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Robust understanding of geometry is important for students' future studies in mathematical sciences, many careers, and for understanding the world around them. Therefore, the aim of this study was to understand the geometric thinking levels of 9th graders in Ghana before they enter the Senior High School. This study used the van Hiele theory (Van Hiele-Geldof, 1957) to understand geometric thinking levels of 400 9th graders in western Ghana. These students were given the van Hiele Geometry Test (VHGT) developed by Usiskin (1982). The results showed that 56.2% of 9th graders demonstrated thinking at the pre-visualization level, 30.75%of the graders attained level 1(visualization), 12.5% reached level 2 and only 0.5% demonstrated level 3 thinking. These findings indicate that students are struggling to meet the Ministry of Education's curriculum standards. Additional analysis points to reasoning about properties of geometric figures using definitions and informal deductive reasoning, instead of relying on visual characteristics of diagrams as a specific obstacle for students. Recommendations are made for improving the teaching and learning geometry based on our findings.

BACKGROUND: The number of youth presenting to hospitals with suicidality and/or self-harm has increased substantially in recent years. We implemented a multihospital quality improvement (QI) collaborative from February 1, 2018 to January 31, 2019, aiming for an absolute increase in hospitals mean rate of caregiver lethal means counseling (LMC) of 10 percentage points (from a baseline mean performance of 68% to 78%) by the end of the collaborative, and to evaluate the effectiveness of the collaborative on LMC, adjusting for secular trends. METHODS: This 8 hospital collaborative used a structured process of alternating learning sessions and action periods to improve LMC across hospitals. Electronic medical record documentation of caregiver LMC was evaluated during 3 phases: precollaborative, active QI collaborative, and postcollaborative. We used statistical process control to evaluate changes in LMC monthly. Following collaborative completion, interrupted time series analyses were used to evaluate changes in the level and trend and slope of LMC, adjusting for covariates. RESULTS: In the study, 4208 children and adolescents were included-1314 (31.2%) precollaborative, 1335 (31.7%) during the active QI collaborative, and 1559 (37.0%) postcollaborative. Statistical process control analyses demonstrated that LMC increased from a hospital-level mean of 68% precollaborative to 75% (February 2018) and then 86% (October 2018) during the collaborative. In interrupted time series analyses, there were no significant differences in LMC during and following the collaborative beyond those expected based on pre-collaborative trends. CONCLUSIONS: LMC increased during the collaborative, but the increase did not exceed expected trends. Interventions developed by participating hospitals may be beneficial to others aiming to improve LMC for caregivers of hospitalized youth with suicidality.

ObjectiveTo develop and test a new quality measure assessing timeliness of follow-up mental health care for youth presenting to the emergency department (ED) with suicidal ideation or self-harm.MethodsBased on a conceptual framework, evidence review, and a modified Delphi process, we developed a quality measure assessing whether youth 5 to 17 years old evaluated for suicidal ideation or self-harm in the ED and discharged to home had a follow-up mental health care visit within 7 days. The measure was tested in 4 geographically dispersed states (California, Pennsylvania, South Carolina, Tennessee) using Medicaid administrative data. We examined measure feasibility of implementation, variation, reliability, and validity. To test validity, adjusted regression models examined associations between quality measure scores and subsequent all-cause and same-cause hospital readmissions/ED return visits.ResultsOverall, there were 16,486 eligible ED visits between September 1, 2014 and July 31, 2016; 53.5% of eligible ED visits had an associated mental health care follow-up visit within 7 days. Measure scores varied by state, ranging from 26.3% to 66.5%, and by youth characteristics: visits by youth who were non-White, male, and living in an urban area were significantly less likely to be associated with a follow-up visit within 7 days. Better quality measure performance was not associated with decreased reutilization.ConclusionsThis new ED quality measure may be useful for monitoring and improving the quality of care for this vulnerable population; however, future work is needed to establish the measure's predictive validity using more prevalent outcomes such as recurrence of suicidal ideation or deliberate self-harm.

In the study reported on here, we investigated the effects of the use of dynamic geometry software (DGS) (i.e., GeoGebra) on learners' learning and a teacher's beliefs. The learners and teacher involved in the study were from a high-poverty, rural high school in South Africa. We compared grade 11 learners (N = 56) who used GeoGebra in the context of learning circle geometry with learners who experienced geometry through traditional lecture-based instruction. Participating learners were from classes in a public school located in the rural Umkhanyakude district of KwaZulu-Natal, Republic of South Africa. Results showed that learners using GeoGebra were more successful at solving problems and justifying their statements, while the other learners provided a limited justification for their answers. In a parallel and complementary investigation the teacher's attitudes toward using GeoGebra as an instructional tool were considered qualitatively. Results showed that even in high-poverty, rural settings where the availability of technological resources are limited, the use of GeoGebra affected learners' learning and had positive effects on the teacher's beliefs regarding teaching and learning.

Proof plays many important roles in mathematics. Proofs should do more than simply verify that a statement is true; instead, a proof should also explain why a statement is true and enrich both the author's and the readers' understanding of the statement and important mathematical ideas within it. Common practice in high school geometry classrooms is to introduce proof by defining important terms, stating essential properties or axioms, and using deductive reasoning to verify given claims. The proving process is amplified by providing students with opportunities to explore, make, test, and verify conjectures and by positioning students to engage with the reasoning of others (Sinclair, Pimm, and Skelin 2012). Although this process attends to the Standards for Mathematical Practice (NGA Center and CCSSO 2010) and promotes the development of students' deductive reasoning and proving skills, students are often left unimpressed by the results because they are investigating properties of objects with which they are very familiar (Knuth 2002). The authors brainstormed an approach to introducing proof in a world that was likely new to our students. They implemented a two-day lesson on taxicab geometry in the second author's (Kelly Fulton) geometry classes to overcome the obstacle of students' familiarity with common geometric objects while also positioning students for developing essential understandings of definitions, axiomatic systems, and deduction.

This paper examines university faculty perceptions on whether preservice teachers are sufficiently prepared to use information and communication technology (ICT) for teaching in early grades and barriers faced in incorporating these technological interventions in classroom settings. This study employed a qualitative research approach and semi-structured questionnaires to investigate faculty perceptions from a teacher education university and considered their responses through the lens of growth and fixed mindsets. The findings revealed that, despite preservice teachers being exposed to instructional technology as part of their academic preparation for early grades teaching, faculty perceived that challenges exist that inhibit preservice teachers' readiness to integrate technologies in their teaching of mathematics. In particular, many significant disagreements existed among the teacher education faculty as to how prepared they perceived their preservice teachers to be in the use of technology in their future classrooms. Findings from this study led to additional observations regarding university faculty opinions regarding their own use of ICT and its implementation in the department and programme.