• Tutoring

    The PhilScience online tutoring program for the conceptual understanding of mathematics complements class teaching in the conceptual-explicative aspects, with the goal of full understanding. Our tutoring sessions insist on conceptual understanding as well as explanation and justification of the concepts and procedures. Our instructors are licensed in mathematics, with competencies in the methodology of teaching mathematics, fundamentals of mathematics, and epistemology and philosophy of mathematics.

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  • Problem solving

    Get your homework done while understanding and learning mathematics! The solutions are explained entirely in detail, with respect to theoretical framing, application of procedures, strategy of solving, recalling the concepts and theoretical results that are used. The solutions are such edited for the pedagogical content to can be separated from the formal-mathematical solution. A fully explained solution is equivalent to a classical tutoring session with respect to the knowledge you gain.

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Course for teachers

Our course Conceptual-holistic knowledge for teaching school mathematics is addressed to mathematics teachers of any professional level, for improving the quality of the teaching of school mathematics – in both official school institutions and in private tutoring – in regard to the conceptual understanding of mathematics on the basis of scientific criteria targeting content and didactical methods as well. Attendance in this course also ensures eligibility for the position of PhilScience math tutor.

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Online tutoring for conceptual understanding of mathematics

Learning starts with conceptual understanding and progresses only along with it. However pragmatic the goals of learning might be, the lack of understanding of the discipline being taught – in detail and as a whole – will sooner or later have implications for acquiring the knowledge, communication, and application of that knowledge. We have to follow the ideal path, not the pragmatic one. Mathematics is indeed a complex discipline, but it is not incomprehensible because we are biologically built to understand it. Let the experts guide your child's path to understanding mathematics! Register for PhilScience tutoring!

About mathematics, mathematics education, and understanding mathematics

  • The actual state of mathematics education

    Mathematics education poses the greatest challenge worldwide. Traditional teaching methods as well as curriculum development have proved ineffective for the majority of students – and this has been true for generations. [...]

  • What is mathematics? Can anyone understand it?

    Nobody has offered a precise definition of mathematics which reflects its nature and its entire specificity among the other disciplines – neither mathematicians nor philosophers. Therefore, we should not wonder much when our child does not understand a great deal from math class. But we must ask what the student is being taught and how it can ensure an adequate understanding. [...]

  • Theory, principles, research, and application

    Research from education sciences has not shaped a unitary concept of mathematical understanding because it has kept the same separation between the conceptual and procedural aspects of teaching mathematics. Both inter- and trans-disciplinary research pursued by mathematicians and philosophers have concluded, even since the 1990s, that [...]

  • A guide to conceptual understanding of mathematics – for students and teachers

    [...] a didactical unit conceived as a starting point and orientation guide to acquiring a holistic understanding of mathematics (for the student), and (for the teacher) a conceptual-epistemic approach to teaching in which conceptual understanding is as important as applicative-procedural skills.

  • • News and announcements

    - The course for teachers is presently being developed, and we take registrations for the first series of students. We estimate the start of the course for April 2021.

  • Articles