Learning Theories

Learning TheoriesThe thought of how we learn can be described in a battalion of different ways. Andrew Pollard describes larning â€Å"as the procedure by which cognition, constructs, accomplishments and attitudes are acquired, understood, applied and extended. Children besides discover their feeling towards themselves, towards each other and towards larning itself. Learning is therefore partially a cognitive, partially societal and affective.† Therefore a brooding professional must concentrate on these major concerns by concentrating on student public presentation within course of study based undertakings and in the long term developing each kid ‘s ability to come on as a successful scholar. Another of import facet for the instructor is the ability to decently understand the procedure of acquisition, as this should enable the professional to cognize best how to prosecute students in the acquisition experience. This thought of acquisition is non new and has been around since the beginning of world, be that the passing on cognition of fire devising to the acquisition of basic linguistic communication within early adult male. It is merely in more recent times that bookmans have attempted to make theories which describe this act that most people carry out without truly believing about. Some of these theories will be looked at in this piece, nevertheless it is of import to observe that the thought of one theory that fits all persons is in its ego a misnomer, as people and the universe they live in alteration faster than these theories can maintain up.Multiple intelligences: Howard GardnerThis theory of Multiple Intelligences was suggested in 1983 by the American psychologist Howard Gardener in his book Frames of the Mind. Gardner ‘s theory proposed that scholars have peculiar types of intelligences that can be classified, and each person has differing degrees of competency within each int elligence type or profile.Gardner identified 8 intelligences:Linguistic – the capacity to utilize words efficaciously Logical-mathematical – the capacity to utilize Numberss efficaciously Spatial – the ability to comprehend the visual-spatial universe accurately Bodily-kinaesthetic – expertness in utilizing one ‘s whole organic structure to show thoughts and feelings. Musical – the capacity to comprehend, discriminate, transform and express musical signifiers. Interpersonal – the ability to comprehend and do differentiations in the tempers, purposes and feelings of other people. Intrapersonal – self-knowledge and the ability to move on that cognition. Naturalistic – expertness in the acknowledgment and categorization of the legion species. ( Definitions from Multiple Intelligences in the Classroom – Thomas Armstrong ) Gardner ‘s theory proposed that the thought of I.Q. does non take into history the broad scope of abilities worlds display. In the multiple intelligences theory Gardner states that each intelligence profile can be improved to a high degree and suggests that learning should integrate all intelligences into the schoolroom so as to provide to a broad scope of abilities and intelligences. This will enable the scholar to larn in a manner that bests suits his or her single intelligence profile. Gardner highlights the importance of the instructor admiting that persons have different degrees of competency within certain intelligences, and suggests lessons should be planned to assist the scholar better in the intelligences in which they are weaker. This thought has been reinforced by research that proposes intelligence is developed though chance and the scholar ‘s experience ( Shayer and Addy, 2002 ) Some of the thoughts behind this theory of multiple intelligences have been criticized in the psychological science and educational theory communities ( White, 1998 ) , a common unfavorable judgment is that the theory is based on the theorist personal sentiment. Psychologist such as George Miller believe Gardner ‘s theory is based on his intuition and provinces that the theory lacks empirical informations. Gardner ‘s responds to his critics saying. â€Å" The testimonies and s are legion plenty from tonss of different topographic points to propose it ‘s deserving taking earnestly. † There is a batch of anecdotal grounds in support of MI, but no formal surveies. At the really least, many believe that MI theory virtues farther probe and large-scale research† . Other unfavorable judgments are based on instructors seting students into fixed intelligence profiles. This does non let the scholar to better in intelligences in which they are deemed to be less ab le, taking to a non-inclusive environment.Constructivism and Social Constructivism: Piaget VygotskyConstructivism theory suggests that people learn through an interaction between believing and experience, and through the consecutive development of more complex cognitive constructions ( Pollard 2002 ) . The most influential constructivist theoretician was Piaget. Jean Piaget ( 1896-1980 ) was a Swiss psychologist, philosopher and instructor. He taught at Grange-Aux-Belles school for male childs, he noticed when taging the students work that immature kids would systematically give the incorrect replies to certain inquiries. When he looked closer at these consequences he found that there was a form to the errors that immature kids made, that older kids did non. This led him to believe that there was an built-in difference in the manner younger people learn than that of grownups. Piaget proposed through a procedure of â€Å"accommodation and â€Å"assimilation† kids construct their ain world by agencies of experimenting on their ain environment. Piaget proposed that there are four cardinal developmental phases in which kids process their experience. 1 Sensorimotor – From birth to age 2 old ages. The baby builds an apprehension of himself or herself and world ( and how things work ) through interactions with the environment. It is able to distinguish between itself and other objects. Learning takes topographic point via assimilation ( the organisation of information and absorbing it into bing scheme ) and adjustment ( when an object can non be assimilated and the schemes have to be modified to include the object. 2 Pre-operational phase – From 2 to 7 old ages The kid is non yet able to gestate abstractly and needs concrete physical state of affairss. Objects are classified in simple ways, particularly by of import characteristics 3 Concrete operations phase – ( 7 to 12 old ages ) . As physical experience accumulates, adjustment is increased. The kid begins to believe abstractly and gestate, making logical constructions that explain his or her physical experiences. 4 Formal operations stage – ( 12 to 15 old ages ) Cognition reaches its concluding signifier. By this phase, the individual no longer requires concrete objects to do rational opinions. He or she is capable of deductive and conjectural logical thinking. His or her ability for abstract thought is really similar to an grownup. The effect of Piaget work has lead to the thought of a kid centred attack to instruction, this is particularly true in Primary school categories. It has promoted the usage of varied and stimulating schoolroom environments from which kids can deduce ambitious experiences. Some restrictions of Piagets work have been highlighted, one such unfavorable judgment is that due to the fact that the abilitiy of a kid to larn is structured into phases, it can take to the under appraisal of their capacities. Surveies have shown that kids ‘s capacities are much greater than those suggested by Piaget ( Tizard and Hughes ) Another unfavorable judgment of Piagets work is that as it can be hard to run into the demands of all persons in a category, the demand for a trim acquisition experience for each single category can take to a damaging state of affairs whereby the instructor spends so much clip pull offing the category room they are non able to pass adequate clip learning their students. Social Constructivism is a alteration of Piaget ‘s theory and was proposed by Russian psychologist Lev Vygotsky. He believed that Piaget ‘s theory did non take into history a kid ‘s societal interactions which he believed besides had an consequence on cognitive development. Vygotsky ‘s theory proposed that. * interaction and civilization have a dramatic consequence on cognitive development. * Cognitive procedures ( linguistic communication, thought and concluding ) develop though societal interaction. * Learning is a shared societal activity embedded in schoolroom interactions. * The relationship between scholar and instructor is important. Within Vygotsky ‘s theory he introduces the thought of the zone of proximal development ( ZPD ) in larning this is stated as. â€Å" The distance between the existent development degree as determined by independent job resolution and the degree of possible development as determined through job work outing under grownup counsel or in coaction with more capable equals † ( Vygotsky, 1978, p. 86 ) . This helping the scholar by a more capable other has been termed â€Å"scaffolding† . Scaffolding is a procedure whereby the scholar is provided with construction and support which allows them to understand undertaking they could non make entirely. As the scholar develops an apprehension of the undertaking the staging can be removed this consequences in â€Å"more sophisticated cognitive systems†¦ the system of cognition itself becomes portion of the scaffold or societal support for the new learning† ( Raymond, 2000, p. 176 ) . Curriculum for Excellence lends to a great extent from these thoughts with its AifL and inclusion enterprises. AifL formative appraisal constabularies should convey more balance to the place of more knowing other as it aims to hold category equals every bit good as the instructor make fulling this function. The active function of the scholar in this theory should let for a better apprehension of what is being taught and why ensuing in an improved acquisition environment.Theories used in the schoolroomMultiple IntelligencesDuring my clip on SE1A I tried to suit a figure of different intelligences into my lesson. During planning of any lesson I would implement different manners of acquisition, this was non ever possible due to resource and clip restraints, nevertheless in the cases where it was possible I noticed positive consequences. Whilst taking a S1 category covering human organic structure systems, I was able to utilize a choice of larning stuffs. I made certain that all students were exposed to all larning types, the purpose of the lesson was to let all students to make the success standards utilizing three different larning manners. The manners I adopted were the usage of a picture ( Visual ) theoretical accounts of the human organic structure ( kinesthetic ) and group treatment ( Linguistic-Intrapersonal ) . I found this to be a successful lesson as during plenary students were able to joint which larning manner they found most good and which they found least. With this in head I will go on to use the multiple intelligences theory when be aftering my lessons and will seek to suit as many larning intelligences as possible.Social constructivismI implemented societal constructivist theory when puting a undertaking to a S1 category I was learning, the category was split into groups A, B, C, D, E each group was given the undertaking of happening out about a particular cell type/s, during this clip I moved around the category staging. Once the group collected all the information that was required, the groups were rearranged so each member of the group had looked at a different cell. The purpose of the lesson was for each member of the group to learn the remainder of the group what they had found out. Each group successfully completed the acquisition and success standards. The whole category were engaged and there was a high grade of larning taking topographic point, holding seen this theory in pattern I will be go oning to utilize and better it in my pattern.Appraisal schemesIn recent old ages appraisal has become the primary focal point in instruction. This has occurred for two grounds ( Pollard 2008 ) . The first and most important has been the demand for authoritiess to hold a manner of mensurating educational end product. This was seen as a manner for parents to be able to compare between different schools trial consequences, and hence be able to do an informed pick as to what school to direct their kids to. The hope was that the publication of conference tabular arraies would promote all schools to raise criterions and invariably better on consequences to raise their place in the school evaluations tabular arraies. The 2nd ground for the increased involvement in appraisal came from the realization of the value of continual appraisal in informing instruction and bettering acquisition ( Black and William 1998 ) . Their research highlighted that appraisal can be used as a tool to find non merely what has been learned i.e . terminal of subject trials and tests, but appraisal can besides be used as a tool for acquisition.Appraisal is for Learning ( AifL )Appraisal is for larning ( AifL ) is an effort to seek and hold more balance in the Scots course of study, the over accent of summational appraisals schemes, such as terminal of subject trials and tests, does non needfully give a good indicant to the degree of larning that takes topographic point in the category room. Alternatively the usage of formative appraisal schemes should be at the nucleus of effectual instruction pattern. The work of Black and William in 1998 established that there was strong grounds that formative appraisal can raise criterions of student ‘s accomplishment. Appraisal can be said to be formative when the consequences from the instructors and pupils measuring themselves generate an adaptation to the learning methods later employed to run into the demands of the students. ( Inside the Black Box ) . It is this thought of co ntinual student instructor interactions taking to version of learning to run into the demands of single students that lies at the bosom of effectual instruction.The AifL model incorporates three different facets of appraisal:* appraisal FOR larning * appraisal OF larning * appraisal AS acquisition,Appraisal For larningThe intent of appraisal for acquisition is to â€Å"focus on the spread between where a scholar is in their acquisition, and where they need to be- the coveted goal† ( LTScotland ) . This end can be attained by a assortment of agencies such as feedback to pupils, guaranting the students are cognizant of the acquisition purposes and effectual inquiring among others. Black and William have defined appraisal for larning as â€Å"all those activities undertaken by instructors and/or by their pupils, which provide information to be used as feedback to modify the instruction and acquisition activities in which they are engaged†Key characteristicsThe cardinal characteristics as stated by LTS web site are as follows Focus on high quality interactions – Successful appraisal in the schoolroom should affect high quality interactions based on thoughtful inquiries, careful hearing and effectual responses. This should affect giving students equal â€Å"wait time† before seeking to reply inquiries as suggested by Mary Budd Rowe ( â€Å"Wait Time and Rewards as Instructional Variables, Their Influence on Language, Logic, and Fate Control, † Journal of Researching Science Teaching, vol. 11, 1974, pp. 81-94 ) . This could besides be the usage of a no custodies policy when replying inquiries Involving students in their acquisition – Focus on the extent your students and staff are to the full involved in make up one's minding following stairss in their acquisition and identifying who can assist. This should affect the scholars holding a active function in what they are being taught were possible, and giving the scholar pick in the ways which they learn as stated by Gardner ‘s theory of multiple intelligences Feedback – Students and staff are given timely feedback about the quality of their work and how to do it better. This thought of positive support sing students work it portion of Skinner ‘s behaviorist theory. The importance of both verbal and written feedback allows the scholar to cognize if there are any spreads in their cognition, but besides lets them cognize what countries they perform good in. Sharing standards – â€Å"Pupils, staff and parents are clear about what is to be learned and what success would be like† It is of import that students are made cognizant of the undertaking they are transporting out and what is to be learned by sharing larning purposes, in add-on it is besides of import that they are cognizant of what the success standards are for said undertaking. This pattern of sharing larning purposes and success standards is a critical portion of the appraisal for larning scheme and is similar to Vygotsky ‘s Zone of Proximal Development.Appraisal in the schoolroomDuring my clip on SE1A I implemented a figure of different formative appraisal techniques, I ever shared the learning purposes with the category, they would be written on the white board leting me to transport out the lesson on the smart board. This would let the students to hold a mention point which they could easy see throughout the lesson, helped the students to set the lesson into context. In my first lessons I did non portion the success standard with the students and would alternatively travel over them in the plenary, nevertheless holding spoken to co-workers I was advised that it would be good to portion the success standard with the students this was reinforced when I went back to the literature which resulted in me watching instructors Television picture ( hypertext transfer protocol: //www.teachers.tv/video/3311 ) . The sharing of acquisition and success standards did better the categories apprehension of a peculiar subject as they had a clear thought of what was expected of them. With both my S1 and S2 I implemented a no-hands up policy, I would get down by inquiring the students a inquiry I would so give them at least a minute to believe of an reply, so I would inquire an person for an reply. This took a spot of clip for the students to acquire used to as certain students were acquiring frustrated by the delay clip as they knew the reply. I think overall this scheme worked good for most kids as it gave the whole category clip to believe and as they did non cognize who would be asked the inquiry it led to a high degree of battle. In a S2 category I was responsible for a alteration lesson for an terminal of topic trial. I implemented a quiz that was to be created by the category, this involved dividing the category into groups and acquiring them to come up with inquiries refering to the subject. This worked good as there was a high degree of competition for the place of top squad. Once I had made certain the students knew the nature of the inquiries they could inquire they were left to come up with inquiries themselves. This really challenged the students as they wanted to come up with ambitious inquiries for their equals, which lead to some high degree acquisition and a high degree of battle. Other schemes I have used include the usage of a traffic visible radiation system whereby students who showed a green visible radiation for understanding a peculiar subject paired up with students who showed ruddy visible radiation. The green visible radiation students would so assist explicate facets of the subject. I will be implementing other assessment schemes in my go oning pattern, such as issue inquiries, demo me boards and head maps, while invariably bettering my oppugning accomplishments.A Curriculum For ExcellenceThe Curriculum for Excellence ( CfE ) is the new Scottish course of study to be taught in all public Scottish schools by August 2010. CfE came approximately due to the â€Å"National Argument on Education† this argument was launched by the Scots Executive in 2002, the purpose of the argument was to construct on the high quality instruction that was being provided to many of the immature people in Scotland but besides to guarantee that â€Å"all immature people were being offered a welcoming and stimulating environment for the 21st century.† ( Scots Executive, 2002 ) . The consequence of this argument was that although there were many positive facets of the current course of study there was a demand for alteration. In November 2004 the proposal for CfE was approved and published, it was implemented to broaden the acquisition experiences of immature people and to do these experiences more gratifying and relevant to a quickly altering environment. CfE has been designed to develop four chief capacities in all immature people between the ages of 3 and 18, these capacities being successful scholars, confident persons, responsible citizens and effectual subscribers. To accomplish this end CfE has 7 rules of course of study design that have been devised to guarantee the four capacities are met. 1. Challenge and enjoyment – Young people should happen their acquisition challenging, prosecuting and actuating. The lessons planned by instructors should reflect this rule by promoting high aspirations and aspirations for all students. 2. Breadth – All immature people should be educated in a wide scope of results and experiences across all course of study countries. The acquisition may be linked to vocational or other specialised contexts and will take topographic point both in the category room and other cross-curricular activities. 3. Progression – The learning experience will take topographic point between the ages of 3 – 18 and will demo a continual patterned advance within a individual curricular model. The rate of patterned advance should be tailored to the person so that it meets their demands and aptitudes, and leaves options open so that no picks within the course of study are closed prematurely. 4. Depth – The scholar should hold chances to derive a deeper apprehension for different types of thought and acquisition. As they progress through the old ages they should be able to make their full capacity by developing cognitive accomplishments, while besides deriving a better apprehension of their moral values and beliefs. 5. Personalisation and Choice – the course of study should suit every single scholars demands and back up their aptitudes and endowments. The scholar should hold an active function in how and what they learn. 6. Coherence – The course of study should be a consistent larning experience from 3-18 and there should be clear links between different facets of their acquisition. This should include lessons which can pull from different strands of larning which cross over traditional capable boundaries 7. Relevance – The leering experienced by immature people should be relevant to them. They should understand why they are larning and it relevancy to their lives both inside and outside the category room. The Curriculum for excellence purposes to give all immature people the accomplishments and cognition they need to win in the modern twenty-four hours universe. If all schools can win at developing the four capacities in all persons so it should give their students an ideal start in life and should do for a shining illustration of what can be achieved.CfE in the category roomAs the CfE results and experiences have non yet been implemented in the school I was at on SE1 I was non able to be after lessons around them. The school I was placed at was still learning the 5-14 National Guidelines, nevertheless this did non halt me from looking at the similarities in each set of results. Looking at the results it became clear that there was an convergence in both sets of results which allowed me to learn lessons which would cover both 5 to 14 and CfE outcomes. During my observations at school it became clear that in many instances the seven rules within CfE were being adhered to, this allowed me to larn from my equals how best to implement them into my categories.Challenge and EnjoymentDuring my observation clip on arrangement I was able to see precisely what was working good within certain categories, although at this point I had a batch of thoughts on how best to set together my lessons acquiring a pupils oculus position on the lesson truly helped me to take activities that would work best. I was responsible for a category of S1 students on SE1, through a series of lessons I implemented a scope of different activities to maintain the category stimulated and motivated. During the lessons the students were involved in card kinds, cut and paste activities, single paired and full category probes, smart board activities, pictures, modeling, postings doing and PowerPoint presentations. Appendix? Shows a posting made by a group of my students, the lesson involved making research for the subject in the ICT suite followed by a presentation to the remainder of the category utilizing postings or PowerPoint. All the students were actively involved in the exercising and students had the pick of how they wished to show their information. I besides left it up to the students to depute certain undertakings to each member of the squad. These activities allowed the scholars to hold an active function in their acquisition and take which method of larning they thought worked best for them. During the plenary session at the terminal of the lesson we would discourse if they had met the success standards and in some instances if their chosen type of larning manner was really effectual.RelevanceWhen be aftering my lesson I ever thought of ways to convey in existent life illustrations to the subjects I was learning. When I was covering the electrochemical series with a S3 category I was able to demo why we use different metals in bring forthing batteries, this lead to me explicating the chemical science of nomadic phone batteries and ways to widen their life. During a lesson on the respiratory system to a S1 category I was able to demo the consequence that smoke has on the lungs, and highlighted the importance of a healthy diet in digestion. During the forces topic we investigated the varying degrees of clash of different stuffs on ice, the students were so able to propose the best types of footwear to either cut down or increase clash if they were out walking on an icy w inter ‘s twenty-four hours.Literacy and numeracyLiteracyWithin CfE literacy had been highlighted as a nucleus accomplishment which is to be embedded throughout the course of study regardless of the topic. Literacy is defined as â€Å"the set of accomplishments which allows an person to prosecute to the full in society and in acquisition, through the different signifiers of linguistic communication, and the scope of texts, which society values and discoveries useful.† ( LTS ) Bettering literacy accomplishments is of critical importance as it enables immature people to â€Å"develop accomplishments for acquisition, accomplishments for life and accomplishments for work, † ( www.ltscotland.org.uk/curriculumforexcellence/buildingthecurriculum/entitlements/skills/index.asp ) Literacy skills enable immature people to better understand and interact with their topics in the course of study, non merely this but these accomplishments are movable to the out of school environment, be that the work topographic point or in mundane life. If a student has problem with literacy accomplishments this can take to a deficiency of patterned advance in a peculiar topic, the feeling that the instructor may hold is that the student is non engagement in the topic. However the root of the job is that the students have hapless reading authorship or listening accomplishments. The results for literacy are: Reading, Writing, Listening and Talking CfE demands that all practicians engage with bettering degrees of literacy, as the betterment in literacy will ensue in an increased apprehension of all topics within the school course of study. By guaranting that all practicians take duty for literacy within schools the student will hold the chance to develop their accomplishments for acquisition, accomplishments for life and accomplishments for the work topographic point.NumeracyAs with Literacy, numeracy is besides a nucleus accomplishment within CfE â€Å"All instructors have duty for advancing the development of numeracy. With an increased accent upon numeracy for all immature people, instructors will necessitate to be after to revisit and consolidate numeracy accomplishments throughout schooling.† ( Constructing the Curriculum I ) Numeracy has been highlighted as a nucleus accomplishment, as like literacy competent numeracy accomplishments are indispensable in mundane life, and as such to be able to lend efficaciously to society immature people should hold a good foundation in these accomplishments. Strong numeracy accomplishments provide immature people with better apprehension of the universe around them and are a footing for womb-to-tomb acquisition. The edifice of strong numeracy accomplishments throughout the course of study should give immature people â€Å"the assurance and competency in utilizing figure which will let persons to work out jobs, analyse information and do informed determinations based on calculations.† CfE bookletDrumheadIt has been shown that strong accomplishments in both literacy and numeracy benefits both the person and the state as a whole. The importance of these accomplishments is highlighted in the ALNIS study which states â€Å"Literacy and numeracy accomplishments are c ritical for grownups to accomplish the ends they set themselves at work, at place, in the community and as scholars. The personal effects of low literacy and numeracy accomplishments can be serious. The national effects for a modern, multicultural, competitory Scotland, and attempts to accomplish societal justness, are far reaching.† ( ALNIS, p 12 )Literacy in the schoolroomDuring placement SE1A, I paid peculiar attending to the literacy results defined by CfE. When lesson planning I integrated literacy results into all my categories be these reading composing speaking or hearing. In one category I used a picture to summarize chief points that had been taught throughout the subject. I asked to take down note sum uping the chief points of the subject, this would let me to estimate whether they had understood the chief learning purpose of the subject. I made certain to halt the picture at cardinal points to let the kids with slower cognitive or composing accomplishments clip to believe and compose. This exercising planned to better the kids ‘s hearing and note taking abilities as this is a of import accomplishment needed in the school and work environment. The kids were so asked to describe back what notes they had taken and why within groups. This exercising was besides developed to better at that place speaking accomplishments as they each had to separately describe back the notes they had taken. I found this exercising priceless as I rapidly realised that there was a broad scope of abilities within the category, as a whole the category found this undert aking hard. There were a figure of facets of the undertaking the kids found hard which arose during the plenary treatment, many of which arose from holding to watch the picture and compose down short concise notes. This undertaking showed me the true extend of the importance of distinction required in lessons, it besides highlighted that note pickings is a accomplishment that may non hold been taught in any deepness within the course of study. In future I will do certain that before transporting out an exercising like this that a important sum of clip is spent learning the accomplishment as I think it will profit students in the short and long term. The creative activity of a lab write up within a category is an first-class manner to better composing accomplishments. Every practical carried out by my categories is accompanied with an experimental write up. The usage of experimental write ups gives kids exposure to an unfamiliar manner of composing. I ever promote my students to compose up studies in a scientific mode with an purpose, hypothesis, consequences and decision. Before the write up I would inquire for suggestion as to how the study should be worded, followed by an illustration provided by myself. This got the kids thin inking about the construction and registry of the piece. In some instances I would inquire an person or group to show their findings to the category. In one category I split the category into four groups and asked each group to compose up the purpose, method and manner to enter consequences for the four different experiments. Once completed the group ‘s swapped studies and tried to transport out experiment utilizing the study they received. I will be go oning to utilize lab study composing as I think it does cover a broad scope of results for literacy, and when carried out good does prosecute students. In a S2 scientific discipline category I took, the students were required to retrieve a peculiar series of reactive metals. To do this easier to retrieve I encouraged the category to come up with acronym to assist them retrieve the series. Before we started I gave them a few illustrations of common acronyms they had likely used such l.o.l and o.m.g. this started a het argument as to the best acronym to utilize for the reactive metals. Each member of the category came up with their ain acronym some more suited than others, nevertheless all students did prosecute and there was a spot of temper in the lesson which is of import when learning some of the more proficient facets of scientific discipline. This undertaking got the kids activity believing about the right pick of words and the usage of their vocabulary, I would state the undertaking worked good and I will be utilizing the technique once more when seeking to assist the kids remember complex scientific sequences.