We investigate students’ misconceptions in electrostatics, direct current (DC) and magnetism which are important in electricity and magnetism. We developed and administered a multiple-choice questionnaire test to reveal students’ misconceptions related to charged bodies, lightning, electric fields, electric potential, forces, DC resistive electric circuits and magnets. This test aimed at obtaining quantitative information about misconceptions and was administered to 380 senior two students from Nine Year Basic Education (9YBE) Schools. The selected students have some experience with the new Rwandan secondary physics Competence Based Curriculum (CBC) that is currently under implementation. We find that senior two students have several common misconceptions related to these concepts. The data indicate that although students have some backgrounds on the subject matter, they still seem to believe that if the two charges are separated by a distance, a large-charged object exerts a greater force of attraction or repulsion on the small one. Considerable number of participated students held the misconception of considering current consumption in the resistor/bulb or the electrical devices in the circuits. They also believed that the battery was a continuous current source. The findings also revealed that students held a misconception that a bar magnet when broken into pieces, it is demagnetized. Moreover, a considerable number of participants hold the misconception that all metals are attracted by a magnet. Our study also revealed some of the statistically significant differences in terms of either gender or location of schools for some items.

The performance in biology at the secondary level has not been as good as expected. This has been a matter of concern. Thus, there has been a continuous focus on exploring newer innovative learner-centered and friendly instructional strategies to enhance understanding and retention in biology. This study, therefore, determined the effects of Concept Mapping (CM) and Cooperative Mastery Learning (CML) on fostering retention in photosynthesis among secondary schools in Nyamagabe district, Rwanda. A pre-test and post-test non-equivalent control group quasi-experimental design was used. Data were obtained from 151 students taught with CM, 144 students taught with CML, and 154 students taught with Conventional Teaching Methods (CTM). The Photosynthesis Retention Test (KR-21= 0.82) was used for data collection. The data were mainly analyze d using mean and Analysis of Covariance (ANCOVA). The results showed that the CM and CML treatment groups outperformed the CTM group in retention in photosynthesis. There was a statistically significant difference in favor of the CM between the two experimental groups. The male and female students taught using CM retained equally in photosynthesis while gender difference was revealed in the mean retention scores of the students exposed to the CML, with females retained significantly higher than males. The study concluded that the CM and CML strategies were more effective than CTM. It was suggested, among other things, that teachers should be encouraged to apply CM and CML strategies when teaching biology.

This paper investigates the quantitative literacy and reasoning (QLR) of freshmen students pursuing a Science, Technology, Engineering, and Mathematics (STEM)–related degree but do not necessarily have a Senior High School (SHS) STEM background. QLR is described as a multi-faceted skill focused on the application of Mathematics and Statistics rather than just a mere mastery of the content domains of these fields. This article compares the QLR performance between STEM and non-STEM SHS graduates. Further, this quantitative-correlational study involves 255 freshman students, of which 115 have non-STEM academic background from the SHS. Results reveal that students with a SHS STEM background had significantly higher QLR performance. Nevertheless, this difference does not cloud the fact that their overall QLR performance marks the lowest when compared to results of similar studies. This paper also shows whether achievement in SHS courses such as General Mathematics, and Statistics and Probability are significant predictors of QLR. Multivariate regression analysis discloses that achievement in the latter significantly relates to QLR. However, the low coefficient of determination (10.30%) suggests that achievement in these courses alone does not account to the students’ QLR. As supported by a deeper investigation of the students’ answers, it is concluded that QLR indeed involves complex processes and is more than just being proficient in Mathematics and Statistics.

Evolution is one of the most difficult and controversial topics. Scientific knowledge of evolution should belong to general knowledge of people, it should be the part of their natural science knowledge or biological education because it is the basis for accepting or refusing of other important topics such as genetical modification, global climatic change and others. Our aim was to analyse the inclusion of evolution in the teaching process in Slovakia in the subjects of history and biology and the associated potential threats to the formation of misconceptions. We measured the level of knowledge and understanding of evolution and evolutionary processes among high school graduates (N = 200). In doing so, we hypothesized that graduating high school students who have received evolutionary education achieve higher levels of both knowledge and understanding of evolutionary processes compared to those who have not received such education. We hypothesized that interest in science and acceptance of evolution would also positively influence levels of knowledge about evolutionary phenomena and understanding of evolutionary processes. Having used research, we claimed the impact of interest in natural science. We suggest to include the evolution as a main topic of biology into education through exploration- oriented teaching.

Misconceptions are one of the biggest obstacles in learning mathematics. This study aimed to investigate students’ common errors and misunderstandings they cause when defining the angle and the triangle. In addition, we investigated the metacognition/ drawing/ writing/ intervention (MDWI) strategy to change students’ understanding of the wrong concepts to the correct ones. A research design was used to achieve this goal. It identified and solved the errors in the definition of angle and triangle among first-year students in the Department of Mathematics Education at an excellent private college in Mataram, Indonesia. The steps were as follows: A test instrument with open-ended questions and in-depth interviews were used to identify the errors, causes, and reasons for the students’ misconceptions. Then, the MDWI approach was used to identify a way to correct these errors. It was found that students generally failed in interpreting the concept images, reasoning, and knowledge connection needed to define angles and triangles. The MDWI approach eliminated the misconceptions in generalization, errors in concept images, and incompetence in linking geometry features.

This research is a developmental research aiming at developing a good mathematical test instrument using polytomous responses based on classical and modern theories. This research design uses the Plomp model, which consists of five stages, (1) preliminary investigation, (2) design, (3) realization/construction, (4) revision, and (5) implementation (testing). The study was conducted in three vocational schools in Lampung Province, Indonesia. The study involved 413 students, consisting of 191 male and 222 female students. The data were collected through questionnaire and test. The questionnaire was used to identify the assessment instruments currently employed by teachers and to be validated by the experts of mathematics and educational evaluation. The test used an open polytomous response test numbering of 40 items. The data were analyzed using both classical and modern theories. The results show that (1) the open polytomous response test has a good category according to classical and modern theory. However, the discrimination power of test items in classical theory needs several revisions, (2) the assessment instrument using the polytomous response of open multiple choice can guarantee information on the actual competence of students. This is proven by the fact that there is a harmony between the analysis result obtained from classical and modern theory from the students' arguments when giving reasons for their choices. Therefore, the open polytomous response test can be used as an alternative to learning assessment.

Algebraic knowledge transfer is considered an important skill in problem-solving. Using algebraic knowledge transfer, students can connect concepts using common procedural similarities. This quasi-experimental study investigates the influence of algebraic knowledge in solving problems in a chemistry context by using analogical transformations. The impact of structured steps that students need to take during the process of solving stoichiometric problems was explicitly analyzed. A total of 108 eighth-grade students participated in the study. Of the overall number of students, half of them were included in the experimental classes, whereas the other half were part of the control classes. Before and after the intervention, contextual problems were administered twice to all the student participants. The study results indicate that the students of the experimental classes exposed to structured steps in solving algebraic problems and the procedural transformations scored better results in solving problems in mathematics for chemistry compared to their peers who did not receive such instruction. Nevertheless, the result shows that although the intervention was carried out in mathematics classes, its effect was more significant on students' achievements in chemistry. The findings and their practical implications are discussed at the end of the study.

We developed a Quantum Mechanics Conceptual Understanding Survey (QMCUS) in this study. The survey was conducted using a quantitative methodology. A multiple-choice survey of 35 questions was administered to 338 undergraduate students. Three experienced quantum mechanics instructors examined the validity of the survey. The reliability of our survey was measured using Cronbach's alpha, the Fergusson delta index, the discrimination index, and the point biserial correlation coefficient. These indices showed that the developed survey is reliable. The statistical analysis of the students' results using SPSS shows that the scores obtained by the students have a normal distribution, around the score of 7.14. The results of the t-test show that the students' scores are below the required threshold, which means that it is still difficult for the students to understand the concepts of quantum mechanics. The obtained results allow us to draw some conclusions. The students' difficulties in understanding the quantum concepts are due to the nature of these concepts; they are abstract and counterintuitive. In addition, the learners did not have frequent contact with the subatomic world, which led them to adopt misconceptions. Moreover, students find it difficult to imagine and conceptualize quantum concepts. Therefore, subatomic phenomena are still explained with classical paradigms. Another difficulty is the lack of prerequisites and the difficulties in using the mathematical formalism and its translation into Dirac notation.

Mathematics teachers’ instructional strategies lack in-depth knowledge of algebraic systems and hold misconceptions about solving two algebraic equations simultaneously. This study aimed to gain an in-depth analysis of teachers’ knowledge and perceptions about the promotion of conceptual learning and effective teaching of algebraic equations. The main question was, ‘How do junior secondary school mathematics teachers manifest their pedagogical practices when teaching algebraic equations? This article reports on a qualitative, underpinned by the knowledge quartet model study, that sought to explore how junior secondary school teachers’ pedagogical practices manifested in the teaching of algebraic equations. Data were collected from observations, semi-structured interviews, and document analysis of two mathematics teachers purposely selected from two schools. The collected data were analysed using a statistical analysis software called Atlas-ti. (Version 8) and triangulated through thematic analysis. The study revealed that teachers’ choices of representations, examples, and tasks used did not expose learners to hands-on activities that promote understanding and making connections from the underlying algebraic equation concepts. The study proposed Penta-Knowledge Collaborative Planning and Reflective Teaching and Learning Models to enable teachers to collaborate with their peers from the planning stage to lesson delivery reflecting on good practices and strategies for teaching algebraic equations.

Diagnostic tests are generally two or three-tier and based on classical test theory. In this research, the Four-Tier Diagnostic Test (FTDT) was developed based on modern test theory to determine understanding of physics levels: scientific conception (SC), lack of knowledge (LK), misconception (MSC), false negatives (FN), and false positives (FP). The goals of the FTDT are to (a) find FTDT constructs, (b) test the quality of the FTDT, and (c) describe students' conceptual understanding of physics. The development process was conducted in the planning, testing, and measurement phases. The FTDT consists of four-layer multiple-choice with 100 items tested on 700 high school students in Yogyakarta. According to the partial credit models (PCM), the student's responses are in the form of eight categories of polytomous data. The results of the study show that (a) FTDT is built on the aspects of translation, interpretation, extrapolation, and explanation, with each aspect consisting of 25 items with five anchor items; (b) FTDT is valid with an Aiken's V value in the range of 0.85-0.94, and the items fit PCM with Infit Mean Square (INFIT MNSQ) of 0.77-1.30, item difficulty index of 0.12-0.38, and the reliability coefficient of Cronbach's alpha FTDT is 0.9; (c) the percentage of conceptual understanding of physics from large to small is LK type 2 (LK2), FP, LK type 1 (LK1), FN, LK type 3 (LK3), SC, LK type 4 (LK4), and MSC. The percentage sequence of MSC based on the successive material is momentum, Newton's law, particle dynamics, harmonic motion, work, and energy. In addition, failure to understand the concept sequentially is due to Newton's law, particle dynamics, work and energy, momentum, and harmonic motion.

The various intuitive reasoning types in many cases comprise the core of students’ misconceptions about concepts, procedures and phenomena that pertain to natural sciences. Some researchers support the existence of a relatively closer connection between the right hemisphere and intuitive thought, mainly due to a notably closer relation of individual intuitive cognitive processes with specific right hemisphere regions. It has been suggested that individuals show a different preference in making use of each hemisphere’s cognitive capacity, a tendency which has been termed Hemisphericity or Hemisphere Preference. The purpose of the present study was to examine the association between hemispheric preference and students’ misconceptions. A correlational explanatory research approach was implemented involving 100 seventh grade students from a public secondary school. Participants completed a hemispheric preference test and a misconceptions documentation tool. The results revealed that there wasn’t any differentiation in the mean score of misconceptions among the students with right hemispheric dominance and those with left hemispheric dominance. These findings imply a number of things: (a) the potential types of intuitive processes, that might be activated by the students, in interpreting the biology procedures and phenomena and their total resultant effect on students’ answers, probably do not have any deep connection with the right hemisphere; (b) it is also possible that students might use reflective and analytic thought more frequently than we would have expected.

Many students have misconceptions about mathematics, so preservice teachers should be developing the skills to notice mathematical misconceptions. This qualitative study analyzed preservice teachers' skills in noticing student misconceptions about algebra, according to three aspects of noticing found in the literature: attending, interpreting and responding. Participants in this study were seven preservice teachers from one university in the capital of Aceh province, Indonesia, who were in their eighth semester and had participated in teaching practicums. Data was collected through questionnaires and interviews, which were analyzed descriptively. The results revealed the preservice teachers had varying levels of skill for the three aspects of noticing. Overall, the seven preservice teachers' noticing skills were fair, but many needed further development of their skills in interpreting and responding in particular. This university’s mathematics teacher education program should design appropriate assessment for preservice teachers’ noticing skills, as well as design and implement learning activities targeted at the varying needs of individual preservice teachers regarding noticing student misconceptions, in order to improve their overall teaching skills.

This research aims to describe secondary school students' functional thinking in generating patterns in learning algebra, particularly in solving mathematical word problems. In addressing this aim, a phenomenological approach was conducted to investigate the meaning of functional relationships provided by students. The data were collected from 39 ninth graders (13-14 years old) through a written test about generating patterns in linear functions. The following steps were conducting interviews with ten representative students to get detailed information about their answers to the written test. All students' responses were then analyzed using the thematic analysis software ATLAS.ti. The findings illustrate that students employed two types of approaches in solving the problem: recursive patterns and correspondence. Students favored the recursive patterns approach in identifying the pattern. They provided arithmetic computation by counting term-to-term but could not represent generalities with algebraic symbols. Meanwhile, students evidenced for correspondence managed to observe the relation between two variables and create the symbolic representation to express the generality. The study concludes that these differences exist due to their focus on identifying patterns: the recursive pattern students tend to see the changes in one variable, whereas the correspondence ones relate to the corresponding pair of variables.

Research on conceptual understanding is one of the first steps in designing materials to improve learning. Literature reports that students have difficulties analyzing and describing phenomena in electric circuits. This report contributes to students' conceptual difficulties regarding simple electrical circuits by systematically analyzing an open conceptual test answered by 531 first-year engineering students. We found students' reasoning that has not yet been reported in the literature as misconceptions or difficulties. To deepen our understanding of students' difficulties, we chose five students by convenience to interview. We present evidence that there are two main contributions to the taxonomy in this study: the Series Circuit Misconception, which is when students convey that the current through bulbs is the same because they are in series, using that as a mnemonic ignoring any change in the circuit; and the Inverse Parallel Circuit Misconception, that is when students mention that the resistance of the circuit decreases when disconnecting bulbs in parallel, neither are reported in the literature. The results of this study have implications for physics education research in electric circuits and educational practice in the classroom.

This study aims to produce a product to evaluate students' critical thinking skills that departs from physics content where students often have misconceptions. This research is a development research with research stages covering a) research and review literature; (b) planning chapter objectives; (c) developing a preliminary form; (d) field-testing the preliminary form; (e) Revise the preliminary form; (f) conducting a main field-test. The Waves Critical Thinking (WCT) test developed consists of 7 questions with 15 specific domains. Total percentage of content validity test was obtained 87.98% with appropriate criteria and based on the construct validity WCT test, the Goodness of Fit criteria were obtained which were classified as fit. The test instrument being tested consists of 15 objective items. The reliability of WCT test results 0.597 as a Cronbach's alpha score with the medium category and all the components have a good level of composite reliability. The outcome of the study was the WCT test with a valid state for measuring students' CT in a specific domain of physics wave material.

In this article, we present the results of empirical research using a combination of quantitative and qualitative methodology, in which we examined the achievements and difficulties of sixth-grade Slovenian primary school students in decimal numbers at the conceptual and procedural knowledge level. The achievements of the students (N = 100) showed that they statistically significantly (z = -7,53, p < .001) better mastered procedural knowledge (M = 0.60, SD = 0.22) than conceptual knowledge (M = 0.37, SD = 0.17) of decimal numbers. Difficulties are related to both procedural and conceptual knowledge, but significantly more students have difficulties at the level of conceptual knowledge. At the level of procedural knowledge, or in the execution of arithmetic operations with decimal numbers, we observed difficulties in transforming text notation into numerical expressions, difficulties in placing the decimal point in multiplication and division, and insufficient automation of mathematical operations with decimal numbers. At the level of conceptual knowledge of decimal numbers, the results indicate difficulties for students in understanding the place values of decimal numbers, in estimating the sum, product and quotient of decimals with reflection and in mathematical justification. In relation to difficulties in justification, we observed an insufficient understanding of the size relationship between decimal numbers and difficulties in expressing them in mathematical language. The results indicate that to overcome such difficulties in the learning and teaching of mathematics, more balance between procedural and conceptual knowledge is needed.

Understanding graphs in the dynamics of market (DM) is a challenge to learners; its teaching demands a specific kind of teacher’s knowledge. This study aims to examine the topic-specific pedagogical content knowledge (TSPCK) of experienced economics teachers in teaching graphs in DM to enhance learners’ understanding of the topic. It reports using a qualitative approach underpinned by the TSPCK framework for teaching specific topics developed by Mavhunga. Data were collected through classroom observations and analyzed thematically using a case study of two economics teachers. The study revealed that adopting a step-by-step approach and the use of worked graphical examples promote an understanding of graphs in DM. It also established that active learning is preferable to the predominant chalk-and-talk (lecture) method of teaching graphs in DM. The study proposed a Dynamics of Market Graphical Framework (DMG-Framework) to enable teachers, particularly pre-service teachers in lesson delivery, to enhance learners’ understanding of graphs in DM. The result of this study will broaden the international view in the teaching of graphs in DM.

<p style="text-align:justify">This study aimed to assess the geometric knowledge of student teachers from a university in the Eastern Cape province of South Africa. The study used a sample of 225 first-year student teachers who completed school mathematics baseline assessments on a computer- aided mathematics instruction (CAMI) software. The study adopted a descriptive cross-sectional research design, using quantitative data to measure student teachers&rsquo; geometry achievement level, and qualitative data to explain the challenges encountered. The results show that student teachers exhibited a low level of understanding of school-level geometry. The low achievement levels were linked to various factors, such as insufficient grasp of geometry concepts in their secondary school education, difficulty in remembering what was done years ago, low self-confidence, and lack of Information and Communications Technology (ICT) skills along with the limited time for the baseline tests. These results suggest that appropriate measures should be taken to ensure that student teachers acquire the necessary subject-matter knowledge to teach effectively in their future classrooms.</p>