This project is dedicated to the enhancement of mathematics education through interdisciplinary theoretical contributions regarding a conceptual-holistic understanding.
The project is led by Dr. Cătălin Bărboianu with the support of the Theoretical Philosophy Department of University of Bucharest. PhilScience tutors are certified in mathematics, with competencies in the methodology of teaching mathematics, fundamentals of mathematics, epistemology, and philosophy of mathematics.
How we proceed, what we do, and what we don't do
Tutoring sessions run on the internet (on specialized platforms) in groups of a maximum of five students. A tutoring session consists of two consecutive 40-minute segments running as closely parallel as possible with the school math classes.
Tutoring for conceptual understanding of mathematics does not follow the pattern of the traditional math tutoring, but rather, it supplements the class teaching in content and helps to overcome the methodological deficit by aiming for complete understanding. Our tutoring sessions insist on conceptual understanding, explication, and justification of the concepts and procedures. Thus, within the sessions we do not teach exclusively problem-solving and do not concentrate on the homework entirely (but we do explain procedures and steps of the solutions or proofs; tips and progressive solutions for the homework problems are also offered).
Problems and exercises are solved entirely in the complete conceptual explanation mode. This mode applies to the formal-theoretical part employed (by recalling the definitions and properties of the mathematical concepts involved in their applicative aspects), the solving procedures (by explaining and justifying each step and method used), and the contribution of that problem to previous mathematical knowledge (generalizations, particularizations, special cases, examples and counterexamples, relationships with other mathematical concepts learned or subsequently to be taught, distinctions from similar problems, etc.). During the period of tutoring, periodic tests are scheduled to evaluate both conceptual-theoretical understanding and procedural and problem-solving skills.
The principle driving the collaboration between teacher and student is to offer guidance for the student toward a conceptual clarification which will ultimately induce the procedural skills necessary for becoming an autonomous problem solver; these latter skills are consolidated through personal training and in class. If a student is able to "do" mathematics while understanding it, s/he will do it eventually without direct help, this status of independence being in fact the ultimate target of this approach.
For the students/parents who still want that additional teaching of mathematics to concentrate on problem solving, or do not want to attend tutoring sessions, we offer the service of problem solving with fully explained solutions.
How it works
To participate in a tutoring group, you must first choose your preferred instructor from the availability table, where you may also view the CVs of the listed instructors. After the first two sessions, the instructor may propose regrouping the students in order to have students of about the same level within the same group.
A daily full tutoring session consists of two consecutive 40-minute segments, according to the schedule established by the instructor.
A daily full session of tutoring assumes three stages: the first stage consists of explaining those concepts and procedures taught in class, with the goal of holistic conceptual understanding (teaching stage); the second stage consists of a round of questions posed by the student with regard to the aspects still not understood from the class, as well as from the current tutoring session (the clarification stage);
the third stage is dedicated to problem solving and applications, explained in their conceptual and procedural aspects (the application stage).
Evaluation tests will be given approximately every two weeks and will be followed by personalized recommendations for improving the student’s results.
The minimum computer requirements are: video camera and microphone, operating system Windows 7 or higher, e-mail address, a Google account, MS Word, and Adobe Reader. .