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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. Elementary Teachers’ Verbal Support of Engineering Integration in an Interdisciplinary Project

   Lilly, S. C. ; McAlister, A. M. ; Chiu, J. L. ( July 2021 , 2021 ASEE Annual Conference proceedings)

   null (Ed.)

   This study investigates how teachers verbally support students to engage in integrated engineering, science, and computer science activities across the implementation of an engineering project. This is important as recent research has focused on understanding how precollege students’ engagement in engineering practices is supported by teachers (Watkins et al., 2018) and the benefits of integrating engineering in precollege classes, including improved achievement in science, ability to engage in science and engineering practices inherent to engineering (i.e., engineering design), and increased awareness of engineering (National Academy of Engineering and the National Research Council; Katehi et al., 2009). Further, there is a national emphasis on integrating engineering, science, and computer science practices and concepts in science classrooms (NGSS Lead States, 2013). Yet little research has considered how teachers implement these disciplines together within one classroom, particularly elementary teachers who often have little prior experience in teaching engineering and may need support to integrate engineering design into elementary science classroom settings. In particular, this study explores how elementary teachers verbally support science and computer science concepts and practices to be implicitly and explicitly integrated into an engineering project by implementing support intended by curricular materials and/or adding their own verbal support. Implicit use of integration included students engaging in integrated practices without support to know that they were doing so; explicit use of integration included teachers providing support for students to know how and why they were integrating disciplines. Our research questions include: (1) To what extent did teachers provide implicit and explicit verbal support of integration in implementation versus how it was intended in curricular materials? (2) Does this look different between two differently-tracked class sections? Participants include two fifth-grade teachers who co-led two fifth-grade classes through a four-week engineering project. The project focused on redesigning school surfaces to mitigate water runoff. Teachers integrated disciplines by supporting students to create computational models of underlying scientific concepts to develop engineering solutions. One class had a larger proportion of students who were tracked into accelerated mathematics; the other class had a larger proportion of students with individualized educational plans (IEPs). Transcripts of whole class discussion were analyzed for instances that addressed the integration of disciplines or supported students to engage in integrated activities. Results show that all instances of integration were implicit for the class with students in advanced mathematics while most were explicit for the class with students with IEPs. Additionally, support was mainly added by the teachers rather than suggested by curricular materials. Most commonly, teachers added integration between computer science and engineering. Implications of this study are an important consideration for the support that teachers need to engage in the important, but challenging, work of integrating science and computer science practices through engineering lessons within elementary science classrooms. Particularly, we consider how to assist teachers with their verbal supports of integrated curricula through engineering lessons in elementary classrooms. This study then has the potential to significantly impact the state of knowledge in interdisciplinary learning through engineering for elementary students. 

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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)

   Math anxiety (MA) and math achievement are generally negatively associated.

   This study investigated whether and how classroom engagement behaviors mediate the negative association between MA and math achievement.

   Data 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).

   Math 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.

   Students 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.

   Overall, 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. Noticing mathematics from multiple perspectives

   Kosko, K. W. ; Ferdig, R. E. ; Gandolfi, E. ( January 2022 , Psychology of Mathematics Education - North America)

   Olanoff, D. ; Johnson, K. ; Spitzer, S. (Ed.)

   A key aspect of professional noticing includes attending to students’ mathematics (Jacobs et al., 2010). Initially, preservice teachers (PSTs) may attend to non-mathematics specific aspects of a classroom before attending to children’s procedures and then, eventually their conceptual reasoning (Barnhart & van Es, 2015). Use of 360 videos has been observed to increase the likelihood that PSTs will attend to more mathematics-specific student actions. This is due to an increased perceptual capacity, or the capacity of a representation to convey what is perceivable in a scenario (Kosko et al., in press). A 360 camera records a classroom omnidirectionally, allowing PSTs viewing the video to look in any direction. Moreover, several 360 cameras can be used in a single room to allow the viewer to move from one point in the recorded classroom to another; defined by Zolfaghari et al., 2020 as multi-perspective 360 video. Although multiperspective 360 has tremendous potential for immersion and presence (Gandolfi et al., 2021), we have not located empirical research clarifying whether or how this may affect PSTs’ professional noticing. Rather, most published research focuses on the use of a single camera. Given the dearth of research, we explored PSTs’ viewing of and teacher noticing related to a six-camera multiperspective 360 video. We examined 22 early childhood PSTs’ viewing of a 4th grade class using pattern blocks to find an equivalent fraction to 3/4. Towards the end of the video, one student suggested 8/12 as an equivalent fraction, but a peer claimed it was 9/12. The teacher prompts the peer to “prove it” and a brief discussion ensues before the video ends. After viewing the video, PSTs’ written noticings were solicited and coded. In our initial analysis, we examined whether PSTs attended to students’ fraction reasoning. Although many PSTs attended to whether 8/12 or 9/12 was the correct answer, only 7 of 22 attended to students’ part-whole reasoning of the fractions. Next, we examined the variance in how frequently PSTs switched their camera perspective using the unalikeability statistic. Unalikeability (U2) is a nonparametric measure of variance, ranging from 0 to 1, for nominal variables (Kader & Perry, 2007). Participants scores ranged from 0 to 0.80 (Median=0.47). We then compared participants’ U2 statistics for whether they attended (or not) to students mathematical reasoning in their written noticing. Findings revealed no statistically significant difference (U=38.5, p=0.316). On average, PSTs used 2-3 camera perspectives, and there was no observable benefit to using a higher number of cameras. These findings suggest that multiple perspectives may be useful for some, but not all PSTs’. 

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5. Multi-Disciplinary Summer Orientation Sessions for First-Year Students in Engineering, Engineering Technology, Physics, and Computer Science

   https://doi.org/10.18260/p.25760  

   Novoa, Clara ; Ortiz, Araceli ; Talley, Kimberly ( January 2016 , American Society of Engineering Education)

   This work in progress is motivated by a self-study conducted at Texas State University. The study revealed that the average second year science, technology, engineering and math (STEM) student retention rate is 56% vs. 67% for all majors, and that 16% of STEM majors are female while 57% of all undergraduate students are female. Using these statistics, the authors identified the need to offer motivating experiences to freshman in STEM while creating a sense of community among other STEM students. This paper reports on the impact of two interventions designed by the authors and aligned with this need. The interventions are: (1) a one-day multi- disciplinary summer orientation (summer15) to give participants the opportunity to undertake projects that demonstrate the relevance of spatial and computational thinking skills and (2) a subsequent six-week spatial visualization skills training (fall 2015) for students in need to refine these skills. The interventions have spatial skills as a common topic and introduce participants to career applications through laboratory tours and talks. Swail et al.1 mentions that the three elements to address in order to best support students’ persistence and achievement are cognitive, social, and institutional factors. The interventions address all elements to some extent and are part of an NSF IUSE grant (2015-2018) to improve STEM retention. The summer 2015 orientation was attended by 17 freshmen level students in Physics, Engineering, Engineering Technology, and Computer Science. The orientation was in addition to “Bobcat Preview”, a separate mandatory one-week length freshman orientation that includes academic advising and educational and spirit sessions to acclimate students to the campus. The effectiveness of the orientation was assessed through exit surveys administered to participants. Current results are encouraging; 100% of the participants answered that the orientation created a space to learn about science and engineering, facilitated them to make friends and encouraged peer interaction. Eighty percent indicated that the orientation helped them to build confidence in their majors. Exit survey findings were positively linked to a former exit survey from an orientation given to a group of 18 talented and low-income students in 2013. The training on refining spatial visualization skills connects to the summer orientation by its goals. It offers freshman students in need to refine spatial skills a further way to increase motivation to STEM and create community among other students. It is also an effective approach to support students’ persistence and achievement. Bairaktarova et al.2 mention that spatial skills ability is gradually becoming a standard assessment of an individual’s likelihood to succeed as an engineer. Metz et al.3 report that well-developed spatial skills have been shown to lead to success in Engineering and Technology, Computer Science, Chemistry, Computer Aided Design and Mathematics. The effectiveness of the fall 2015 training was assessed through comparison between pre and post tests results and exit surveys administered to participants. All participants improved their pre-training scores and average improvement in students’ scores was 18.334%. 

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