Scientific Research

–The whole story. 

An exper­i­men­tal study on The Expert Math­e­mati­cian is reviewed on the US Depart­ment of Edu­ca­tion’s “What Works Clear­ing­house” web­site (click for report).

The study, con­duct­ed over the major­i­ty of a school year, com­pared a com­put­er-medi­at­ed “gen­er­a­tive learn­ing” intervention–The Expert Math­e­mati­cian (TEM)–vs. the UCSMP Tran­si­tion Math­e­mat­ics text­book-based pro­gram. The two treat­ment groups of ran­dom­ly assigned stu­dents were taught by the same teacher, using a block sched­ule model.

While stu­dents were not offi­cial­ly receiv­ing spe­cial ed. sup­port, the teacher indi­cat­ed that most were “at-risk” for aca­d­e­m­ic fail­ure, though tech­ni­cal­ly, they were “main­streamed.”

Achieve­ment vari­ables. Stu­dents’ acqui­si­tion of con­cep­tu­al knowl­edge as mea­sured on a stan­dard­ized math­e­mat­ics achieve­ment test was the main research inter­est. Stu­dents in both the exper­i­men­tal treat­ment and con­trol groups achieved sta­tis­ti­cal­ly sig­nif­i­cant gains on con­cep­tu­al mea­sures.. There was no sta­tis­ti­cal­ly sig­nif­i­cant dif­fer­ence between posttest scores for the two com­par­i­son groups, though raw gains showed an 18% increase for the text­book group, and 29% for the TEM group–the dif­fer­ences owing to much low­er pretest scores for the TEM group. Females were over­rep­re­sent­ed in the TEM treat­ment, and account­ed for both low­er pretest scores and high­er total gains than the males in their group. The pretest dif­fer­ences raise a valid­i­ty issue that is addressed in the final analy­sis by redis­trib­ut­ing pretest scores to equal­ize pretest totals in both groups–here, elim­i­nat­ing gain differences.

The find­ing that stu­dents in the TEM group came from behind to equal­ize total achieve­ment with the well-regard­ed Tran­si­tion Math­e­mat­ics con­trol treatment–while exper­i­men­tal­ly inadmissable–should not be dis­re­gard­ed. In fact, the nov­el inter­ven­tion group did accom­plish more than the tra­di­tion­al group in the same time peri­od with the same teacher who was wide­ly expe­ri­enced in and enjoyed teach­ing the Tran­si­tion Math­e­mat­ics program.

From a sci­en­tif­ic point of view, even after covary­ing out pretest dif­fer­ences, TEM passed a crti­cial test of sci­en­tif­ic mer­it: “First do no harm.” Although the teacher had no pre­vi­ous teach­ing expe­ri­ence with the TEM pro­gram, the pro­gram’s “pro­duci­tiv­i­ty” equaled that of a high­ly regard­ed pro­gram in which the teacher was trained and experienced.

The Depart­ment of Edu­ca­tion review also does­n’t report affec­tive data, which was con­sid­ered by the researcher an impor­tant part of this study.

A 7 dimen­sion atti­tude sur­vey probed stu­dents’ changes on a vari­ety of psy­cho­log­i­cal and social mea­sures relat­ing to the study of math­e­mat­ics at the then present time and into the future. While fur­ther devel­op­ment of a sound inter­pre­tive frame­work for these affec­tive mea­sures would be use­ful, the find­ing that the TEM media—which afford­ed stu­dents greater per­son­al con­trol over the hard work of learning—is viewed by stu­dents as sig­nif­i­cant­ly more favor­able than those that offers less con­trol, has impor­tant impli­ca­tions for study.

Total Scores on Math­e­mat­i­cal Con­cepts and Gain Scores on Atti­tudes About Study­ing Math­e­mat­ics Concepts.