteered and were interviewed for an average of 49 minutes. They all coached an athlete that participated either in the world championships or Olympic games since 2008. Participants reported that mental toughness was the ability of a diver to perform a movement in a crucial moment that requires focus, extending beyond their comfort zone, overcoming fear, and never giving up. Mentaltoughness may not be the appropriate term due to its lack of multicultural sensitivity. Participants felt that dealing with adversity was something divers would have to constantly process. Mental toughness can be developed by the coach, the environment, or individual athlete. Unique attributes specific to divers were an awareness of self and a distinct level of knowing what the athlete was going to do. More research needs to be conducted to determine if these concepts can be generalized to other high risk sports. Future research could help establish a valid quantitative measure of mental toughness development.