How to teach Logic

Hi Rose,

CM’s schools covered logic in formal geometry (called ‘Euclid’ on the timetables) beginning in Form III (Year 7).  Years 7 & 8 had one 30-minute lesson taking place every Friday with an additional 10 minutes if the school ran on Saturday, perhaps to finish up or go over work begun the day before.  From Year 9 through the remainder of their schooling Geometry  was increased to two thirty-minute lessons.  Years 7 and up also had ten minutes a week of recitatation of Euclidian proofs.

Practical Geometry (inductive reasoning) came before Formal Geometry (deductive).  It’s study took place once a week in Form IIA (approx. our grades 5 & 6) which provided some foundational ideas to be developed later, gaining a child’s interest in the study, as well as training some physical and mental habits while learning to work with mathematical tools.

The Formal Geometry was not all proofs though as, when I went through the books Charlotte used, it appears the knowledge was then applied in practical exercises alongside deductive ones.  This, coupled with short histories of leading thinkers, ensured the “living” treatment we think of with CM math.

If I get the chance, I will tell you what this looks like as played out in our home.

Best,

Richele

Hi Rose,

Logic looks quite differently played out in a Charlotte Mason education because her starting point begins with the way of the will rather than reason and she also believed the reasoning powers in children do not wait upon our training.

Your arrival at a right destination does not depend upon your choice of a good road, or upon your journeying at a good pace, but entirely upon your starting in the right direction (Vol. 4, p. 64).

Charlotte Mason’s “A Philosophy of Education” includes Chapter 8,  “The Way of the Will”, and Chapter 9, “The Way of Reason”, if you want to have it straight from the source.  A very good overview of this and how it can look  practically in one’s home school can be heard in the “A Delectable Education” podcast, The Way of the Will and the Way of Reason.   SCM also has a very encouraging and free ebook on The Way of the Will.

You can see its import to Charlotte as it is addressed in Principles 17 and 18 of her 20 Principles.

The way of reason: We teach children, too, not to ‘lean (too confidently) to their own understanding’; because the function of reason is to give logical demonstration (a) of mathematical truth, (b) of an initial idea, accepted by the will. In the former case, reason is, practically, an infallible guide, but in the latter, it is not always a safe one; for, whether that idea be right or wrong, reason will confirm it by irrefragable proofs (Principle 18).

When we speak of logical demonstration of mathematical truth, it was taught in her schools through proof-based Geometry.  Since her math was “living” it was found helpful in the elementary years to teach paper sloyd as it helped with neatness, accuracy and measuring; additionally, ideas of distance and direction came from their hours out-of-doors and their early geography lessons.   I spoke of practical geometry leading into the formal study already.  We begin proof-based geometry this year with our eldest son and have chosen Harold Jacob’s “Geometry:  Seeing, Doing, Understanding” but so far, I can only tell you that is our choice as we have yet to see how that goes.  It appears that Jacobs presents the subject in a lively and logical fashion that leads a student through in a way that one should not get lost.  Ask Dr. Callahan has dvd’s that go through the Jacobs’ book but I haven’t used them so can’t speak to them.

Anyhow, I hope this helps some in your quest.

Warmly,

Richele