@ELCBK and others.  

Untrained small fingers have a difficult time holding down strings tuned to conventional a=440 hertz.  Tuning down to a=432 hertz or so makes playing a lot easier.  Ear training is much better if strings adjusted on the Pythagoras scale (you may need a smart phone app for this as most electronic tuners are programmed for chromatic scales).

A chin rest which centers the chin on the instrument (over the tail piece) maximizes the effectiveness for short arms.  A piece of foam held on with rubber bands makes for an excellent shoulder rest for the young.

If the child establishes an interest, replacing conventional pegs with planetary adjustment pegs (which also allows the removal of tail piece fine tuners) makes tuning faster and generally improves sound on a fractional sized instrument.  Your glasser violin has this type of peg (for comparison).  Even greater improvement can be gained by undersizing the tailpiece (1/2 sized on 3/4 instrument or similar).

It is difficult to obtain good sound from a small instrument.  Typical misadjustment of cheaper instruments (poorly shaped bridge, nut, and soundpost) can make the item unplayable.  Fiddlerman strings are a good upgrade from standard (make sure to get spare e strings).

The addition of note position fingerboard tapes is a hotly contested issue.  I do not see the harm.  Others do.

If paper business cards remain available, it is a good idea to test 90 degree angle bridge position with each tuning.

@ELCBK and others.  It would be useful if you took a photo of the bridge and space between fingerboard and strings (bass and treble sides).  A flat bridge makes for difficult bowing and too much string clearance makes it difficult to finger notes.

Small violins are very strong devices.  To not leave in a hot car or the glue will lose grip.  

@ELCBK and @Mouse et al.  I just began the book “measure for measure” by Thomas Levenson.  It is about the science of music.  The first nugget gleamed from the book involved a Norton Lecture at Harvard given by Leonard Bernstein.  It took a bit of investigation but I found the snippet of referenced lecture on YouTube.  

No clue on how to link it here but if you look up “the unanswered question 1973 1 musical phonology bernstein norton” by the submitter “cagin,” you will find it.  Advance video to the 30 minute mark and play until the 45 minute mark.  You will find a very clear demonstration of string overtones and the difference between Pythagorean and chromatic tuning (I brought cid into this because she thinks my stressing of Pythagorean tuning for string instruments is bunk).

@ELCBK and others.  Not particularly violin related, but this poem embraces the spirit of this thread.

To a Child

The greatest poem ever known,

Is one all poets have outgrown:

The poetry, innate, untold,

Of being only four years old.

Still young enough to be a part

Of nature’s great impulsive heart,

Born comrade of bird, beast and tree

And unselfconscious as the bee—

And yet with lovely reason skilled

Each day new paradise to build;

Elate explorer of each sense,

Without dismay, without pretense!

In your untainted transparent eyes

There is no conscience, no surprise:

Life’s queer conundrums you accept,

Your strange divinity still kept.

Being, that now absorbs you, all

Harmonious, unit, integral,

Will shred into perplexing bits,—

Oh, contradictions of the wits!

And life, that sets all things in rhyme,

May make you poet, too, in time —

But there were days, O tender elf,

When you were Poetry itself.

Christopher Morley, 1922