Jerome Seymour Bruner was an American psychologist who made significant contributions to human cognitive psychology and cognitive learning theory in educational psychology. Bruner was a senior research fellow at the New York University School of Law, he received a B. A. in 1937 from Duke University and a Ph. D. from Harvard University in 1941. A Review of General Psychology survey, published in 2002, ranked Bruner as the 28th most cited psychologist of the 20th century. Bruner was born blind on October 1, 1915, in New York City, to Herman and Rose Bruner, who were Polish Jewish immigrants. An operation at age 2 restored his vision, he received a bachelor's of arts degree in Psychology, in 1937 from Duke University, went on to earn a master's degree in Psychology in 1939 and a doctorate in Psychology in 1941 from Harvard University. In 1939, Bruner published his first psychological article on the effect of thymus extract on the sexual behavior of the female rat. During World War II, Bruner served on the Psychological Warfare Division of the Supreme Headquarters Allied Expeditionary Force committee under General Dwight D. Eisenhower, researching social psychological phenomena.
In 1945, Bruner returned to Harvard as a psychology professor and was involved in research relating to cognitive psychology and educational psychology. In 1970, Bruner left Harvard to teach at the University of Oxford in the United Kingdom, he returned to the United States in 1980. In 1991, Bruner joined the faculty at New York University, where he taught in the School of Law; as an adjunct professor at NYU School of Law, Bruner studied. During his career, Bruner was awarded honorary doctorates from Yale University, Columbia University, The New School, the Sorbonne, the ISPA Instituto Universitário, as well as colleges and universities in such locations as Berlin and Rome, was a Fellow of the American Academy of Arts and Sciences, he turned 100 in October 2015 and died on June 5, 2016. Bruner is one of the pioneers of cognitive psychology in the United States, which began through his own early research on sensation and perception as being active, rather than passive processes. In 1947, Bruner published his study Value and Need as Organizing Factors in Perception, in which poor and rich children were asked to estimate the size of coins or wooden disks the size of American pennies, dimes and half-dollars.
The results showed that the value and need the poor and rich children associated with coins caused them to overestimate the size of the coins when compared to their more accurate estimations of the same size disks. Another study conducted by Bruner and Leo Postman showed slower reaction times and less accurate answers when a deck of playing cards reversed the color of the suit symbol for some cards; these series of experiments issued in what some called the'New Look' psychology, which challenged psychologists to study not just an organism's response to a stimulus, but its internal interpretation. After these experiments on perception, Bruner turned his attention to the actual cognitions that he had indirectly studied in his perception studies. In 1956, Bruner published the book A Study of Thinking, which formally initiated the study of cognitive psychology. Soon afterward Bruner helped. After a time, Bruner began to research other topics in psychology, but in 1990 he returned to the subject and gave a series of lectures compiled into the book Acts of Meaning.
In these lectures, Bruner refuted the computer model for studying the mind, advocating a more holistic understanding of the mind and its cognitions. Beginning around 1967, Bruner turned his attention to the subject of developmental psychology and studied the way children learn, he coined the term "scaffolding" to describe the instructional process where the instructor provides the appropriate amount of guidance to help the student achieve the task. The instructor reduces the amount of assistance provided as the student progresses through the instruction. In his research on the development of children Bruner proposed three modes of representation: enactive representation, iconic representation, symbolic representation. Rather than neatly delineated stages, the modes of representation are integrated and only loosely sequential as they "translate" into each other. Symbolic representation remains the ultimate mode, for it "is the most mysterious of the three." Bruner's theory suggests it is efficacious, when faced with new material, to follow a progression from enactive to iconic to symbolic representation.
A true instructional designer, Bruner's work suggests that a learner is capable of learning any material so long as the instruction is organized appropriately, in sharp contrast to the beliefs of Piaget and other stage theorists.. Like Bloom's Taxonomy, Bruner suggests a system of coding in which people form a hierarchical arrangement of related categories; each successively higher level of categories becomes more specific, echoing Benjamin Bloom's understanding of knowledge acquisition as well as the related idea of instructional scaffolding. In accordance with this understanding of learning, Bruner proposed the spiral curriculum, a teaching approach in which each subject or skill area is revisited at intervals, at a more sophisticated level each time. First there is basic knowledge of a subject more sophistication is added, reinforcing principles that were first discussed; this sy
A standardized test is a test, administered and scored in a consistent, or "standard", manner. Standardized tests are designed in such a way that the questions, conditions for administering, scoring procedures, interpretations are consistent and are administered and scored in a predetermined, standard manner. Any test in which the same test is given in the same manner to all test takers, graded in the same manner for everyone, is a standardized test. Standardized tests do not need to be high-stakes tests, time-limited tests, or multiple-choice tests; the questions can be complex. The subject matter among school-age students is academic skills, but a standardized test can be given on nearly any topic, including driving tests, personality, professional ethics, or other attributes; the opposite of standardized testing is non-standardized testing, in which either different tests are given to different test takers, or the same test is assigned under different conditions or evaluated differently. Most everyday quizzes and tests taken by students meet the definition of a standardized test: everyone in the class takes the same test, at the same time, under the same circumstances, all of the students are graded by their teacher in the same way.
However, the term standardized test is most used to refer to tests that are given to larger groups, such as a test taken by all adults who wish to acquire a license to have a particular kind of job, or by all students of a certain age. Because everyone gets the same test and the same grading system, standardized tests are perceived as being fairer than non-standardized test; such tests are thought of as fairer and more objective than a system in which some students get an easier test and others get a more difficult test. That perception, which may or may not be accurate, depends on the purpose for the test. If a teacher wishes to determine individual children's skills with respect to a specific activity, tests other than those that are standardized are more effective. Standardized tests are designed to permit reliable comparison of outcomes across all test takers, because everyone is taking the same test. While that point is granted the children tested have not been exposed to the same materials found on those standardized tests.
Such tests are constructed by individuals who have no knowledge of the test-takers beyond their age and/or grade level. Age and/or grade level, are poor indicators of what children have learned; as a result, conclusions drawn from the results can be wrong. The prevalence of standardized testing in formal education has been criticized for many reasons; the definition of a standardized test has changed somewhat over time. In 1960, standardized tests were defined as those in which the conditions and content were equal for everyone taking the test, regardless of when, where, or by whom the test was given or graded; the purpose of this standardization is to make sure that the scores reliably indicate the abilities or skills being measured, not other things, such as different instructions about what to do if the test taker does not know the answer to a question. By the beginning of the 21st century, the focus shifted away from a strict sameness of conditions towards equal fairness of conditions. For example, a test taker with a broken wrist might write more because of the injury, it would be more fair, produce a more reliable understanding of the test taker's actual knowledge, if that person were given a few more minutes to write down the answers to a most test.
However, if the purpose of the test is to see how the student could write this would become a modification of the content, no longer a standardized test. The earliest evidence of standardized testing was in China, during the Han Dynasty, where the imperial examinations covered the Six Arts which included music, horsemanship, arithmetic and knowledge of the rituals and ceremonies of both public and private parts; these exams were used to select employees for the state bureaucracy. Sections on military strategies, civil law and taxation, agriculture and geography were added to the testing. In this form, the examinations were institutionalized for more than a millennium. Today, standardized testing remains used, most famously in the Gaokao system. Standardized testing was introduced into Europe in the early 19th century, modeled on the Chinese mandarin examinations, through the advocacy of British colonial administrators, the most "persistent" of, Britain's consul in Guangzhou, Thomas Taylor Meadows.
Meadows warned of the collapse of the British Empire if standardized testing was not implemented throughout the empire immediately. Prior to their adoption, standardized testing was not traditionally a part of Western pedagogy, it is because of this, that the first European implementation of standardized testing did not occur in Europe proper, but in British India. Inspired by the Chinese use of standardized testing, in the early 19th century, British "company managers hired and promoted employees based on competitive examinations in order to prevent corruption and favoritism." This practice of standardized testing was adopted in the late 19th century by the British mainland. The parliamentary debates that ensued made many references to the "Chinese mandarin system", it was from B
Arithmetic is a branch of mathematics that consists of the study of numbers the properties of the traditional operations on them—addition, subtraction and division. Arithmetic is an elementary part of number theory, number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra and analysis; the terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are sometimes still used to refer to a wider part of number theory. The prehistory of arithmetic is limited to a small number of artifacts which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed; the earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but the characteristics of the particular numeral system influence the complexity of the methods.
The hieroglyphic system for Egyptian numerals, like the Roman numerals, descended from tally marks used for counting. In both cases, this origin resulted in values that used a decimal base but did not include positional notation. Complex calculations with Roman numerals required the assistance of a counting board or the Roman abacus to obtain the results. Early number systems that included positional notation were not decimal, including the sexagesimal system for Babylonian numerals and the vigesimal system that defined Maya numerals; because of this place-value concept, the ability to reuse the same digits for different values contributed to simpler and more efficient methods of calculation. The continuous historical development of modern arithmetic starts with the Hellenistic civilization of ancient Greece, although it originated much than the Babylonian and Egyptian examples. Prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs.
For example, Nicomachus summarized the viewpoint of the earlier Pythagorean approach to numbers, their relationships to each other, in his Introduction to Arithmetic. Greek numerals were used by Archimedes and others in a positional notation not different from ours; the ancient Greeks lacked a symbol for zero until the Hellenistic period, they used three separate sets of symbols as digits: one set for the units place, one for the tens place, one for the hundreds. For the thousands place they would reuse the symbols for the units place, so on, their addition algorithm was identical to ours, their multiplication algorithm was only slightly different. Their long division algorithm was the same, the digit-by-digit square root algorithm, popularly used as as the 20th century, was known to Archimedes, who may have invented it, he preferred it to Hero's method of successive approximation because, once computed, a digit doesn't change, the square roots of perfect squares, such as 7485696, terminate as 2736.
For numbers with a fractional part, such as 546.934, they used negative powers of 60 instead of negative powers of 10 for the fractional part 0.934. The ancient Chinese had advanced arithmetic studies dating from the Shang Dynasty and continuing through the Tang Dynasty, from basic numbers to advanced algebra; the ancient Chinese used a positional notation similar to that of the Greeks. Since they lacked a symbol for zero, they had one set of symbols for the unit's place, a second set for the ten's place. For the hundred's place they reused the symbols for the unit's place, so on, their symbols were based on the ancient counting rods. It is a complicated question to determine when the Chinese started calculating with positional representation, but it was before 400 BC; the ancient Chinese were the first to meaningfully discover and apply negative numbers as explained in the Nine Chapters on the Mathematical Art, written by Liu Hui. The gradual development of the Hindu–Arabic numeral system independently devised the place-value concept and positional notation, which combined the simpler methods for computations with a decimal base and the use of a digit representing 0.
This allowed the system to represent both large and small integers. This approach replaced all other systems. In the early 6th century AD, the Indian mathematician Aryabhata incorporated an existing version of this system in his work, experimented with different notations. In the 7th century, Brahmagupta established the use of 0 as a separate number and determined the results for multiplication, division and subtraction of zero and all other numbers, except for the result of division by 0, his contemporary, the Syriac bishop Severus Sebokht said, "Indians possess a method of calculation that no word can praise enough. Their rational system of mathematics, or of their method of calculation. I mean the system using nine symbols." The Arabs learned this new method and called it hesab. Although the Codex Vigilanus described an early form of Arabic numerals by 976 AD, Leonardo of Pisa was responsible for spreading their use throughout Europe after the publication of his book Liber Abaci in 1202, he wrote, "The method of the Indians surpasses any known method to compute.
It's a marvelous method. They do their computations using nine figures and symbol zero". In the Middle Ages, arithmetic was one of the seven
Maria Tecla Artemisia Montessori was an Italian physician and educator best known for the philosophy of education that bears her name, her writing on scientific pedagogy. At an early age, Montessori broke gender barriers and expectations when she enrolled in classes at an all-boys technical school, with hopes of becoming an engineer, she soon had a change of heart and began medical school at the University of Rome, where she graduated – with honors – in 1896. Her educational method is still in use today in many public and private schools throughout the world. Montessori was born on August 1870 in Chiaravalle, Italy, her father, Alessandro Montessori, 33 years old at the time, was an official of the Ministry of Finance working in the local state-run tobacco factory. Her mother, Renilde Stoppani, 25 years old, was well educated for the times and was the great-niece of Italian geologist and paleontologist Antonio Stoppani. While she did not have any particular mentor, she was close to her mother who encouraged her.
She had a loving relationship with her father, although he disagreed with her choice to continue her education. The Montessori family moved to Florence in 1873 and to Rome in 1875 because of her father's work. Montessori entered a public elementary school at the age of 6 in 1876, her early school record was "not noteworthy", although she was awarded certificates for good behavior in the 1st grade and for "lavori donneschi", or "women's work", the next year. In 1883 or 1884, at the age of 13, Montessori entered a secondary, technical school, Regia Scuola Tecnica Michelangelo Buonarroti, where she studied Italian, algebra, accounting, history and sciences, she graduated in 1886 with good grades and examination results. That year, at the age of 16, she continued at the technical institute Regio Istituto Tecnico Leonardo da Vinci, studying Italian, history, geography and ornate drawing, chemistry, botany and two foreign languages, she did well in the sciences and in mathematics. She intended to pursue the study of engineering upon graduation, an unusual aspiration for a woman in her time and place.
However, by the time she graduated in 1890 at the age of 20, with a certificate in physics–mathematics, she had decided to study medicine instead, an more unlikely pursuit given cultural norms at the time. Montessori moved forward with her intention to study medicine, she appealed to Guido Baccelli, the professor of clinical medicine at the University of Rome, but was discouraged. Nonetheless, in 1890, she enrolled in the University of Rome in a degree course in natural sciences, passing examinations in botany, experimental physics, histology and general and organic chemistry, earning her diploma di licenza in 1892; this degree, along with additional studies in Italian and Latin, qualified her for entrance into the medical program at the University in 1893. She was met with hostility and harassment from some medical students and professors because of her gender; because her attendance of classes with men in the presence of a naked body was deemed inappropriate, she was required to perform her dissections of cadavers alone, after hours.
She resorted to smoking tobacco to mask the offensive odor of formaldehyde. Montessori won an academic prize in her first year, in 1895 secured a position as a hospital assistant, gaining early clinical experience. In her last two years she studied pediatrics and psychiatry, worked in the pediatric consulting room and emergency service, becoming an expert in pediatric medicine. Montessori graduated from the University of Rome in 1896 as a doctor of medicine, her thesis was published in 1897 in the journal Policlinico. She found employment as an assistant at the University hospital and started a private practice.) From 1896 to 1901, Montessori worked with and researched so-called "phrenasthenic" children—in modern terms, children experiencing some form of mental retardation, illness, or disability. She began to travel, study and publish nationally and internationally, coming to prominence as an advocate for women's rights and education for mentally disabled children. On March 31, 1898, her only child -- a son named.
Mario Montessori was born out of her love affair with Giuseppe Montesano, a fellow doctor, co-director with her of the Orthophrenic School of Rome. If Montessori married, she would be expected to cease working professionally. Montessori wanted to keep the relationship with her child's father secret under the condition that neither of them would marry anyone else; when the father of her child fell in love and subsequently married, Montessori was left feeling betrayed and decided to leave the university hospital and place her son into foster care with a family living in the countryside opting to miss the first few years of his life. She would be reunited with her son in his teenage years, where he proved to be a great assistant in her research. After graduating from the University of Rome in 1896, Montessori continued with her research at the University's psychiatric clinic, in 1897 she was accepted as a voluntary assistant there; as part of her work, she visited asylums in Rome where she observed children with mental disabilities, observations which were fundamental to her future educational work.
She read and studied the works of 19th-century physicians and educators Jean Marc Gaspard Itard and Édouard Séguin, who influenced her work. Maria was intrigued by Itard's ideas and created a far more specific an
Problem-based learning is a student-centered pedagogy in which students learn about a subject through the experience of solving an open-ended problem found in trigger material. The PBL process does not focus on problem solving with a defined solution, but it allows for the development of other desirable skills and attributes; this includes enhanced group collaboration and communication. The PBL process was developed for medical education and has since been broadened in applications for other programs of learning; the process allows for learners to develop skills used for their future practice. It enhances critical appraisal, literature retrieval and encourages ongoing learning within a team environment; the PBL tutorial process involves working in small groups of learners. Each student takes on a role within the group that may be formal or informal and the role alternates, it is focused on the student's reasoning to construct their own learning. The Maastricht seven-jump process involves clarifying terms, defining problem, brainstorming and hypothesis, learning objectives, independent study and synthesis.
In short, it is identifying what they know, what they need to know, how and where to access new information that may lead to the resolution of the problem. The role of the tutor is to facilitate learning by supporting and monitoring the learning process; the tutor aims to build students' confidence when addressing problems, while expanding their understanding. This process is based on constructivism. PBL represents a paradigm shift from traditional teaching and learning philosophy, more lecture-based; the constructs for teaching PBL are different from traditional classroom or lecture teaching and require more preparation time and resources to support small group learning. Wood defines problem-based learning as a process that uses identified issues within a scenario to increase knowledge and understanding; the principles of this process are listed below: Learner-driven self-identified goals and outcomes Students do independent, self-directed study before returning to larger group Learning is done in small groups of 8–10 people, with a tutor to facilitate discussion Trigger materials such as paper-based clinical scenarios, lab data, articles or videos or patients can be used The Maastricht 7 jump process helps to guide the PBL tutorial process Based on principles of adult learning theory All members of the group have a role to play Allows for knowledge acquisition through combined work and intellect Enhances teamwork and communication, problem-solving and encourages independent responsibility for shared learning - all essential skills for future practice Anyone can do it as long it is right depending on the given causes and scenario We can be champions and holders of a vocational degree It depends upon the cases and the scenario the building of curriculum lesson The PBL process was pioneered by Barrows and Tamblyn at the medical school program at McMaster University in Hamilton in the 1960s.
Traditional medical education disenchanted students, who perceived the vast amount of material presented in the first three years of medical school as having little relevance to the practice of medicine and clinically based medicine. The PBL curriculum was developed in order to stimulate learning by allowing students to see the relevance and application to future roles, it maintains a higher level of motivation towards learning, shows the importance of responsible, professional attitudes with teamwork values. The motivation for learning drives interest because it allows for selection of problems that have real-world application. Problem-based learning has subsequently been adopted by other medical school programs adapted for undergraduate instruction, as well as K-12; the use of PBL has expanded from its initial introduction into medical school programs to include education in the areas of other health sciences, law, economics, social studies, engineering. PBL includes problems that can be solved in many different ways depending on the initial identification of the problem and may have more than one solution.
There are advantages of PBL. It is student-focused, which allows for active learning and better understanding and retention of knowledge, it helps to develop life skills that are applicable to many domains. It can be used to enhance content knowledge while fostering the development of communication, problem-solving, critical thinking and self-directed learning skills. PBL may position students to optimally function using real-world experiences. By harnessing collective group intellect, differing perspectives may offer different perceptions and solutions to a problem. Following are the advantages and limitations of problem-based learning. In problem-based learning the students are involved and they like this method, it fosters active learning, retention and development of lifelong learning skills. It encourages self-directed learning by confronting students with problems and stimulates the development of deep learning. Problem-based learning gives emphasis to lifelong learning by developing in students the potential to determine their own goals, locate appropriate resources for learning and assume responsibility for what they need to know.
It greatly helps them better long term knowledge retention. Problem-based learning focuses on engaging students in finding solutions to real life situations and pertinent contextualized problems. In this method discussion forums collaborative research take the place of lecturing. PBL fosters learning by involving students with the interaction of learning materials, they relate the concept they study with ever
Outcome-based education is an educational theory that bases each part of an educational system around goals. By the end of the educational experience, each student should have achieved the goal. There is no single specified style of teaching or assessment in OBE; the role of the faculty adapts into instructor, facilitator, and/or mentor based on the outcomes targeted. Outcome-based methods have been adopted in education systems at multiple levels. Australia and South Africa have since been phased out; the United States has had an OBE program in place since 1994, adapted over the years. In 2005, Hong Kong adopted an outcome-based approach for its universities. Malaysia implemented OBE in all of their public schools systems in 2008; the European Union has proposed an education shift to focus on outcomes, across the EU. In an international effort to accept OBE, The Washington Accord was created in 1989; as of 2017, the full signatories are Australia, Taiwan, Hong Kong, Ireland, Korea, New Zealand, Singapore, South Africa, Sri Lanka, the United Kingdom, Pakistan and the United States.
In a regional/local/foundational/electrical education system, students are given grades and rankings compared to each other. Content and performance expectations are based on what was taught in the past to students of a given age of 12-18; the goal of this education was to present the knowledge and skills of an older generation to the new generation of students, to provide students with an environment in which to learn. The process paid little attention to; the focus on outcomes creates a clear expectation of what needs to be accomplished by the end of the course. Students will understand what is expected of them and teachers will know what they need to teach during the course. Clarity is important over years of schooling; each team member, or year in school, will have a clear understanding of what needs to be accomplished in each class, or at each level, allowing students to progress. Those designing and planning the curriculum are expected to work backwards once an outcome has been decided upon.
With a clear sense of what needs to be accomplished, instructors will be able to structure their lessons around the student’s needs. OBE does not specify a specific method of instruction, leaving instructors free to teach their students using any method. Instructors will be able to recognize diversity among students by using various teaching and assessment techniques during their class. OBE is meant to be a student-centered learning model. Teachers are meant to guide and help the students understand the material in any way necessary, study guides, group work are some of the methods instructors can use to facilitate students learning. OBE can be compared across different institutions. On an individual level, institutions can look at what outcomes a student has achieved to decide what level the student would be at within a new institution. On an institutional level, institutions can compare themselves, by checking to see what outcomes they have in common, find places where they may need improvement, based on the achievement of outcomes at other institutions.
The ability to compare across institutions allows students to move between institutions with relative ease. The institutions can compare outcomes to determine; the articulated outcomes should allow institutions to assess the student’s achievements leading to increased movement of students. These outcomes work for school to work transitions. A potential employer can look at records of the potential employee to determine what outcomes they have achieved, they can determine if the potential employee has the skills necessary for the job. Student involvement in the classroom is a key part of OBE. Students are expected to do their own learning, so that they gain a full understanding of the material. Increased student involvement allows students to feel responsible for their own learning, they should learn more through this individual learning. Other aspects of involvement are parental and community, through developing curriculum, or making changes to it. OBE outcomes are meant to be decided at a local level.
Parents and community members are asked to give input in order to uphold the standards of education within a community and to ensure that students will be prepared for life after school. The definitions of the outcomes decided upon are subject to interpretation by those implementing them. Across different programs or different instructors outcomes could be interpreted differently, leading to a difference in education though the same outcomes were said to be achieved. By outlining specific outcomes, a holistic approach to learning is lost. Learning can find itself reduced to something, specific and observable; as a result, outcomes are not yet recognized as a valid way of conceptualizing what learning is about. When determining if an outcome has been achieved, assessments may become too mechanical, looking only to see if the student has acquired the knowledge; the ability to use and apply the knowledge in different ways may not be the focus of the assessment. The focus on determining if the outcome has been achieved leads to a loss of understanding
Caleb Gattegno was one of the most influential and prolific mathematics educators of the twentieth century. He is best known for his innovative approaches to teaching and learning mathematics, foreign languages and reading, he is the inventor of pedagogical materials for each of these approaches, the author of more than 120 books and hundreds of articles on the topics of education and human development. Gattegno’s pedagogical approach is characterised by propositions based on the observation of human learning in many and varied situations; this is a description of three of these propositions. Gattegno noticed. Human beings have a developed sense of the economics of their own energy and are sensitive to the cost involved in using it, it is therefore essential to teach in ways that are efficient in terms of the amount of energy spent by learners. To be able to mathematically determine whether one method was more efficient than another, he created a unit of measurement for the effort used to learn.
He called that unit an ogden, one can only say an ogden has been spent if the learning was done outside of ordinary functionings, was retained. For example, learning one word in a foreign language costs one ogden, but if the word cannot be recalled, the ogden has not been spent. Gattegno's teaching materials and techniques were designed to be economical with ogdens, so that the most information can be recalled with the least sense of effort. Certain kinds of learning are expensive in terms of energy, i.e. ogdens, while others are free. Memorization is a expensive way to learn; the energy cost can be high when the content is of no particular interest to the learner. Memorizing dates in history or major exports of foreign countries is for most people. School is not the only place. Learning somebody's name or telephone number is arbitrary. We have to use our own energy to make such arbitrary items stick in our memories; the "mental glue" necessary is expensive. Not only is that type of learning expensive, it tends to be fragile.
It is difficult to remember those kinds of items. When we make a great effort, we do not always succeed. We recognise a face without being able to remember the name of the person... not to mention all that all of us have forgotten much of what we "learned" at school. It is not unusual. However, there is another way of functioning. An example of retention is the reception of sensory images; when we look at something – a street, a film, a person, a fine view – photons move from what we are contemplating and enter our eyes to strike the retina. When we listen to something, we create auditory images in a similar way, that is, through energy that enters our system, rather than energy we allocate from inside, to memorize an arbitrary item. To retain an auditory or visual image, we have to use only an insignificant amount of our own to retain it; such images are acquired and remain for long periods. We all have experiences similar to the following examples Gattegno offered: First experience: "I visited a village in the south of France where I had not been for over 10 years and I was able to say,'Oh, yes, I know.
The pharmacy is over there beyond the baker’s.' I went to see and there it was. I had made no effort to memorise this village square, it had entered my mind during my previous visits and it had remained there." Second experience: "I visit a supermarket and go down the aisles. I see an unexceptional woman with a trolley. Three aisles further on, I see her again. I have not tried to remember her, but I have seen her and I can recognise her again a little later." Our system of retention is efficient. We keep in our minds a huge quantity of information because we have seen, tasted, smelled or felt it; that ability is part of human nature. It enables us to ski or to read a book. Gattegno proposed that we base education, not on memorization, which has a high energetic cost and is unreliable, but on retention; the learning tools and techniques Gattegno proposed rely systematically on retention. Gattegno argued that for pedagogical actions to be effective, teaching should be subordinated to learning, which requires that as an absolute prerequisite teachers must understand how people learn.
Rather than present facts for memorization, teachers construct challenges for students to conquer. If the student cannot conquer the challenge the teacher does not tell the answer, but observes and asks questions to determine where the confusion lies, what awareness needs to be triggered in the student; the role of teachers is not to try to transmit knowledge, but to engender acts of awareness in their students, for only awareness is educable. Gattegno created pedagogical materials designed to provoke awarenesses; the materials are intended to be used along with techniques aimed at leading students through a succession of awarenesses. As the students progress, teachers who observe their students can see when and how they can induce a new act of awareness. For example, he created Words in Colour for learning to read, it consists of a series of word charts using a colour code in which each colour represents a phoneme of the language. The charts are used to provoke the phonological awareness in students of the sounds they are making and the order in which they are making them thus engendering all the awarenesse