There are several studies evaluating the effectiveness of in-office vision therapy vs pencil pushups. One such study revealed that after 12 weeks of therapy the convergence insufficiency score was significantly reduced in the in-office vision therapy group from 32.1 to 9.5. However, after 12 weeks of pencil pushups the convergence insufficiency score decreased from 29.3 to 25.9. It is of particular interest to note that pencil pushup therapy was found to be no more effective than the placebo therapy.
It is important to remember that the Convergence Insufficiency Symptom Survey used for the Convergence Insufficiency Treatment Trial established that a score of 16 or greater is considered significant for symptoms associated with Convergence Insufficiency. Comparing the established score of 16 to the score of 9.5 following 12 weeks of in-office vision therapy and to the score of 25.9 following 12 weeks of pencil pushups, it is easy to understand why pencil pushups are considered an ineffective form of therapeutic treatment.
Studies indicate that office-based vision therapy with home reinforcement is the most effective treatment for convergence insufficiency. Home-based treatment with pencil pushups hasn't been shown to be as effective. But home treatment costs less and is more convenient and more readily available.
The Effectiveness of Home-based Pencil Push-up Therapy Versus Office-based Therapy for the Treatment of Symptomatic Convergence Insufficiency in Young Adults: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4302485/
THE EFFECTIVENESS OF PENCIL PUSHUPS TREATMENT FOR CONVERGENCE INSUFFICIENCY: https://www.aaopt.org/detail/knowledge-base-article/effectiveness-pencil-pushups-treatment-convergence-insufficiency
Pencil Push-Ups Not Helpful for Convergence Insufficiency https://www.medscape.com/viewarticle/455363