the assumption of lecturers studying via educating (LTT) – while awarded to a naïve bystander – seems to be as an oxymoron. Are we now not imagined to study ahead of we train? finally, lower than the standard situations, studying is the duty in case you are being taught, now not of these who train. in spite of the fact that, this e-book is set the training of lecturers, now not the educational of scholars. it truly is an historic knowledge that how to “truly examine” anything is to educate it to others. however, as soon as a instructor has taught a selected subject or idea and, for this reason, “truly realized” it, what's left for this instructor to profit? As obtrusive during this publication, the event of training offers lecturers with a thrilling opp- tunity for studying all through their complete profession. this suggests buying a “better” figuring out of what's being taught, and, additionally, studying various new issues. What those new issues can be and the way they're discovered is addressed within the number of chapters during this quantity. LTT is stated by means of a number of researchers and arithmetic educators. within the rst bankruptcy, Leikin and Zazkis overview literature that acknowledges this phenomenon and rigidity that just a small variety of experiences attend systematically to LTT p- cesses. The authors during this quantity purposefully research the instructing of arithmetic as a resource for academics’ personal learning.