This study investigated secondary school students’ errors and misconceptions in algebra with a view to expose the nature and origin of those errors and to make suggestions for classroom teaching. The study used a mixed method research design. An algebra test which was pilot-tested for its validity and reliability was given to a sample of grade 11 students in an urban secondary school in Ontario. The test contained questions from four main areas of algebra: variables, algebraic expressions, equations, and word problems. A rubric containing the observed errors was prepared for each conceptual area. Two weeks after the test, six students were interviewed to identify their misconceptions and their reasoning. In the interview process, students were asked to explain their thinking while they were doing the same problems again. Some prompting questions were asked to facilitate this process and to clarify more about students’ claims. The results indicated a number of error categories under each area. Some errors emanated from misconceptions. Under variables, the main reason for misconceptions was the lack of understanding of the basic concept of the variable in different contexts. The abstract structure of algebraic expressions posed many problems to students such as understanding or manipulating them according to accepted rules, procedures, or algorithms. Inadequate understanding of the uses of the equal sign and its properties when it is used in an equation was a major problem that hindered solving equations correctly. The main difficulty in word problems was translating them from natural language to algebraic language. Students used guessing or trial and error methods extensively in solving word problems. Some other difficulties for students which are non-algebraic in nature were also found in this study. Some of these features were: unstable conceptual models, haphazard reasoning, lack of arithmetic skills, lack or non-use of metacognitive skills, and test anxiety. Having the correct conceptual (why), procedural (how), declarative (what), and conditional knowledge (when) based on the stage of the problem solving process will allow students to avoid many errors and misconceptions. Conducting individual interviews in classroom situations is important not only to identify errors and misconceptions but also to recognize individual differences.

This research reviewed the neglect of cities in the mission work of the Reformed Churches in Southern Africa with a special reference to churches of Synod Soutpansberg. The biblical passage, Jeremiah 29:1-14 was used, as a representative of other biblical passages, to shed light on the role of cities in mission work of the church while addressing misconceptions and false theology about the cities and the role they played and still play in the mission work of the church. The same biblical message is confirmed by many missiology literature, including, "Cities, Missions' New Frontier" by R.S. Greenway and T.M. Monsma (1989); "City of God - City of Satan" by R.C. Linthicum(1991) and "Discipling the City" by R.S. Greenway (1992). The biblical message and the missiology literature mentioned above were the basis from which the neglect of the role of the cities in the history of the mission work of the Reformed Churches in Southern Africa was studied. From these basis, the causes, implementations and effects of such neglect in the mission work of the Soutpansberg churches was studied in Chapter 3. The empirical research was conducted using the interview questionnaire in Chapter 4. The empirical results and findings, which were presented in this research, can direct churches towards a remedy of the neglect of the cities in their mission work as far as the strategies is concerned. The neglect of the cities in the history of the mission work of the Reformed Churches in Southern Africa was studied with an aim that churches learn from it and hence avoid the past neglect in their present and future mission plans, strategies and programs. In other words, the lesson is important for churches to view the role of the secular cities as important instruments used by God to speed up not only the planting and growing big holy churches from those secular cities outwards, but also the biblical reformation of the rural - orientated theories, strategies and practice! / Thesis (M.A. (Theology))--North-West University, Vaal Triangle Campus, 2008.

The study assessed the knowledge structure of Grade 11 physics students and their instructors using Pathfinder networks. Instructors’ structural knowledge was averaged to create a referent pathfinder network. Each student’s pathfinder network was compared with the referent pathfinder network in order to identify misconceptions. These misconceptions served as the basis for remedial instruction. The study was conducted in six sections of Grade 11. Three different types of remedial instruction based on three different chapters from the Grade 11 physics textbook were given to the students at three separate stages. In the first section, students were shown their own and referent pathfinder networks as an intervention during the first stage. The students were asked to reflect on the similarities and differences between them. The researcher gave written concept-oriented exercises based on the differences at the second stage, and multimedia concept-oriented instruction based on the differences was given to the students at the third stage. The order of instruction was counterbalanced in all the six sections. After each stage, students’ pathfinder networks were reassessed and the similarities between students’ and the referent pathfinder networks were calculated to measure the effect of a particular intervention. The study tried to determine which type of remedial instruction given to students best improved the knowledge structure of the students in the domain of physics. Results revealed that the similarity indices around the treatment concepts in the pathfinder networks of the students increased the most from pre- to post-intervention phase because of their reflections, followed by multimedia concept-oriented instruction and written concept-oriented exercises. Most likely, the major reason for this change was the interventions around the treatment concepts by the researcher at three different stages which stimulated and probably changed some of students’ misconceptions. To address the issue of validity, the similarity indices of control concepts in the students’ pathfinder networks were also checked for improvement. The result shows that there is no appreciable improvement in control concepts as there was no intervention around those concepts. Findings support the use of structural assessment of knowledge with pathfinder scaling technique to check the effectiveness of a classroom instruction.

This study aimed to explore the effectiveness one of the interactive engagement method which is peer instruction enriched by concept test on students&#039 / achievement and attitudes toward physics. In this study two types of teaching were used. These are / (1) Peer Instruction enriched by concept test, and (2) Traditional Instruction. For this study, Physics Attitude Test (PAT), Physics Achievement Test (PACT), Observation Checklist (OC), Teaching/Learning Materials were developed. Physics Attitude Test, Physics Achievement Test and Observation Checklist were used as measuring tools. The PACT and PAT were used to assess students&#039 / achievement and their attitudes toward Newton&#039 / s Laws of Motion respectively. The OC was used for treatment verification. The PACT was developed by the help of the findings from the literature. The OC was developed by the researcher. The PAT was adapted from TaSlidere&#039 / s thesis. This study was conducted with 3 teachers, 6 classes and total of 192 10th grade students in the public high schools at Yenimahalle district of Ankara in the fall semester of 2002-2003 academic years. For each teacher, 2 classes were used in the study. The teachers were trained for how to implement Peer Instruction in the classroom. Students from 3 classes participated in Traditional Instruction group and referred as control group, whereas the other 3 classes instructed by Peer Instruction referred as experimental group. The PAT and PACT were applied twice as pre-test and after a three-week treatment period as a post-test to both groups to assess and compare the effectiveness of two different types of teaching utilized in physics course. The data obtained from the administration of post-tests were analyzed by statistical techniques of Multivariate Analyses of Covariance (MANCOVA). The statistical results indicated that Peer Instruction was more effective than Traditional Instruction. Whereas the statistical analysis failed to show a significant differences between the experimental and control groups attitudes toward physics.

This thesis reports on a longitudinal study of students’ understanding of decimal notation. Over 3000 students, from a volunteer sample of 12 schools in Victoria, Australia, completed nearly 10000 tests over a 4-year period. The number of tests completed by individual students varied from 1 to 7 and the average inter-test time was 8 months. The diagnostic test used in this study, (Decimal Comparison Test), was created by extending and refining tests in the literature to identify students with one of 12 misconceptions about decimal notation. (For complete abstract open document)

Thesis (M.J.)--Carleton University, 2003. / Includes bibliographical references (p. 161-170). Also available in electronic format on the Internet.

Title from first page of PDF document. Includes bibliographical references (p. 57-58).

Title: Electricity and magnetism: Hands-on minds-on approach Author: Věra Koudelková Department: Department of Physics Education Supervisor: Doc. RNDr. Leoš Dvořák, CSc., KDF Abstract: The PhD. thesis is focused on high school students' understanding of electricity and magnetism and on experiments which can help students to develop this understanding. The thesis can be divided into two parts: In the first research part typical misconceptions of high school students in the area of electricity and magnetism are described, both misconceptions known from foreign literature and results of Czech Conceptual Test of Electricity and Magnetism. This test is based on the known Conceptual Survey of Electricity and Magnetism, but unlike it and other conceptual tests in electricity and magnetism this new Czech test is intended for high school students. The second part of the thesis is developmental. It contains methodical materials, lab works and experiments which partly arise from the discovered misconceptions. In this part of the work four learning sequences (we chose topics, which were identified as problematic for students), four laboratory works and 13 experiments are described. Prepared materials were verified during instructions in high school and during conferences for physics teachers. Experiences with them are...

Exploratory testing (ET) is an agile approach towards software testing. It is simultaneous learning, testing, reporting of problems and then generating new tests based on the learning. The aim of this thesis is to investigate exploratory testing in the industry. This thesis was proposed by Sogeti AB in Lund. Therefore the research questions were formulated and finalized according to their requirements and consent. Initially, a literature survey was conducted to study the different concepts of ET. After that a descriptive case study was conducted to investigate ET practices in an industrial environment. The research methodology used is qualitative. It comprises of ten semistructured interviews with industrial practitioners including both ET testers and customers having different perspectives. The study explores the misconceptions about ET and also identifies its claimed pros and cons. The investigation also studies its suitability with different types of testing and its effective combination with other techniques. In addition to the interviews, a survey was conducted to further investigate and analyze our findings with a larger sample of 25 practitioners. A framework for a session-based exploratory testing as practiced by the industrial partner is presented as part of our results. ET has different opinions and it is hard to say whether they are misconceptions or not. The most prominent advantage of ET from the testers view point is utilization of tester’s creativity and experience however, customers think the biggest benefit of ET approach is its ability to provide focused testing. The major disadvantage according to the testers resulted to be, difficulty in finding testers with appropriate experience, skill set and knowledge. On the other hand Inability to produce decision material was the biggest concern of the customers. The results also showed that ET approach was preferred to be used in combination with other testing techniques. Combination of Risk Based Testing and ET was reported to be used the most. ET was considered very suitable for situations where the testing requirements included learning of the system, time constraints and complementary testing. It was considered unsuitable for testing critical systems. / +46- (0)762005979

The study assessed the knowledge structure of Grade 11 physics students and their instructors using Pathfinder networks. Instructors’ structural knowledge was averaged to create a referent pathfinder network. Each student’s pathfinder network was compared with the referent pathfinder network in order to identify misconceptions. These misconceptions served as the basis for remedial instruction. The study was conducted in six sections of Grade 11. Three different types of remedial instruction based on three different chapters from the Grade 11 physics textbook were given to the students at three separate stages. In the first section, students were shown their own and referent pathfinder networks as an intervention during the first stage. The students were asked to reflect on the similarities and differences between them. The researcher gave written concept-oriented exercises based on the differences at the second stage, and multimedia concept-oriented instruction based on the differences was given to the students at the third stage. The order of instruction was counterbalanced in all the six sections. After each stage, students’ pathfinder networks were reassessed and the similarities between students’ and the referent pathfinder networks were calculated to measure the effect of a particular intervention. The study tried to determine which type of remedial instruction given to students best improved the knowledge structure of the students in the domain of physics. Results revealed that the similarity indices around the treatment concepts in the pathfinder networks of the students increased the most from pre- to post-intervention phase because of their reflections, followed by multimedia concept-oriented instruction and written concept-oriented exercises. Most likely, the major reason for this change was the interventions around the treatment concepts by the researcher at three different stages which stimulated and probably changed some of students’ misconceptions. To address the issue of validity, the similarity indices of control concepts in the students’ pathfinder networks were also checked for improvement. The result shows that there is no appreciable improvement in control concepts as there was no intervention around those concepts. Findings support the use of structural assessment of knowledge with pathfinder scaling technique to check the effectiveness of a classroom instruction.