Recently there has been a keen interest in the area of mathematics and finding the best methods of instruction. For instance, the No Child Left Behind Act (NCLB) has placed new levels of accountability on educators for the success of students with their education, especially in mathematics. Certain areas of mathematics, such as Algebra, have been known to challenge students to think abstractly. This has become a difficult task for educators to accomplish. The challenge of teaching algebra becomes apparent when students do not comprehend the abstract reasoning of algebra. Many students need help with the transition from numerical calculation to the abstract reasoning required for algebra. This dissertation focuses on the best approaches to helping students with this transition. This dissertation investigates a mathematics program called Hands-On Equations (HOE), which is designed to help students learn abstract concepts taught in algebra with less difficulty. The program concentrates on the transition from numerical calculation to abstract reasoning by utilizing manipulatives. The objective of the study is to investigate the effectiveness of HOE in 9 th and 10 th grade. The research uses three pretests, three posttests, a three week retention test, a six week retention test, and benchmark tests to evaluate the academic growth of students in two set groups. The collected data is then quantitatively analyzed by applying simple t-tests and an ANOVA. Analysis of the data endorses HOE as being effective with solving linear equations at Level 1, Level 2, Level 3, and with the three-week retention tests, which indicates HOE may be a positive factor in achieving success with linear equations. However, analysis of the data revealed HOE is not as effective with the six-week retention test or the benchmark test which indicates after six weeks and beyond, students do not retain the information to be successful on end of the year exams such as benchmarks. The findings from this study may be useful to educators who are contemplating implementing HOE or other such programs at their schools.
","abstract_html":"<p>Recently there has been a keen interest in the area of mathematics and finding the best methods of instruction. For instance, the No Child Left Behind Act (NCLB) has placed new levels of accountability on educators for the success of students with their education, especially in mathematics. Certain areas of mathematics, such as Algebra, have been known to challenge students to think abstractly. This has become a difficult task for educators to accomplish. The challenge of teaching algebra becomes apparent when students do not comprehend the abstract reasoning of algebra. Many students need help with the transition from numerical calculation to the abstract reasoning required for algebra. This dissertation focuses on the best approaches to helping students with this transition. This dissertation investigates a mathematics program called Hands-On Equations (HOE), which is designed to help students learn abstract concepts taught in algebra with less difficulty. The program concentrates on the transition from numerical calculation to abstract reasoning by utilizing manipulatives. The objective of the study is to investigate the effectiveness of HOE in 9 th and 10 th grade. The research uses three pretests, three posttests, a three week retention test, a six week retention test, and benchmark tests to evaluate the academic growth of students in two set groups. The collected data is then quantitatively analyzed by applying simple t-tests and an ANOVA. Analysis of the data endorses HOE as being effective with solving linear equations at Level 1, Level 2, Level 3, and with the three-week retention tests, which indicates HOE may be a positive factor in achieving success with linear equations. However, analysis of the data revealed HOE is not as effective with the six-week retention test or the benchmark test which indicates after six weeks and beyond, students do not retain the information to be successful on end of the year exams such as benchmarks. The findings from this study may be useful to educators who are contemplating implementing HOE or other such programs at their schools.</p>","abstract_has_math":false,"creators":["Jimenez, Amelia"],"institution":null,"degree_name":"Doctor of Education (Ed.D.)","degree_level":"Dissertation - Pacific Access Restricted","degree_discipline":"Educational Administration and Leadership","degree_department":null,"school":null,"contributors":["Dennis Brennan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T05:35:52Z","subjects":["Mathematics education","Mathematics teachers","Linear equations","Education","Hands-on programs","Manipulatives","Educational Administration and Supervision","Educational Leadership"],"languages":[],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["9781267217639"],"render_values":[{"text":"9781267217639","href":null,"code":true}]}]},"links":{"outbound_url":"https://scholarlycommons.pacific.edu/uop_etds/94","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dennis Brennan"]},{"key":"dc:creator","label":"Author","values":["Jimenez, Amelia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-06-29T08:55:23Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Educational Administration and Leadership"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation - Pacific Access Restricted"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Education (Ed.D.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics education","Mathematics teachers","Linear equations","Education","Hands-on programs","Manipulatives","Educational Administration and Supervision","Educational Leadership"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["9781267217639","https://scholarlycommons.pacific.edu/uop_etds/94"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Recently there has been a keen interest in the area of mathematics and finding the best methods of instruction. For instance, the No Child Left Behind Act (NCLB) has placed new levels of accountability on educators for the success of students with their education, especially in mathematics. Certain areas of mathematics, such as Algebra, have been known to challenge students to think abstractly. This has become a difficult task for educators to accomplish. The challenge of teaching algebra becomes apparent when students do not comprehend the abstract reasoning of algebra. Many students need help with the transition from numerical calculation to the abstract reasoning required for algebra. This dissertation focuses on the best approaches to helping students with this transition. This dissertation investigates a mathematics program called Hands-On Equations (HOE), which is designed to help students learn abstract concepts taught in algebra with less difficulty. The program concentrates on the transition from numerical calculation to abstract reasoning by utilizing manipulatives. The objective of the study is to investigate the effectiveness of HOE in 9 th and 10 th grade. The research uses three pretests, three posttests, a three week retention test, a six week retention test, and benchmark tests to evaluate the academic growth of students in two set groups. The collected data is then quantitatively analyzed by applying simple t-tests and an ANOVA. Analysis of the data endorses HOE as being effective with solving linear equations at Level 1, Level 2, Level 3, and with the three-week retention tests, which indicates HOE may be a positive factor in achieving success with linear equations. However, analysis of the data revealed HOE is not as effective with the six-week retention test or the benchmark test which indicates after six weeks and beyond, students do not retain the information to be successful on end of the year exams such as benchmarks. The findings from this study may be useful to educators who are contemplating implementing HOE or other such programs at their schools.
"]},{"key":"dc:source","label":"Dc Source","values":["114"]},{"key":"dc:title","label":"Title","values":["Hands-on equations program: An approach to teaching linear equations using manipulatives"]}]}],"canonical_facts":{"dc:contributor":["Dennis Brennan"],"dc:creator":["Jimenez, Amelia"],"dc:date.available":["2018-06-29T08:55:23Z"],"dc:description.abstract":["Recently there has been a keen interest in the area of mathematics and finding the best methods of instruction. For instance, the No Child Left Behind Act (NCLB) has placed new levels of accountability on educators for the success of students with their education, especially in mathematics. Certain areas of mathematics, such as Algebra, have been known to challenge students to think abstractly. This has become a difficult task for educators to accomplish. The challenge of teaching algebra becomes apparent when students do not comprehend the abstract reasoning of algebra. Many students need help with the transition from numerical calculation to the abstract reasoning required for algebra. This dissertation focuses on the best approaches to helping students with this transition. This dissertation investigates a mathematics program called Hands-On Equations (HOE), which is designed to help students learn abstract concepts taught in algebra with less difficulty. The program concentrates on the transition from numerical calculation to abstract reasoning by utilizing manipulatives. The objective of the study is to investigate the effectiveness of HOE in 9 th and 10 th grade. The research uses three pretests, three posttests, a three week retention test, a six week retention test, and benchmark tests to evaluate the academic growth of students in two set groups. The collected data is then quantitatively analyzed by applying simple t-tests and an ANOVA. Analysis of the data endorses HOE as being effective with solving linear equations at Level 1, Level 2, Level 3, and with the three-week retention tests, which indicates HOE may be a positive factor in achieving success with linear equations. However, analysis of the data revealed HOE is not as effective with the six-week retention test or the benchmark test which indicates after six weeks and beyond, students do not retain the information to be successful on end of the year exams such as benchmarks. The findings from this study may be useful to educators who are contemplating implementing HOE or other such programs at their schools.
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