This research study was built upon findings in neuroscience of the brain's natural ability to physically change itself through cognitive modifiability by creating new pathways and neural connections. The purpose of the research was to investigate instructional music applications for improvement in basic math skills with students who are on the autism spectrum and have intellectual development disorder with significant cognitive/language delays. Seventy-seven (N = 77) high school-aged students from a center-based special education program in Nassau County, Long Island, participated in this mixed methodology study. A purposeful sample of six students was selected for case studies from the research participants. The eight-week study took place over the last marking period of the school year, May-June 2013 in the principal investigator's music classroom. Pre-tests and post-tests were given in two areas: music aptitude and mathematics. The Primary Measures of Music Audiation (PMMA) was used to test music aptitude. The New York State Common Core Learning Standards Math and Music Data Sheets were used to record quantitative and prompting measures of teacher-designed math tests. The following research questions guided this study. Can music aptitude be measured in students with significant cognitive/language delays including autism spectrum disorders? How does rhythmic and tonal training help students with significant cognitive/language delay, including autism spectrum disorders, make developmental/academic gains in basic math skills? What does teaching and learning look like in a MLE (mediated learning experience) special education music classroom? What other cross-curricular academic benefits can be evidenced by student work to indicate higher levels of independent functioning and cognitive understanding? Research findings through both inferential statistical and descriptive analysis of data point towards student improvement with standards-based classroom music instruction taught through mediated learning experiences. Significant growth towards functional independence was seen in pre- and post-basic math counting skills. Educational implications of the research represent a paradigm shift for expectations of this student population. The research opens possibilities for alternate ways to teach and to interact with students with intellectual disabilities on the autism spectrum in order to increase their learning capacity to reach curriculum content expectations. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]