Design, integration and assessment of mathematical investigations in secondary mathematics classes

The study designed, described, and analyzed the integration of mathematical investigation (MI) and its assessment in secondary mathematics classes. It adopted a qualitative research design in describing and analyzing the nature of the products and processes of MI and in documenting the experiences, constraints, challenges, and changes the teacher and students underwent in the process. Data were collected from two geometry classes and the mathematics teachers of Las Pinas East National High School in Las Pinas City however, data analysis was restricted to 22 students comprising two groups per class. The results of the study provided evidence to the conjecture on the interplay of factors in MI that was proposed in the framework. Further, the results suggested the inclusion of the students metacognitive ability and both the teachers and students communicative competence as factors in MI. To assess MI products and processes, a scoring framework and rubric were developed and validated in this study and a process for assessing MI was proposed. Results indicated that the teachers and students beliefs and attitudes came into play, and were challenged, as they engaged in MIs. Their attitudes towards MI were generally positive. On the average per task, each group of students posed three to four problems, which were generally highly original with moderate to high complexity. The proof schemes used by the students to prove their conjectures, improved with some training from examples-based to transformational in the numeric task. In the non-numeric tasks, students used mostly perceptual and examples-based proof scheme. Finally, the study proposed a design for the initial integration of MI in schools

Exploring mathematical investigations among selected students

An excellent activity that can develop students\u27 investigative skills, mathematical thinking processes and good mental habits is to engage them in mathematical investigations. Mathematical investigation is a sustained exploration of an open-ended mathematical situation where students investigate, look for patterns, explore possibilities and establish relationships. Two groups of freshmen students were given pre-activity and post-activity interviews regarding their views in doing mathematics. The activity consisted of a mathematical investigation task, the task being complex, gave students opportunities to make their own decisions of which particular situation to explore. Both groups made choices that are consistent with established truths and from their existing knowledge, they were able to construct new ones through reasoning and argumentation, and through deliberate application of problem-solving strategies. Students in both groups went through the creative and inventive phases and writing their report on the activity through collaborative learning. They were able to negotiate the task requirements with their peers and the teacher. Through relating their ideas to others, they were able to internalize and transform learning into something that has personal relevance and meaning. Moreover, they also developed their social skills and dispositions such as respect for others, reliance on others for assistance and sensitivity to, group discussions. After doing the mathematical investigations, the participants had a change of views regarding doing mathematics. Instead of viewing mathematics as a body of facts and formulas, they view mathematics as a growing and dynamic body of knowledge. Observations from their activity and the analysis of their output in the given task indicated that they used scientific method and inquiry. Steps and processes in doing mathematical investigations were evident as students investigated the situation, formulated problems and conjectures, verified relationships, were able to explain and justify conjectures, and reorganized or synthesized these conjectures with previous results already established

Futures for Post-Pandemic Mathematics Teacher Education: Responsiveness and Responsibility in the Face of a Crisis

COVID-19 has caused unprecedented disruption to mathematics teacher education worldwide. This paper is anchored in our learnings from the experiences of teacher educators at four major universities from the Association of Southeast Asian Nations as they dealt with changes in their programs’ delivery triggered by the pandemic, and raises challenges that remain for the futures of post-pandemic mathematics teacher education. Here, we use the two ethical constructs of responsiveness and responsibility to guide actions in response to a crisis, in order to discuss a range of decisions the participants made to respond to the crisis. Behind their initial response to the emergent conditions, the participants were concerned about maintaining the continuity of their students’ education. Further, we identify remaining challenges for mathematics teacher educators to re-imagine their curriculum, teaching, assessment, and equitable access towards a more relevant, productive, and equitable mathematics teacher education. This study adds to the rapidly increasing literature on the effect of the pandemic on mathematics education in the following three ways: (1) here we take a comprehensive view of the disruptions instigated by the pandemic;, (2) we pay special attention to issues of equity; and (3) we address concerns about possible and desirable post-pandemic futures

Towards developing science of survival (SOS) pamphlets for typhoon, flashflood, storm surge and tsunami for earthquakes and their aftermath: A pilot study

The catastrophic devastation from recent natural calamities in the Philippines such as Typhoon Yolanda and Central Visayas earthquake in 2013 had made disaster preparedness a primary concern in the country. Prompted by the critical need to use science to save lives, this study developed Science of Survival (SOS) pamphlets titled When the Wind Rages and Water Rises: A Science of Survival Pamphlet for Typhoon, Flashflood, Storm Surge and Tsunami and When the Earth Moves: A Science of Survival Pamphlet for Earthquakes and Their Aftermath (Liquefaction, Fire, Landslide and Tsunami). The study used the` developmental research design consisting of three phases: needs and context analysis phase, design, development and formative evaluation phase, and semi-summative evaluation phase. By carefully documenting the iterative process of analysis, design, evaluation and revision, insights were sought with regard to the development of pamphlets that provide useful and scientifically accurate information about surviving natural calamities such as typhoons and earthquakes. Experts from government agencies involved in disaster risk reduction and management, science experts in the university, and students who were victims of major disasters reviewed and evaluated the pamphlets. The results of the semi-summative quantitative evaluation showed that both pamphlets are highly acceptable as supplementary resourc