Differential Item Functioning on mathematics items using multilevel SIBTEST

(ProQuest: . denotes formulae omitted.)Interest in the examination of performance differences on mathematics assessments related to sex is strong given the current assessment climate. Sex differences in mathematics assessments are being examined at national (e.g., Scholastic Aptitude Test; Rinn, McQueen, Clark & Rumsey, 2008) and at international (e.g., PISA-Mathematics; Liu, Wilson & Paek, 2008) levels. These differences are examined regardless of a student's grade level. Evaluations start as early as preschool (e.g. number exposure; Chang, Sandhofer, & Brown, 2011) with an aim to determining strengths and weaknesses of students and understanding why differences exist between groups, including differences between boys and girls.Sex differences in mathematics scores have been associated with social (e.g. stereotypes; Cvencek & Meltzoff, 2012), cognitive (e.g., spatial reasoning; Klein, Adi-Japha & Hakak-Benizri, 2010), and affective (e.g., mathematics ability attribution; Dickhauser & Wulf-Uwe, 2006) aspects of mathematical learning. However, although documented, it is not clear what causes these sex differences in scores. Possible reasons include adult's expectations towards a child's mathematics performance (Ambady, Shih, Kim & Pittinsky, 2001; Penner & Paret, 2008). Such expectations can influence girls' and boys' mathematics achievement starting in the early stages of development (Keller, 2012). Parents, for instance, work on mathematical concepts with boys more often than with girls (Watt et al., 2012), and teacher beliefs reflect student's math-related attitudes (Gunderson, Ramirez, Levine & Beilock, 2012). When examining sex differences in mathematical ability measured by standardized tests, outcomes can become ambiguous. Systematic reviews evaluating information from large datasets including international assessments created to measure mathematical performance (e.g., TIMMS, PISA) have shown sex differences in mathematics scores can be small (i.e., Cohen's d ranging from .05 to .15; Else-Quest, Hyde & Linn, 2010; Lindberg, Hyde, Petersen & Linn; 2010). In contrast, evidence also suggests the use of standardized assessments can perpetuate gender differences given the impact an item's format may have on gender responses. Item format (e.g., constructed-response), content (e.g. algebra), or objectives (e.g. evaluating "real life" mathematical problems) can favor boys and girls differently (Harris & Carlton, 1993; Taylor & Lee, 2012). Such results are supported when systematic reviews consider a test's format at an item level when examining outcomes (Zhang & French, 2010). Thus, sex differences in mathematics scores may, in part, be attributed to a lack of measurement invariance at the item level driven by such item components as item format.At the item level, measurement invariance in mathematic tasks can be evaluated via differential item functioning (DIF) analysis. DIF refers to the situation where examinees from two groups (e.g., boys and girls) with equal levels on the measured trait (e.g., mathematics ability) have different probabilities of endorsing a specific level or response to an item (e.g., correct response). DIF can be found in the item difficulty and the item discrimination parameters, which are labeled as uniform DIF and non-uniform DIF, respectively. The former occurs when the probability of endorsing an item, conditioned on underlying ability, differs for members of the reference and focal groups, whereas the latter is present when group differences in the probability of endorsement conditioned on ability are not constant across the entire spectrum of abilities.DIF methodology is frequently used to: evaluate sex differences across cultures (Lyons-Thomas, Sandilands & Ercikan, 2014); examine how these differences are developed through student's educational advancement (e.g. elementary and secondary schooling; Robinson & Lubieski, 2010); or understand how mathematics achievement gaps increase longitudinally (Carmichael, 2013). …