On the differences between correct student solutions.

ABSTRACT We know that students solve problems in different ways, but we know little about the kinds of variation, or the degree of variation between these student generated solutions. In this paper, we propose a taxonomy that classifies the variation between correct student solutions in objective terms, and we show how the application of the taxonomy provides instructors with additional insight about the differences between student solutions. This taxonomy may be used to inform instructors in selecting examples of code for teaching purposes, and provides the possibility of automatically applying the taxonomy to existing solution sets

Proses Interpretasi Siswa SMP dalam Menyelesaikan Masalah Numerasi

The interpretation process is the process of interpreting the problem, information in the form of a representation, and communicating the proposed interpretation according to the context of the problem. Interpretation plays a role in solving numeracy problems, namely by analyzing information, predicting, and making decisions in solving problems. This research is a qualitative research with the aim of describing the interpretation process of junior high school students in solving numeracy problems. The research subjects were three grade VIII students of SMP Negeri in Surabaya, taking into account the various interpretations of students. Data on students' interpretation processes in solving numeracy problems were obtained through task-based interviews and analyzed using indicators of the interpretation process in solving numeration problems. The results showed that each student had read the graphs provided, and compared the two graphs by determining the differences and similarities between the two graphs. Students analyze the relationship between variables by associating information on graphs and student experiences. The results of the conclusions of each student vary due to the different interpretations of students on graphs. In presenting arguments students have difficulty with questions that require steps and evidence in drawing conclusions. Students check the correct interpretation of information and questions in problems by reflecting on solutions to questions and student experiences

Graduate teaching assistants use different criteria when grading introductory physics vs. quantum mechanics problems

Physics graduate teaching assistants (TAs) are often responsible for grading. Physics education research suggests that grading practices that place the burden of proof for explicating the problem solving process on students can help them develop problem solving skills and learn physics. However, TAs may not have developed effective grading practices and may grade student solutions in introductory and advanced courses differently. In the context of a TA professional development course, we asked TAs to grade student solutions to introductory physics and quantum mechanics problems and explain why their grading approaches were different or similar in the two contexts. TAs expected and rewarded reasoning more frequently in the QM context. Our findings suggest that these differences may at least partly be due to the TAs not realizing that grading can serve as a formative assessment tool and also not thinking about the difficulty of an introductory physics problem from an introductory physics student's perspective

An Analysis of Mathematics Interventions: Increased Time-on-Task Compared with Computer-Assisted Mathematics Instruction

Student achievement is not progressing on mathematics as measured by state, national, and international assessments. Much of the research points to mathematics curriculum and instruction as the root cause of student failure to achieve at levels comparable to other nations. Since mathematics is regarded as a gate keeper to many educational opportunities as well as, eventually, potential job prospects, critics are asking schools to fix the problem. This research project is a comparison of two different interventions used to improve student performance as tested on the Colorado State Assessment Program (CSAP). The first intervention, increased time-on-task, was used at Freedom High School for the school years 2004-2005 until 2008-2009. In those years, mathematics achievement did not improve and CSAP scores showed a negative trend. In the school year 2009-2010, Freedom High School used a computer-assisted instruction program as an intervention for low performing students. A matched-pair design was used to compare these two interventions to determine if the new intervention would improve student achievement. Eighth grade CSAP scale scores for both groups were used as a pre-test and ninth grade CSAP scale scores were used as a post-test. Pre-test mean scale scores were compared to determine variance between the groups. An analysis of covariance was used as a control for the mean differences. The statistical analysis showed that the computerassisted instructional program was ineffectual in improving student achievement in the sample group selected. Chapter Five offers discussion focused on the reasons why the computer-assisted instruction program did not work and possible solutions to correct the problems in the future. References are made to the fact that pedagogy must change if real achievement gains are going to be made by students

Reforming Physics Exams Using Openly Accessible Large Isomorphic Problem Banks created with the assistance of Generative AI: an Explorative Study

This paper explores using large isomorphic problem banks to overcome many challenges of traditional exams in large STEM classes, especially the threat of content sharing websites and generative AI to the security of exam items. We first introduce an efficient procedure for creating large numbers of isomorphic physics problems, assisted by the large language model GPT-3 and several other open-source tools. We then propose that if exam items are randomly drawn from large enough problem banks, then giving students open access to problem banks prior to the exam will not dramatically impact students' performance on the exam or lead to wide-spread rote-memorization of solutions. We tested this hypothesis on two mid-term physics exams, comparing students' performance on problems drawn from open isomorphic problem banks to similar transfer problems that were not accessible to students prior to the exam. We found that on both exams, both open bank and transfer problems had the highest difficulty. The differences in percent correct were between 5% to 10%, which is comparable to the differences between different isomorphic versions of the same problem type. Item response theory analysis found that both types of problem have high discrimination (>1.5) with no significant differences. Student performance on open-bank and transfer problems are highly correlated with each other, and the correlations are stronger than average correlations between problems on the exam. Exploratory factor analysis also found that open-bank and transfer problems load on the same factor, and even formed their own factor on the second exam. Those observations all suggest that giving students open access to large isomorphic problem banks only had a small impact on students' performance on the exam but could have significant potential in reforming traditional classroom exams

Investigating the effectiveness of teaching methods based on a four-step constructivist strategy

This paper reports on an investigation of the effectiveness an intervention using several different methods for teaching solution chemistry. The teaching strategy comprised a four-step approach derived from a constructivist view of learning. A sample consisting of 44 students (18 boys and 26 girls) was selected purposively from two different Grade 9 classes in the city of Trabzon, Turkey. Data collection employed a purpose-designed ‘solution chemistry concept test’, consisting of 17 items, with the quantitative data from the survey supported by qualitative interview data. The findings suggest that using different methods embedded within the four-step constructivist-based teaching strategy enables students to refute some alternative conceptions, but does not completely eliminate student alternative conceptions for solution chemistry

Improving performance in quantum mechanics with explicit incentives to correct mistakes

An earlier investigation found that the performance of advanced students in a quantum mechanics course did not automatically improve from midterm to final exam on identical problems even when they were provided the correct solutions and their own graded exams. Here, we describe a study, which extended over four years, in which upper-level undergraduate students in a quantum physics course were given four identical problems in both the midterm exam and final exam. Approximately half of the students were given explicit incentives to correct their mistakes in the midterm exam. In particular, they could get back up to 50\% of the points lost on each midterm exam problem. The solutions to the midterm exam problems were provided to all students in both groups but those who corrected their mistakes were provided the solution after they submitted their corrections to the instructor. The performance on the same problems on the final exam suggests that students who were given incentives to correct their mistakes significantly outperformed those who were not given an incentive. The incentive to correct the mistakes had greater impact on the final exam performance of students who had not performed well on the midterm exam.Comment: accepted for publication Physical Review Physics Education Research in 2016, 20 pages, PACS: 01.40Fk,01.40.gb,01.40G-, Keywords: physics education research, learning from mistakes, pedagogy, quantum mechanics, teaching, learnin