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1. Exploring the Association between Upper Elementary Students’ Mature Number Sense and Grade-Level Mathematics Achievement.

   Kirkland, Patrick K.; Guang, C.; McNeil, N.M. (October 2023, Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lamberg, T.; Moss, D. (Ed.)

   Students with mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000), the association between students’ mature number sense and other important outcomes is not well specified. For example, how does students’ mature number sense relate to their grade-level mathematics achievement? We analyzed 153 upper elementary school students’ scores on measures of mature number sense, fraction and decimal knowledge, multiplication fluency, and grade-level mathematics achievement. We found mature number sense to be measurably distinct from their fraction and decimal knowledge and uniquely associated with students’ grade-level mathematics achievement. 

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2. A brief, multiple-choice assessment of mature number sense is strongly correlated with more resource-intensive measures

   https://doi.org/10.5964/jnc.12679  

   Kirkland, Patrick K.; Guang, Claire; Otuonye, Chineme; McNeil, Nicole M. (January 2024, Journal of Numerical Cognition)

   Students who exhibit mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly choose effective problem-solving strategies (McIntosh et al., 1997, https://ro.ecu.edu.au/ecuworks/6819). Due to its dispositional nature, mature number sense is typically measured through in-depth interviews or tests of strategy usage. Yet, the lack of an efficient, rigorously developed measure has made it difficult to collect systematic, replicable evidence on students’ mature number sense. To address this, we developed a brief assessment of mature number sense. The present study provides additional convergent evidence of validity for this measure with US students in grades 3-8 (8–14 years old). We compared middle school (N = 40) and upper elementary school (N = 41) scores from the brief assessment with an established, time-intensive measure (Yang, 2019, https://doi.org/10.1007/s10649-018-9874-8) and an in-depth interview of student strategy usage (Markovits & Sowder, 1994, https://doi.org/10.2307/749290). We found strong correlations (r > 0.7) across all three measures, and this held even when controlling for students’ arithmetic scores (pr > 0.6). Researchers and educators can now use the brief assessment to investigate students’ mathematical thinking and advance knowledge of a key aspect of mathematical cognition. 

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3. A multidimensional examination of math anxiety and engagement on math achievement

   https://doi.org/10.1111/bjep.12482  

   Quintero, Michaela; Hasty, Leslie; Li, Tianyu; Song, Seowon; Wang, Zhe (December 2021, British Journal of Educational Psychology)

   BackgroundMath anxiety (MA) and math achievement are generally negatively associated. AimsThis study investigated whether and how classroom engagement behaviors mediate the negative association between MA and math achievement. SampleData were drawn from an ongoing longitudinal study that examines the roles of affective factors in math learning. Participants consisted of 207 students from 4th through 6th grade (50% female). MethodsMath anxiety was measured by self‐report using the Mathematics Anxiety Scale for Children (Chiu & Henry, 1990,Measurement and valuation in Counseling and Development, 23, 121). Students self‐reported their engagement in math classrooms using a modified version of the Math and Science Engagement Scale (Wang et al., 2016,Learning and Instruction, 43, 16). Math achievement was assessed using the Applied Problem, Calculations, and Number Matrices subtests from the Woodcock‐Johnson IV Tests of Achievement (Schrank et al., 2014,Woodcock‐Johnson IV Tests of Achievement. Riverside). Mediation analyses were conducted to examine the mediating role of classroom engagement in the association between MA and math achievement. ResultsStudents with higher MA demonstrated less cognitive‐behavioral and emotional engagement compared to students with lower MA. Achievement differences among students with various levels of MA were partly accounted for by their cognitive‐behavioral engagement in the math classroom. ConclusionsOverall, students with high MA exhibit avoidance patterns in everyday learning, which may act as a potential mechanism for explaining why high MA students underperform their low MA peers. 

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4. Developing a problem-solving measure for grade 4.

   Bostic, J. (July 2019, Proceedings of the 43rd Meeting of the International Group for the Psychology of Mathematics Education)

   Problem solving is central to mathematics learning (NCTM, 2014). Assessments are needed that appropriately measure students’ problem-solving performance. More importantly, assessments must be grounded in robust validity evidence that justifies their interpretations and outcomes (AERA et al., 2014). Thus, measures that are grounded in validity evidence are warranted for use by practitioners and scholars. The purpose of this presentation is to convey validity evidence for a new measure titled Problem-Solving Measure for grade four (PSM4). The research question is: What validity evidence supports PSM4 administration? The PSM4 is one assessment within the previously published PSM series designed for elementary and middle grades students. Problems are grounded in Schoenfeld’s (2011) framework and rely upon Verschaffel et al. (1999) perspective that word problems be open, complex, and realistic. The mathematics in the problems is tied to USA grade-level content and practice standards (CCSSI, 2010). 

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5. Changing populations: Using the PSMs with teachers.

   Bostic, J.; Folger, T.; Matney, G.; May, T.; Koskey, K.; Stone, G. (October 2022, Psychology of Mathematics Education North America)

   Lischka, A; Dyer, E.; Jones, E.; Lovett, J.; Strayer, J.; Drown, S. (Ed.)

   Using a test for a purpose it was not intended for can promote misleading results and interpretations, potentially leading to negative consequences from testing (AERA et al., 2014). For example, a mathematics test designed for use with grade 7 students is likely inappropriate for use with grade 3 students. There may be cases when a test can be used with a population related to the intended one; however, validity evidence and claims must be examined. We explored the use of student measures with preservice teachers (PSTs) in a teacher-education context. The present study intends to spark a discussion about using some student measures with teachers. The Problem-solving Measures (PSMs) were developed for use with grades 3-8 students. They measure students’ problem-solving performance within the context of the Common Core State Standards for Mathematics (CCSSI, 2010; see Bostic & Sondergeld, 2015; Bostic et al., 2017; Bostic et al., 2021). After their construction, the developers wondered: If students were expected to engage successfully on the PSMs, then might future grades 3-8 teachers also demonstrate proficiency? 

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