The fundamental goal of this study is to explore why so many students have difficulty learning mathematics. To achieve this goal, this study focuses on why so many students keep making the same errors over a long period of time. To explore such issues, three basic algebra concepts - variable, equation, and function – are used to analyze students’ errors, possible buggy algorithms, and the conceptual basis of these errors: misconceptions. Through the research on these three basic concepts, it is expected that a more general principle of understanding and the corresponding learning difficulties can be illustrated by the case studies. Although students’ errors varied to a great extent, certain types of errors related to students’ misconceptions occurred frequently and repeatedly after one year of additional instruction. Thus, it is possible to identify students’ misconceptions through working on students’ systematic errors. The causes of students’ robust misconceptions were explored by comparing high-achieving and low-achieving students’ understanding of these three concepts at the object (structural) or process (operational) levels. In addition, high achieving students were found to prefer using object (structural) thinking to solve problems even if the problems could be solved through both algebra and arithmetic approaches. It was also found that the relationship between students’ misconception and object-process thinking explained why some misconceptions were particularly difficult to change. Students’ understanding of concepts at either of two stages (process and object) interacted with either of two aspects (correct conception and misconception). When students had understood a concept as a process with misconception, such misconception was particularly hard to change. In addition, other concerns, such as rethinking the misconception of the “equal sign,” the influence of prior experience on students’ learning, misconceptions and recycling curriculum, and developing teachers’ initial subject knowledge were also discussed. The findings of this study demonstrated that the fundamental reason of misconception of “equal sign” was the misunderstanding of either side of equation as a process rather than as an object. Due to the existence of robust misconceptions as stated in this study, the use of recycling curriculum may have negative effect on students’ understanding of mathematics.

Abstract This research is to explore the high school student potential misconceptions on evolution, based on the two-tier diagnostic test and diagnostic interview. Through a proper teaching design, the researcher has developed an untraditional teaching method. The effects of the untraditional teaching method and the traditional teaching method were compared. With the retest of two-tier diagnostic test, a survey was conducted to evaluate the students¡¦ achievement resulting from the teaching strategy designed by the researcher. The survey can also be consulted and used in the improvement of future teaching activities. This research adopted a Quasi-experimental research method. Data included the analysis of quantity and the description of quality. The research tool is a two-tier diagnostic questionable. The sample groups consist of two classes in the grade-10 and two classes in the grade-12 with 35 students in each class, taught by the researcher. The results of this research indicate that (1) in general , the students are in lack of the structural knowledge of evolution in their prior learning especially¡§the relationship between organism and organism¡¨and the concept of human selection; (2) the comparison of learning results brought about between the untraditional teaching method and traditional teaching method, apparently shows that the experimental group students are far better than the control group students in understanding the connection of evolutional concepts and the abundance of conceptive maps; (3) the difference of student learning process of the two teaching methods , compared by the quiz results on each unit, are not significantly different between the two groups of students; and (4) as far as the teaching of the concept of evolution is concerned, the improved teaching method design is appreciated by the experiment group students and is highly expected by the control group students.

I was concerned with the preconceptions of the pupils in the area of geometric optics in my diploma work. I did the research among the pupils of grammar schools and multi-annual secondary schools. The used test contained ten questions. My choice of the questions was based on the researches concerning the misconceptions in optics that have been already done. I also mention the survey of these researches in my diploma work. I compiled the summary of the textbooks that are used at grammar schools and in the lower degrees of secondary schools in the next part. These textbooks are focused on the topics contained in the questions of the test. The survey of the testing results creates main part of my diploma work. I tested before and after the teaching of optics 162 pupils from eight classes of grammar schools and multi-annual secondary schools took part in the investigation. The table with the most frequent misconceptions that were ascertained during the testing is part of this survey. I devoted to the differences in the results between the pupils from grammar schools and multi-annual secondary schools and also the differences in the results of boys and girls.

Magister Educationis - MEd / Every year there is a national outcry by educationists in South Africa relating to the poor performance of grade 12 mathematics learners. This is an unsatisfactory state of affairs in a country where mathematics is seen as playing a pivotal role in the preparation of students in disciplines for careers in science and technology. Interventions by the Department of Basic Education as well as by provincial education departments do not seem to be successful in stemming the tide in the decline of standards in the mathematical performance of learners. It is this which has motivated this study.The aim of this study was to identify the types of errors committed by students in their responses to question one of Paper 1 in the final Grade 12 mathematics examinations of 2010. By reviewing the work done by different authors, an analytical framework was compiled that was used to identify and to label errors in the written responses of learners. This study has adopted a documentary analysis approach and has selected a representative sample of examination scripts of Western Cape students who wrote the first paper of the grade 12 mathematics examination in 2010. The result shows that during the analysis of 1959 scripts (the sample taken from different educational departments and districts), 4163 errors were identified. These errors have been identified based on the above-mentioned analytical framework. Comparisons were labeled according to the different types of errors, across the different ex- department schools and per districts. If the percentage is calculated based on the number of scripts analyzed, the number of errors varies from 12% careless errors to 40% calculation errors. It was also noticed that the number of errors found in the urban districts was higher than all of the errors found in the different rural districts. In return, in the urban districts, the numbers of errors found were evenly distributed over the four districts. When the different ex-department schools were compared, the numbers of application and procedural errors were significantly higher in the DET schools(Department of Education and Training, which consists of mostly black disadvantaged learners) than all the other schools. The rest of the errors were evenly distributed over all the exdepartment schools. The inability of learners solving inequality equations stood out as a major concern.

This article provides five common grad school misconceptions: more of the same, it's all bench research, research is boring, what about patient care?, and grad school delays life.

Simulated learning environments are becoming a more popular format for the delivery of healthcare education. These environments include but are not limited to simulated online learning environments, serious games, task trainers, and, electronic mannequins. Presently there is a lack of understanding of how the learning environment impacts students’ disposition to engage in learning processes and how learner satisfaction with the environment impacts learning outcomes. This preliminary descriptive study utilizes methods such as traditional statistical analysis and Association Rule mining. This study will investigate how students perceptions of the simulative learning environment IPSims (Interprofessional Simulations) usability impacts learning outcomes, and how these environments may impact student disposition to engage in learning. The participants (n= 58) were undergraduate health science students studying at the University of Ontario Institute of Technology. The data analysis provides insight into how simulative learning environments can impact student engagement in learning processes. Study strengths and limitations are identified along with future considerations. / UOIT

The objective of this thesis was to investigate pre-service teachers and student misconceptions of the equal sign, and then offer suggestions to pre-service teachers, teachers, university programs, and schools to prevent common misconceptions from occurring in classrooms. Some students do not realize the equal sign can have two different functions, operational and relational. There are several different reasons for this misconception, beginning with the lack of defining what the equal sign is and what it means in the classroom. In the first study, eighteen participants were interviewed to explain their responses when evaluating student work to gain an in-depth knowledge of pre-service teachers' perceptions of the equal sign and their ability to evaluate a students' response to a specific math task. Results showed that pre-service teachers have a better understanding of the equal sign and may be ready to teach the equal sign as a relationship between numbers. Furthermore, pre-service teachers would benefit greatly from evaluating students' work and looking for common misperceptions that students may have. In the second study, six fifth grade classes were studied to determine if there was a positive relationship for teaching atypical type equivalence statements to students and performing better on equivalence questions. Three classes from Spring 2011, were administered a test; two of the test items were used to analyze their understanding of the equal sign. In Fall 2011, another three fifth grade classes participated in lessons, which required students to analyze atypical type equivalence statements, and then they were given the same two test items. Results from this study supported the use of atypical type equivalence statements because more students in the experimental group correctly responded to the two items and were also able to justify their responses with work that exemplified good understanding of the equal sign as being a relationship. Both of these studies support increasing student and pre-service teachers understanding of the equal sign and the misconceptions students have regarding the equal sign. University programs and schools should utilize these results to require preservice teachers and teachers to evaluate student work to identify common misconceptions and teach the equal sign as a relationship between both sides and not as an operation.

abstract: The semiconductor field of Photovoltaics (PV) has experienced tremendous growth, requiring curricula to consider ways to promote student success. One major barrier to success students may face when learning PV is the development of misconceptions. The purpose of this work was to determine the presence and prevalence of misconceptions students may have for three PV semiconductor phenomena; Diffusion, Drift and Excitation. These phenomena are emergent, a class of phenomena that have certain characteristics. In emergent phenomena, the individual entities in the phenomena interact and aggregate to form a self-organizing pattern that can be observed at a higher level. Learners develop a different type of misconception for these phenomena, an emergent misconception. Participants (N=41) completed a written protocol. The pilot study utilized half of these protocols (n = 20) to determine the presence of both general and emergent misconceptions for the three phenomena. Once the presence of both general and emergent misconceptions was confirmed, all protocols (N=41) were analyzed to determine the presence and prevalence of general and emergent misconceptions, and to note any relationships among these misconceptions (full study). Through written protocol analysis of participants' responses, numerous codes emerged from the data for both general and emergent misconceptions. General and emergent misconceptions were found in 80% and 55% of participants' responses, respectively. General misconceptions indicated limited understandings of chemical bonding, electricity and magnetism, energy, and the nature of science. Participants also described the phenomena using teleological, predictable, and causal traits, indicating participants had misconceptions regarding the emergent aspects of the phenomena. For both general and emergent misconceptions, relationships were observed between similar misconceptions within and across the three phenomena, and differences in misconceptions were observed across the phenomena. Overall, the presence and prevalence of both general and emergent misconceptions indicates that learners have limited understandings of the physical and emergent mechanisms for the phenomena. Even though additional work is required, the identification of specific misconceptions can be utilized to enhance semiconductor and PV course content. Specifically, changes can be made to curriculum in order to limit the formation of misconceptions as well as promote conceptual change. / Dissertation/Thesis / Ph.D. Curriculum and Instruction 2014

Social attitudes towards child sexual abuse (CSA) tend to reflect a wide variety of misconceptions. These not only play a highly significant role in the etiology and maintenance of sexual offending against children, they also contribute to under reporting and promote the silence that generally surrounds CSA. They further predict unfair treatment of victims, and compromise adaptive resolution in both victim and offender. The main purpose of this study was to investigate the existence of misconceptions surrounding CSA amongst the general public of Durban in South Africa. A further purpose was to explore differences in rates of myth endorsement in this context, firstly between males and females, and secondly between two levels of education. The research design was conceptualised within a positivist paradigm with the use of quantitative data collected through questionnaire method. The research instrument was developed by the researcher within the framework of four empirical studies, with input from two professors with extensive research experience. The sample consisted of members and staff of a public library; clothing factory workers; staff in two elementary schools; and employees in a retail outlet. The research sites were located in three different geographical areas of the city to maximise generalisation of findings. Although previous studies have indicated high rates of myth endorsement amongst the general public and gender differences in rates of myth endorsement, the present study xiv did not yield significant results in these two areas. This may have been due to the composition of the sample which was largely representative of educators and other school personnel (n = 80). This population has more exposure to victims of CSA than the average member of the public, and may well have a wider knowledge in issues surrounding CSA, as a consequence of this. In terms of differences in rates of myth endorsement according to levels of education, findings in this study have indicated a higher rate of myth endorsement in those with a lower level of education. This is consistent with findings in previous studies amongst the general public in the USA and Australia. This suggests a priority for the development of programs to disseminate accurate information in issues surrounding CSA at all levels of public education. The literature additionally indicates an urgent need for the development and implementation of comprehensive programs to elucidate issues in CSA amongst the general public. It has been suggested that these public programs be based on the educational initiatives employed in antismoking campaigns, since these have proven efficacy. / National Research Foundation

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