"I used the Mally books for a while (although I found the way the instructions were set out a bit clumsy) and was very glad to have the technique of cross-row playing explained to me at an early stage - I've seen too many players who can't manage it because the single-row style of playing has become so habitual that it's difficult to unlearn later. I liked being able to get the "right" chords more easily."

Far be it from me to knock Mally, who is a good guy and whose books have set many beginners on their way. Nor to knock cross-row playing, which is vital technique that any good player should master. However, it is not necessarily the most appropriate technique for punchy English dance playing, and my experience with a good many students is the converse of the above, namely, that having learned cross-row style, they find it difficult to unlearn in order to get the rhythm they want. A morris dance musician, for instance, doesn't need to sacrifice rhythmic drive in order to achieve the "right" chords.

I would also suggest that the process of unlearning one style in order to accommodate a different one is a vital part of understanding the instrument properly. Learning an alternative fingering for a particular passage enables you to choose the kind of phrasing you need, or which chords you have available. So my schedule with a student (unless they were irreversibly committed to continental music) would be: learn 'along-the-row' playing, get it sounding rhythmic, tight and musical, and then learn cross-row.