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Home > Developing Students Conceptual Understanding and Reasoning Skills of Geometrical Proofs Through Integrating Geogebra Software in Grade 10 in a Private Higher Secondary School Situated in Chitral, Pakistan

Developing Students Conceptual Understanding and Reasoning Skills of Geometrical Proofs Through Integrating Geogebra Software in Grade 10 in a Private Higher Secondary School Situated in Chitral, Pakistan

Thesis Info

Author

Muhammad, Noor

Department

Institute for Educational Development, Karachi

Program

MEd

Institute

Aga Khan University

Institute Type

Private

City

Karachi

Province

Sindh

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Education

Language

English

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676728018885

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Mathematics is one of the compulsory subjects taught from kindergarten to matriculation level in the schools of Pakistan. Teaching mathematics remained a challenge generally and geometry, particularly due to the abstract nature of the topics. The board and chalk method of teaching is not enough to develop the conceptual understanding and the reasoning skills of students. For this purpose, the integration of the Dynamic Geometry Software's (DGS) are introduced to enrich and enhance the learning of students in classroom teaching, along with the traditional instructional methods. Geogebra is one of the Dynamic Geometry software, which is famous for its freeware, offline use and versatile features to construct analyse and visualize the geometrical objects. An action research based on qualitative approach has been conducted on grade 10 students to develop their understanding of geometrical proofs through integrating the Geogebra software in a private secondary school, Chitral. The data has been collected in two phases and comprises 12 lessons on circle theorems taken from the National Curriculum of Mathematics i.e., NCM (2006). The data collection tools includes focused group discussion of six research participants, interviews of mathematics teacher, feedback from critical friend, students 'work on the software and their written reflections after each phase. The findings revealed that the integration of the software enhanced the understanding of geometrical proofs and their reasoning skills in the students. The students found the software friendly, interactive, and helpful in understanding the abstract topics. The use of the Van Hiele's geometrical thinking model enhanced the understanding of the students in the systematic using of Geogebra. For example, the students visualized the geometrical objects, analysed the properties through dragging and flipping and then informally deduced the relative changes in the figures to formally provide arguments or reasons for their geometrical works in solving problems related to circle theorems. Furthermore, this software helped the teachers to utilize the teaching time effectively through engaging the students individually in the learning process. In addition, the integration of the software filled the gap of conversation between the students and teacher while teaching abstract topics in geometry, making them tangible and visible. Finally, the success of the integration of software in teaching depends on the motivational power and skills of teachers in designing the tasks to scaffold the students' learning vividly.
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Analytical Characerization of Some Indiginous Oils for Their Commercial Exploitation

Oil and fats whether for human consumption or for industrial purposes are largely derived from plant sources. To meet the increasing demand for edible oils and oilcakes, improvements are being made with conventional crops, as well as with other new sources of plant species, that have the ability to produce unique desirable oils. Therefore, several plants are now grown not only for food and fodder but also for a striking variety of products, including oils with nutritional and pharmaceutical attributes. This necessitates the search of new sources of indigenous oils. In the present study new native resource of oil i.e. Bauhinia seeds and apple seeds have been explored. The study is divided into five parts. In first and second part the physiochemical characteristics, fatty acid composition, lipid bioactive, unsaponifiable content of extracted oil of three locally grown Bauhinia species (B. purpurea, B. variegata and B. linnaei) were evaluated. Analysis of fatty acid composition of oil samples revealed 13 fatty acids with chain length C14 to C24. The major fatty acids were Myristoleic acid (C14:1) and lignoceric acid (C24:0), linoleic, oleic and palmitic acid. Tocopherols (α-tocopherol, γ+β-tocopherol and δ-tocopherols) were identified and α-tocopherol is reported first time in this study. The unsaponifiable lipid fraction of Bauhinia species ranged 1.8-3.2%, β-sitosterol, campesterol and stigmasterol were the major sterols which accounted for 84-92%. The proximate compositions of meal residue of all samples were also analyzed to determine the suitability of these seeds meal in animal feed formulations. The results revealed that Bauhinia species could be helpful in understanding the influence of cultivar / variety on the quality of oil. The study revealed that the seed oils of the Bauhinia species grown in Pakistan were found nutritionally important with higher amount of PUFA, tocopherols and sterols. In the third part of study the oxidative stability assessment was done by Differential scanning calorimetry (DSC) and oxidative stability index (OSI) method among three Bauhinia species (B. purpurea, B. variegata and B. linnaei), rice bran and cotton seed oil. B. purpurea oil showed highest oxidative stability. Excellent calibration was achieved between ivDSC T 0 and OSI measurements. The coefficients of correlation were highly significant (P < 0.01) for each evaluation. The coefficient of the determination (R 2 ) for analyzed oils was above 0.9956, showing good linear regression, which revealed that oxidative stability of the oils can be accurately determined by DSC in a short time as compared to OSI method. In fourth part of study Infraspecific variation in composition of Bauhinia purpurea Linn. (B. purpurea L.) seed oil was assessed for regional discrimination. Samples were collected from five cities of Pakistan (Hyderabad, Tandojam, Multan, Pakpattan and Abbotabad). Linoleic acid, α-tocopherol, and β-sitosterol contents were used to find variability and significant difference among five regions and was found to be p<0.0001. On the basis of fatty acid composition, five regions could not be discriminated using PCA, LDA on fatty acids discriminated the regions and cross-validation was found to be 99%. Using tocopherols only one PCA component was extracted and LDA on tocopherols discriminated within the regions and cross-validation was found to be 100% perfect. PCA and LDA plots for sterol composition showed five distinct groups for both statistical protocols and all cases were 100% correctly classified. The results of present study indicated that tocopherols and sterols are better chemotaxonomic marker as compared to fatty acids for regional discrimination of B. purpurea L. In fifth part of study the extracted oil from four apple seed varieties (Royal Gala, Red Delicious, Pyrus Malus and Golden Delicious) from Pakistan, total forty two samples were investigated for their physiochemical characteristics, fatty acids profile and lipid bioactive by GC-MS. The oil content in the seeds of apple varieties ranged from 26.8-28.7%. The results revealed that linoleic acid (40.5-49.6%) was the main fatty acid. The unsaponifiable lipid fraction of apple seed oils ranged from 1.8-2.1%, squalene, β-tocopherol, α-tocopherol, campesterol, avenasterol, β-sitosterol, 9,19-Cyclolanost-24-en-3-ol and Stigmast-4-en-3-one were identified, which accounted for 98- 100%. The variation among the results of both fatty acids and lipid bioactive for four varieties was assessed by principal component analysis, discriminant analysis and cluster analyses. The results conclude that both oil fractions could be applied as a useful tool to discriminate the apple seed varieties.