The main purpose of the study was to investigate the effects of a dynamic instructional environment (based on use of Geometer&rsquo / s Sketchpad) on 7th grade students&rsquo / understandings of lines, angles, and polygons and their retention. Besides that, the students&rsquo / attitudes towards computer instruction and its relation with students&rsquo / performance on geometry and retention were investigated. The study was carried out with 63 7th grade students from two classes taught by the same teacher in a state elementary school. One class was assigned as the experimental group (EG), the other as the control group (CG). Students in CG received the instruction on lines, angles, and polygons by the regular traditional method used at the school. In the EG, students worked on the computer activities named as &ldquo / Sketchsheets&rdquo / , prepared by the researcher, with computers provided at the computer-lab. The usage of GSP with Sketchsheets enabled students to create the shapes first and after they explored and discovered the properties of shapes and make generalisations for the development of conjectures. Geometry Performance Test (GPT) and Computer Attitude Scale (CAS) were used in this study. The GPT was administered to both groups of students as a pre-test, post-test, and a delayed post-test. CAS was administered only to the EG students as a post-test. Furthermore, interviews were carried out with three students from EG in order to get their feelings about the dynamic instructional environment. Besides that, both of these classroom and computer sessions were observed and recorded with camera. The results of t-test suggest that GPT mean scores in EG and CG did not significantly differ in pre-test, but EG achieved significantly better than the CG in post and delay-post tests. CAS mean scores and interviews showed that students had positive feelings and decisions towards computer instruction and they preferred computer instruction to traditional instruction. Furthermore, Pearson product-moment correlation coefficient was performed in order to investigate the relationship between GPT scores and CAS scores. From this analysis, a significant correlation was observed between the GPT scores and CAS scores. This means that the students who had positive attitudes towards computer instruction, achieved significantly better at GPT. The results of this study revealed that Geometer&rsquo / s Sketchpad for learning and teaching geometry in elementary school level is an effective tool.

In this quantitative study, the relationships between high school students' preference for solution methods, geometry performance, task difficulty, and gender were investigated. The data was collected from 161 high school students from six different schools at a county located in central Florida in the United States. The study was conducted during the 2013-2014 school year. The participants represented a wide range in socioeconomic status, were from a range of grades (10-12), and were enrolled in different mathematics courses (Algebra 2, Geometry, Financial Algebra, and Pre-calculus). Data were collected primarily with the aid of a geometry test and a geometry questionnaire. Using a think-aloud protocol, a short interview was also conducted with some students. For the purpose of statistical analysis, students' preferences for solution methods were quantified into numeric values, and then a visuality score was obtained for each student. Students' visuality scores ranged from -12 to +12. The visuality scores were used to assess students' preference for solution methods. A standardized test score was used to measure students' geometry performance. The data analysis indicated that the majority of students were visualizers. The statistical analysis revealed that there was not an association between preference for solution methods and students' geometry performance. The preference for solving geometry problems using either visual or nonvisual methods was not influenced by task difficulty. Students were equally likely to employ visual as well as nonvisual solution methods regardless of the task difficulty. Gender was significant in geometry performance but not in preference for solution methods. Female students' geometry performance was significantly higher than male students' geometry performance. The findings of this study suggested that instruction should be focused on incorporating both visual and nonvisual teaching strategies in mathematics lesson activities in order to develop preference for both visual and nonvisual solution methods.

The study investigated the strategies used in teaching geometry in primary six as well as the perception of teachers on geometry vocabulary teaching, how geometry vocabularies were taught and, lastly, how the teaching of geometry vocabulary influenced primary six learners’ performance in geometry. The Van Hiele Theory of geometrical thinking and the Constructivist Theory of learning guided the study. The study conveniently sampled 250 primary 6 learners and 7 primary 6 mathematics teachers from three privately-owned primary schools in the Greater Accra Region of Ghana. It combined quantitative and qualitative approaches, using O1–X–O2 design. Data collection instruments were 5-point Likert type scale questionnaires (one for teachers, one for learners), a pre-test and post-test of basic geometry, and a semi-structured one-on-one audio-recorded interview of a selected number of learners and all seven teachers. An intervention was carried out in-between the pre-test and post-test, where the researcher taught geometry vocabulary to participants. Quantitative data were analysed using tables, charts, and simple tests while the qualitative analysis involved the transcription of interviews that were coded, categorised and themed. The study found that geometry vocabularies were not taught and that the most commonly used strategy for teaching geometry was the drawing of 2-D shapes and models of 3-D objects on the board. The pre-test and post-test scores were analysed using a paired t-test and the results indicated that the intervention had a positive effect. The qualitative and quantitative results confirmed that the teaching of geometry vocabulary improved learners’ performance in geometry. The study developed a prototype lesson plan for teaching 3-D objects, a geometry vocabulary activity sheet, a sample assessment for prisms and pyramids and recommends a curricular reform to inculcate the teaching of geometry vocabulary in the curriculum with a geometry vocabulary list for learners in each year group, as contribution to knowledge in mathematics education. The study recommends further research to investigate the effect of geometry vocabulary teaching on learners’ performance in geometry across all year groups in the primary school. / Dyondzo a yi lavisisa maendlelo lawa ya tirhisiwaka ku dyondzisa geometry ya tidyondzo ta le hansi ta ka ntsevu, mavonelo ya vadyondzisi eka madyondziselo ya marito ya geometry, tindlela leti tirhisiweke ku dyondzisa marito ya geometry xikan’we ni ndlela leyi madyondziselo ya marito ya geometry ya khumbheke matirhelo ya vadyondzi va tidyondzo ta le hansi ta ka ntsevu. Dyondzo ya ndzavisiso yi leteriwile hi ehleketelelo ra Van Heile ra maehleketelelo ra ndlela ya geometry ni ndlela yo dyondzisa leyi pfumelelaka vadyondzi ku vumba vutivi ku nga ri ntsena ku teka vutivi ku suka eka mudyondzisi. Dyondzo ya vulavisisi yi hlawurile vana va 250 va tidyondzo ta le hansi ta ka ntsevu na 7 wa vadyondzisi va tnhlayo ta tidyondzo ta le hansi ta ka ntsevu kusuka eka swikolo swinharhu swo ka swi nga ri swa mfumo e Greater Accra etikweni ra Ghana. Yi hlanganisile qualitative na quantiutative aapproach, yi tirhisa O1–X–O2 design. Switirhisiwa swo hlengeleta data a swi ri swivutiso hi muxaka wa 5-point scale(yin’we ya vadyondizi, yin’we ya vadyondzi), xikambelwana xo rhanga na xo hetelela xa geometry ya masungulo, xikan’we na nkandziyiso wa mburisano wa vanhu vambirhi eka nhlayo ya vadyondzi ni vadzyondzisi hinkwavo va nkombo. Ntirho wo nghenelerisa wu endliwile exikarhi ka xikambelwana xo rhanga ni xo hetelela laha mulavisisi a nga dyondzisa marito ya geometry eka vanhu lava ngheneleleke. Quantitative data yi hleriwile hi ku tirhisa matafula, ti charts ni swikambelwana swo olova kasi vuhleri bya qualitative byi nghenise kutsariwa ka miburisano leyi hundzuluxiweke yi nyika tinhlamuselo leti tumbeleke. Leti vekiweke hi ku ya hi mintlawa ni maendlelo ya tona. Dyondzo ya ndzavisiso yi kume leswaku marito ya geometry a ya dyondzisiwanga ni leswaku maendlelo yo toloveleka ya ku dyondzisa geomeyry i ya drawing ya xivumbeko xa 2-D ni mfanekiso wa nchumu wa 3-D eka bodo. Mbuyelo wa Xikambelwana xo sungula na xo hetelela wu hleriwile hi ku tirhisa t-test (xikambelwana xa T) lexi hlanganisiweke naswona mbuyelo wu komba leswaku maendlelo himkwawo ya vile ni xiave lexinene. Mbuyelo wa Qualitative na Quantitative wu tiyisisile leswaku ku dyondzisiwa ka marito ya geometry swi antswisa matirhelo ya vadyondzi eka dyondzo ya geometry. Dyondzo ya vulavisisi yi antswisile kumbe ku kurisa prototype lesson plan ya ku dyondzisa 3-D objects, sheet ya migingiriko ya marito ya geometry na ku bumabumela circular reform ku dyondzisa madyondziselo ya marito ya geometry eka kharikhulamu leyi ng na nxaxamelo wa marito ya geometry ya vadyondzi eka ntlawa wa lembe na lembe, ta ni hi mpfuneto wa vutivi eka dyondzo ya tinhlayo. Dyondzo ya vulavisisi yi bumabumela leswaku vulavisisi byi ya emahlweni ku lavisisa xiave xa madyondziselo ya marito ya geometry eka matirhelo ya vadzyondzi eka geometry eka malembe ni mintlawa hinkwayo exikolweni xa le hansi. / Thuto ye e nyakisisitse ditsela tseo di somiswago go ruteng ga geometry go mphato wa bo tshelela, temogo ya barutisi go ruteng tlotlontsu ya geometry, tsela yeo ditlotlontsu tsa geometry di rutilwego ka gona go akaretswa le, sa mafelelo, ka mokgwa wo thuto ya tlotlontsu ya geometry e tutueditsego mabokgoni a barutwana ba mphato wa bo tshelela go dithuto tsa geometry. Thuto ya van Hiele ya geometrical thinking le ya constructivist theory of learning di hlahlile thuto ye. Thuto ye e somisitse ga bonolo mohlala wa barutwana ba 250 ba mphato wa 6 le barutisi ba dipalo ba supa ba go ruta mphato wa 6 go tswa dikolong tsa tlase tse tharo tsa go ikema seleteng sa Greater Accra Region of Ghana. Thuto ye e kopantse mekgwa ya bontsi/dipalopalo (quantitative) le boleng (qualitative), go somiswa tlhamo ya O1-X-O2. Didiriswa tsa kgobaketso ya boitsebiso e bile 5-point Likert Type Scale Questionnaire (ye tee ya barutisi, ye tee ya barutwana), moleko wa pele le moleko wa morago wa geometry ya motheo, le poledisano yeo e gatisitswego ya tlhamego ya sewelo (semi-structured) ya barutwana bao ba kgethilwego ga mmogo le barutisi ka moka ba supa. Thekgo e ile ya phethagatswa/fiwa magareng ga moleko wa pele le moleko wa morago moo monyakisisi a rutilego tlotlontsu ya geometry go batseakarolo. Boitsebiso bja bontsi (quantitative data) bo sekasekilwe ka go somisa ditafola, ditshate, le teko e bonolo mola ditshekatsheko tsa boleng (qualitative analysis) di akareditse go ngwalolla dipoledisano tseo di thulagantswego, tsa hlophiwa le go beakanywa ka sehlogo. Thuto ye e itullotse gore ditlotlontsu tsa geometry ga se tsa rutwa ebile mekgwana yeo e somisitswego ya setlwaedi go ruta geometry ebile go thala dibopego tsa 2-D le mehlala ya didiriswa tsa 3-D letlapeng. Dintlha tsa moleko wa pele le moleko wa bobedi di sekasekilwe ka go somisa mokgwa wa go phera moleko wa t (t-test). Dipoelo di supeditse gore thekgo yeo e filwego e bile le khuetso ye botse. Dipoelo tsa bontsi le boleng di netefaditse gore go ruta tlotlontsu ya geometry go kaonafatsa mabokgoni a barutwana dithutong tsa geometry. Nyakisiso ye e tsweleditse lenaneothuto la go dira diteko go ruteng didiritswa tsa 3-D le papetlatshomelo ya tlotlontsu ya geometry gape le go kgothaletsa mpshafatso ya lenaneo-thuto go tsenyeletsa thuto ya tlotlontsu ya geometry ka gare ga lenaneo-thuto gammogo le lelokelelo la tlotlontsu ya geometry ya barutwana go dihlopha tsa mengwageng ka moka. Se e tla ba e le tlaleletso ya tsebo go thuto ya dipalo. Thuto ye e kgothaletsa dinyakisiso tsa go ya pele go nyakolla mafelelo a go ruta tlotlontsu ya geometry go tiro ya, goba dipoelo tsa, barutwana go thuto ya geometry go dihlopha tsa mengwaga ka moka tsa sekolo sa tlase. / Mathematics Education / Ph. D. (Mathematics Education)