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1. Middle School Students’ Mature Number Sense is Uniquely Associated with Grade-Level Mathematics Achievement.

   Kirkland, P.K.; Guang, C.; Cheng, Y.; Trinter, C.; Kumar, S.; Nakfoor, S.; Sullivan, T.; McNeil, N.M (January 2022, Proceedings of the Forty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.)

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

   Students exhibiting 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; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014), students’ mature number sense and its nomological network are not yet well specified. For example, how does students’ mature number sense relate to their knowledge of fractions and their grade-level mathematics achievement? We analyzed 129 middle school students’ scores on measures of mature number sense, fraction and decimal computation, 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. "Oh! That's Interesting!"; Captivating students who hate mathematics with mathematical ideas

   Claiborne-Naranjo, B.; Barstow, A.; & Dietiker, L. (October 2023, Psychology of Mathematics Education - North American Chapter)

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

   The positive relationship between students’ attitudes toward mathematics and mathematics achievement is well documented. Yet there is a worsening problem of low appeal of mathematics especially at the secondary level. Therefore, in this paper we focus on three high school students who report a strong dislike of mathematics. By analyzing student surveys, interviews, and lesson observation data, we examined how some mathematical lessons improved these students’ experiences (i.e., their aesthetic dimensions). We found that while student preferences varied, each student was interested in lessons that centered them as sense-makers and in which the content unfolded with suspense. Such lessons led to positive aesthetic responses such as surprise, curiosity, and satisfaction. Thus, lessons can be designed in which even students with the most negative views of mathematics can find mathematical concepts interesting. 

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3. Comorbid learning difficulties in reading and mathematics: The role of intelligence and in-class attentive behavior

   https://doi.org/doi/10.3389/fpsyg.2020.572099  

   Geary, D. C. (October 2020, Frontiers in psychology)

   null (Ed.)

   The goal was to identify the domain-general cognitive abilities and academic attitudes that are common and unique to reading and mathematics learning difficulties that in turn will have implications for intervention development. Across seventh and eighth grade, 315 (155 boys) adolescents (M age = 12.75 years) were administered intelligence, verbal short-term and working memory, and visuospatial memory, attention, and ability measures, along with measures of English and mathematics attitudes and mathematics anxiety. Teachers reported on students’ in-class attentive behavior. A combination of Bayesian and multi-level models revealed that intelligence and in-class attentive behavior were common predictors of reading accuracy, reading fluency, and mathematics achievement. Verbal short-term memory was more critical for reading accuracy and fluency, whereas spatial ability and mathematics self-efficacy were more critical for mathematics achievement. The combination of intelligence and in-class attentive behavior discriminated typically-achieving students from students with comorbid (D = 2.44) or mathematics (D = 1.59) learning difficulties, whereas intelligence, visuospatial attention, and verbal short-term memory discriminated typically-achieving students from students with reading disability (D = 1.08). The combination of in-class attentive behavior, verbal short-term memory, and mathematics self-efficacy discriminated students with mathematics difficulties from their peers with reading difficulties (D = 1.16). Given the consistent importance of in-class attentive behavior, we conducted post hoc follow-up analyses. The results suggested that students with poor in-class attentive behavior were disengaging from academic learning which in turn contributed to their risk of learning difficulties. 

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4. A Validity Argument for a Brief Assessment of Mature Number Sense

   https://doi.org/10.5951/jresematheduc-2022-0071  

   Kirkland, Patrick K.; Cheng, Ying; McNeil, Nicole M. (January 2024, Journal for Research in Mathematics Education)

   This Brief Report presents an example of assessment validation using an argument-based approach. The instrument we developed is a Brief Assessment of Students’ Mature Number Sense, which measures a central goal in mathematics education. We chose to develop this assessment to provide an efficient way to measure the effect of instructional practices designed to improve students’ number sense. Using an argument-based framework, we first identify our proposed interpretations and uses of student scores. We then outline our argument with three claims that provide evidence connecting students’ responses on the assessment with its intended uses. Finally, we highlight why using argument-based validation benefits measure developers as well as the broader mathematics education community. 

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5. *Racial and Ethnic Disparities in Advanced Science and Mathematics Achievement During Elementary School

   https://doi.org/10.1177/00169862221128299  

   Morgan, Paul L.; Hu, Eric Hengyu; Farkas, George; Hillemeier, Marianne M.; Oh, Yoonkyung; Gloski, Cecelia A. (April 2023, Gifted Child Quarterly)

   We analyzed a population-based cohort ( N = 10,922) to investigate the onset and stability of racial and ethnic disparities in advanced (i.e., above the 90 th percentile) science and mathematics achievement during elementary school as well as the antecedent, opportunity, and propensity factors that explained these disparities. About 13% to 16% of White students versus 3% to 4% of Black or Hispanic students displayed advanced science or mathematics achievement during kindergarten. The antecedent factor of family socioeconomic status and the propensity factors of student science, mathematics, and reading achievement by kindergarten consistently explained whether students displayed advanced science or mathematics achievement during first, second, third, fourth, or fifth grade. These and additional factors substantially or fully explained initially observed disparities between Black or Hispanic and White students in advanced science or mathematics achievement during elementary school. Economic and educational policies designed to increase racial and ethnic representation in STEM course taking, degree completion, and workforce participation may need to begin by elementary school. 

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