This study examined the relationship between maternal education, the home environment, educational expectations and children’s math skills. The aim of this research was to determine how well these measures individually and collectively explained the variation in children’s mathematical achievement at the start of kindergarten. This analysis was done within the context of the unique biological mother-child relationship, how frequently they engaged with their children in shared activities at home, the warmth of their relationship with their children, their perspectives on parenting, and finally their aspirations for their children’s educational attainment. Relying on a large, nationally representative sample of 10,863 biological mothers and their children, this study found a persistent and moderate association between maternal education and children’s mathematical skills, even after adjusting for both the home environment and educational expectations measures, and several other select maternal, child, and family characteristics. The home environment, measured by maternal self-reports of the frequency of engagement in eight pre-selected activities and by maternal self-ratings of the warmth of the relationship with their children, was addressed using Principal Component Analysis. The findings in this area were mixed. A higher self-reported frequency of time spent playing games, talking about nature, playing with construction toys, and helping with arts and crafts was positively linked to children’s early math achievement. The frequency of shared book reading, storytelling, and working with numbers was negatively linked to children’s mathematical achievement. Both of these effect sizes were statistically significant, yet quite small. No relationship was found between maternal warmth and children’s mathematical skills or between parenting perspectives and children’s math achievement. The findings also demonstrated a small, positive association between maternal expectations and children’s mathematical achievement. Children whose mothers believed they would graduate from college or beyond had stronger math skills than those whose mothers expected them to experience some college. This finding was more pronounced among mothers from different cultural backgrounds. The continued significance of both the maternal education and maternal expectations effects helped to explain some of the variation in children’s math achievement and contributed to the important research aimed at reducing these gaps early in children’s formative education.

In this investigation an attempt was made to determine how learners and teachers use computers in the teaching and learning of hyperbolic graphs in Mathematics. A comprehensive literature study showed that there are many benefits in using computers to study Mathematics. The investigation was done in two phases. In the first phase, a questionnaire was given to learners. The second phase involved interviewing learners and teachers. Findings indicate that learners and teachers enjoy using computers in the teaching and learning of Mathematics. Analysis of the results shows that the use of computers in teaching and learning of Mathematics, in particular the teaching and learning of hyperbolic graphs is beneficial. / Mathematical Sciences / M.Sc. (Mathematics Education)

In three experiments, I first examined the correlation between the presence of transformation of stimulus function (TSF) across computation and the presence of TSF across saying and writing for spelling words, and then tested the effects of the establishment of TSF across saying and writing on the establishment of TSF across math operants. Eight middle school students with learning disabilities participated in experiments I and II. All participants demonstrated reader/writer and math skills such as textual responding and using counting strategies to solve one-step word problems. Four of the eight participants also demonstrated TSF across saying and writing for spelling. The dependent variables of Experiment I were the accuracy and fluency of solving word problems after receiving fluency training on math facts, as well as the number of counting strategies used when solving word problems. Results showed that all participants with TSF across saying and writing for spelling demonstrated significant increases in both their accuracy and fluency when responding to word problems (i.e., ES = 1) whereas participants who did not demonstrate TSF across saying and writing for spelling demonstrated minimal gain from accuracy and fluency training of math facts (i.e., mean ES = 0.3). Experiment II tested the effects of fluency and accuracy training of word problems on the accurate and fluent responding to math facts and other math operants. Results showed that accuracy and fluency training had large effects on all participants (i.e., ES = 1). Participants who did not demonstrate TSF also demonstrated larger improvement (i.e., ES > 0.67) compared to Experiment I. The results of Experiments I and II demonstrated an association between TSF across math operants and TSF across saying and writing for spelling. Experiment III further tested for a functional relation by examining the effects of the establishment of TSF across saying and writing for spelling on the establishment of TSF across math operants with three of the participants who did not demonstrate TSF across saying and writing for spelling in the first two experiments. Upon establishment of TSF across saying and writing for spelling words, all three participants demonstrated TSF across math operants (i.e., increased accuracy and fluency of word problems, extinction of counting strategies). The results of the three experiments suggest the importance of teaching math as a verbal behavior, more specifically, as a speaker-as-own-listener behavior instead of as visual match-to-sample repertoires. Future replication of the procedure is needed to extend the external validity of the current experiments.

Close to a decade ago Hong Kong completed the implementation of a New three-year Senior Secondary (NSS) curriculum by introducing the Hong Kong Diploma of Secondary Education (HKDSE) examination. Because mathematics is one of the core subjects intricately involved in this education reform, it is necessary to evaluate the connection between the Hong Kong S1 – S6 mathematics curriculum and the mathematics compulsory portion of the HKDSE examination. A curricular alignment study can provide insight to policymakers, students, teachers, and schools concerning agreement between the intended curriculum and the assessed curriculum. This research study adopted a combination of criteria from the Achieve’s alignment protocol and Webb’s alignment method to determine the alignment between the Hong Kong S1 – S6 mathematics curriculum and the mathematics compulsory part of the 2018 HKDSE examination. A panel of three mathematics educators identified the assessment item/learning objective match, classified the content centrality value of each match, and identified the Depth of Knowledge of each assessment item. The alignment results indicate a wide range from no to strong indication of alignment between the Hong Kong S1 – S6 mathematics curriculum standards and the 2018 HKDSE examination. Areas of misalignment were found within the Measures, Shape and Space strand and the Data Handling strand of the Hong Kong S1 – S6 mathematics curriculum, where both show deficiencies in meeting the minimum benchmark for the categorical concurrence and the range of knowledge correspondence.

The purpose of this research study was to increase the overall achievement gains of my students who are currently receiving overall grades below a 69% in my middle school mathematics class by promoting parental involvement. The purpose of my action-research study was to answer the following three research questions: 1. What changes occur in students‟ test scores and overall grades when a variety of parental contacts are made over a six-week period? 2. How can I promote parental involvement? 3. What can I do to educate parents on how to become more effectively involved in their child‟s education? To answer these questions I selected ten parents, whose children were currently receiving grades below a 69% in 7th grade mathematics and who have not contacted me after the first nine weeks of the semester. I used three different methods to contact the parents, phones call, emails, and notes in students‟ planners. All three methods showed a lack of parental feedback and involvement. Nevertheless, five students showed an increase in the second marking period, four showed a decrease, and one stayed the same.

published_or_final_version / Education / Master / Master of Education

This multiple case study investigated pedagogical differences and similarities among practices used to teach word problems in private schools of Turkey and the United States, the factors impacting teachers’ instructional decisions, and their approaches to teaching word problems as well as the role of culture in teaching and learning word problems. Quantitative survey data were collected from 28 Turkish and 27 U.S. high school mathematics teachers from private or independent schools. The survey investigated teachers’ background information, resources used, and their use of teaching practices (teacher-centered, student-centered, concrete-visualizing, analytical) and types of word problems (true or practice-oriented) as well as their thoughts about the structure of word problems. Qualitative data were collected through classroom observations, videotaping, and focus-group interviews from four ninth grade algebra teachers in Turkey and the United States. Qualitative data helped the researcher expand upon the quantitative findings and examine how word problems actually were being taught in the classroom, the factors impacting teachers’ instruction and approaches to teaching word problems, and participants’ reflections on their own practices as well as on their international partners’ word problems instruction. The findings indicated no significant difference for most survey items, but descriptive statistical analysis revealed that Turkish survey participants incorporated teacher-centered, concrete-visualizing practices, and practice-oriented word problems more often in their instruction, while U.S. survey participants frequently used student centered, concrete-visualizing practices, and true problems. Qualitative findings pointed out what specific teaching practices were evident in the classrooms observed and videotaped in Turkey and the United States. While Turkish teachers thought the university entrance examination and national curriculum had the biggest impact on their teaching, U.S. teachers found school environment (traditional versus progressive) and student perception of word problems as influential on their instruction. The role of culture on teaching and learning word problems was observed in regard to teacher centered versus student-centered instruction, teacher versus student role, and student engagement. Study findings also indicated that cross-examination of teaching promotes teachers’ reflection on their own practices and, thus, should be encouraged and promoted across STEM disciplines and throughout a teaching career. Implications and recommendations for future research, curriculum developers, and mathematics teachers are discussed. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

published_or_final_version / Education / Master / Master of Education

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Text in Afrikaans / 'n Leerling se wiskunde-selfkonsep wys heen na die konsep wat hy van homself op wiskundige vakgebied het. Die kwaliteit van hierdie konsep word bepaal deur die kwaliteit van sy eie betrokkenheid by, belewing van en sin- en betekenisgewing aan wiskundige vakinhoud. Wanneer die kwaliteit van 'n leerling se wiskunde-selfkonsep ontoereikend is, word sy onvermoe om op daardie tydstip sukses op wiskundige vakgebied te behaal, geopenbaar. Dit plaas die opvoeder voor die opgawe om bemoeienis met die leerling te maak en hom ten aansien van sy probleem te help. In die lig hiervan is 'n hulpverleningsprogram ter bevordering van die wiskunde-selfkonsep ontwerp. Aangesien leerlinge in Suid-Afrikaanse skole tans gedurende die st.7-skooljaar die besluit neem om die studie van wiskunde te staak of daarmee voort te gaan, is die inhoud van die program derhalwe op die st.7-leerling van toepassing gemaak. Spesifieke doelsteilings wat in die ontwerp van die program nagestreef is, is die volgende: Om die leerling te begelei tot insig in en die begryp van die kwaliteit van sy eie wiskunde-selfkonsep en grondliggende oorsake vir die vorming daarvan, ten einde hom in staat te stel om sy eie situasie in perspektief te plaas. Om die leerling te begelei tot die ontwikkeling van spesifieke vaardighede aan die hand waarvan hy homself op 'n meer selfstandige wyse kan handhaaf ten aansien van die begripmatige bemeestering van wiskunde as vak. By wyse van 'n loodsondersoek is die toepasbaarheid van die onderhawige program ondersoek. Uit die terugvoergesprekke met die leerlinge tydens die groepsessies en die inligtingstukke wat hulle voltooi het, blyk dit dat hulle baat gevind het by hulle deelname aan die program. Met die oog op moontlike toekomstige navorsing is spesifieke leemtes ten opsigte van die onderhawige studie uitgelig en aanbevelings gedoen wat as verdere riglyne geimplementeer kan word. / A pupil's mathematical self-concept is the concept a pupil has of himself in the sphere of Mathematics as a subject. The quality of this concept is determined by the quality of his own involvement in, live-experiencing of, and significance attribution in respect of mathematical subject content. When the quality of a pupil's mathematical self-concept is inadequate, his inability is manifested in his failure to master Mathematics as a subject. This confronts the educator with the task of becoming involved with the pupil and helping him with his problem. In view of this, an aid programme was designed to improve the mathematical self-concept. Owing to the fact that, at present, pupils in South African schools have to decide during their Std 7 school year whether they are going to continue with their study of Mathematics or discontinue these studies, the content of the programme was aimed at the Std 7 age group. The following are the specific aims that were pursued in the designing of the programme: To guide the pupil to insight in and understanding of the quality of his own mathematical self-concept and its underlying causes, in order to enable him to place his own situation in perspective. To guide the pupil in the development of specific skills to help him cope more independently with the successful mastery of Mathematics as a subject. The possibility of implementing such a programme in practice was established by means of a pilot investigation. From feedback discussions with the sample group during group sessions and from questionnaires they filled in, it appears that they benefited from their participation in the programme. With a view to possible future research, specific shortcomings with respect to the investigation were highlighted and recommendations made which can be implemented as further guidelines. / Psychology of Education / M. Ed. (Sielkundige Opvoedkunde)