Children can clap the beat to music when they can feel the pulse. This is an important part of being able to play with good rhythm. Clapping and dancing to the Suzuki music are natural ways for children to connect with the beat in the music they are learning to play. The twinkle variations are a wonderful way to learn to feel beat/rhythm with a good tone on just one note.  This is a good example of an integral learning experience where the student can feel the rhythm/beat, hear the tone, and connect this with the tactile sense in the finger. 

When we clap the beat to music we are feeling music that is already on the rhythm, already made.  This is much easier than creating the correct steady tempo oneself.   The ready position is the best way to enable the student to play with good beat.  This is because in ready position the body is balanced and still.  When a conductor is going to start an orchestra they first raise their hands in gesture to have everyone’s attention and stillness on the ready.  Next the conductor gives an indication of the rhythm with just one beat, such as an up feeling for example, and then the first sound is the down. Everyone can play together on the rhythm this way.  This is the “go” part of practicing with students.  Please observe in the lessons how to say go effectively so that the child can play with good rhythm.  The “go” needs to be in tempo of the piece.  This one signal teaches the child to play with rhythm.

When children first learn to play the right hand melodies in Book 1, they find the pitch (notes) first. They may be finding the correct notes totally by ear, or with the help of a parent singing the pitch. Part of this learning of the notes is getting the correct fingerings. Next, they can develop the ability to play the notes with the feeling of the rhythm.

Feeling deep and light sounds is important for the natural flow in the music in the same way that inflection is important in speech. The best way to help with this is to sing the pieces with a natural emphasis on the metrical placement (first beat in each measure) as well as the rising and falling of the melodic phrase.  A good way to practice is to sing along with the disc using the solfege, humming, or singing “la la la”.  So, the singing is not just for learning the pitch/notes, but also will help the child feel the rhythm, and connect with the broader feeling of the meter and phrases in the notes they are learning to play.
The phrases are the equivalent of sentences.
In this regard, words to the songs are ok to sing too, especially for fun while not at the piano.  It is best for children to understand the language of music without actual words.  So after the notes can be played with some fluency, singing along by humming/solfege/la-la as your child plays will help your child play in a good tempo which is not too fast or too slow, and has natural emphasis on the deep and light sounds, and breadth on the phrases.

When the teacher plays with the student at the lesson it also helps them to play with the steady rhythm.  This may be more difficult for them than playing by themselves because they have to keep the tempo on the “hard part”.  This process helps the parent and child understand where to focus more time and energy in the home learning. So, in the learning at home, please practice extra on the parts where the beat/rhythm is not felt.

Most importantly continued listening to a piece after the notes are learned is the most important tool for helping the child progress from just the notes to playing and feeling the rhythm. Lastly, it is important that the teacher and parent do not give the child too many instructions that may take away from their natural ability to feel the beat because they are thinking too much as they are playing. This way they can play by heart.

Related Post with more explanation of meter and research on babies and rhythm:

Twinkle Lessons:  On the Rhythm