Development and use of Test Instruments to measure Algebraic Reasoning Based on Cognitive Systems in Marzano’s Taxonomy

<p style="text-align: justify;">Algebraic reasoning involves representation, generalization, formalization of patterns and order in all aspects of mathematics. Hence, the focus of algebraic reasoning is on patterns, functions, and the ability to analyze situations with the help of symbols. The purpose of this study was to develop a test instrument to measure students' algebraic reasoning abilities based on cognitive systems in Marzano's taxonomy. The cognitive system in Marzano's taxonomy consists of four levels, including retrieval, comprehension, analysis, and knowledge utilization. According to the stage of cognitive development, students are at the level of knowledge utilization. At this level, students can make decisions, solve problems, generates and test hypotheses, as well as carry out investigations that are in line with indicators of algebraic reasoning abilities. The stages in developing the test instrument were based on three phases: preliminary investigation phase, prototyping phase, and assessment phase. The study obtains a set of valid and reliable algebraic reasoning test instruments for students based on the cognitive system in Marzano's taxonomy. Through the development of an algebraic reasoning test instrument based on Marzano's taxonomy, students can build' thinking habits so that active learning exercises occurs.</p>

Differences and Similarities in Scientists’ Images Among Popular USA Middle Grades Science Textbooks

<p style="text-align: justify;">Research on students’ perceptions of scientists is ongoing, starting with early research by Mead and Metraux in the 1950s and continuing in the present. Continued research interest in this area is likely due to scholarship suggesting adolescents’ impressions of scientists are sourced in-part from media, which influence their interests in science and identity in becoming a scientist. A significant source of images, in which adolescents (or middle school students) view science and scientists, is in their science textbooks. A qualitative content analysis explored images of scientists in three of the major U.S.-based middle grade science textbooks published in the new millennium: sixth grade biology, seventh grade earth science, and eighth grade physical science. The Draw A Scientist Test (DAST) Checklist was employed to assess scientists’ images and the stereotypes therein. From nine textbooks, 435 images of scientists were coded and analyzed by publisher and grade level / area by DAST constructs of appearance, location, careers, and scientific activities. Statistical analyses showed significant variances between grade levels and textbook publishers of scientists. Despite scientists portrayed in active endeavors, traditional tropes of the scowling, older, solitary, white male scientist persist. This study offers insight in leveraging improved images of scientists in textbooks.</p>

Exploring Zimbabwean A-Level Mathematics Learners’ Understanding of the Determinant Concept

<p style="text-align: justify;">Learners bring prior knowledge to their learning environments. This prior knowledge is said to have an effect on how they encode and later retrieve new information learned. This research aimed at exploring ‘A’ level mathematics learners’ understanding of the determinant concept of 3×3 matrices. A problem-solving approach was used to determine learners' conceptions and errors made in calculating the determinant. To identify the conceptions; a paper and pencil test, learner interviews, and learner questionnaires were used. Ten learners participated in the research and purposive sampling was used to select learners who are doing the syllabus 6042/2 Zimbabwe School Examination Council (ZIMSEC). Data was analyzed qualitatively through an analysis of each learners' problem-solving performance where common themes were identified amongst the learners’ work. Results from the themes showed that Advanced level learners faced some challenges in calculating the determinant of 3×3 matrices. Learners were having challenges with the place signs used in 3×3 matrices, especially when using the method of cofactors. The findings reveal that learners had low levels of engagement with the concepts and the abstract nature of the concepts was the major source of these challenges. The study recommends that; teachers should engage learners for lifelong learning and apply some mathematical definitions in real-world problems. Teachers should address the issues raised in this research during the teaching and learning process. In addition, teachers should engage learners more through seminars where learners get to mingle with others from other schools.</p>

Alignment of the Philippine Mathematics Teacher Education Curriculum with the Programme for International Student Assessment

<p style="text-align: justify;">This study aimed to examine the alignment of the Philippine mathematics teacher education curriculum with the 2021 mathematics literacy framework of the Programme for International Student Assessment (PISA). Such study could inform the Philippine Commission on Higher Education (CHED) if its mandated bachelor’s degree in secondary education major in mathematics could produce teachers at the secondary level prepared to deliver the expectations of PISA to mathematically literate 15-year-old learners. Through document analysis, the researcher reviewed the alignment of two official documents accessible online: the 2017 Philippine mathematics teacher education curriculum and the 2021 PISA mathematics literacy framework. Three mathematics education experts validated the researcher’s analysis. The results revealed alignment of the content and competencies covered by the teacher education curriculum and PISA mathematics literacy framework. However, the researcher found gaps in the curriculum in terms of its responsiveness in capturing some contexts and 21st century skills emphasized in PISA 2021 mathematics literacy framework. The study provided recommendations in addressing the gaps to inform needed updating in the teacher education curriculum to meet the expectations of PISA as a step to meeting the international standards of quality educational program.</p>

The Effect of a Change in Virtual Learning Environment on Innovative Digital Teaching Practice: A Case Study of Academic Staff in an Irish University

<p style="text-align: justify;">This mixed-methods, investigative case study explores the experience of a virtual learning environment (VLE) change and its effect on the use of digital learning tools specifically, and teaching practice more generally, for chemistry lecturers at TU Dublin (Ireland) prior to pandemic of the coronavirus disease COVID-19. Initially, a questionnaire examined the different teaching identities the participating lecturers might have and how they relate to the literature. These identities were examined under the following themes: sense of achievement, motivational factors for innovation, innovation positioning, as well as social and organizational factors influencing the decision making. A visual approach of representing the questionnaire data, termed ‘Lecturer Landscapes’, was developed which uncovered new trends based on the biographical descriptors of the research population. Subsequent interviews led to a more detailed investigation of the themes noted in the questionnaire and the Lecturer Landscapes to more holistically capture the professional identity of each respondent. The lens of experience during a VLE change was used to frame each respondent’s professional identity in context. Overall, a VLE change does not have to effect teaching practice and can be experienced as a positive change in teaching and learning. It was also noted that innovation can only occur when specific, and individual, needs and problems are addressed and when personal development is promoted by intrinsic, rather than extrinsic, motivational factors.</p>

The Effects of Mathematical Modelling in Mathematics Teaching of Linear, Quadratic and Logarithmic Functions

<p style="text-align: justify;">This study aims to acquaint high school students with the process of modelling in mathematics teaching. The research lasted 5 weeks with a group of (N=36) high school students of Zenica-Doboj Canton (Bosnia and Herzegovina). Students had an opportunity to learn about functions and their properties, and subsequently about mathematical modelling with linear, quadratic, and logarithmic functions. Examples in the research were related to real-world phenomena and processes. The problems were composed of the following subtasks: creating or testing a model, explaining the results, finding the domain and range, and critical thinking about the model. The research identifies the importance of mathematical modelling in teaching. The results display a positive impact of such an approach on students, their thinking, attitude towards teaching, understanding of the materials, motivation and examination scores. The experiences that both students and teachers may have in a mathematical modelling framework could be extremely important for the academic success. A control group of 36 students took the final exam as well. The students of the experimental group got much better results than the students of the control group. Indeed, learning through mathematical modelling has been shown to contribute to all the aspects of students' expected development.</p>