The Relationship between Middle Grades Algebra and Advanced Carnegie Credits: A QuantCrit Analysis

We investigated the impacts of a peer-facilitated instructional intervention in mathematics on progress towards readiness for college among 10th graders who facilitated instruction for 9th graders in algebra classrooms in urban secondary schools. A goal of the intervention is to promote readiness for college by placing middle-performing students in the role of instructional facilitators. The program draws on theory that holds that instructional facilitation helps facilitators enhance their content knowledge and develop in metacognitive and social-emotional domains. We used propensity score matching to evaluate the program’s impact on facilitators’ achievement of outcomes that represent early high school “on-track for college” benchmarks, benchmarks for college readiness, and college entry without need for remediation. Acting as a 10th grade instructional facilitator increased students’ likelihood of meeting near-term, intermediate, and long-term indicators of college readiness. These results indicate that intensive long-term interventions in early high school that draw on students as resources can having lasting impacts on real-world metrics for college-readiness.

The current study explored the impact that algebra knowledge in 1st and 2nd grade can have in growth and achievement in mathematics through 5th grade. Previous studies have shown the positive impact of teaching algebra in middle school (e.g. Smith, 1996). Other studies have shown that students can learn and apply fundamental algebra concepts even earlier, including early elementary grades (e.g. Schifter et al., 2008; Brizuela and Earnest, 2008). The current study aimed to expand upon this research by showing students' knowledge of early algebra concepts can predict positive longitudinal outcomes. This would support cognitive and education theories that students can use algebraic concepts to structure their overall mathematics knowledge. The current study utilized an archival dataset with five years of student data from one district. District assessments measured student knowledge of algebra in 1st and 2nd grade. Students' standardized mathematics test scores and district assessments for mathematics were collected for 3rd, 4th, and 5th grade. Algebra knowledge in 1st and 2nd grade predicted students' mathematics ability on the state standardized assessment in 5th grade. It also predicted growth in scores from 3rd through 5th grade. Algebra was a significant predictor in a model that included students' abilities in other areas of mathematics, reading ability, and race. The model also included school level socioeconomic data. Parallel models were done using the district assessments in 3rd through 5th grade as the outcome measure. Algebra knowledge in 1st and 2nd grade was a significant predictor of 5th grade mathematics knowledge on these assessments. Algebra knowledge did not predict growth from 3rd through 5th grade. Overall, this study underlines the importance of including algebra in early elementary teaching, standards, and assessment. Early algebra may help students structure their mathematics knowledge from the beginning of their education. This can lead to improved longitudinal mathematics knowledge and performance.

Problem statement: Although there have been increases in student enrollment in tertiary (university) educational settings in many countries, there continues to be students who experience challenges bridging secondary (high school) and university education. Approach: This study includes a description of strategies used in a Gaining Early Awareness and Readiness for Undergraduates Program (GEAR UP) that assisted students whose parents did not continue education beyond high school to pursue a college or university education. Results: The relationship between both student academic support and parent support of students attending college and students’ participation in the college preparation activities (termed university preparedness) in 10 and 11th grades were examined. Conclusion: The analyses showed that higher levels of both types of supports are associating with higher student university preparedness scores and that parent-related supports proved especially important as a determinant of pursuing a tertiary degree.

This research explored the experiences of students in a school district that limited early access to the study of algebra and to inform education policymakers of the impact of such tracking policies on the lives and futures of the students. Quantitative analysis had already yielded a snapshot of inequities deriving from the policies surrounding placement in 8th grade as well as significant benefits deriving from that placement. Subsequent interviews with students provided a vital portrait of the faces behind this analysis. The candid and reflective interviews with these graduating seniors suggest that 8th-grade mathematics experiences impacted their academic and social experiences as well as their future plans. Regardless of their group, the students concluded that the policy of assigning students to algebra in the 8th grade was based on developmental behaviors, like study habits and self-discipline, rather than on cognitive ability. Students in both groups criticized the school’s emphasis on the state’s standardized tests and regarded those tests as basic and minimal. The students also chronicled the long-term effects of studying 8th-grade algebra in 8th grade, primarily the academic benefits of the type and number of mathematics courses afforded early algebra students. According to students in both tracks, algebra instruction for all students in eighth grade would level the playing field and open the gates to advanced study for those students who choose to take advantage of those opportunities. Providing algebra to all students, with additional academic and institutional support if necessary, would diminish the disparity of outcomes and promote more equitable opportunities for all students.

In a recent article entitled “Racial Inequality in 8th-Grade Math Course-Taking: Between-School Inequality, Local Achievement Queues, and Course Placements,” Carbonaro et al. (2024) argue that African American 8th-grade students are less likely to be enrolled in algebra or geometry courses compared to White students with similar prior achievement levels. Carbonaro, Lee and Langenkamp claim that this racial disadvantage derives from “structural inequality” because “racialized sorting” results in Black students encountering greater constraints due to queuing for “course-taking opportunities.” However, Carbonaro, Lee and Langenkamp’s investigation is not convincing. Their statistical methods do not fit their theory, which is ad hoc and inadequately developed. Their regression equations resemble mis-specified status attainment models rather than queuing models. Their empirical results, in any event, do not provide adequate support for their emphasis on structural inequality in terms of being enrolled in advanced math courses in the 8th grade. Their assertion that “discrimination and structural inequality” are “the primary drivers of racial inequality” does not explain why their findings show that Asian Americans are consistently advantaged over Whites. Sociologists’ enduring interest in structural inequality may be laudable, but Carbonaro, Lee and Langenkamp’s investigation of it is not informative.

Middle level educators must find ways to integrate postsecondary education and career exploration throughout the curriculum.One can never consent to creep when one feels the impulse to soar.Helen Keller (1954, p. 335)One major aspect of the education policy of the Obama administration involves promoting greater high school graduation rates nationwide and expanding access to postsecondary options (e.g., junior colleges, four-year universities, trade schools, vocational training programs) through college and career readiness programs (U.S. Department of Education, 2010). These also important aims of the Common Core State Standards, which are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and (Common Core State Standards Initiative, 2012, Mission Statement section). The administration contends that one factor essential to attaining this formidable goal is middle grades student achievement, particularly in low-performing schools. This focus on the middle grades seems appropriate because high school-based career and college education often may be ineffective for high-risk students who may already be considering dropping out of school as early as ninth grade (Legum & Hoare, 2004).While these policies focus on achievement of content knowledge, the changing world of work also requires attention to certain types of skills taught in the classroom. Johnson (2000) noted that rather than finding stable, long-term employment, workers in the future will encounter more contractual work, temporary assignments, and decentralized work locations. This means that, in addition to having knowledge of their fields, future workers will need to be more flexible, be committed to ongoing learning and development, be able to problem solve, be good communicators, be able to quickly analyze data, and possess collaborative decision-making skills. Content knowledge alone will not be enough to sustain and to make workers effective.Middle grades educators may wonder how they can impact students' progress toward postsecondary success and career readiness. Moreover, they may feel inadequately prepared to foster the knowledge and skill development students need to prepare for postsecondary success in the 21st century, especially for at-risk students (Legum & Hoare, 2004). In addition, educators may be uncertain how to teach the skills needed for future careers while, at the same time, balancing the fundamental, accountability-driven content standards. There a limited number of hours in a school day. How can middle grades teachers possibly fit more into the curriculum? In this article, we argue for a greater emphasis on career-related education and suggest practical strategies for integrating postsecondary education and career with the existing middle level curriculum.Arguments for career-related education in the middle gradesCareer and college readiness encompasses an array of knowledge, skills, and attitudes. Yet, in a study of sixth and ninth grade students' career development awareness, only about half could identify a skill needed for career success (Johnson, 2000). Even more disheartening was the finding that approximately 88% of the students participating in the study reflected little or no awareness of how the skills, knowledge, or attitudes learned in the subject coursework might relate to future employment (p. 269). Another finding that raised concern was that sixth graders found school work more useful to their future than did ninth graders. Johnson considered this finding to be evidence of students' growing discontentment with the school experience between their sixth and ninth grade years. This finding illustrates why it is essential to keep students engaged in activities that connect academics to career and college preparation throughout the middle grades. This is especially of concern to educators because, by ninth grade, many students who feel disconnected from school may be considering dropping out. …

Using multilevel analysis on a sample of academic-track 12th graders in 1989, this article compares gender inequality in course taking of mathematics and sciences in Arab and Jewish high schools. The findings show that gender inequality is almost nonexistent in Arab schools, whereas it is very prominent in Jewish, particularly secular, schools. The differences in gender inequality are explained by the differences in the curriculum. In contrast with Jewish high schools that offer a rich curriculum, Arab schools offer few advanced courses in humanities and social sciences. Consequently, male and female students who wish to take advanced courses have to choose mathematics and sciences. The findings point to a sociological paradox; the poor curriculum of Arab high schools enhances the chances of Arab female students to be exposed to highly valued knowledge. These findings shed an additional light on the beneficial effect that a restricted curriculum can have for members of disadvantaged groups.

Despite some gains, women continue to be underrepresented in many science, technology, engineering, and math (STEM) fields. Using a national longitudinal dataset of 690 participants born in 1991, we tested whether spatial skills, measured in middle childhood, would help explain this gender gap. We modeled the relation between 4th-grade spatial skills and STEM majors while simultaneously accounting for competing cognitive and motivational mechanisms. Strong spatial skills in 4th grade directly increased the likelihood of choosing STEM college majors, above and beyond math achievement and motivation, verbal achievement and motivation, and family background. Additionally, 4th-grade spatial skills indirectly predicted STEM major choice via math achievement and motivation in the intervening years. Further, our findings suggest that gender differences in 4th-grade spatial skills contribute to women's underrepresentation in STEM majors. RESEARCH HIGHLIGHTS: Using a national longitudinal dataset, we found 4th-grade spatial skills directly predicted STEM college major choice after accounting for multiple cognitive and motivational mechanisms. Strong spatial skills in 4th grade also elevated STEM major choice via enhanced math achievement and motivation in the intervening years. Gender differences in 4th-grade spatial skills contributed to women's underrepresentation in STEM college majors.

In the United States,the American College Test (ACT)is a standardized test that is used primarily as an indicator of college readiness and as a gauge for college admission. The governing bodies for Louisiana’s public schools—The Louisiana Department of Education (LDOE)and the Board of Elementary and Secondary Education (BESE)—made the ACT a requirement—effective spring 2013—for Louisiana’s public high school 11th grade students regardless of their postsecondary intentions. The primary purpose of this study was to ascertain from Louisiana high school seniors’ whether the Louisiana Department of Education’s ACT mandate is perceived as a factor influencing their postsecondary decisions or affecting their postsecondary trajectory. A qualitative case study was used for this research. The cases were two Louisiana schools which were designated by the Louisiana Department of Education as economically disadvantaged. One economically disadvantaged school from two different school districts was included in this research. The study participants were seniors who participated in the mandatory ACT in the 11th grade and were at least 18 years of age. Six seniors from each school—for a total of twelve participants—were interviewed using semi-structured interviews. The interviews were conducted at the school site during normal school operation hours. Participants in this study indicated that the ACT mandate was not a determinant in their postsecondary decisions, in relation to what they wanted to do after high school. The participants, however, did indicate that their ACT outcomes were affecting their postsecondary education route or choices. All of the participants, except one indicated that they were planning to attend college, regardless of the ACT mandate. The participants perceived the attainment of a specific ACT score as an admission requirement—to the institutions of their choice—as the factor affecting their postsecondary trajectories.

Ethnic and racial disparities in children's education: Comparative evidence from Ethiopia, India, Peru and Viet Nam

The relationship between the dental caries and the physical constitution together with the incidence of absence to school, which might be connected with learning, was investigated by making use of individual records of both physical and dental states at the time of the periodical health examination in 1963 on 259 pupils, the second- to the 6th-year graded, of a certain elementary school at a central part of Tokyo City.As for the classification of caries proceeding grades, deciduous teeth and permanent teeth were separately divided into either the treatment teeth or the carious teeth. In particular, carious teeth among permanent teeth were subdivided into the dental caries of the first grade (C1), of the second grade (C2), of the third grade (C3) and of the fourth grade (C4). Concerning to each grade, the average number of carious teeth per person was calculated and checked in relation to the physical constitution such as the height, the weight and the girth of the chest and to the incidence of absence to school, obtaining the following results.1. In the height, as compared with those who showed higher values than the national average value, those who showed lower values had more carious teeth. In deciduous teeth, the number of carious teeth was larger equally in pupils of all the year grades, while in permanent teeth the number of carious teeth of C2 and C3 was larger in them except for the 5th year grade.2. In the weight, those pupils who showed lower values than the national value of average, as compared with those who showed higher values, had more carious teeth in deciduous teeth throughout the year grades. Meanwhile, in case of their permanent teeth, the number of treatment teeth were smaller in the 2nd, 4th and 6th year grades. However, the 6th-year graded pupils showed a little larger number of C2, C3 and C4 carious teeth.3. In the girth of the chest, those pupils who showed lower values than the national average value, when they were compared with those who showed higher values, had generally more carious teeth in deciduous teeth throughout the year grades. In permanent teeth they exhibited a small number of treatment teeth except for pupils of the 3rd year grade. At the same time, it may be said that C1 was rare except for the 5th-year graded pupils, while C2, C3 and C4 occurred in general frequently.4. As described above, it was observed that carious teeth appeared rather often in case of the poor physical constitution at the time of the examination, that means, in pupils showing a poor bodily development, suggesting the importance in the protection of deciduous teeth during the elementary school period.5. During one year before the physical examination, those pupils who were never absent to school showed, in comparison with those who made as many as more than 10 times of absence, more numerous carious teeth of deciduous teeth in the 2nd, 3rd and 4th year grades and C1, C2 and C3 of permanent teeth in the 5th and 6th year grades. Therefore, it is assumed that the absence to school may be connected with the caries of the deciduous tooth in pupils of the low and middle year grades and of the permanent tooth in those of the high year grade.6. Similarly, if the R.I.D. Index (1961) of pupils making no absence was compared with that of pupils showing many times of absence, the former exhibited lower values throughout the year grades. Consequently, those who showed high caries proceeding grades of both deciduous and permanent teeth, showed also frequent absence to school.

Estimates of contact among children, used for infectious disease transmission models and understanding social patterns, historically rely on self-report logs. Recently, wireless sensor technology has enabled objective measurement of proximal contact and comparison of data from the two methods. These are mostly small-scale studies, and knowledge gaps remain in understanding contact and mixing patterns and also in the advantages and disadvantages of data collection methods. We collected contact data from a middle school, with 7th and 8th grades, for one day using self-report contact logs and wireless sensors. The data were linked for students with unique initials, gender, and grade within the school. This paper presents the results of a comparison of two approaches to characterize school contact networks, wireless proximity sensors and self-report logs. Accounting for incomplete capture and lack of participation, we estimate that “sensor-detectable”, proximal contacts longer than 20 seconds during lunch and class-time occurred at 2 fold higher frequency than “self-reportable” talk/touch contacts. Overall, 55% of estimated talk-touch contacts were also sensor-detectable whereas only 15% of estimated sensor-detectable contacts were also talk-touch. Contacts detected by sensors and also in self-report logs had longer mean duration than contacts detected only by sensors (6.3 vs 2.4 minutes). During both lunch and class-time, sensor-detectable contacts demonstrated substantially less gender and grade assortativity than talk-touch contacts. Hallway contacts, which were ascertainable only by proximity sensors, were characterized by extremely high degree and short duration. We conclude that the use of wireless sensors and self-report logs provide complementary insight on in-school mixing patterns and contact frequency.

BackgroundInclusive STEM high schools seek to broaden STEM participation by accepting students on the basis of interest rather than test scores and providing a program sufficient to prepare students for a STEM major in college. Almost nonexistent before the present century, these high schools have proliferated over the last two decades as a strategy for addressing gaps in STEM education and career participation. This study uses a meta-analytic approach to investigate the relationship between attending an inclusive STEM high school and a set of high school outcomes known to predict college entry and declaration of a STEM college major.ResultsCombining effect estimates from five separate datasets of students from inclusive STEM high schools and matched comparison schools, the analysis reported here used data from administrative records and survey data for 9719 students in 94 high schools to obtain estimates of the average impact of attending an inclusive STEM high school on STEM-related high school outcomes. Positive effects for inclusive STEM high schools were found for completion of key STEM courses and for likelihood that students would engage in self-selected STEM activities. Students who attended an inclusive STEM high school also identified more strongly with mathematics and science and were more likely as high school seniors to be very interested in one or more STEM careers. Importantly, these positive impacts were found for low-income, under-represented minority, and female students as well as for students overall. Attending an inclusive STEM high school appeared to have a small positive impact on science test scores for students overall and for economically disadvantaged students, but there were no discernible impacts on mathematics test scores.ConclusionsThese findings suggest that the inclusive STEM high school model can be implemented broadly with positive impacts for students, including low-income, female, and under-represented minority students. Positive impacts on the odds of taking advanced mathematics and science courses in high school and on interest in entering a STEM profession are of particular importance, given the strong association between these variables and entry into a STEM major in college.

Introduction. The current, rapidly changing world is faced with global changes taking place in various spheres of human activity and bearing a spiritual, moral, ontological character. Insufficient level of spiritual and moral culture, uncertainty in the choice of life-meaning orientations, change of value attitudes, manifestation of egocentricity generates quasi-needs and destructive behavior among students. This is the reason for the problem of studying the prevention of destructive behavior of students, which has become particularly relevant. The purpose of the article is to test a practice–oriented model of prevention of destructive behavior of students in the process of formation of spiritual and moral culture (PDPO in the process of FDNA). Materials and methods. The study involved 287 5th grade students and 48 teachers of the educational organization of the city of Krasnodar (Russian Federation). The research methods are based on a rational combination of theoretical and experimental methods of studying objects corresponding to the set goals and objectives, aimed at determining the level of development of spiritual and moral qualities, the formation of vital functions in students, their value orientations and destructive manifestations (test «Value orientations» by M. Rokich; card «Spiritual and moral development of a student» by V.I. Andreev; diagnostic card of readiness of a student and a teacher to prevent destructive behavior in the process of forming a spiritual and moral culture by Yu.N. Sinitsyn; methodology for assessing the formation of vital functions, spiritual and moral development and destructive manifestations of a student by V.I. Andreev, Yu.N. Sinitsyn). The method of mathematical statistics is the Kramer-Welch T-test. Results. The analysis of the problem of preventing destructive behavior of students in the process of forming a spiritual and moral culture allowed us to develop and test a practice-oriented model of PDPO in the process of FDNA, which is based on objective and subjective pedagogical conditions, using integrative technology for preventing destructive behavior of students. As a result of the implementation: 1) a decrease in the level of destructive behavior of students by 60,7%, the effectiveness of experimental exposure is represented by changes in the difference in characteristics according to the coefficients ТEMP before = 0,009 and ТEMP after = 4,59; 2) an increase in the levels of vital functions by 12,1% (ТEMP before = 0,24, ТEMP after = 6,23), the formation of moral qualities in students by 13,2% (ТEMP before = 0,03, ТEMP after = 8,24), the readiness of students for PDPO in the FDNA process by 15,7% (ТEMP before = 0,45, ТEMP after = 8,15). Conclusion. The created practice-oriented model of PDPO in the process of FDNA allows to expand the understanding of the prevention of destructive behavior of students in the process of forming a spiritual and moral culture and can act as a prerequisite for: the development of network interaction of educational organizations in the systems of general and vocational education on this issue; the continuity of FDNA of students in educational organizations at all levels; conducting advanced training courses qualifications of teaching staff, parental training. Keywords: spiritual and moral culture, prevention of destructive behavior, students, conceptual model, pedagogical system, criteria and indicators of readiness for the prevention of destructive behavior, practical recommendations

Educators and policymakers alike recognize that algebra is an important gatekeeper course, not only for college preparation but also for preparation for the world of work. To prepare students for future success, many school districts and state legislatures now make algebra a graduation requirement for all high school students. Of course, the burden for preparing all students in algebra falls on the shoulders of the classroom teacher. Whether an algebrafor-all initiative is school-, district-, or state-based, a teacher faces the difficult challenge of teaching a high-standards course to a classroom of students whose beginning knowledge may range from far below to far above the course prerequisites.