Understanding the concepts of proportion and ratio among grade nine students in Malaysia

The purpose of the study was to investigate the concepts of ratio and proportion constructed by grade nine students by investigating grade nine students proportional reasoning schemes and procedures on three types of tasks: missing value, numerical comparison and qualitative reasoning. Comparisons among the different categories were made and the strategies used in solving these problems were identified. The relationship between student grades on a national examination and their knowledge of proportional reasoning was determined. The results of the quantitative analysis indicated that students performed generally well on the missing value tasks but their scores on the numerical comparison and qualitative tasks were much lower. The results indicate that only a small percentage of students who did well on the national exams were able to solve complex proportional problems and the grades obtained were not indicative of their knowledge of ratio and proportion. The difficulty experienced by the ninth graders indicated that students frequently used additive reasoning, that is a comparison of two numbers by subtraction rather than division. It appears that students cannot begin to understand the functional and scalar relationship inherent in a proportion until they first develop multiplicative reasoning.     

School mathematics and creativity at the elementary and middle-grade levels: how are they related?

In this study, we evaluated students’ creativity, as expressed in the solution methods of three problems for groups of students in different grades. Posing the same problems to students of similar (advanced) mathematical abilities in different grades allowed us to look for possible connections between creativity and mathematical knowledge. The findings indicate that at the elementary school level, the number of solution methods and creativity scores increased with age. The collective methods space of the eighth graders seemed to narrow almost exclusively to algebraic methods, but the increase in the number of solutions was renewed in the ninth grade.     

The effect of attending tutoring on course grades in Calculus I

Tutoring centres are common in universities in the United States, but there are few published studies that statistically examine the effects of tutoring on student success. This study utilizes multiple regression analysis to model the effect of tutoring attendance on final course grades in Calculus I. Our model predicted that every three visits to the tutoring centre is correlated with an increase of a students’ course grade by one per cent, after controlling for prior academic ability. We also found that for lower-achieving students, attending tutoring had a greater impact on final grades.     

Three methods for robust grading

We propose three strategies by which a professor of a university course can assign final letter grades taking into account the natural uncertainty in students’ individual assignment and final numerical grades. The first strategy formalizes a common technique that identifies large gaps in the final numerical grades. For the second and third strategies, we introduce the notion of a borderline student, that is, a student who is close to, but below, the breakpoint for the next highest letter grade. Using mixed-integer linear programming and a tailor-made branch-and-bound algorithm, we choose the letter-grade breakpoints to minimize the number of borderline students. In particular, the second strategy treats the uncertainty implicitly and minimizes the number of borderline students, while the third strategy uses a robust-optimization approach to minimize the maximum number of borderline students that could occur based on an explicit uncertainty set. We compare the three strategies on realistic instances and identify overall trends as well as some interesting exceptions. While no strategy appears best in all cases, each can be computed in a reasonable amount of time for a moderately sized course. Moreover, they collectively provide the professor important insight into how uncertainty affects the assignment of final letter grades.     

Student Initiatives in Urban Elementary Science Classrooms

Student initiatives play an important role in inquiry‐based science with all students, including English language learning (ELL) students. This study examined initiatives that elementary students made as they participated in an intervention to promote science learning and English language development over a three‐year period. In addition, the study examined whether student initiatives were related to other domains of classroom practices. The study involved 70 third‐, fourth‐, and fifth‐grade classrooms with ELL students in six urban elementary schools. Results indicated that students generally made few, low‐quality initiatives. Student initiatives were generally not related to the other domains of classroom practices for grades 3 and 4, whereas initiatives were significantly related to almost all the other domains for grade 5. These results contribute to the knowledge base for fostering ELL students' initiatives in science classrooms.     

The Cumulative and Residual Impact of a Systemic Reform Program on Teacher Change and Student Learning of Science

This longitudinal, five‐year study of teachers and students who had participated in a systemic reform program in science explored if (1) teacher change in practice realized during a three‐year program is sustained one, two, and three years following the program, (2) student performance on state science assessments two years following studying with teachers at this school still demonstrated significant differences from students who attended the control school, and (3) student performance continued to be enhanced for both White and Minority students. Student achievement was assessed using the Discovery Inquiry Test in Science during sixth through eighth grades and the Ohio Graduation Test was used in 10th grade. The same students completed the test in grades 6–8 and 10th grade. Students from the Program school significantly outperformed students who attended the control school on the 10th grade state assessment in science. Findings in this study revealed the ability for sustained, whole‐school, professional development programs to have a cumulative and residual impact on teacher change and student learning of science.     

The incoming statistical knowledge of undergraduate majors in a department of mathematics and statistics

Studies have shown that at the end of an introductory statistics course, students struggle with building block concepts, such as mean and standard deviation, and rely on procedural understandings of the concepts. This study aims to investigate the understandings entering freshman of a department of mathematics and statistics (including mathematics education), students who are presumably better prepared in terms of mathematics and statistics than the average university student, have of introductory statistics. This case study found that these students enter college with common statistical misunderstandings, lack of knowledge, and idiosyncratic collections of correct statistical knowledge. Moreover, they also have a wide range of beliefs about their knowledge with some of the students who believe that they have the strongest knowledge also having significant misconceptions. More attention to these statistical building blocks may be required in a university introduction statistics course.     

The benefit to consumers from generic scoring models based on credit reports

Received on 1 July 1991. The benefit to consumers from the use of informative creditreports is demonstrated by showing the improvement in creditdecisions when generic scoring models based on credit reportsare implemented. If these models are highly predictive, thenthe truncation of credit reports will reduce the predictivepower of bureau-based generic scoring systems. As a result,more good credit risks will be denied credit, and more poorcredit risks will be granted credit. It is shown that, evenwhen applied to credit applications that had already been screenedand approved, the use of generic scoring models significantlyimproves credit grantors' ability to predict and eliminate bankruptcies,charge-offs, and delinquencies. As applied to existing accounts,bureau-based generic scores are shown to have predictive valuefor at least 3 months, while scores 12 months old may not bevery powerful. Even though bureau-based scores shift towardsthe high-risk end of the distribution during a recession, theycontinue to rank risk very well. When coupled with application-basedcredit-scoring models, scores based on credit-bureau data furtherimprove the predictive power of the model-the improvements beinggreater with more complete bureau information. We conclude thatgovernment-imposed limits on credit information are anti-consumerby fostering more errors in credit decisions.     

Investigating the impact of an urban community school effort on middle school STEM-related student outcomes over time through propensity score matched methods

This study investigates the impact of an urban community school reform initiative that focuses on an immigrant and refugee population in middle school. A 6th–8th grade cohort of students in the community school are followed over time and compared to a propensity score matched group on overall GPA, mathematics, and science academic outcomes and traditional college preparedness indicators. Further, a deeper dive into the intersection of gender and race/ethnicity was examined on all outcomes. Findings revealed that students in the urban community school demonstrated significantly more preparedness to enroll in college and move into a STEM field if they desired compared to the matched students. All gender/racial groups in the community school performed significantly higher than those in the matched group. Further, all gender/racial groups of students in the urban community school defied standard academic achievement drops common over time in middle school, and instead increase overall, math, and science grades from 6th to 8th grade.     

Elementary school students engaging in making generalisation: a glimpse from a Singapore classroom

This article reports on the generalisation strategies used by students in a grade five class in an elementary school in Singapore and the factors that seemed to influence the use of these strategies. Each student completed a novel task that required generalisation after which they were interviewed. The findings indicated that the students were using strategies that had been reported in the literature. However, this study was able to provide further understanding into factors that influence generalisation strategy use, which included: (1) the ability to see structures and relationships; (2) prior knowledge; (3) metacognitive strategies; (4) critical-thinking strategies; (5) the use of organizing heuristics such as a table; (6) the use of simplifying heuristics such as trying out simpler cases; (7) task familiarity; and (8) technology.     

Relationships Between Inquiry‐Based Teaching and Physical Science Standardized Test Scores

This exploratory case study investigates relationships between use of an inquiry‐based instructional style and student scores on standardized multiple‐choice tests. The study takes the form of a case study of physical science classes taught by one of the authors over a span of four school years. The first 2 years were taught using traditional instruction with low levels of inquiry (non‐inquiry group), and the last 2 years of classes were taught by inquiry methods. Students' physical science test scores, achievement data, and attendance data were examined and compared across both instructional styles. Results suggest that for this teacher the use of an inquiry‐based teaching style did not dramatically alter students' overall achievement, as measured by North Carolina's standardized test in physical science. However, inquiry‐based instruction had other positive effects, such as a dramatic improvement in student participation and higher classroom grades earned by students. In additional inquiry‐based instruction resulted in more uniform achievement than did traditional instruction, both in classroom measures and in more objective standardized test measures.     

Evaluating Mathematics Achievement of Middle School Students in a Looping Environment

Looping, a school structure where students remain with one group of teachers for two or more school years, is used by middle schools to meet the diverse needs of young adolescents. However, little research exists on how looping effects the academic performance of students. This study was designed to determine if looping influenced middle school students' mathematical academic achievement. Student scores on the Mississippi Curriculum Test (MCT) were compared between sixth and eighth grade years for 69 students who looped during the seventh and eighth grades with a group of 137 students who did not loop. Looping students achieved statistically significantly greater growth on the MCT than their nonlooping counterparts between sixth and eighth grades. Further, the data were disaggregated by gender, ethnicity, and socioeconomic status. Findings indicate that looping may academically reengage students during the middle school years. Advantages and disadvantages of looping at the middle grades are discussed.     

Changes in Student Attitudes Regarding Science When Taught by Teachers Without Experiences With a Model Professional Development Program

This study focuses on two main issues concerning changes in student attitudes toward science study and their perceptions of its usefulness in their lives. Information has been gathered concerning how student attitudes toward science have changed for teachers and schools not involved with any funded professional development project. Pretesting and posttesting were administered with such “control” groups at the same intervals corresponding with the data collected from students with teachers enrolled in five funded Professional Development projects over the 1981–2008 interim. The grade levels used by the National Assessment of Education Progress in their 1977 assessment of science were used; it focused on students in grades 3, 7, and 11. The results indicate a steady decline in student positive attitudes concerning their science study as grade levels increase. Conversely, the student perceptions of the usefulness of their science study as related to daily living, further science study, and for potential careers remained much the same over the 30‐year interim is a second focus. Generally, results indicate that traditional teaching and major use of textbooks cause increasingly negative student attitudes about science while not producing major changes in their perceptions of its usefulness in their lives.     

Characteristics of good mathematics teaching in Singapore grade 8 classrooms: a juxtaposition of teachers’ practice and students’ perception

This paper examines the instructional approaches of three competent grade 8 mathematics teachers. It also examines their students’ perception of the lessons they taught as well as characteristics of good lessons. The findings of teachers’ practice and students’ perception are juxtaposed to elicit characteristics of good teaching in Singapore grade 8 classrooms. With limitation, the findings of the paper suggests that good mathematics teaching in Singapore schools centres around building understanding and is teacher-centred but student focused. Some characteristic features of good lessons are that their instructional cycles have specific instructional objectives such that subsequent cycles incrementally build on the knowledge. The examples used in such lessons are carefully selected and vary in complexity from low to high. Teachers actively monitor their student’s understanding during seatwork, by moving from desk to desk guiding those with difficulties and selecting appropriate student work for subsequent whole-class review and discussion. Finally, during such lessons teachers reinforce their students’ understanding of knowledge expounded during whole-class demonstration by detailed review of student work done in class or as homework.     

Factors contributing to academic achievement: a Bayesian structure equation modelling study

In Iran, high school graduates enter university after taking a very difficult entrance exam called the Konkoor. Therefore, only the top-performing students are admitted by universities to continue their bachelor's education in statistics. Surprisingly, statistically, most of such students fall into the following categories: (1) do not succeed in their education despite their excellent performance on the Konkoor and in high school; (2) graduate with a grade point average (GPA) that is considerably lower than their high school GPA; (3) continue their master's education in majors other than statistics and (4) try to find jobs unrelated to statistics. This article employs the well-known and powerful statistical technique, the Bayesian structural equation modelling (SEM), to study the academic success of recent graduates who have studied statistics at Shahid Beheshti University in Iran. This research: (i) considered academic success as a latent variable, which was measured by GPA and other academic success (see below) of students in the target population; (ii) employed the Bayesian SEM, which works properly for small sample sizes and ordinal variables; (iii), which is taken from the literature, developed five main factors that affected academic success and (iv) considered several standard psychological tests and measured characteristics such as ‘self-esteem’ and ‘anxiety’. We then study the impact of such factors on the academic success of the target population. Six factors that positively impact student academic success were identified in the following order of relative impact (from greatest to least): ‘Teaching–Evaluation’, ‘Learner’, ‘Environment’, ‘Family’, ‘Curriculum’ and ‘Teaching Knowledge’. Particularly, influential variables within each factor have also been noted.     

Perform ance in identifying surface plots of a function of two variables and its first-order partial derivatives

Undergraduates enrolled in two sections of an elementary differential equations course completed a sequence of tasks to identify the surface plots of selected functions of two variables and the first-order partial derivatives. Average scores on the series of tasks exceeded chance-level expected values and showed an increase over time. Participants' suggestions for improving performance on the identification tasks included increasing student feedback and interaction among students, and a review of the graphics literature pointed to the potential for improvement offered by adaptive surface plotting, graphical design variations, and attention to contour diagrams.     

The Contribution of Conceptual Change Texts Accompanied by Concept Mapping to Students' Understanding of the Human Circulatory System

The present study was conducted to investigate the contribution of conceptual change texts accompanied by concept mapping instruction to 10^th— grade students' understanding of the human circulatory system. To determine misconceptions concerning the human circulatory system, 10 eleventh-grade students were interviewed. In the light of the findings obtained from student interviews and related literature, the Human Circulatory System Concepts Test was developed. The data were obtained from 26 students in the experimental group taught with the conceptual change texts accompanied by concept mapping, and 23 students in the control group taught with the traditional instruction. Besides treatment, previous learning in biology and science process skills were other independent variables involved in this study. Multiple Regression Correlation analysis revealed that science process skill, the treatment, and previous learning in biology each made a statistically significant contribution to the variation in students' understanding of the human circulatory system. It was found that the conceptual change texts accompanied by concept mapping instruction produced a positive effect on students' understanding of concepts. The mean scores of experimental and control groups showed that students in the experimental group performed better with respect to the human circulatory system. Item analysis was carried out to determine and compare the proportion of correct responses and misconceptions of students in both groups. The average percent of correct responses of the experimental group was 59.8%, and that of the control group was 51.6% after treatment.     

Scoring by usage

This paper aims to discover whether the predictive accuracy of a new applicant scoring model for a credit card can be improved by estimating separate scoring models for applicants who are predicted to have high or low usage of the card. Two models are estimated. First we estimate a model to explain the desired usage of a card, and second we estimate separately two further scoring models, one for those applicants whose usage is predicted to be high, and one for those for whom it is predicted to be low. The desired usage model is a two-stage Heckman model to take into account the fact that the observed usage of accepted applicants is constrained by their credit limit. Thus a model of the determinants of the credit limit, and one of usage, are both estimated using Heckman's ML estimator. We find a large number of variables to be correlated with desired usage. We also find that the two stage scoring methodology gives only very marginal improvements over a single stage scoring model, that we are able to predict a greater percentage of bad payers for low users than for high users and a greater percentage of good payers for high users than for low users.     

Assessments accompanying published textbooks: the extent to which mathematical processes are evident

Assessments accompanying published textbooks are often used by teachers in the USA as a primary means to evaluate students’ mathematical knowledge. In addition to assessing content knowledge, assessments should provide insight into students’ ability to engage with mathematical processes such as reasoning, communication, connections, and representations. We report here an analysis of the extent to which the assessments accompanying published textbooks in the USA at the elementary, middle grades, and high school levels provide opportunities for students to engage with these mathematical processes. Results indicate that in elementary grades, communication, connections, and graphics are not consistently emphasized across grade levels and publishers. In middle grades, students are rarely asked to record their reasoning or translate among representational forms of a concept. In high school geometry, students are given many opportunities to interpret and create graphics, but the same is not true for algebra. With the exception of connections, the results suggest that inconsistent emphasis is placed on the mathematical processes within assessments accompanying commercial textbooks in the USA.