The main purpose of this study is to determine the amount of time-dependent learning of "solving problems that require establishing of single variable equations of the first order" of the seventh grade students. The study, adopting the screening model, consisted of a total of 84 students, including 42 female and 42 male students at the seventh grade. Data was collected using an assessment tool consisting of 10 open-ended questions. The findings show that the learning group of 84 students were behind the value closest to the full learning level by a score of 0.013. While the female students reached the lower limit of 0.987 specified for the full learning level in a period of 3.2 course hours, the male students reached this limit in 4.0 course hours. The learning amount of 0.999, which is the closest value to the full learning level, was reached by the learning group in a period of 9.7 course hours, the female students in 8.5 course hours, and the male students in 11.3 course hours. In addition to this, the data obtained showed that learning difficulties among to the learning groups decreased as the space below the curve of time and learning amount decreased. As a result of the study, it was recommended that it is possible to determine the closest course periods for the full learning level for each of the gains found in all levels of education and all teaching programmes, which define certain learning outcomes within a certain time.

Technological Pedagogical Content Knowledge (TPACK) is a model that explains how teachers use technology more effectively in the context of technological, pedagogical, and content knowledge. Teachers' TPACK competencies play great importance in this regard. Lesson study has also been playing significant roles in the development of teachers' professional trainings. When the researches on TPACK and lesson study have been analyzed, the research is expected to provide significant contributions to the literature. This study aims to present reflections from a lesson study practice that carried out to urge techno-pedagogical competencies of the secondary school mathematics teachers and to reveal the development of teachers’ progress. The study used case study method, and it was conducted with three in-service teachers. The research data were collected through semi-structured interviews, voice recorder, and observation notes. To analyze the collected data, descriptive analysis method was used. The results have revealed that teachers have made much more progress in designing, implementing, and problem solving in terms of TPACK competencies. It has also been determined that teachers’ development of openness to the innovations was limited. This limitation appeared to emerge as a result of teachers’ time anxiety and insufficient knowledge regarding the use of technology.

In order to reflect the integration of the teachers’ content knowledge, pedagogical knowledge, and technology usage skills to the class context and to provide the expected outputs for the program's purposes, it is needed to be revealed the different dimensions of Technological Pedagogical Content Knowledge (TPACK). In this study, it was aimed to investigate the teacher training programmes related to pre-service science teachers’ TPACK. This study was designed as a cross-sectional study. In the 2015-2016 academic year, a total of 269 pre-service teachers (73 of them from 1st grade, 73 of them from 2nd grade, 87 of them from 3rd and 36 of them from 4th grade students) attending Science Education Department participated in this study. As a data collection tool, 7 subscales of “Technological Pedagogical Content Knowledge Scale of Pre-Service Teachers”; namely, technology knowledge, pedagogical knowledge, content knowledge, technological pedagogical knowledge, technological content knowledge, pedagogical content knowledge, and technological pedagogical content knowledge were used. According to the results, as the class level of pre-service teacher increases, their level of technological pedagogical content knowledge increases as well. Moreover, there is a significant difference on behalf of pre-service teachers at the 1st grade in all dimensions of technological pedagogical content knowledge scale.

It is important for pre-service teachers to know the conceptual difficulties they have experienced regarding the concepts of multiplication and division in fractions and problem posing is a way to learn these conceptual difficulties. Problem posing is a synthetic activity that fundamentally has multiple answers. The purpose of this study is to analyze the multiplication and division of fractions problems posed by pre-service elementary mathematics teachers and to investigate how the problems posed change according to the year of study the pre-service teachers are in. The study employed developmental research methods. A total of 213 pre-service teachers enrolled in different years of the Elementary Mathematics Teaching program at a state university in Turkey took part in the study. The “Problem Posing Test” was used as the data collecting tool. In this test, there are 3 multiplication and 3 division operations. The data were analyzed using qualitative descriptive analysis. The findings suggest that, regardless of the year, pre-service teachers had more conceptual difficulties in problem posing about the division of fractions than in problem posing about the multiplication of fractions.

This study aims to determine the impact of the ECIRR(Elicit, Confront, Identify, Resolve, Reinforce) learning model on students' mathematical reasoning abilities in terms of student motivation. The research method used was a quasy-experimental method with a post-test only control design research design. The population of this study was all students in five classes XII Private School. The Samples were taken at class XII AP-2 and XII MM-1 as the experimental class, and class XII AP-1 and XII MM-2 as the control class. The data analysis technique used is hypothesis testing using ANAVA 2 paths. Based on the research results obtained that (a) There is an influence of the ECIRR (Elicit, Confront, Identify, Resolve, Reinforce) learning model on mathematical reasoning abilities. (b) There is an influence of student learning motivation on mathematical reasoning abilities. (c) There is no interaction between the treatment of learning models and categories of students' learning motivation towards mathematical reasoning abilities. So as a whole it can be concluded that the ECIRR (Elicit, Confront, Identify, Resolve, Reinforce) learning model influences the ability of mathematical reasoning and can increase students' learning motivation.

The identification of students’ mental models is crucial in understanding their knowledge of scientific concepts. This research aimed to develop a Mental Models Representation Instrument on Newton's Laws (MeMoRI-NL). The ADDIE (Analyzing, Designing, Developing, Implementing and Evaluating) model was used as a research method. The sample consisted of 30 students of 15-16 years-old at one of senior high school in Tatar Pasundan. The data was examined using Rasch analysis on validity, reliability, level of difficulty, and distributions of students’ mental models. Students’ mental models were classified as Scientific (SC), Synthetic (SY), Synthetic almost Misconception (SYM), and Initial (IN) model. Based on the evaluating stage, students’ mental models are mostly in the SYM and IN model. Consequently, it can be concluded that the Mental Models Representation Instrument on Newton's Laws (MeMoRI-NL) can be developed using the ADDIE model and most of the students' mental model has not been following scientific knowledge. Based on this research, teachers or educators should enhance students' mental models, especially for female students.

This research aims to describe the expectations of prospective teachers for students' mathematical thinking processes in solving problem-based on the Polya model. This model is perceived by the theory of mathematical thought processes proposed by Mason. A descriptive method with a qualitative approach was used in this research. The research subjects were 25 students from the Department of Mathematics Education, Ibrahimy University. The test was given to collect data related to mathematical thinking processes expected by prospective teachers to students. Collected data including observations, tests, and interviews were tested in the aspect of their validity by triangulation. The qualitative descriptive was used to analyze the data. The results indicated that: (1) The average GPA (Grade Point Average) of the high, medium, and low group prospective teachers' were 93.25; 89.89; and 83.63 with a standard deviation of 1.754 each; 1.054; and 5.370, respectively (2) The prospective teachers expected that the students' mathematical thinking processes were able to carry out all of four mathematical thinking processes based on Mason Theory; (3) The prospective teachers expected that students were able to use Mason Theory on every stage of the Polya model problem solving; and (4) The expectation of prospective teachers were specializing (89%), generalizing (75%), conjecturing (62%), and convincing (59%). The results suggest for following up in a teachers or lecturer’s meeting in order to find out the expectations of their students' mathematical thinking processes, both in mathematics or other disciplines.

Considering the low achievement of Indonesian students in international studies (PISA), which measures Higher-Order Thinking Skill (HOTS) in solving the problem, improving the quality of mathematics learning in Indonesia is very important. The purpose of this research was conducted to explore the variations in students’ learning strategies and students’ Self–Regulated Learning (SRL) in solving mathematical HOT problems. The study employed a mixed-method, namely quantitative and qualitative methods were applied through five tests and seven interviews for over eight weeks. Two types of instruments were employed in this study, and they include tests and interviews. At the initial stage, we randomly selected 30 students from all those in grade 10 (Senior High School ), after which 12 were chosen purposively after the pre-test for an interview, having satisfied all complete group, middle group, and lower group. All of them were treated using metacognitive questions. Data analysis techniques used were percentage, data reduction, presentation, and conclusion. The quantitative results showed the students could generally use orientation, organization, and elaboration learning strategies as observed with 68.3%, 60%, and 56.7% for complete, middle, and lower groups. Moreover, the students were also observed to have conducted three cognitive processes in selecting the rules for solving the mathematical HOT problem, namely using models and drawing, written texts, and combining both. Furthermore, their final solution failures were affected by their misconceptions and errors in creating the mathematical model. The interview results on designing the learning procedures, monitoring the progress, and evaluating the outcomes, show that the students’ SRL level is good for complete (89.3%), middle (75%), and lower groups (60.7%).

An evidence-based, interactive teaching method peer instruction (PI) is promoted to support effectiveness over more commonly used teaching methods. Usually it is proposed for the university and upper secondary school. The research reports on the implementation of the PI approach in teaching subject Science and Technology (S&T) in the 4th grade of primary school. The aim of this research was to verify the feasibility of this approach for much younger students in primary school by evaluating the students’ progress in the subject S&T, identifying the differences in individual progress in relation to students’ general learning success, and determining students’ opinions about the approach and where no desired progress has been made. In a selected Slovenian primary school, a classroom with 26 students (age 9 – 10) was included in the study and 5 different content areas (Earth’s motion, Matter, Magnetism, Forces and motion, and Electricity) were taught using this PI approach. Results show that students made progress in all content areas and no differences were identified in the progress of individual students in terms of general learning success. Students were satisfied with the approach, although more than half of them found the multiple-choice questions as too difficult. Although the PI approach is successful, teachers must be aware that some persistent and widespread misunderstandings may still remain and require additional intervention.

One of the issues that hinder the students’ learning progress is the inability to construct an epistemological explanation of a scientific phenomenon. Four-tier multiple-choice (hereinafter, 4TMC) instrument and Partial-Credit Model were employed to elaborate on the diagnosis process of the aforementioned problem. This study was to develop and implement the four-tier multiple-choice instrument with Partial-Credit Model to evaluate students’ learning progress in explaining the conceptual change of state of matter. This research applied a development research referring to the test development model by Wilson. The data were obtained through development and validation techniques on 20 4TMC items tested to 427 students. On each item, the study applied diagnostic-summative assessment and certainty response index. The students’ conceptual understanding level was categorized based on the combination of their answer choices; the measurement generated Partial-Credit Model for 1 parameter logistic (IPL) data. Analysis of differences was based on the student level class using Analysis of Variants (One-way ANOVA). This study resulted in 20 valid and reliable 4TMC instruments. The result revealed that the integration of 4TMC test and Partial-Credit Model was effective to be treated as the instrument to measure students’ learning progress. One-way ANOVA test indicated the differences among the students’ competence based on the academic level. On top of that, it was discovered that low-ability students showed slow progress due to the lack of knowledge as well as a misconception in explaining the Concept of Change of State of Matter. All in all, the research regarded that the diagnostic information was necessary for teachers in prospective development of learning strategies and evaluation of science learning.

We investigated the effects of just-in-time guidance at various stages of inquiry learning by novice learners. Thirteen participants, randomly assigned to an intervention (n = 8) or control (n = 5) group, were observed as they learned about DC electric circuits using a web-based simulation. Just-in-time instructional prompts to observe, predict, explain, systematically test, collect evidence, and generate rules were strongly associated with diagnosing and correcting misconceptions, and constructing correct scientific concepts. Students’ repeated use of predictions, systematic testing, and evidence-coordinated reasoning often led to formulating new principles, generalizing from observed patterns, verifying comprehension, and experiencing “Aha!” moments. Just-in-time prompts helped learners manage embedded cognitive challenges in inquiry tasks, achieve a comprehensive understanding of the model represented in the simulation, and show significantly higher knowledge gain. Just-in-time prompts also promoted rejection of incorrect models of inquiry and construction of robust scientific mental models. The results suggest ways of customizing guidance to promote scientific learning within simulation environments.

This paper explores misconceptions and errors (M/Es) of eighth-grade students in Nepal with a quasi-experimental design with nonequivalent control and experimental groups. The treatment was implemented with teaching episodes based on different remedial strategies of addressing students' M/Es. Students of control groups were taught under conventional teaching-learning method, whereas experimental groups were treated with a guided method to treat with misconceptions and errors. The effectiveness of treatment was tested at the end of the intervention. The results showed that the new guided treatment approach was found to be significant to address students' M/Es. Consequently, the students of experimental groups made significant progress in dealing with M/Es in mathematical problem-solving at conceptual, procedural, and application levels.

The equal symbol has been used in diverse mathematical frameworks, such as arithmetic, algebra, trigonometry, set theory, and so on. In mathematical terms, the equal sign has been used in fixed command of standings. The study reports on the students meaning and interpretations of the equal sign. The study involved Grade 6, 7, and 8 students in a secondary school in Alain, United Arab Emirates (UAE). Much of the earlier research done on the equal sign has focused on the primary school level, but this one focuses on middle school students. The study shows that the maximum foremost understanding of the equal sign amongst Grade 6, 7, and 8 students is a do-something, unidirectional symbol. Students realize the equal sign as an instrument for marking the response moderately than as an interpersonal symbol to associate extents.

The cooperative learning (CL) is an advanced instructional approach that uses different motivational procedures to make instruction significant and learners more responsible. This study aimed to investigate the effects of cooperative learning on students' achievement in chemistry among the advanced level in 12-year basic education schools; it engaged a quasi-experimental design with one treatment group and a comparison group (control); the first applied cooperative learning in teaching organic chemistry while in the control group, organic chemistry was taught by the conventional teaching methods (CTM). A sample of 257 students participated in the study. The data collected used an organic Chemistry Achievement Test, and its data were analyzed using SPSS version 23.0 and MS Excel 2016. The ANCOVA results showed that learners taught using cooperative learning achieved better than their counterparts in the control group (F=78.07, df=1, 256, p<.001) with the learning gains of 16.0% in traditional methods and 53.6% of cooperative learning approach, respectively. However, there was no statistically significant difference in gender of students. It is recommended that chemistry teachers be trained on cooperative learning and encouraged to apply it in their teaching methods to enhance students' academic achievement.

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.

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.

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.