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The purpose of this paper is to show the similarities as well as the differences of fundamental fraction knowledge owned by preservice elementary teachers from the United States (N= 89) and Taiwan (N= 85). To this end, we examined and compared their performance on an instrument including 15 multiple‐choice test items. The items were categorized into four different types of fundamental fraction constructs, including part–whole relationship, quotient, equivalence, and meanings of operations. Each item was embedded in the area, linear, or set model except for the items constructed out of the meaning of operations. Several items were featured with a pictorial illustration. Quantitative analysis showed that U.S. preservice teachers were significantly outperformed by their Taiwanese counterparts overall. The difference between the two groups was statistically significant on 12 of 15 items. Findings suggest that preservice elementary teachers from both countries need to be better prepared in their understanding of the meaning of fraction multiplication or division operations. Findings also suggest that U.S. preservice elementary teachers need to be more knowledgeable in dealing with fraction problems embedded in a linear model. Further research is suggested to study the issues raised from the findings.

Rural students account for almost 20% of the US K-12 students, but rural context varies from state to state. This study uses a statewide longitudinal sample (N = 3,119) to analyze college enrollment and STEM major choice patterns of Montana’s public high school students in the academic years of 2013-2017. The binary logistic regressions showed that Montanan students are more likely to enroll into a 4-year institution than a 2-year institution. Also, students enrolled at a 4-year institution are more likely to consider STEM majors than students at a 2-year institution. Although high school GPA and ACT STEM scores are strong predictors for both college enrollment and STEM major choice, findings for race/ethnicity, gender, and free or reduced-price lunch status varied across the two outcomes. Specifically, race/ethnicity contributes to variation in college enrollment, but not STEM major choice. Similarly, free or reduced-price lunch status in high school is predictive of college enrollment, but not for STEM major choice. Although there was no difference in college enrollment type for gender, male students are more likely to select a STEM major, and this trend occurs at a rate of three times higher at a 4-year institution versus a 2-year institution. Our findings provide additional nuances of rural students, contributing to the understanding of their college enrollment and STEM major choices in the context of Montana - a large geographic, low populous state - which has received less attention than urban and high-density states.

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This case study explored the efficacy of web-based instruction on preservice elementary teachers’ mathematics learning. Web-based instruction is appealing to many schools in urban settings because it helps them to face the two big challenges most akin to their schools: to motivate students’ interests and to meet the diverse students needs with its interactive feature and adaptive capability. Ten preservice elementary teachers were interviewed regarding their ability to model and reason with fractions after receiving web-based instruction on these topics in their regular mathematics method course. The interview transcripts were used to provide information about the strength and weakness of participants’ conceptual and procedural understanding of fractions. The findings of this case study identify promises and challenges in supporting the recommendations of many national reports, such as the NCTM Professional Standards for School Mathematics (2000) and the National Mathematics Advisory Panel (2008), in incorporating technology into the compulsory mathematics classrooms.