By Heidi Trude, M.Ed, French Teacher at Skyline High School, Front Royal, VA and Certificate Student at the University of Colorado Boulder.
Imagine putting on a headset and being transported into another world. That’s what virtual reality does for you. According to the Merriam-Webster Dictionary, virtual reality (VR) is “an artificial environment which is experienced through sensory stimuli (as sights and sounds) provided by a computer and in which one’s actions partially determine what happens in the environment”. In other words, virtual reality relies on a computing device to stimulate and immerse an individual in a virtual environment.
Virtual reality is different from augmented reality or mixed reality. Virtual reality immerses users in a completely digital and artificial environment. Unlike virtual reality, augmented reality (AR) overlays virtual objects on the real-world environment. Mixed reality (MR) combines virtual environments with the real-world and allows for interaction between both.
Virtual reality has significant educational potential. As Bell (2017) explained, “These tools can help flatten the walls of our classrooms and allow us to take students on virtual reality field trips and engage students in new ways. Virtual reality is one of the fastest growing areas of technology! VR is in its infancy and we are just scratching the surface of what this technology can do and how it will transform learning in our classrooms.” As individuals continue to study virtual reality and experiment with it, there will be even more uses for virtual reality. Thompson (2018) states, “ The market for virtual reality applications is growing at a rapid pace, and is expected to double in the next five years. As the cost of equipment falls and schools have greater access to technology, there is a great interest in virtual reality as an educational tool.” Virtual reality is changing the way in which individuals experience the world, as well as the way educators are sharing the world with their students.
GOOGLE VR TOOLS
Different types of viewers or headsets can be used for virtual reality; one of the most popular among educators is Google Cardboard. According to Google, Google Cardboard allows users to “experience virtual reality in a simple, fun, and affordable way”. Google Cardboard was created as a 20% project by Googlers, David Coz and Damian Henry of Paris, France. After pitching their idea to Google’s executives, the Google Cardboard Viewer and app were born in 2014. Google Cardboard viewers are relatively inexpensive and can be purchased for $10-15 per viewer.
As children, many of us experienced other places through the Viewmaster. With a single click of a button, the image changed and the user was transported to another world. David Hotler describes his experiences, “No other toy succeeded in removing me so completely from my current reality. Like the stereoscopic viewers of our childhood, Google Cardboard and other virtual reality (VR) viewers serve a similar purpose: to transplant users into a new reality by engaging their senses. What has changed is the technology behind these devices, which allows for an even more immersive experience” (5). Google Cardboard takes the experiences of the Viewmaster and amplifies it. Individuals are no longer relying on paper discs, but rather their smartphones. Google Cardboard uses a “split-screen format to create photospheres that offer a three-dimensional view of the scene” (Hotler, 6). With Google Cardboard, the viewer feels as if they were a part of the scene that they are viewing.
Google Cardboard provided viewers with immersive experiences, but there was still a missing piece for educators who needed a tool to create guided immersive experiences in the classroom. Google recognized this need and launched Google Expeditions. As Duckworth explains, “ Google responded to educators’ interest by making the Google Expeditions app available to teachers. Expeditions is an all-inclusive app that allows teachers to guide and control a classroom full of students using VR headsets on a journey around major landmarks on earth and in space” (8).
Within the Expeditions app, individuals decide whether to be a guide or an explorer. There are guided scripts and questions for the teacher to use while students are following along using the Google Cardboard viewers.
All of the scripts and questions are contained within each individual expedition. While the scripts are already created for the teachers, each teacher has the option to skip parts of the expedition. In addition, the comprehension questions are differentiated based on the level of the students participating in the expedition. Teachers can easily search within the app for an expedition connected to their curriculum. Duckworth states, “Teacher controls are extensive, including the ability to see where children are looking (happy face icons), turning on/off ambient sound, opening teacher notes, blacking out students’ views, and navigating to the main menu of the destination” (9). With Google Cardboard and Google Expeditions, lessons come alive and students truly experience what they are studying. By simply putting on the Google Cardboard viewer and following the teacher’s voice, students are transported to another world and are given experiences that were previously unavailable to them.
The majority of Google Expeditions are available in English; however Google is starting to create Expedition scripts in multiple languages. There are plenty of cultural expeditions that could be used in the language classroom either in the target language or with wraparound activities to be completed in the target language.
WHO’S USING IT?
Using Twitter, Google Forms, Google Hangouts, email, and Flipgrid, I reached out to educators across the globe to learn how they are using virtual reality in their classrooms. I did not limit my search to classroom teachers. I also reached out to instructional designers and technology experts. I have come to realize that Virtual Reality in conjunction with Google Cardboard, StreetView, and Expeditions, is an extremely powerful learning tool for students and allows them to be immersed in the content.
Virtual reality allows students to be creators and not merely consumers. According to Geoff Derry, an IT Integration Specialist at the IGB International School, in Kuala Lumpur, Malaysia, the true benefits of virtual reality is the students’ ability to create these immersive experiences. Derry exclaimed, “Students create their own VR experiences, either tours of the school or experiences for teachers or reflections or interesting ways to present their learning (360 videos)” (Derry interview). He continued “They love it [virtual reality}, but I am sure the novelty of just consuming VR and AR will wear off, that is why we have now focused on creating VR.” (Derry interview). Derry went on to explain how his students are creating 360 photo spheres and then giving their classmates’ the immersive experience. During our exchange, Derry stressed that the importance is on “student creation rather than just consumption”. He explained how his students are now creating their own Google Expeditions using RoundMe and Thinglink. Derry also shared how some of his students are creating 360 YouTube videos by using iMovie.
In my conversations with teachers and instructional technology coaches, all agreed that Google Expeditions has allowed students to experiences things that typically would not be possible within the classroom setting. Ben Friesen, Summit Lead at the EdTechTeam and former middle school teacher, shared how powerful Expeditions can be for both the students and the teacher. Friesen states, “I think one of the best ways to use Virtual Reality in the classroom is Google Expeditions. You can do class tours where everybody looks at the same tour lead by the teacher. But, also what is new is that you can go and explore that on your own as a teacher. You can also view it as a student and explore on your own. So play with it!” (Friesen interview). Friesen also remarked that Google Expeditions is a great way to differentiate the curriculum for the students by allowing them to explore based on their personal interest. Sam Northern, a teacher librarian from Kentucky, shared how his students use VR in the library in conjunction with project-based learning: “students have access to Google Cardboard to use with Street View and Google Expeditions. This has been a great way to connect students to the world” (Northern interview). The largest benefit of using Google expeditions is its ability to provide virtual field trips for students. As Brian Costello, a middle school Digital Integration Specialist remarked, “Virtual Reality brings kids to places they cannot otherwise go. By creating their own experiences, it gives them an opportunity to engage in the planning, visual/spatial thinking, coding, and more.” (Costello interview). Sandra Chow, an instructional liaison at TVO in Toronto, Canada, shared how Google Expeditions allow for field trips to be possible without all the hassle. She remarked, “Google Cardboard allows students to access things more quickly and easily without having to go through the logistics of signing permission forms, paying for a bus, or flying somewhere. It gives students the opportunity to visit anywhere in the world and experience things that they may never have the chance to experience” (Chow interview). The enthusiasm that each of these educators showed regarding the use of virtual reality and Google Geo tools was overwhelming at times, but made me realize what a powerful tool this can be in the language classroom.
In all of my conversations, the students’ reaction to Virtual Reality whether they were elementary or secondary students, was practically the same. Brian Costello shared, “They were excited about the consumption, but their ability to create and share in virtual reality is incredibly engaging. Students voluntarily come in at lunch and during free time to work with VR for projects.” (Costello interview). Jamie Donally, an elementary teacher and author of the upcoming book, Learning Transported, remarked “Students want to explore the world, and they just need the opportunity. They love the experiences but more importantly, they love to create the experiences” (Donally interview). After hearing from all these educators about the power of Virtual Reality and how much their students enjoyed it, I clearly saw the transformative potential of VR for language teachers and their students.
HOW TO USE VR IN THE CLASSROOM
There are many ways that world language educators can integrate these tools into their classrooms. Not only do I see the potential for virtual field trips, but also for digital storytelling, telecollaborative exchanges, and cultural explorations.
Idea 1: Google Expedition: Field Trip to Paris, French, level I
In this activity, I use Google Cardboard viewers and Google Expeditions to create an immersive field trip for my French students. This expedition goes perfectly with one of the chapters in my French 1 book that shows where individuals go in Paris and what they do at the various monuments. In the past, I have shown students images on my SmartBoard, as well as video clips. However by using the Cardboard viewers and Google Expeditions, the students would feel like they really are in Paris. The expedition, Field Trip to Paris, is created by Houghton Mifflin Harcourt. It is composed of eight scenes which explore the Arc de Triomphe, Sacré Coeur, the Louvre, the Centre Pompidou, the Musée d’Orsay, the Panthéon, the jardin du Luxembourg, and the stade de France. Upon completion of this expedition, the students will be able to describe important landmarks in Paris and explain what one can do at each site.
During the activity, students complete a See, Think, Wonder chart using Padlet. Under the See column, students record what they see in each scene. In the “Think” column, students share what they are thinking about the landmarks. In the “Wonder” column, students ask questions about the various landmarks. After completing the Expedition, I can ask the students to create a presentation highlighting each site and describing in French where they are going to visit and what they are going to do there. In the Expeditions that I have found, I use the script that is provided, which is in English, and then create the wraparound activities in the target language for the students to complete.
Idea 2: Google Cardboard with Story Spheres, French, level III
Students in French III are asked to create 360 Story Spheres detailing how they spent their weekend. A Story Sphere is a 360 image that contains audio files and can be viewed on a computer or with a Cardboard viewer. Prior to starting this project, I teach the students how to upload their images and audio files to Story Sphere, as well as how to share their finished product. Once the students have an understanding of Story Spheres, they are able to focus on the task of narrating past events.
Students take a series of 360 photos using either a 360 camera or using their smart phones and then upload the images to Story Spheres. The students then record an audio file describing what they did in each photo and then upload the audio file to Story Spheres. In Story Spheres, the students link the audio files into the images. Students then embed their Story Spheres onto the class Google Site to keep all the images in one place. Students view each image and listen to the audio using their Google Cardboard viewers. After watching the videos, students work in pairs to ask each other questions about what they did over the weekend.
Idea 3: StreetView Scavenger Hunt, French, all levels
In this activity, students complete a scavenger hunt in order to better understand historical sites and landmarks throughout France and the French-speaking world. I create a Google Form with the clues the students need to solve the scavenger hunt. Using data validation, I “lock” the responses and the students are only able to move onto the next clue if they enter the correct answer. Students use Google StreetView and Google Cardboard viewers to look for the various landmarks and sites. They work in teams to complete the tasks. Once a team unlocks a clue, they are directed to a page of the Google Form that shares additional information about the historical site or landmark. Within that page, there is a YouTube 360 video that allows students to immersive themselves in that site. After completing the activity associated with the site or landmark, the students move onto the next clue, solve it, and continue to the activity. This cycle continues until the students have finished the scavenger hunt. This activity allows the students to gain a better understanding of France, its history, its landmarks, and its culture.
Idea 4: StreetView Town Tours: Front Royal & Charleville-Mézières, French, all levels
Google Cardboard, along with Google Streetview and the Cardboard Camera app allow my students and the students at our partner school, the Lycée Bazin in Charleville-Mézières, France to tour where each other lives. By taking 360 photos using either StreetView or Cardboard Camera, the students feel like they are in each other’s town. By viewing all the images from each town, the students are able to understand the similarities and differences between Front Royal, Virginia and Charleville-Mézières, France.
During the activity, each student takes one 360 photo using StreetView or Cardboard Camera. If the students choose to use Cardboard Camera, they are also able to record audio within the 360 photo, so they can describe where they are and why they selected the location. Once all students have taken their photos, my students and the students at theLycée Bazin view the photos using our Google Cardboard viewers. If possible, we organize a live Google Hangout to discuss the similarities and differences between the two cities. I also create a Flipgrid topic where the students ask each other video questions. The virtual tours and live discussions help the students understand where their peers come from and help them to develop a better cultural understanding.
DOWNSIDES AND CHALLENGES OF VR
Even though virtual reality in combination with Google Cardboard, Expeditions, StreetView, and Youtube 360 allows the creation of immersive experiences, educators may face challenges when trying to implement virtual reality into the classroom.
After researching virtual reality and the Google Geo tools, as well as communicating with educators who are using virtual reality in the classroom, I have found that one of the biggest challenges educators face in integrating virtual reality is access to devices. Many of the educators that I communicated with shared that funding can be an issue when trying to purchase devices for their classrooms. While the Google Cardboard viewers are relatively inexpensive, the cost comes from acquiring the devices to use with the Google Cardboard viewers. Like several of the educators I interviewed, I was able to get a classroom set of Google Cardboard viewers through a grant, however, not all my students have a device with which to use the Google Cardboard viewers. I plan to apply for a grant to purchase devices for the students, as well as a tablet and router, so I can run Expeditions in my classroom. Jen Caruthers, an educator and technology leader at Mahopac School District, shared that she actually purchased devices for her classes on Amazon Prime Day. Other educators explained how they asked for donations and set up Donors Choose pages to acquire the devices for their students.
While acquiring the necessary hardware can be a challenge, having access to reliable wifi can prove equally challenging. In my own building, students do not have access to the wifi on their personal devices. Other educators I spoke with also shared how issues such as unstable wifi and bandwidth created hindrances when incorporating virtual reality into the classroom.
Despite these challenges, the benefits of virtual reality ultimately outweigh the downfalls that educators may face in incorporating virtual reality into their classrooms. As virtual reality becomes more prevalent as an educational technology tool, I believe there will be fewer issues regarding accessibility to devices, as well as internet access.
Virtual reality is changing the way in which educators and students experience the world. No longer does the learning have to stay within the four walls of the classroom. Virtual reality, along with Google Cardboard and Google Expeditions allows teachers and students to experience places that were previously inaccessible to them. According to Ashley McCann (2017), “Although still an emerging technology in terms of recognizing its full potential, virtual reality offers the opportunity to step into places, roles, and experiences that were previously impossible, or at the very least, inaccessible to most.” Furthermore, “…virtual realities can be designed precisely for human interaction for very specific reasons to create experiences not otherwise possible” (McCann, 2017).
Virtual reality has the capability to allow teachers to transform their students’ understanding of the world and allows for curiosity and wonder to enter the classroom. No longer are students just reading about places in a textbook, instead, they are immersing themselves in those places through Google Cardboard and Google Expeditions. By using virtual reality in conjunction with Google Cardboard and Google Expeditions, educators can empower students to travel to other countries, be inside the space shuttle, or even explore the ocean.
While there is no specific research on the impact of virtual reality and telecollaboration on proficiency, it appears that adding the element of virtual reality into such partnerships could allow students to experience each other’s cultures, including the sights and sounds of their towns as if they were actually there. This technology could make it possible for those students who do not have the means to travel abroad or to complete an exchange, and to experience another country and culture. Students could create virtual immersive tours and share those live over a Google Hangout. Not only would the students be experiencing each other’s towns and cultures, but would also have an immersive language experience. Students could also create YouTube 360 videos in the target language and view those using a Google Cardboard viewer to create a language-rich and immersive cultural experience. Imagine the power of those experiences for the students! Virtual reality, Google Cardboard, and Google Expeditions allows educators to inspire and engage students in a way that many never dreamed was possible.
As virtual reality continues to emerge and develop, more and more educators will start to use virtual reality and Google Geo Tools in the classroom. Holly Clark writes, “While being transported to amazing and far away places is the wow factor that captures students’ attention, VR is not all about traveling somewhere or seeing something for the first time. What Google Cardboard viewers create is the opportunity for students to become creators – creators of content and information they can share with the world” (Clark, 55). By using virtual reality as a creation tool, educators will allow their students to foster the 21st Century skills of creativity, collaboration, critical thinking, and communication, and ultimately develop a better sense of the global society in which they live.
So often individuals remark that “a picture is worth a thousand words”. In thinking about this statement, one could say that the immersive experiences provided by virtual reality through the use of Google Cardboard viewers and the Google Geo tools are truly providing users with unforgettable experiences. With all the challenges of arranging trips for students in light of society today, teachers are able to bring those immersive experiences to their students. Even though there are some challenges in implementing virtual reality into the language classroom, the benefits of using virtual reality outweigh those challenges. Virtual reality in combination with Google Geo Tools is truly allowing language students to experience another culture and language in ways that had not been possible in the past.
Clark, H., Duckworth, S. Heil, J. Hotler, D. Piercey, D. & Thumann, L. (2017). The Google Cardboard Book: Explore, Engage, and Educate with Virtual Reality. The EdTechTeam Press, Irvine, California.
Bell, K. (2016). Getting Started with Google Expeditions and Virtual Reality. Shake Up Learning. Retreived from http://shakeuplearning.com/blog/getting-started-google-expeditions-virtual-reality/
Bell, K. (2016). How to Use Virtual Reality and Google Expeditions in the Classroom. Shake Up Learning. Retrieved from http://shakeuplearning.com/blog/use-virtual-reality-google-expeditions-classroom/
Bell, K. (2016). How to Choose a Virtual Reality Device for Your Classroom. Shake Up Learning. Retrieved from http://shakeuplearning.com/blog/choose-virtual-reality-device-classroom/
Bell, K. (2017). The Ultimate Google Cardboard and Expeditions Resource Guide. Shake Up Learning. Retrieved from http://shakeuplearning.com/blog/ultimate-google-cardboard-expeditions-resource-guide/
Caruthers, B. personal communication. February 20, 2018.
Caruthers, J. personal communication. February 20, 2018.
Chow, S. personal communication. February 26, 2018.
Chute, E. (2018). How one high-poverty district is adding virtual reality to its classrooms. Hechinger Report. Retrieved from http://hechingerreport.org/one-high-poverty-district-adding-virtual-reality-classrooms/
Costello, B. personal communication. February 19, 2018
Danhoff, C. personal communication. February 21, 2018.
Derry, G. personal communication. February 22, 2018.
Donally, J. personal communication. February, 19, 2018.
Fricano, M. personal communication. March 8, 2018.
Friesen, B. personal communication. February 21, 2018.
Google. (2018). Google Cardboard. Retrieved from https://vr.google.com/cardboard/
McCann, A. (2017). 10 Reasons to Use Virtual Reality in the Classroom. Teach Thought. Retrieved from https://www.teachthought.com/technology/10-reasons-use-virtual-reality-classroom/
Northern, S. personal communication. February 23, 2018.
Thompson, M. (2018). Making Virtual Reality a Reality in Today’s Classrooms. THE Journal. Retrieved from http://thejournal.com/Articles/2018/01/11/Making-Virtual-Reality-a-Reality-in-Todays-Classrooms
Tokareva, J. (2018).The Difference between Virtual Reality, Augmented Reality, and Mixed Reality. Forbes Magazine. Retrieved from https://www.forbes.com/sites/quora/2018/02/02/the-difference-between-virtual-reality-augmented-reality-and-mixed-reality/#62cac0712d07


LEARNING CYCLE MODEL
FOR LEARNING SURFACE AREA OF TRIANGULAR PRISM
WORKSHOP ON DEVELOPING LEARNING MODEL
BASED ON REALISTIC MATHEMATICS EDUCATION APPROACH
REGIONAL CENTER OF QITEP IN MATHEMATICS
LEARNING CYCLE MODEL
Realistic Mathematics Education was underlined by the idea of Hans
Freudenthal that viewed mathematics as human activity, instead as subject matter that
must be transferred from teachers to students (Freudenthal, 1973). Based on
Freudenthal’s idea, the teaching and learning process of mathematics should be
connected to realistic problem. The term “reality” as the focus of Realistic
Mathematics Education means that the problem situation must be experientially real
for students. The main focus of the teaching and learning process is activities that lead
to the process of mathematization.
There are five tenets of realistic mathematics education defined by Treffers
1. Phenomenological exploration
Contextual problems are used as the base and starting point for the teaching and
learning process. The teaching and learning process is not started from formal level
but from a situation that is experientially real for student.
2. Using models and symbols for progressive mathematization
The aim of this tenet is bridging from concrete level to more formal level using
models and symbols.
3. Using students’ own construction
The freedom for students to use their own strategies could direct to the emergence
of various solutions that can be used to develop the next learning process. The
students’ strategies in the activities are discussed in the following class discussion to
support students’ acquisition of the formal level of mathematics concepts.
The learning process of students is not merely an individual process, but it is also a
social process. The learning process of students can be shortened when students
communicate their works and thoughts in the social interaction emerged in
The activities used in the teaching and learning process do not merely support
learning for a single mathematics topic, but they also should support the learning
process of other mathematics topics or concepts.
Interactivity, as one of the five tenets of realistic mathematics education,
emphasizes on the learners’ social interaction to support the individual’s learning
process. This idea is in line with social constructivism that views an individual's
cognitive development as a result of communication in social groups and it cannot be
separated from social life. The learning process of learners is not merely an individual
process, but it is also a social process, and these both perform simultaneously (Cooke
& Buchholz, 2005 and Zack & Graves, 2002). Social interaction is a prerequisite to the
individuals' cognitive development through internalization of ideas in the community.
The learning process of learners can be shortened when they communicate their works
and thoughts in the social interaction. However, social constructivism should not
merely focus on the individual part and the social interaction the learning systems, but
should also focus on the knowledge and skills to be learned as the social products.
Considering the importance of exploration, social interaction and knowledge
development, as emphasized by RME and social constructivism, it is important to use a
learning model that integrates these three components. One of learning model that is
suitable for this objective is learning cycle model.
II. THEORETICAL REVIEW
Learning cycle model is a learning model that encourages students to develop
their own understanding of a scientific concept, explore and deepen that understanding,
and then apply the concept to new situations. There two types of learning cycle, the
first type is the old learning cycle model and the second type is the new learning cycle
The old learning cycle model has three phases, namely: exploration, concept
development and concept application.
In the first phase, students work in small groups to explore the given problems and
attempt to solve problems. The teacher acts as facilitator, posing questions and
providing assistance as needed. Students have the opportunity to develop their own
hypotheses and to test them through a hands-on experiment or observation.
b) Concept development
In the second phase of the learning cycle, the teacher leads the students through
the introduction and development of the scientific concepts central to the lesson.
This phase can be facilitated in a class discussion. The students may begin by
sharing their observations and ideas from the exploration phase.
c) Concept application
The teacher now poses a new problem or situation for the students to solve based
on their initial exploration and on the concepts they refined in the second phase. In
this phase the students work individually or in small groups while the teacher acts
as facilitator. The learning cycle may then begin again, as these hands-on activities
become the starting point for the exploration and development of a related
The three phases of old learning cycle are developed into five phases in the new
type of learning cycle model, namely: engagement, exploration, explanation,
elaboration or extension, evaluation.
In this phase problem is used to stimulate students’ interest and curiosity in the
topic of study. However, there must be a connection between what students know
and what students can do. Therefore, teacher needs to investigate students’ pre
knowledge before posing the problem. Students have a need to relate their pre
knowledge to the given problem.
During this phase students should be given opportunities to work together. Teacher
should act as facilitator and do not give direct instruction to help students solving
the problem. In this stage students cooperate to explore, analyze and solve the
problem. Students may do hands-on activities to solve the problem.
During this phase students have to present and explain concepts in their own
words, provide evidence and clarification for their explanation, and listen critically
to one another's explanation. At this phase teacher should bring students’ ideas
into more general and formal mathematical concept.
During this phase students should apply the learned concepts and skills in new (but
similar) situations and use formal mathematical concept. Exploration phase may
reapply here because students should be using the previous information to solve
the new problem.
Teacher should observe students' knowledge and/or skills, application of new
concepts and a change in thinking and students should assess their own learning.
Teacher may pose open-ended questions that involve observation, evidence, and
previously accepted explanations. Questions that would encourage future
investigations are also important in this phase.
The implementation of the five phases of learning cycle model in mathematics
teaching and learning can be formulated in the following sequence:
1. Teacher gives apperception
Apperception is an initial step of engagement phase. There are two main aims of
apperception, namely stimulating students’ interest and investigating students’ pre
2. Teacher poses the problem and ask the students to think individually
After knowing that students’ already have required pre knowledge, teacher poses
the problem and let students think individually. Students have a need to relate their
pre knowledge to the given problem. Students are not asked to find the answer of
the problem, but they are asked to analyze what the problem is and what kind of
knowledge or strategies they need to solve the problem
3. Teacher makes group of four students and asks students to solve the problem in
This activity aims to facilitate the exploration phase of learning cycle model,
namely giving students opportunities to work together. Students may do hands-on
activities or other strategies to solve the problem. Students are asked to make
4. Teacher conduct students’ presentation and class discussion
Students’ presentation and class discussion aims to facilitate explanation phase of
learning cycle. Students have to present and explain their work and listen critically
to one another's explanation. Students’ ideas should be bridged to the more general
and formal mathematical concept.
5. Teacher gives new problems
The new problems have to aims, namely providing students opportunities to extend
and apply their knowledge in new situation and to evaluate students’ achievement.
When solving the new problems, students apply the learned concept and also do reexploration
process. Therefore, new cycle of learning begins.
This document contains short description of Realistic Mathematics Education and
Learning Cycle model, lesson plan and worksheets. This document is aimed to give
examples of learning scenario for teaching and learning of the surface area of
triangular prism by using learning cycle model.
Bybee, R.W. et al. (1989). Science and technology education for the elementary years:
Frameworks for curriculum and instruction. Washington, D.C.: The National Center
for Improving Instruction.
Cooke, B.D. & Buchholz, D. (2005). Mathematical communication in the classroom:
Teacher makes a difference. Early Childhood Education Journal, Vol. 32 No. 6: 365
Freudenthal, H. (1973). Mathematics as an Educational Task. Dordrecht: Reidel Publishing
Treffers, A. (1987). Three Dimensions. A Model of Goal and Theory Description in
Mathematics Instruction – The Wiskobas Project. Dordrecht, The Netherlands: Reidel
Zack, V. & Graves, B. (2001). Making mathematical meaning through dialogues: “Once
you think of it the Z minus three seems pretty weird”. Educational studies in
mathematics 46: 229-271
: SMP …..
Grade/Semester : 8/2
Standard of competence : Understanding the characteristics of cube, cuboids, prism,
pyramid and their parts with determined dimension
Basic competence : calculating the surface area and volume of cube, cuboids, prism,
Indicators : - Students are able to reinvent the formula to calculate the
surface area of a triangular prism
- Student are able to calculate the surface area of a triangular
: 2 x 40 minutes (1 meeting)
A. Learning objectives
1. Students are able to reinvent the formula of surface area of triangular prism.
2. Students are able to use the formula of surface area of triangular prism.
3. Students are able to use the formula of surface area of triangular prism to solve
related problem in daily life.
The surface area of triangular prism
C. Learning approach and model
1. Learning approach : Realistic Mathematics Education
2. Learning model : learning cycle
D. Teaching Materials
Marsigit ,2009 Mathematics 2 For Junior High School, Jakarta,Yudistira
2. Media: worksheet
E. Summary of material
A prism is a three dimensional shape in which each flat
surface is a polygon, the across faces are congruent, and every
two lateral faces intersects each other parallel lines.
A triangular prism is a prism composed of triangular bases and
three rectangular sides.
The elements of triangular prism are:
1. Face of prism, contains the base of prism (ABC), the top of prism (DEF) and
lateral sides (ABED, BCFE, ACFD).
2. Lateral edges are intersect of lateral sides ( AD, BE, CF ) , base edges
3. Vertex ( A, B, C, D, E, F, )
Surface area of the triangular prism is the sum of base area, top area and lateral
sides area. The volume of a triangular prism is product of base area and the height
of triangular prism.
F. Learning Activities
Teacher shows a picture of house and asks the following question:
a. What geometrical shape is the roof of the house?
This question is aimed to recall students about triangular prism and its components
b. If students answer that the roof is a triangular prism, then teacher asks students to
give the other examples of triangular prism in daily life.
This question is aimed to check students’ understanding about the characteristics of a
triangular prism by asking to give examples of triangular prism.
c. The dimension of living room is 3 m x 4 m. How many tiles do we need to buy if the
dimension of the tile is 20 cm x 20 cm?
This question is used to stimulate students to recall the concept of area of a rectangle
because the area of rectangle and triangle are the prerequisite to learn the surface
area of triangular prism.
d. Teacher shows picture of a part of the roof and asks students calculate the height of
This question aims to recall students about the concept of Pythagorean Theorem.
The entire problem in this apperception is not only aimed to recall some mathematics
concepts and to investigate students’ pre-knowledge, but it also aimed to create a
contextual-realistic learning atmosphere or situation. From contextual-realistic problem,
it is expected that students do not only think about formula and other formal concept of
mathematics. Instead, students are stimulated to analyze the problem and identify what
mathematics concept they need to solve the contextual-realistic problem.
For time efficiency, teacher can give the problem above by displaying on LCD screen,
instead of storytelling. Other alternative is that teacher gives the problem in a hand out
and asks students to work on the hand out.
1. Teacher poses the problem and asks students to think individually (note: the problem
is problem number 1 on worksheet A).
Students are not asked to find the answer of the problem, but they are asked to
analyze what the problem is and what kind of knowledge or strategies they need to
solve the problem. Problem number 1 is the most important problem that will be used
as the base for the formation of mathematics concepts (i.e. surface area of a triangular
prism). Consequently, teacher should encourage students to give extra consideration
to this problem.
2. Teacher makes groups of 4 students and asks students to share their individual ideas
and solve the problem.
After students understand the problem, then they start solving the problem in groups.
Students’ individual ideas are shared and developed to solve the problem. Students
may do hands-on activity or make drawings to solve the problem. Teacher facilitates
the group discussion (i.e. provides guidance, etc)
During group discussion, teacher should clarify students’ idea and also scaffold
students in solving the problem.
Teacher may provide some teaching aids/materials that can be used by students when
working on hands-on activities. Teacher may provide a model of triangular prism as
the representation of the tent and a roll of tape as the representation of the
cloth/fabric. Students may cut the tape and glue it on the model of triangular prism
when determining they cloth needed to make the tent.
3. Teacher conducts presentation or class discussion.
Several groups of students are asked to present their work. Teacher should bring and
bridge students’ idea to the more general and formal mathematical concepts by
posing question or other guidance.
There are two possible alternative of facilitating the explanation phase:
- Teacher selects some interesting work of students to be presented in the
classroom discussion. (Note: interesting does not only mean correct solution, but
any solution that will contribute to the formation of mathematics concepts).
- Teacher asks all group to display or hang their work on the wall, then they can
visit, observe and discuss the others’ work. Students can record their question
and then pose it in the classroom discussion.
4. Teacher gives new problems (see Task 1)
Note: if the time is not enough, the problems can be used for the next meeting
This activity aims to :
− provide students opportunities to extend and apply their knowledge in new
− stimulate students to do new exploration to solve the problem and, therefore, the
new cycle of learning begins.
− evaluate students’ achievement
− Teacher and students make a summary and conclusion about the learned topic
− Teacher gives homework
1. The technical assessment : written test
2. Instrument :
Homework is used to assess individual’s achievement
− Task 1
Task 1 is used to stimulate students to do re-exploration to develop new concept (i.e. the concept of volume)
Solve the following problems by using your own strategies and use drawing if it is needed.
1. For the next Pramuka camping, our scout team will make our own tent. The dimension
of the tent will be 4 meters long, 3 meters wide and 2 meters high. How long do we
need to buy the cloth/fabric to make our tent?
Note: the wide of the special cloth to make the tenth is 1 meter.
2. If we would also like to make the base of our tent from the same cloth/fabric, how long
do we need to buy the cloth/fabric for our tent? How many meter of cloth/fabric we
need in total (for the tent and its base)?
3. All members of the scout team agree to express their creativity by making the tent
colorful. If a bottle of paint is enough to paint 4 m 2 of cloth/fabric, how many bottles of
paint do we need to buy to paint the tent and its base?
4. A tailor is asked to make the tent. Can you help the tailor draw the pattern of the tent?
5. Find the formula to calculate the surface area of a triangular prism
Time allocation: 40 minutes.
To help you manage your time, you can follow the following guide:
Problem 1 and problem 3: approximately you need 10 minutes for each problem
Problem 2: approximately you need 10 minutes
Problem 4 and 5: approximately you need 15 minutes for both problems
Note for teacher about the worksheet:
− Problem (1) involves two tenets of Realistic Mathematics Education, namely:
phenomenological exploration and intertwinement. The phenomenological exploration
is reflected from the use of contextual/realistic problem and the intertwinement is
reflected how students to use the Pythagorean Theorem and the concept of area to solve
− Problem (1) and (2) is aimed to stimulate students’ sense of surface area of triangular
prism. When we discuss three dimensional objects, a question about their capacity or
content is related to the concept of volume and a question about materials needed to
make non-solid objects or a question about the amount of paint to paint the surface of
the object is related to the concept of surface area. Therefore, the amount of cloth/fabric
that is needed to make the tent (and its base) is related to the surface area of a triangular
prism. Students may use hands-on activities and various strategies to solve problem (1).
For the doors of the tent:
1 m 1 m
- For problem (1) and (2), students’ answer is still about the length of cloth (e.g. they
need to buy 38 meter of cloth). Therefore, problem (3) is aimed to bridge students from
length (of cloth) problem to area problem. To solve problem (3), students need to
“convert” the length of cloth into the area of cloth, namely: from 38 meter long of cloth
into 38 × 1 of cloth (note: the width of the cloth is 1 meter). At the beginning students
may solve the problem by calculating the area of each piece of cloth/fabric.
- Problem (4) is aimed to guide students to make the net of a triangular prism. This
question is important to help students to formulate the formula of triangular prism’s
surface area in more formal way since this problem will help students think that a
triangular prism compounded by two triangles and three rectangles. Therefore, it is
expected that students are able to find that the surface area of a triangular prism is the
sum of the area of two triangles and the area of three rectangles.
- Problem (5) is aimed to guide students to conclude what they have done on problem
(1) to problem (4).
1. Our scout team wants to make a tent that is made of 100 sacks.
Every sack has size 60cm× 40cm. Determine possible
dimension(s) of our tent that can be made of 100 sacks without
leaving any sacks.
Note: we should split every sack.
Suppose every sack is split, so the size of the sack will be 60cm× 80cm.
Arrange the sacks so we will get a rectangle with size:
length = 80cm × 10 = 800 cm = 8 m
width = 60cm×10 = 600 cm = 6 m
We can make a tent without base in triangular prism with size:
The net of the tent could be:
R : part that remain
2. Eighteen centimeter square of aluminium foil is needed to pack a triangular prism-
chocolate bar. Determine the possible dimensions of the cartoon package that can
contain 10 triangular prism-chocolate bars.
18 cm 2
The area of aluminium foil is the surface area of a chocolate bar. Therefore:
18 = 2 area of triangles + 2 area of rectangular sides + 1 area of rectangular base
One possible dimension for a chocolate bar is:
Therefore one of the possible dimensions of the cartoon package is
SCORING FOR THE TASK 1
1. Splitting sack 5
2. Drawing the result of merging 100 sacks 10
3. Predicting possible dimension of tent 15
4. Argument of prediction 20
1. Illustrating/drawing 5
2. Formulating dimension of one chocolate 20
3. Predicting dimension of cartoon package 15
4. Final answer 10
Homework (individual task):
1. Given a triangular prism which its base is equilateral triangle. If the sides of the
triangles are 4 cm and the height of prism is 12 cm, find the area of triangular prism.
2. The base of a triangular prism is a right triangle. The right sides are 6 cm and 8 cm. If
the height of the triangular prism is 15 cm, find the area of triangular prism.
3. ABC is an isosceles triangle.
AB = BC = 5 cm and AC = 8 cm
The base-side and top-side of a prism made of triangle above.
Find the surface area of the prism, if its height is 20 cm.
1. First, the altitude of the equilateral triangle must be calculated by using Pythagorean
Theorem. The altitude of the equilateral triangle: √4 − 2 = 2√3 cm.
Area of the triangular prism =
(2×area of triangle) + (3×area of rectangle)
(2×( × 4 × 2√3)) + (3×(12 ×4)) = 144+8√3 cm2
2. Area of triangular prism =
(2×area of triangle) + area of 3 rectangles
) + (8×15) + (6×15) + (10×15) = 48+120+90+150 = 378 cm2
3. Area of triangular prism =
(2×area of triangle) + area of 3 rectangle
(2×( 1 × 8× 3 ) ) + (2×5×10) + (8×10) = 24+100+80 = 204 cm2
4. Area of triangular prism =
(2×area of triangle) + area of 3 rectangles
(2×( 1 × 14× 12 ) ) + (14×20) + (15×20) + (13×20) = 168+280+300+260 = 1008cm2


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|Predominant national and selected regional or minority scripts|
A writing system is a method of visually representing verbal communication. While both writing and speech are useful in conveying messages, writing differs in also being a reliable form of information storage and transfer. Writing systems require shared understanding between writers and readers of the meaning behind the sets of characters that make up a script. Writing is usually recorded onto a durable medium, such as paper or electronic storage, although non-durable methods may also be used, such as writing on a computer display, on a blackboard, in sand, or by skywriting. Reading a text can be accomplished purely in the mind as an internal process, or expressed orally.
Writing systems can be placed into broad categories such as alphabets, syllabaries, or logographies, although any particular system may have attributes of more than one category. In the alphabetic category, a standard set of letters represent speech sounds. In a syllabary, each symbol correlates to a syllable or mora. In a logography, each character represents a semantic unit such as a word or morpheme. Abjads differ from alphabets in that vowels are not indicated, and in abugidas or alphasyllabaries each character represents a consonant–vowel pairing. Alphabets typically use a set of less than 100 symbols to fully express a language, whereas syllabaries can have several hundred, and logographies can have thousands of symbols. Many writing systems also include a special set of symbols known as punctuation which is used to aid interpretation and help capture nuances and variations in the message's meaning that are communicated verbally by cues in timing, tone, accent, inflection or intonation.
Writing systems were preceded by proto-writing, which used pictograms, ideograms and other mnemonic symbols. Proto-writing lacked the ability to capture and express a full range of thoughts and ideas. The invention of writing systems, which dates back to the beginning of the Bronze Age in the late Neolithic Era of the late 4th millennium BC, enabled the accurate durable recording of human history in a manner that was not prone to the same types of error to which oral history is vulnerable. Soon after, writing provided a reliable form of long distance communication. With the advent of publishing, it provided the medium for an early form of mass communication.
Writing systems are distinguished from other possible symbolic communication systems in that a writing system is always associated with at least one spoken language. In contrast, visual representations such as drawings, paintings, and non-verbal items on maps, such as contour lines, are not language-related. Some symbols on information signs, such as the symbols for male and female, are also not language related, but can grow to become part of language if they are often used in conjunction with other language elements. Some other symbols, such as numerals and the ampersand, are not directly linked to any specific language, but are often used in writing and thus must be considered part of writing systems.
Every human community possesses language, which many regard as an innate and defining condition of humanity. However, the development of writing systems, and the process by which they have supplanted traditional oral systems of communication, have been sporadic, uneven and slow. Once established, writing systems generally change more slowly than their spoken counterparts. Thus they often preserve features and expressions which are no longer current in the spoken language. One of the great benefits of writing systems is that they can preserve a permanent record of information expressed in a language.
All writing systems require:
- at least one set of defined base elements or symbols, individually termed signs and collectively called a script;
- at least one set of rules and conventions (orthography) understood and shared by a community, which assigns meaning to the base elements (graphemes), their ordering and relations to one another;
- at least one language (generally spoken) whose constructions are represented and can be recalled by the interpretation of these elements and rules;
- some physical means of distinctly representing the symbols by application to a permanent or semi-permanent medium, so they may be interpreted (usually visually, but tactile systems have also been devised).
In the examination of individual scripts, the study of writing systems has developed along partially independent lines. Thus, the terminology employed differs somewhat from field to field.
Text, writing, reading and orthography
The generic term text refers to an instance of written or spoken material with the latter having been transcribed in some way. The act of composing and recording a text may be referred to as writing, and the act of viewing and interpreting the text as reading. Orthography refers to the method and rules of observed writing structure (literal meaning, "correct writing"), and particularly for alphabetic systems, includes the concept of spelling.
Grapheme and phoneme
A grapheme is a specific base unit of a writing system. Graphemes are the minimally significant elements which taken together comprise the set of "building blocks" out of which texts made up of one or more writing systems may be constructed, along with rules of correspondence and use. The concept is similar to that of the phoneme used in the study of spoken languages. For example, in the Latin-based writing system of standard contemporary English, examples of graphemes include the majuscule and minuscule forms of the twenty-six letters of the alphabet (corresponding to various phonemes), marks of punctuation (mostly non-phonemic), and a few other symbols such as those for numerals (logograms for numbers).
An individual grapheme may be represented in a wide variety of ways, where each variation is visually distinct in some regard, but all are interpreted as representing the "same" grapheme. These individual variations are known as allographs of a grapheme (compare with the term allophone used in linguistic study). For example, the minuscule letter a has different allographs when written as a cursive, block, or typed letter. The choice of a particular allograph may be influenced by the medium used, the writing instrument, the stylistic choice of the writer, the preceding and following graphemes in the text, the time available for writing, the intended audience, and the largely unconscious features of an individual's handwriting.
Glyph, sign and character
The terms glyph, sign and character are sometimes used to refer to a grapheme. Common usage varies from discipline to discipline; compare cuneiform sign, Maya glyph, Chinese character. The glyphs of most writing systems are made up of lines (or strokes) and are therefore called linear, but there are glyphs in non-linear writing systems made up of other types of marks, such as Cuneiform and Braille.
Complete and partial writing systems
Writing systems may be regarded as complete according to the extent to which they are able to represent all that may be expressed in the spoken language, while a partial writing system is limited in what it can convey.
Writing systems, languages and conceptual systems
Writing systems can be independent from languages, one can have multiple writing systems for a language, e.g., Hindi and Urdu; and one can also have one writing system for multiple languages, e.g., the Arabic script. Chinese characters were also borrowed by variant countries as their early writing systems, e.g., the early writing systems of Vietnamese language until the beginning of the 20th century.
- Jiahu symbols, carved on tortoise shells in Jiahu, c. 6600 BC
- Vinča symbols (Tărtăria tablets), c.5300 BC
- Early Indus script, c. 3500 BC.
- Nsibidi script, c. before 500 AD
The invention of the first writing systems is roughly contemporary with the beginning of the Bronze Age in the late Neolithic[dubious ] of the late 4th millennium BC. The Sumerian archaic cuneiform script and the Egyptian hieroglyphs are generally considered the earliest writing systems, both emerging out of their ancestral proto-literate symbol systems from 3400 to 3200 BC with earliest coherent texts from about 2600 BC. It is generally agreed that Sumerian writing was an independent invention; however, it is debated whether Egyptian writing was developed completely independently of Sumerian, or was a case of cultural diffusion.
A similar debate exists for the Chinese script, which developed around 1200 BC. Chinese script is probably an independent invention, because there is no evidence of contact between China and the literate civilizations of the Near East, and because of the distinct differences between the Mesopotamian and Chinese approaches to logography and phonetic representation.
A hieroglyphic writing system used by pre-colonial Mi'kmaq, that was observed by missionaries from the 17th to 19th centuries, is thought to have developed independently. Although, there is some debate over whether or not this was a fully formed system or just a series of mnemonic pictographs.
It is thought that the first consonantal alphabetic writing appeared before 2000 BC, as a representation of language developed by Semitic tribes in the Sinai-peninsula (see History of the alphabet). Most other alphabets in the world today either descended from this one innovation, many via the Phoenician alphabet, or were directly inspired by its design.
Several approaches have been taken to classify writing systems, the most common and basic one is a broad division into three categories: logographic, syllabic, and alphabetic (or segmental); however, all three may be found in any given writing system in varying proportions, often making it difficult to categorise a system uniquely. The term complex system is sometimes used to describe those where the admixture makes classification problematic. Modern linguists regard such approaches, including Diringer's
- pictographic script
- ideographic script
- analytic transitional script
- phonetic script
- alphabetic script
as too simplistic, often considering the categories to be incomparable. Hill split writing into three major categories of linguistic analysis, one of which covers discourses and is not usually considered writing proper:
- discourse system
- morphemic writing system, e.g. Egyptian, Sumerian, Maya, Chinese
- phonemic writing system
Sampson draws a distinction between semasiography and glottography
- semasiography, relating visible marks to meaning directly without reference to any specific spoken language
- glottography, using visible marks to represent forms of a spoken language
- logography, representing a spoken language by assigning distinctive visible marks to linguistic elements of André Martinet's "first articulation" (Martinet 1949), i.e. morphemes or words
- phonography, achieving the same goal by assigning marks to elements of the "second articulation", e.g. phonemes, syllables
- syllabic systems
- pure syllabic, e.g. Linear B, Yi, Kana, Cherokee
- morpho-syllabic, e.g. Sumerian, Chinese, Mayan
- morpho-consonantal, e.g. Egyptian
- pure consonantal, e.g. Phoenician
- pure phonemic, e.g. Greek
- morpho-phonemic, e.g. English
- syllabic systems
Faber categorizes phonographic writing by two levels, linearity and coding:
- logographic, e.g. Chinese, Ancient Egyptian
|Type||Each symbol represents||Example|
|Logosyllabary||word or morpheme as well as syllable||Chinese characters|
|Abjad (consonantary)||consonant||Arabic alphabet|
|Alphabet||consonant or vowel||Latin alphabet|
|Abugida||consonant accompanied by specific vowel,
modifying symbols represent other vowels
|Featural system||distinctive feature of segment||Korean Hangul|
A logogram is a single written character which represents a complete grammatical word. Most traditional Chinese characters are classified as logograms.
As each character represents a single word (or, more precisely, a morpheme), many logograms are required to write all the words of language. The vast array of logograms and the memorization of what they mean are major disadvantages of logographic systems over alphabetic systems. However, since the meaning is inherent to the symbol, the same logographic system can theoretically be used to represent different languages. In practice, the ability to communicate across languages only works for the closely related varieties of Chinese, as differences in syntax reduce the crosslinguistic portability of a given logographic system. Japanese uses Chinese logograms extensively in its writing systems, with most of the symbols carrying the same or similar meanings. However, the grammatical differences between Japanese and Chinese are significant enough that a long Chinese text is not readily understandable to a Japanese reader without any knowledge of basic Chinese grammar, though short and concise phrases such as those on signs and newspaper headlines are much easier to comprehend.
While most languages do not use wholly logographic writing systems, many languages use some logograms. A good example of modern western logograms are the Arabic numerals: everyone who uses those symbols understands what 1 means whether they call it one, eins, uno, yi, ichi, ehad, ena, or jedan. Other western logograms include the ampersand &, used for and, the at sign @, used in many contexts for at, the percent sign % and the many signs representing units of currency ($, ¢, €, £, ¥ and so on.)
Logograms are sometimes called ideograms, a word that refers to symbols which graphically represent abstract ideas, but linguists avoid this use, as Chinese characters are often semantic–phonetic compounds, symbols which include an element that represents the meaning and a phonetic complement element that represents the pronunciation. Some nonlinguists distinguish between lexigraphy and ideography, where symbols in lexigraphies represent words and symbols in ideographies represent words or morphemes.
The most important (and, to a degree, the only surviving) modern logographic writing system is the Chinese one, whose characters have been used with varying degrees of modification in varieties of Chinese, Japanese, Korean, Vietnamese, and other east Asian languages. Ancient Egyptian hieroglyphs and the Mayan writing system are also systems with certain logographic features, although they have marked phonetic features as well and are no longer in current use. Vietnamese speakers switched to the Latin alphabet in the 20th century and the use of Chinese characters in Korean is increasingly rare. The Japanese writing system includes several distinct forms of writing including logography.
Syllabic systems: syllabary
Another type of writing system with systematic syllabic linear symbols, the abugidas, is discussed below as well.
As logographic writing systems use a single symbol for an entire word, a syllabary is a set of written symbols that represent (or approximate) syllables, which make up words. A symbol in a syllabary typically represents a consonant sound followed by a vowel sound, or just a vowel alone.
In a "true syllabary", there is no systematic graphic similarity between phonetically related characters (though some do have graphic similarity for the vowels). That is, the characters for /ke/, /ka/ and /ko/ have no similarity to indicate their common "k" sound (voiceless velar plosive). More recent creations such as the Cree syllabary embody a system of varying signs, which can best be seen when arranging the syllabogram set in an onset–coda or onset–rime table.
Syllabaries are best suited to languages with relatively simple syllable structure, such as Japanese. The English language, on the other hand, allows complex syllable structures, with a relatively large inventory of vowels and complex consonant clusters, making it cumbersome to write English words with a syllabary. To write English using a syllabary, every possible syllable in English would have to have a separate symbol, and whereas the number of possible syllables in Japanese is around 100, in English there are approximately 15,000 to 16,000.
However, syllabaries with much larger inventories do exist. The Yi script, for example, contains 756 different symbols (or 1,164, if symbols with a particular tone diacritic are counted as separate syllables, as in Unicode). The Chinese script, when used to write Middle Chinese and the modern varieties of Chinese, also represents syllables, and includes separate glyphs for nearly all of the many thousands of syllables in Middle Chinese; however, because it primarily represents morphemes and includes different characters to represent homophonous morphemes with different meanings, it is normally considered a logographic script rather than a syllabary.
Other languages that use true syllabaries include Mycenaean Greek (Linear B) and Indigenous languages of the Americas such as Cherokee. Several languages of the Ancient Near East used forms of cuneiform, which is a syllabary with some non-syllabic elements.
Segmental systems: alphabets
An alphabet is a small set of letters (basic written symbols), each of which roughly represents or represented historically a segmental phoneme of a spoken language. The word alphabet is derived from alpha and beta, the first two symbols of the Greek alphabet.
The first type of alphabet that was developed was the abjad. An abjad is an alphabetic writing system where there is one symbol per consonant. Abjads differ from other alphabets in that they have characters only for consonantal sounds. Vowels are not usually marked in abjads.
All known abjads (except maybe Tifinagh) belong to the Semitic family of scripts, and derive from the original Northern Linear Abjad. The reason for this is that Semitic languages and the related Berber languages have a morphemic structure which makes the denotation of vowels redundant in most cases.
Some abjads, like Arabic and Hebrew, have markings for vowels as well. However, they use them only in special contexts, such as for teaching. Many scripts derived from abjads have been extended with vowel symbols to become full alphabets. Of these, the most famous example is the derivation of the Greek alphabet from the Phoenician abjad. This has mostly happened when the script was adapted to a non-Semitic language.
The term abjad takes its name from the old order of the Arabic alphabet's consonants 'alif, bā', jīm, dāl, though the word may have earlier roots in Phoenician or Ugaritic. "Abjad" is still the word for alphabet in Arabic, Malay and Indonesian.
An abugida is an alphabetic writing system whose basic signs denote consonants with an inherent vowel and where consistent modifications of the basic sign indicate other following vowels than the inherent one.
Thus, in an abugida there may or may not be a sign for "k" with no vowel, but also one for "ka" (if "a" is the inherent vowel), and "ke" is written by modifying the "ka" sign in a way that is consistent with how one would modify "la" to get "le". In many abugidas the modification is the addition of a vowel sign, but other possibilities are imaginable (and used), such as rotation of the basic sign, addition of diacritical marks and so on.
The contrast with "true syllabaries" is that the latter have one distinct symbol per possible syllable, and the signs for each syllable have no systematic graphic similarity. The graphic similarity of most abugidas comes from the fact that they are derived from abjads, and the consonants make up the symbols with the inherent vowel and the new vowel symbols are markings added on to the base symbol.
In the Ge'ez script, for which the linguistic term abugida was named, the vowel modifications do not always appear systematic, although they originally were more so. Canadian Aboriginal syllabics can be considered abugidas, although they are rarely thought of in those terms. The largest single group of abugidas is the Brahmic family of scripts, however, which includes nearly all the scripts used in India and Southeast Asia.
The name abugida is derived from the first four characters of an order of the Ge'ez script used in some contexts. It was borrowed from Ethiopian languages as a linguistic term by Peter T. Daniels.
A featural script represents finer detail than an alphabet. Here symbols do not represent whole phonemes, but rather the elements (features) that make up the phonemes, such as voicing or its place of articulation. Theoretically, each feature could be written with a separate letter; and abjads or abugidas, or indeed syllabaries, could be featural, but the only prominent system of this sort is Korean hangul. In hangul, the featural symbols are combined into alphabetic letters, and these letters are in turn joined into syllabic blocks, so that the system combines three levels of phonological representation.
Many scholars, e.g. John DeFrancis, reject this class or at least labeling hangul as such. The Korean script is a conscious script creation by literate experts, which Daniels calls a "sophisticated grammatogeny". These include stenographies and constructed scripts of hobbyists and fiction writers (such as Tengwar), many of which feature advanced graphic designs corresponding to phonologic properties. The basic unit of writing in these systems can map to anything from phonemes to words. It has been shown that even the Latin script has sub-character "features".
Most writing systems are not purely one type. The English writing system, for example, includes numerals and other logograms such as #, $, and &, and the written language often does not match well with the spoken one. As mentioned above, all logographic systems have phonetic components as well, whether along the lines of a syllabary, such as Chinese ("logo-syllabic"), or an abjad, as in Egyptian ("logo-consonantal").
Some scripts, however, are truly ambiguous. The semi-syllabaries of ancient Spain were syllabic for plosives such as p, t, k, but alphabetic for other consonants. In some versions, vowels were written redundantly after syllabic letters, conforming to an alphabetic orthography. Old Persian cuneiform was similar. Of 23 consonants (including null), seven were fully syllabic, thirteen were purely alphabetic, and for the other three, there was one letter for /Cu/ and another for both /Ca/ and /Ci/. However, all vowels were written overtly regardless; as in the Brahmic abugidas, the /Ca/ letter was used for a bare consonant.
The zhuyin phonetic glossing script for Chinese divides syllables in two or three, but into onset, medial, and rime rather than consonant and vowel. Pahawh Hmong is similar, but can be considered to divide syllables into either onset-rime or consonant-vowel (all consonant clusters and diphthongs are written with single letters); as the latter, it is equivalent to an abugida but with the roles of consonant and vowel reversed. Other scripts are intermediate between the categories of alphabet, abjad and abugida, so there may be disagreement on how they should be classified.
Perhaps the primary graphic distinction made in classifications is that of linearity. Linear writing systems are those in which the characters are composed of lines, such as the Latin alphabet and Chinese characters. Chinese characters are considered linear whether they are written with a ball-point pen or a calligraphic brush, or cast in bronze. Similarly, Egyptian hieroglyphs and Maya glyphs were often painted in linear outline form, but in formal contexts they were carved in bas-relief. The earliest examples of writing are linear: the Sumerian script of c. 3300 BC was linear, though its cuneiform descendants were not. Non-linear systems, on the other hand, such as braille, are not composed of lines, no matter what instrument is used to write them.
Cuneiform was probably the earliest non-linear writing. Its glyphs were formed by pressing the end of a reed stylus into moist clay, not by tracing lines in the clay with the stylus as had been done previously. The result was a radical transformation of the appearance of the script.
Braille is a non-linear adaptation of the Latin alphabet that completely abandoned the Latin forms. The letters are composed of raised bumps on the writing substrate, which can be leather (Louis Braille's original material), stiff paper, plastic or metal.
There are also transient non-linear adaptations of the Latin alphabet, including Morse code, the manual alphabets of various sign languages, and semaphore, in which flags or bars are positioned at prescribed angles. However, if "writing" is defined as a potentially permanent means of recording information, then these systems do not qualify as writing at all, since the symbols disappear as soon as they are used. (Instead, these transient systems serve as signals.)
Scripts are also graphically characterized by the direction in which they are written. Egyptian hieroglyphs were written either left to right or right to left, with the animal and human glyphs turned to face the beginning of the line. The early alphabet could be written in multiple directions: horizontally (side to side), or vertically (up or down). Prior to standardization, alphabetical writing was done both left-to-right (LTR or sinistrodextrally) and right-to-left (RTL or dextrosinistrally). It was most commonly written boustrophedonically: starting in one (horizontal) direction, then turning at the end of the line and reversing direction.
The Greek alphabet and its successors settled on a left-to-right pattern, from the top to the bottom of the page. Other scripts, such as Arabic and Hebrew, came to be written right-to-left. Scripts that incorporate Chinese characters have traditionally been written vertically (top-to-bottom), from the right to the left of the page, but nowadays are frequently written left-to-right, top-to-bottom, due to Western influence, a growing need to accommodate terms in the Latin script, and technical limitations in popular electronic document formats. Chinese characters sometimes, as in signage, especially when signifying something old or traditional, may also be written from right to left. The Old Uyghur alphabet and its descendants are unique in being written top-to-bottom, left-to-right; this direction originated from an ancestral Semitic direction by rotating the page 90° counter-clockwise to conform to the appearance of vertical Chinese writing. Several scripts used in the Philippines and Indonesia, such as Hanunó'o, are traditionally written with lines moving away from the writer, from bottom to top, but are read horizontally left to right; however, Kulitan, another Philippine script, is written top to bottom and right to left. Ogham is written bottom to top and read vertically, commonly on the corner of a stone.
In computers and telecommunication systems, writing systems are generally not codified as such,[clarification needed] but graphemes and other grapheme-like units that are required for text processing are represented by "characters" that typically manifest in encoded form. There are many character encoding standards and related technologies, such as ISO/IEC 8859-1 (a character repertoire and encoding scheme oriented toward the Latin script), CJK (Chinese, Japanese, Korean) and bi-directional text. Today, many such standards are re-defined in a collective standard, the ISO/IEC 10646 "Universal Character Set", and a parallel, closely related expanded work, The Unicode Standard. Both are generally encompassed by the term Unicode. In Unicode, each character, in every language's writing system, is (simplifying slightly) given a unique identification number, known as its code point. Computer operating systems use code points to look up characters in the font file, so the characters can be displayed on the page or screen.
A keyboard is the device most commonly used for writing via computer. Each key is associated with a standard code which the keyboard sends to the computer when it is pressed. By using a combination of alphabetic keys with modifier keys such as Ctrl, Alt, Shift and AltGr, various character codes are generated and sent to the CPU. The operating system intercepts and converts those signals to the appropriate characters based on the keyboard layout and input method, and then delivers those converted codes and characters to the running application software, which in turn looks up the appropriate glyph in the currently used font file, and requests the operating system to draw these on the screen.
- Artificial script
- Defective script
- Formal language
- International phonetic alphabet
- ISO 15924
- Phonemic orthography
- Phonetic transcription
- Numeral system
- Transcription (linguistics)
- Written language
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