Esperanto

Studies over the decades have found:

1. Esperanto is faster to learn than other European languages (3 studies), and
2. On average Esperanto helps students learn European and Asian languages faster than studying those languages alone (4 studies)
   

The theory is that Esperanto's simplicity shows learners what the basic features are of any language.  Inexpensive courses are available for Esperanto, like other languages.

Alan J. Bishop, "Ekparoli Project Report" 1994 - 1997
angelfire.com/ok/andreo/ekparoli.report.html
web.archive.org/web/20040301110024/http://www.education.monash.edu.au/projects/esperanto/Ekrep97.htm

• 2 years of Esperanto, followed by a year of Japanese, Indonesian, French or German, leads to above-average knowledge of the final language

He reports on 23 students who studied Esperanto for the last 2 years of primary school, and 311 others who studied other languages. Then all studied Japanese, Indonesian, French or German for a year in secondary school. Secondary teachers said 9% of former Esperanto students were at level 5 of 5 in the final language, so were 32% of non-Esperanto students; 70% of Esperanto students were at level 4 or above, 58% of others; 4% of Esperanto students were at level 1 or 2 (worst), so were 19% of other students. So former Esperanto students were generally not the best or worst. No breakdown by final language was given, and no infomation on how many studied the same language in both primary and secondary schools (presumably some of these were in the 32% who did best).

Alvino E. Fantini, and Timothy G. Reagan, "Esperanto and Education: Toward a Research Agenda"
Sponsored by the Esperantic Studies Foundation 31 October 1992
http://web.archive.org/web/20010310011424/http://www.esperantic.org/esf/f-r2.htm#two

Fantini+Reagan report on several studies:

(A) Division of Psychology, Institute of Educational Research, Teachers College, Columbia University. 1933. "Language Learning: Summary of a Report to the International Auxiliary Language Association in the United States." New York: Bureau of Publications, Teachers College, Columbia University.

• "On the whole, with expenditures of from ten to a hundred hours, the achievement in the synthetic language will probably be from five to fifteen times that in a natural language, according to the difficulty of the latter." (p.7)

• "at the end of two years ... the French scores show 9.7 points more progress for the Esperanto group, which had studied French during one of the two years, than was made by the non-Esperanto group, which had studied French during the two years" (p.30)

Fantini+Reagan say, "While these results do appear to be impressive, it should be kept in mind that they were based on a very small sample, and that the study did not involve carefully maintained experimental and control groups. In fact, the authors of the report themselves were clearly very hesitant to draw any substantial conclusions from their data."

(B)  Halloran, J. H. 1952. A four year experiment in Esperanto as an introduction to French. The British Journal of Educational Psychology 22: 200-204.
Williams, Norman. 1965. A language teaching experiment. Canadian Modern Language Review 22, 1: 26-28.

Fantini+Reagan say, "Halloran did find that more academically gifted students tested slightly better in French if they had four years of French instruction rather than a year of Esperanto followed by three years of French. Williams (1965) argued, however, that Halloran's approach was actually biased against the Esperanto group, and that no students were disadvantaged by taking Esperanto first. Halloran and Williams both found that less academically able students benefitted from initial Esperanto instruction. Although a number of methodological problems and limitations in the studies of Halloran and Williams can be raised, it would appear that their results are for the most part reasonable representations of the Denton experience, and would tend to support the claims for the propaedeutic effects of Esperanto study, as well as those concerned with the positive effects of Esperanto study for special needs students."

(C) Sonnabend, Helmut. 1979. Esperanto: Lerneja Eksperimento. Pisa: Edistudio.

Fantini+Reagan quote Maxwell:

• German "Children learning Esperanto were able to learn more in two years than other [German] children learning English in three or four years . . . the Esperanto groups would require a total of 2.5 years to obtain 100% mastery of the material presented in this test, whereas the English groups would require 5.3 years to achieve a corresponding result." (p.58, Maxwell, Dan. 1988. "On the acquisition of Esperanto." Studies in Second Language Acquisition 10, 1:51-61)

Fantini+Reagan note: "This is especially impressive when one takes into account the fact that the Esperanto group were three to four years younger than the English group." [Others might wonder if starting younger contributed to the faster learning.]

(D)  A 1978-87 series of studies in Polish:

1. Frank, Helmar. 1987a. Propedeutika valoro de la internacia lingvo: Kibernetika teorio kaj empiriaj rezultoj de la lingvo-orientiga instruado de la Internacia Lingvo kiel bazo de pli posta lernado de etnaj lingvoj. In Serta Gratvlatoria in Honorem Juan Régulo, II (Esperantismo) (La Laguna: University de La Laguna), pp. 213-222.
2. Frank, Helmar. 1987b. Wartosc propedeutyczna jezyka miedzynarodowego. Miedzynarodowa Komunikacja Jezykowa/Internacia Lingva Komunikado: Materialy Konferencyjne -- IV. Lódz: Uniwersytet Lódzki, Zrzeszenie Studentow Polskich, Studenckie Kolo Naukowe Esperantystów, pp. 124-136.
3. Frank, Helmar. 1978. Grundlagen und sprachpädagogische Anwendung einer informationstheoretischen Transferanalyse. Grundlogenstudien aus Kybernetik und Geisteswissenschaft 19: 75-88.
4. Frank, Helmar. 1976. Mallonga enkonduko en la kibernetikan pedagogion/Kurze Einfuehrung in die Kybernetische Pädagogik. In H. Behrmann and S. Stimec, eds., Bildung und Berechnung/Klerigo kaj Prikalkulado (Alsbach: Leuchtturn-Verlag), pp. 9-55.
5. Frank, Helmar, and Barandovska, Vera. 1991. Lernpliffaciligo pro antaumetitaj lingvokursoj. Internacia Pedagogia Revuo 21, 4: 11-15.
6. Geisler, Evelyn. 1979. La unuaj mezuradoj pri la lernfaciligo internacia kaj angla lingvoj. Europa Dokumentaro 21: 9-10.  Meder, Brigitte. 1978. Efikoj de la lingvo-orientiga instruado al la lernsukceso en la mezgrada lernejo. Europa Dokumentaro 20: 15-18.
7. Meinhardt, Gard. 1978. Latent knowledge of vocabulary of the international language, arising from one's native language. Europa Dokumentaro 18: 13-15.

Fantini+Reagan report,

• "The results obtained by the researchers at the Instituto pri Kibernetika Pedagogio are of quite high quality, and generally appear to support both claims about the ease of learnability of Esperanto and claims about its propaedeutic benefits."

Other reports which I have not been able to find:

1958-63 Finnish students learning German faster by learning Esperanto first, than by just learning German . This would be significant, since Finnish is unrelated to both German and Esperanto.

• J. VILKKI (?), Vilko Setala, "La eksperimenta instruado de Esperanto en la Geknaba Mezgrada Lernejo de Somero" (Suomio). El Popola Åinio, 1963, n. 1, pp. 38-39.
• Vilko Setala, Vizito al la eksperimenta lernejo en Somero, Finnlando. Esperanto, June, 1961, 107 p.

1962-63 Hungarian students learned Esperanto more easily than Russian, German, or English.

• Istvàn Szerdahelyi, La didaktika loko de la Internacia Lingvo en la sistemo de lernejaj studobjektoj. In Esperanto: La internacia lingvo: sciencaj aspektoj, (editor: Detlev Blanke), Kulturbund der DDR, Berlin, 1979, p. 211-219.
• Günter Lobin, "Die Internacia Lingvo als Bildungskybernetisches Sprachmodell," p. 59.

A few other studies are listed in Wikipedia, without findings or citations. The list appears to be translated from an Italian original, or a French translation.