Mathematical learning supported by formative assessment: interactions among feedbacks, exploratory teaching and flipped classroom methodology
Formative assessment in mathematics; Feedback in mathematics; Exploratory Teaching of Mathematics; Flipped classroom; Learning mathematics
This research aims at investigating the processes involved in the resolution of mathematical tasks of a group of high school freshmen of a private school in Brasilia, rooted in continuous assessment through intentional and structured feedback, in the field of plane geometry learning following the flipped classroom methodology. The qualitative and exploratory case study was developed with forty-six learners ranging from 14 to 16 years of age. These students were assigned a set of plane geometry tasks along a period of 10 weeks of lessons with clearly defined goals to be achieved as well as the assessment criteria adopted. Their production was analysed and categorized as follows: unanswered task, task incorrectly answered, partially correct answered, correctly answered. Feedback was offered to students to help them overcome possible learning difficulties involved in the resolution of the tasks assigned. Learner’s production was analysed via content analysis: pre- analysis, exploration of the documents produced, data analysis and discussion. Initial observations showed that the learners were not used to studying with a view to building knowledge and sought teachers’ explanation to clarify their queries. Insecurity as to the procedures adopted in task resolution made the lacunae which called for intervention to foster learning. Geometrical knowledge with incorrect generalizations and algebraic obstacles constituted sources of analysis and debate during the development of the tasks. Using the flipped classroom methodology, students were motivated to do the tasks, individually at first. Gradually though, a collaborative network emerged converting the regular teacher-centered lessons into moments of dialogical learning, favoring the protagonism of learners in class. The diversity of pedagogical spaces and resources allowed for the existence of collaborative and democratic learning, in which continuous assessment made the resource to knowledge with a view to shedding light on the role played by mistakes in learning processes, the structured feedback to learning provided the learner the opportunity to effectively participate in all stages of learning and the teacher/researcher the possibility of reviewing his planning for every lesson, familiarizing himself with the strategies adopted by learners in the resolution of tasks and formulating intentional to every learner or group of learners in the name of learning mathematics. These observations revealed that the learning of mathematics is favoured when the continuous assessment methodology rooted in structured and intentional feedback is adopted in the flipped classroom.