THE EFFECT OF TEACHING SOLID GEOMETRY BY CABRI 3D WITH IPAD

THE EFFECT OF TEACHING SOLID GEOMETRY BY 

CABRI 3D WITH IPAD

Sinan ERASLAN

Ust-Kamenogorsk Kazakh-Turkish High School for gifted boys, Kazakistan

eraslan_s@yahoo.com

Muhammet KULUŞ 

Nurorda International School ,Astana , Kazakistan

mkulush@gmail.com

ABSTRACT 

We unveiled our plans to revolutionize the students’ spatial conception development through the challenge and support of a cooperative learning of practice, the development of the profession as a whole and through sharing innovation and expertise. This unique difference means we can advise on the implementation of those technologies within a live environment. In Kazakhstan, we are experimenting with a high level of technology integration to suit the student’s learning requirements in the solid geometry curriculum. Married to this idea is the use of the iPad. The implementation of a new teaching model using the iPad has been very successful. The devices have been well received by students and by teachers and are increasingly well-used in the solid geometry curriculum as their attributes and limitations are learned. Both pedagogical changes and new ways of learning engender by access to information and learning tools, progress in the implementation of the scheme has been outstanding.

Keywords: iPad, spatial conception, technology integration

Абстракт

Біз оқушылардың кеңестікті, жан жакты пікірінің дамуын жетілдіру және колданылған ақпараттарды біріктіріп оқыту мен тәжірибелік жұмыстар арқылы жаңарту үшін осы жоспарымызды келтірдік. Жалпы мамандырудағы инновацияларды енгізу және тәжірибелердің алмастырылуымен  дамыту  мақсаты көзделген. Бұл оңашаланған тәсіл , біздің күніміздің технологияның орны ереше екенің көрсетіп, біздердің осы мәселеде ұсыныстар ете алуымызды білдіреді. Қазақстанда жоғары деңгейлі технологиялардың интеграциясымен тәжірибелердің жасалу барысындағы мақсаттарымыз, оқушылардың оқу бағдарламасында стереометрияны  үйрену  барысындағы талаптарын қанағаттандыру. Бұл пікірді Ipad қолдануымен байлауға  болады. Жаңа Ipad қолдану тәсілінің оқыту үрдісі жетістікті көрінді. Педагогикалық өзгеріс және жаңа оқыту үрдісі уйрену тәсілі жайлы мәлімет жинап, толықтыруға жол ашқанмен бірге ерекше көрнекті пікір бодып көрінді.

Абстракт

Мы представили наши планы, чтобы реконструировать студентов пространственного развития концепции через вызов и поддержку кооперативного обучения практики, развития профессии в целом и за счет инноваций и обмена опытом. Это единственное отличие значит, мы можем консультировать по вопросам реализации этих технологий в реальных условиях. В Казахстан, мы экспериментируем с высоким уровнем интеграции технологий, чтобы удовлетворить требованиям обучения студента в учебной программе твердой геометрии. Женат на этой идее является использование Ipad. Реализация новой модели обучения с использованием IPad был очень успешным.Устройства были хорошо приняты студентами и преподавателями и все чаще хорошо использовать в твердой учебной программе геометрии как их атрибуты и ограничения узнал. Оба педагогические изменения и новые способы обучения порождают на доступ к информации и средств обучения, прогресс в реализации этой схемы была выдающейся.

ABSTRACT

Bu çalışmadaki planımız öğrencilerin  uzaysal kavramlara bakışlarını, mekansal anlayışı geliştirme adına ve mesleğin gelişmi adına  pratik bir işbirlikli , bir bütün olarak  paylaşım, yenilik   konularında araştırmalar yer almaktadır. Burada asıl fark tavsiyelrimizin  bu teknolojilerin uygulanması   anlamında yapıcı olmaktadır. Kazakistan’da yaptığımız deneylerde yüksek teknolojik entegrasyonlarıyla uzay geometrisi müfradanıda  çalıştık. Bu fikir ile yola çıkarak iPad kullanıldı. IPad kullanarak yeni bir öğretim modeli uygulanması çok başarılı olmuştur.Cihazlar  öğrenciler ve öğretmenler tarafından iyi bir şekilde kullanılarak  daha nitelikli ve uzaygeometrisi eğitiminde sınırları zorlayıcı şekilde iyi sonuçlar elde edildi. Pedagojik değişiklikler  birlikte ve bilgi ve öğrenme araçları yenilenmesi ve gelişmesinde olağanüstü gelişmelerde son derece muazzam bir  ilerleme kaydedilmiştir.

Anahtar kelimeler: Ipad, uzaysal kavramlara bakış, teknolojik entegrasyon

INTRODUCTION

Solid geometry is an important part of the mathematics curriculum, and being the foundation for study in such fields as graphics, geology, science, engineering,  architecture, computer and  astronomy (Banchoff, 1990;Senechal, 1990). However, students are not demonstrating strong conceptual knowledge in reasoning about geometric ideas (Carroll, 1998). Carroll (1998) found that students are capable of developing continued growth and power of reasoning. The visualization of geometry improves students’ perception of spatial relationships. Unfortunately, many students develop misconceptions, and others fail to derive from geometric figures.

Recently, we have relied upon the mobile learning as a way to infuse the technology of the computer and software to the learning objectives found in the various content areas of our curriculum. Staying up to date on new technology, teacher can incorporate geometry software on class to present students the geometry graphics dynamically. When students are poorly prepared in critical order thinking skills and independent inquiry skills, the development can be supported by effective use of mobile technologies. Like the iPod and iPhone, the iPad is a platform intended to support online content including books, magazines, games, music, and video, plus Web access.

The iPad and the Cabri3D software can combine to provide an advantageous alternative to traditional solid geometry teaching. Certainly merging into an iPad environment from a traditional classroom can be challenging. We should explore the instructional implications of a move towards this new option at the Kazakh-Turkish high school. Besides, we will address a gap in the literature by examining the impact on learning and teaching in an innovative school that already has a strong commitment to ICT. In particular, it will focus on changes in teaching and learning styles, impact on standards and on student’s attitudes to learning with the iPad. Melhuish and Falloon (2010) lead us to a consideration of how mobile technologies are redefining what constitutes a learning space, one that is no longer fixed in time but based on connecting people with each other and information through virtual collaborative spaces and communities.

We proposed a new teaching model, is based on the theories of Van Hiele  and Vygotsky. Theoretical foundations such as constructivism, social interaction and discussions, the use of smartboard, iPads, Cabri3D, cooperative learning groups, and higher order thinking are just a few of the theories that support our teaching philosophy and this research. For all the sophistication of our technology, our view of learning is still talking about courses and investigate students’ learning of solid geometry in a phase-based instructional environment using iPad based on the van Hiele theory. This study was undertaken to investigate the following research questions,

1. Is the new teaching model useful in promoting students’ thinking processes on geometry tasks?
2. Can the levels be characterized operationally by student behavior?
3. Can an interview procedure be developed to reveal different levels of reasoning on specific geometry tasks?

We use technology to move from an  event-based learning model that we  know to be ineffective, to a more distributed and contextualized environment that spans the continuum from formal learning to performance support.

THEORETICAL BACKGROUND 

van Hiele theory 

The van Hiele theory of geometric thinking comprises three main components; levels of geometric thinking, characteristics of the levels and phases of learning (Crowley, 1987). The van Hiele defined five phases of reasoning in geometry and the role of instruction in raising levels of thinking. The student passes before jumping to the next level (van Hiele-Geldof, 1957). They believed the developmental model of thought processes were discrete through which student progress as they learn geometry.

1. Level 1 (Visualization).The student reasons about geometric figures, such as simple shapes, by identifying, naming and comparing them according to their appearance. Perception is visual only and primarily by means of visual considerations of the concept as a whole without explicit regard to the properties of its components.
2. Level 2 (Analysis).The student reasons about geometric concepts empirically, such as folding, measuring, analyzing figures in terms of their components and relationships among components. Necessary properties and their attributes are used to describe and established figures.
3. Level 3 (Abstraction).The student logically orders previously discovered properties of concepts, form abstract definitions. By giving informal arguments the student operates with these concepts both within a figure and between related figures.
4. Level 4 (Deduction).The student can manipulate the relationships within the context of a mathematical system rather than a collection of shapes. Reasoning at this level includes complete with undefined terms, axioms, an underlying logical system, definitions, and theorems.
5. Level 5 (Rigor).The student can analyze and compare systems based on different axioms. The student can study various geometries in the highly abstract and does not necessarily involve pictorial models. At this level the axioms themselves become the object of intense rigorous scrutiny.

Vygotsky theory 

Vygotsky (1978) took up the idea of the Zone of Proximal Development (ZPD) as the difference between the level of difficulty of a subject that the student can understand with the help of a teacher or a fellow student. The concept of ZPD emerged as an argument against the use of standardized tests to gauge the human intelligence within our society or culture. The learner proceeds to the next developmental level of participation in activities slightly beyond their competence.

Vygotsky’s theory of individual intellectual development emphasizes the importance of individual cognitive gains occur first through interaction with the social environment and then is internalized in the individual (Vygotsky, 1978; Rogoff, 1990). It is contrasted to Piaget’s supposed tendency to view learning as a primary private affair. Based on Vygotsky’s work, the learning communities can support learning through assisted performance, managed discourse, and reciprocal teaching.

Rather than the push to memorize facts, cognitive psychology advanced beyond behaviorism by positing that students actually could try to find facts and how to distinguish solid from the environment.

By assessing prior knowledge, the teacher is in accordance with both the constructivist view of teaching and learning mathematics will be able to see where the students are cognitively and push to have them work in their zone of proximal development through scaffolding (Vygotsky, 1978; Vygotsky, 1986). Teachers create an attractive scenario and assign students homework to on a daily basis. There is all manner of grunt work that students need to do in terms of time spend interacting with others. They can’t really get rid of much of that grunt work, but it can streamline it. Playful activities in which students can physically practice directional instructions help them develop a kinesthetic understanding of solids.

METHODOLOGY 

Computer Software Current some math software is designed for plane geometry use and is poorly suited to solid geometry. The Cabri3D has become the dominant tool for giving students a tangible, visual way to explore and understand core concepts of geometry (See Fig 1). The Cabri3D’s friendly user interface allows teachers and students to get quickly up to speed so teacher can spend time on teaching mathematics, not software. The teacher can easily generate dynamic instructional materials with accurately measured figures by exporting Cabri3D files to word and PowerPoint programs, and the internet. Teachers can provide engaging learning experiences and explore variables, relationships, and the mathematics of change with their students.

 

Cabri3D, with its dynamic manipulation environments, has three important attributes. First, students can directly manipulate mathematical objects represented on the screen. Second, mathematical objects stay coherent at all

times as they are dragged. Third, students feel that they are involved with the objects they are manipulating, that is, they are immersed in the environment.

For students, it is designed to help explore and understand concepts in mathematics. Students can develop their algebraic equation solving skills through playing Cabri3D and print out (See Fig 2). As shapes and positions

change, all mathematical relationships are preserved, allowing teacher and students to examine an entire set of similar cases in a matter of seconds.

TEACHING STRATEGY 

Our research plan is based on the theories of Van  Hiele and Vygotsky. Theoretical foundations such as constructivism, social interaction and discussions, the use of smartboard, iPads, Cabri3D, cooperative learning groups, and higher order thinking are just a few of the theories that support our teaching philosophy and this research.

We proposed a SIC (smartboard, iPad,  Cabri3D) teaching model which is a blend of classroom materials, self-paced e-learning and assessments. A broader extension of this model is to do more than facilitate performance, by actually promoting learning as well.  As shown in Fig 3, considerable initial and ongoing

training and professional development has been provided. The iPad can support classroom instruction and performance support. It can display HD video. It has a video out via the dock connector, so a teacher can display keynote presentations

from the iPad alone. E-learning on iPad consolidates the delivery of these materials into a single tablet platform and leverages the best the iPad has to offer: ease of distribution, powerful e-reader functionality, rich multi-media and unparalleled navigability.

Evaluation

Over three weeks, we ran an experiment asking students to explore by way of cooperating learning gradually with their iPads that they use in a solid geometry-related context. Clearly the students know what the device is capable of and are keen to exploit that functionality. 

 When the experiment is over, we had a final examination to measure the geometric abilities of students as a function of van Hiele level. One month later, we had a posttest to investigate the effects of instruction on a student’s predominant van Hiele level. Both the two examinations include five parts, each part has four questions, i.e., ‘relations between lines’ (See Fig 9), ‘relations between line and plane’ (See Fig 10), ‘relations between planes’ (See Fig 11), ‘theorem of three perpendiculars’ (See Fig 12), ‘combined concept’ (See Fig 13).

Statistics 

This study is interested in the effect of teaching and level of achievement. Group descriptive statistics, such as mean and standard deviation, were calculated to classify and summarize data. For the comparisons between different teaching and practice activities, Two-way ANOVA with α = 0.01 were conducted.

Two-way ANOVA with unequal number of observations per cell was performed to analyze the data on measurement of Teaching and Level, of each parameter of different group of subjects. The Teaching factor depends on the teaching model use iPad or not. The Level factor includes high grade level, middle grade level, and low grade level. This study does not concern the effect of different grade levels. We prefer to know the interference degree cause by Level. All tests were two-tailed and  p < 0.01 was considered statistically significant. However, the data was not equal across groups. When the sample sizes within the levels of our

independent variables are not equal, we have to handle our ANOVA differently than in the typical two-way case. In our study, three (high, middle, low) grade level students participated in the iPad environment. As such, we should take action to compensate for the unequal sample sizes in order to retain the validity of our analysis.

According to Myers (1979), when the group sizes are sharply unequal (largest/smallest > 2) and a statistical test shows that the population variances are unequal. The ratio of treatment group sizes to control group size in this study was 70/44 = 1.59 (less than 2). This indicated that the F statistic was robust.

The success of the structured interview, using a specific script as a basis, enabled the teachers to compare many students’ responses to the same tasks. Tasks that involved a variety of environments in which the concepts were embodied (drawing, identifying from pictures, sorting, and solving abstract problems) revealed modes of reasoning about specific concepts that the teachers could identify with confidence.

DATA COLLECTION AND ANALYSIS 

1. On the high grade level the treatment group had a mean of 18.3 out of 44 items, with a standard deviation of 1.07. The control group had a mean of 18 with a standard deviation of 1.26. On the middle grade level the treatment group had a mean of 15 out of 70 items, with a standard deviation of 1.37. The control group had a mean of 13.4 with a standard deviation of 2.02. On the low grade level the treatment group had a mean of 9.6 out of 44 items, with a standard deviation of 6.9. The control group had a mean of 18 with a standard deviation of 2.53.

An unweighted mean is calculated by taking the average of the individual group means. Thus, we can derive our unweighted means by summing the means of each level of our independent variables and dividing by the total number of levels. The harmonic mean of n is derived 50.21 (n11 = 44, n12 = 70, n13 = 44, n21 = 44, n22 = 70, n23 = 44).

Another way to say this is that we don’t want the Teaching variable contaminated by the variance it shares with Level: we want to know what the effect of Teaching is holding a Level  constant.

2. A 2×2 (final-posttest by control-treatment) mixed model ANOVA with α = 0.01 was conducted to examine reservation from final to posttest. The posttest is held one month later since final test. The results of the ANOVA indicated a significant main effect for the within factor, F = 4.8132, p = 0.0032 (<0.01).
3. We wonder if changing a teaching formula, process or material might deliver a better learning effect depend on five teaching units. Use one-way ANOVA to determine if there’s a statistically significant difference between two alternatives.

As shown in table 4, both the p-value of unit 1: relation between lines and the p-value of unit 2: relation between line and plane are greater than the significance level (0.01), so we cannot reject the null hypothesis that the means are equivalent. Each p-value of the rest three units are less than the significance level (0.01), so we can reject the null hypothesis and safely assume that SIC teaching model affects learning effect.

4. The accumulated data of the questionnaire.
5. The comments that were listed most often, and include some feedback from teachers regarding their observed students in class.

A1. iPad has the flexibility to meet  teaching needs regardless of subject matter, technological expertise, grade level, or curriculum.

A2. iPad provides a faster, more dynamic and engaging way to demonstrate mathematical concepts than drawing on the board.

A3.Concepts that students frequently find difficult become very clear when they see visual representations on the screen and interact with them using iPads. Students using iPads in the classroom felt better prepared with their homework and that the Cabri3D assisted them with their geometry taking skills.

A4. There is no camera, so the virtual classroom is likely to be an audio-only experience. Because the iPad does incorporate a microphone and speakers, learners should be able to conference via Skype or Google Voice.

A5. The large capacitive screen of the iPads allows more than one person to view and interact with the device without passing it around. Concepts that students frequently find difficult become very clear when they see visual representations on the screen and interact with them using iPad.

A6. It is clearly surprising that some students show such an improvement in their ability to recognize representations of theorems in more complex diagrams, when they could not recognize the same representations in simpler diagrams.

A7. In that way of teamwork and competition, students drive activity and advancement in ways that generate rewards and motivation.

A8.Using smartboard as well as iPads in share activities as well as group work, students will be more likely to develop a critical opinion.

CONCLUSIONS

1. The Cabri3D, in conjunction with the use of the iPad and smartboard, offers new possibilities for our teaching professionals. These essential components of the phase-based instructional environment using iPad helped improve students’

van Hiele levels of geometric thinking about solids. This suggests for this sample that with well-designed instructional activities, appropriate tools, and teacher guidance, students  can learn important solid geometric concepts with increasing understanding. By directly manipulating the Cabri3D to generate many examples of solids, the students were able to recognize its shape and understand that solids by analyzing the measurement of its volumes. Through their dynamic manipulation and reflecting on those actions, students were able to understand properties of solids..

2. Knowledge alone cannot become developed, but it has to be a channel through which intellectual stimulation and development occurs. This concept along with more modifications and changes has played a significant role in the way education has been imparted. Optimizing intellectual capacity that could surpass an instructor is what zone of proximal development aims for. The idea being that an association, if not an immediate then a gradual one has to be built between concepts, experiences and reactions. It is a more challenging task to find ways in which to determine what makes a representation fall within a student’s direct match for their current level of ability, or just a bit beyond. If the challenge is too hard, then a student would become overwhelmed and stressed out by the task. If it was too easy, then this same student would be bored. 3. Teachers have to identify a suite of social-learning skills and teaching styles to develop that is relevant to support the needs of specific classes and students.

The iPad enables a host of activities such as referencing, collaborating, and creating content. Our SIC teaching model includes not only providing the infrastructure, tools, and knowledge, but also developing learners as learners. The students developed their ability to perform, not just their knowledge. E-learning resources don’t replace the classroom experience, but they do provide an extremely wide range of learning resources that teachers and students can take advantage to support classroom learning as well as to develop individual pathways based on actual student need.

4. Encourage students to use iPad across the mathematics curriculum to cover the insufficient of thinking. If students are not familiar with the iPad, they might want to look into life experience with peer. Characterize contexts both geographic and semantic, so that both the type of event students is engaged in as well as where they are and what would be useful to them here and now. The teacher should have the ability to truly create new learning experiences as well as tailor content to their classes, articulating them, assessing them, and developing them.

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