mathematics mobile applications also developed help students learn mathematics '''conventional approach''' gradual systematic guiding hierarchy mathematical notions ideas techniques starts arithmetic followed euclidean geometry elementary algebra taught concurrently requires instructor well informed elementary mathematics since didactic curriculum decisions often dictated logic subject rather pedagogical considerations methods emerge emphasizing aspects approach '''discovery math''' constructivist method teaching discovery learning mathematics centres around problem based inquiry based learning use


open ended questions manipulative tools ref name ansari march math wars evidence based developmental perspective math education ''education digest'' '' '' retrieved https searchproquestcom openview ede afcd bb c dc c baf pdfpq origsite gscholar cbl ref type mathematics education implemented various parts canada beginning discovery based mathematics forefront canadian math wars debate many criticizing effectiveness due declining math scores comparison traditional teaching models value direct instruction rote learning memorization ref name '''exercises''' reinforcement mathematical skills completing large numbers exercises similar type adding

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vulgar fractions solving quadratic equations '''historical method''' teaching development mathematics within historical social cultural context provides human interest conventional approach '''mastery''' approach students expected achieve high level competence progressing '''new math''' method teaching mathematics focuses abstract concepts set theory functions bases ten adopted us response challenge early soviet technical superiority space began challenged late one influential critiques


new math morris kline 's book ''why johnny ca n't add'' new math method topic one tom lehrer 's popular parody songs introductory remarks song new approach know important thing understand 're rather get right answer '''problem solving''' cultivation mathematical ingenuity creativity heuristic thinking setting students open ended unusual sometimes unsolved problems problems range simple word problems problems international mathematics competitions international mathematical olympiad problem solving


used means build new mathematical knowledge typically building students' prior understandings '''recreational mathematics''' mathematical problems fun motivate students learn mathematics increase enjoyment mathematics '''standards based mathematics''' vision pre college mathematics education us canada focused deepening student understanding mathematical ideas procedures formalized national council teachers mathematics created principles standards school mathematics '''relational approach''' uses class topics solve everyday problems relates topic current events approach focuses many


uses mathematics helps students understand need know well helping apply mathematics real world situations outside classroom '''rote learning''' teaching mathematical results definitions concepts repetition memorisation typically without meaning supported mathematical reasoning derisory term ' 'drill kill'' traditional education rote learning used teach multiplication tables definitions formulas aspects mathematics content age levels different levels mathematics taught different ages somewhat different sequences different countries sometimes class may


taught separate courses different years mathematics countries us states integrated topics branches mathematics studied every year students many countries choose option pre defined course study rather choosing courses '' la carte'' united states students science oriented curricula typically study differential calculus trigonometry age integral calculus complex numbers analytic geometry exponential logarithmic functions infinite series final year secondary school probability statistics may taught secondary education classes


countries topics available advanced additional mathematics college university science engineering students required take multivariable calculus differential equations linear algebra several us colleges minor mathematics substantively comprises courses mathematics majors continue study various areas within pure mathematics often applied mathematics requirement specified advanced courses analysis modern algebra applied mathematics may taken major subject right specific topics taught within courses example civil engineers


may required study fluid mechanics math computer science might include graph theory permutation probability formal mathematical proofs pure applied math degrees often include modules probability theory mathematical statistics course numerical methods often requirement applied math theoretical physics mathematics intensive often overlapping substantively pure applied math degree business mathematics usually limited introductory calculus sometimes matrix calculations economics programs additionally cover optimization often differential equations linear algebra sometimes analysis standards throughout history standards mathematics education set


locally individual schools teachers depending levels achievement relevant realistic considered socially appropriate pupils modern times move towards regional national standards usually umbrella wider standard school curriculum england example standards mathematics education set part national curriculum england scotland maintains educational system many countries centralized ministries set national standards curricula sometimes even textbooks summarised research others found based


nationwide data students higher scores standardised mathematics tests taken mathematics courses high school led states require three years mathematics instead two requirement often met taking another lower level mathematics course additional courses diluted effect raising achievement levels north america national council teachers mathematics nctm published ''principles standards school mathematics'' us canada boosted trend towards reform mathematics nctm released ''curriculum focal points'' recommend


important mathematical topics grade level grade however standards guidelines implement american states canadian provinces chose national governors association center best practices council chief state school officers published common core state standards us states subsequently adopted states adoption common core state standards mathematics discretion state mandated federal government states routinely review academic standards may choose change add onto standards


best meet needs students nctm state affiliates different education standards state level example missouri missouri council teachers mathematics mctm pillars standards education listed website mctm also offers membership opportunities teachers future teachers stay date changes math educational standards programme international student assessment pisa created organisation economic co operation development oecd global program studying reading science mathematic abilities


year old students first assessment conducted year countries participating ref name ref pisa repeated assessment every three years provide comparable data helping guide global education better prepare youth future economies many ramifications following results triennial pisa assessments due implicit explicit responses stakeholders led education reform policy change ref name ref name research robust useful theories classroom teaching yet exist ref name hiebertgrouws ref however useful theories children learn mathematics much research


promotion conceptual understanding attending explicitly concepts allowing students struggle important mathematics features confirmed wide variety studies explicit attention concepts involves making connections facts procedures ideas often seen one strong points mathematics teaching east asian countries teachers typically devote half time making connections extreme usa essentially connections made school classrooms connections made explanation meaning


procedure questions comparing strategies solutions problems noticing one problem special case another reminding students main point discussing lessons connect deliberate productive struggle mathematical ideas refers fact students exert effort important mathematical ideas even struggle initially involves confusion errors result greater learning true whether struggle due challenging well implemented teaching due faulty teaching students must struggle make sense formative assessment ref name blackwiliam ref formative assessment best


younger children homework helps simple skills broader measures achievement students difficulties ref name researchclips students genuine difficulties unrelated motivation past instruction struggle basic facts answer impulsively struggle mental representations poor number sense poor short term memory techniques found productive helping students include peer assisted learning explicit teaching visual aids instruction informed formative assessment encouraging students think aloud algebraic reasoning ref name researchclips elementary school children need spend long time learning express algebraic properties without symbols learning algebraic notation learning symbols


many students believe letters always represent unknowns struggle concept variable prefer arithmetic reasoning algebraic equations solving word problems takes time move arithmetic algebraic generalizations describe patterns students often trouble minus sign understand equals sign mean answer methodology educational research social sciences general mathematics education research depends quantitative qualitative studies quantitative research includes studies use inferential statistics answer specific questions whether certain teaching method gives significantly better


results status quo best quantitative studies involve randomized trials students classes randomly assigned different methods test effects depend large samples obtain statistically significant results qualitative research case studies action research discourse analysis clinical interviews depend small focused samples attempt understand student learning look given method gives results studies cannot conclusively establish one method better another randomized trials unless understood ''why'' treatment x


better treatment application results quantitative studies often lead lethal mutations ref name hiebertgrouws finding actual classrooms exploratory qualitative research also useful suggesting new hypotheses eventually tested randomized experiments qualitative quantitative studies therefore considered essential education social sciences many studies mixed simultaneously combining aspects quantitative qualitative research appropriate randomized trials controversy relative strengths different types research randomized trials provide clear objective evidence works


policymakers often consider studies scholars pushed random experiments teaching methods randomly assigned classes ref name cook ref ref name scheaffer ref disciplines concerned human subjects like biomedicine psychology policy evaluation controlled randomized experiments remain preferred method evaluating treatments educational statisticians mathematics educators working increase use randomized experiments evaluate teaching methods ref name scheaffer hand many scholars educational schools argued increasing number randomized experiments often philosophical objections ethical difficulty randomly assigning


students various treatments effects treatments yet known effective difficulty assuring rigid control independent variable fluid real school settings united states national mathematics advisory panel nmap published report based studies used randomized assignment treatments experimental units classrooms students nmap report 's preference randomized experiments received criticism scholars works clearinghouse essentially research arm department education responded ongoing controversy


extending research base include non experimental studies including regression discontinuity designs single case studies organizations advisory committee mathematics education american mathematical association two year colleges association teachers mathematics canadian mathematical society cd howe institute mathematical association national council teachers mathematics oecd see also aspects mathematics education anti racist mathematics using mathematics education fight racism cognitively guided instruction pre math skills north american issues mathematics education united states mathematical difficulties dyscalculia references reading ball lynda et al ''uses technology primary secondary mathematics education'' cham switzerland


springer dreher anika et al kind content knowledge secondary mathematics teachers need ''journal f r mathematik didaktik'' https linkspringercom article online drijvers paul et al ''uses technology lower secondary mathematics education concise topical survey'' springer nature gosztonyi katalin mathematical culture mathematics education hungary xxth century ''mathematical cultures'' birkh user cham pp nbsp https wwwresearchgatenet profile katalin gosztonyi publication mathematical culture mathematics education hungary xxth century links f cd fa mathematical culture mathematics education hungary xxth centurypdf online losano leticia rcia cristina de costa trindade cyrino current research prospective secondary mathematics teachers professional identity ''the mathematics education prospective secondary teachers around world'' springer cham pp strutchens


meat eater ant feeding honey '''myrmecology''' greek ''myrmex'' ant ''logos'' study branch entomology focusing scientific study ants early myrmecologists considered ant society ideal form society sought find solutions human problems studying ants continue model choice study questions evolution social systems complex varied forms eusociality social organization diversity prominence ecosystems also made important components study biodiversity

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Myrmecology


conservation recently ant colonies also studied modeled relevance machine learning complex interactive networks stochasticity encounter interaction networks parallel computing computing fields ref name ant encounters interaction networks ref history word myrmecology coined william morton wheeler although human interest life ants goes back numerous ancient folk references earliest scientific thinking based observation ant life auguste forel swiss psychologist initially interested ideas instinct learning society wrote book


ants switzerland ''les fourmis de la suisse'' named home ''la fourmili re'' ant colony forel 's early studies included attempts mix species ants colony noted polydomy monodomy ants compared structure nations ref name sleigh sleigh charlotte six legs better cultural history myrmecology johns hopkins university press ref wheeler looked ants new light terms social organization delivered lecture woods hole ant colony organism pioneered idea superorganisms wheeler


considered trophallaxis sharing food within colony core ant society studied using dye food observing spread colony ref name sleigh horace donisthorpe worked systematics ants tradition continued many parts world advances aspects biology made advent genetics ideas ethology evolution led new thought line enquiry pioneered e wilson founded field termed sociobiology ref name sleigh interdisciplinary application ants often


studied engineers biomimicry network engineers efficient networking known clearly ants manage avoid congestions optimize movements move efficient ways without central authority would send orders already many applications structure design networking developed studying ants efficiency human created systems still close efficiency ant colonies furthermore efforts use ant algorithms behavioral strategies ants modern management myrmecologists fiction


black white warner bros movie ''them '' describes visiting expert dr harold medford played edmund gwenn department agriculture washington dc myrmecologist dr hank pym fictional character appearing american comic books published marvel comics marvel cinematic universe list notable myrmecologists ''note names listed alphabetically'' ernest andr french entomologist thomas borgmeier german brazilian theologian entomologist william l brown jr american entomologist giovanni cobelli italian entomologist director rovereto museum arthur charles cole jr american entomologist


pierre andr latreille french entomologist sir john lubbock st lord baron avebury wrote hymenoptera sense organs william mann american entomologist gustav mayr austrian entomologist professor pest vienna specialised hymenoptera carlo menozzi also carlo minozzi italian entomologist william nylander finnish botanist biologist mycologist entomologist myrmecologist basil derek wragge morley research included genetics social behaviour animals behaviour agricultural pests fergus o'rourke irish zoologist julius roger german physician entomologist folklorist felix santschi swiss entomologist theodore christian schneirla


american animal psychologist frederick smith worked zoology department british museum specialising hymenoptera roy r snelling american entomologist credited many important finds rare new ant species erich wasmann austrian entomologist neal albert weber american myrmecologist john obadiah westwood english entomologist archaeologist also noted artistic talents william morton wheeler curator invertebrate zoology american museum natural history described many new species edward osborne wilson pulitzer prize winning american myrmecologist revolutionized field sociobiology contemporary myrmecologists


donat agosti swiss entomologist cesare baroni urbani swiss ant taxonomist murray blum american chemical ecologist expert pheromones barry bolton english ant taxonomist alfred buschinger german myrmecologist henri cagniant french myrmecologist john clark scottish myrmecologist cedric alex collingwood british entomologist mark amidon deyrup american myrmecologist francesc xavier espadaler gelabert spanish myrmecologist specialist mediterranean macaronesian ants invasive species deborah gordon studies ant colony behavior ecology william h gotwald jr american entomologist michael j greene studies interactions chemical cues behavior patterns bert h lldobler pulitzer prize winning german


myrmecologist laurent keller swiss evolutionary biologist myrmecologist john e lattke john longino american entomologist mark w moffett american entomologist photographer corrie moreau american evolutionary biologist entomologist wrote evolution diversification ants justin orvel schmidt american entomologist studies chemical behavioral defenses ants wasps arachnids bernhard seifert german entomologist steven shattuck american australian entomologist marion r smith american entomologist robert w taylor australian myrmecologist alberto tinaut ranera spanish myrmecologist walter r tschinkel american myrmecologist laurel hansen american myrmecologist studies carpenter ant biology urban management james c


independent international non profit scientific journal devoted ant research international union study social insects ant colony optimization swarm intelligence references external links http wwwcctvcambridgeorg antsdocumentary documentary myrmecology dead link subfields entomology


rocky side mountain creek near oros costa rica presumably metamorphic rocks '''earth science''' '''geoscience''' includes fields natural science related planet earth branch science dealing physical chemical constitution earth atmosphere earth science considered branch planetary science much older history earth science encompasses four main branches study lithosphere hydrosphere atmosphere biosphere broken specialized fields reductionist holistic


approaches earth sciences also study earth neighbors space earth scientists use knowledge planet locate develop energy mineral resources others study impact human activity earth 's environment design methods protect planet use knowledge earth processes volcanoes earthquakes hurricanes plan communities expose people dangerous events earth sciences include study geology lithosphere large scale structure earth 's interior well atmosphere hydrosphere biosphere


typically earth scientists use tools geology chronology physics chemistry geography biology mathematics build quantitative understanding earth works evolves example meteorologists study weather watch dangerous storms hydrologists examine water warn floods seismologists study earthquakes try understand strike geologists study rocks help locate useful minerals earth scientists often work field perhaps climbing mountains exploring seabed crawling caves wading swamps measure collect samples rocks river water record findings charts


maps fields study following fields science generally categorized within earth sciences geology describes rocky parts earth 's crust lithosphere historic development major subdisciplines mineralogy petrology geomorphology paleontology stratigraphy structural geology engineering geology sedimentology ref name smith ref physical geography focuses geography earth science physical geography study earth 's seasons climate atmosphere soil streams landforms oceans physical geography divided several branches related fields follows geomorphology biogeography environmental geography palaeogeography climatology meteorology coastal geography hydrology ecology glaciology geophysics


geodesy investigate shape earth reaction forces magnetic gravity fields geophysicists explore earth 's core mantle well tectonic seismic activity lithosphere ref name smith geophysics commonly used supplement work geologists developing comprehensive understanding crustal geology particularly mineral petroleum exploration seismologists use geophysics understand plate tectonic shifting well predict seismic activity geochemistry defined study processes control abundance composition distribution chemical compounds isotopes geologic


environments geochemists use tools principles chemistry study composition structure processes physical aspects earth major subdisciplines aqueous geochemistry cosmochemistry isotope geochemistry biogeochemistry soil science covers outermost layer earth 's crust subject soil formation processes pedosphere major subdivisions field study include edaphology pedology ecology covers interactions organisms environment field study differentiates study earth study planets solar system earth planet teeming life hydrology oceanography


limnology studies focus movement distribution quality water involves components hydrologic cycle earth atmosphere hydrosphere sub disciplines hydrology include hydrometeorology surface water hydrology hydrogeology watershed science forest hydrology water chemistry glaciology covers icy parts earth cryosphere atmospheric sciences cover gaseous parts earth atmosphere surface exosphere nbsp km major subdisciplines include meteorology climatology atmospheric chemistry atmospheric physics earth 's interior volcanic eruption release stored energy


earth 's surface plate tectonics mountain ranges volcanoes earthquakes geological phenomena explained terms physical chemical processes earth 's crust beneath earth 's crust lies mantle heated radioactive decay heavy elements mantle quite solid consists magma state semi perpetual convection convection process causes lithospheric plates move albeit slowly resulting process known plate tectonics ref name adams tectonics ref ref name oldroyd tectonics ref plate tectonics might thought process earth


boundaries ref name adams tectonics ref name oldroyd tectonics earthquakes result movement lithospheric plates often occur near convergent boundaries parts crust forced earth part subduction ref name smith subduction ref volcanoes result primarily melting subducted crust material crust material forced asthenosphere melts portion melted material becomes light enough rise surface giving birth volcanoes ref name adams tectonics ref name smith subduction earth 's atmosphere magnetosphere shields surface earth charged particles solar


wind br ''image scale'' troposphere stratosphere mesosphere thermosphere exosphere five layers make earth 's atmosphere gases atmosphere located within troposphere lowest layer atmosphere made nitrogen oxygen argon small amounts gases including co sub sub water vapor ref name adams atmosphere ref water vapor co sub sub allow earth 's atmosphere catch hold sun 's energy greenhouse effect allows earth 's surface warm enough liquid water support life


addition storing heat atmosphere also protects living organisms shielding earth 's surface cosmic rays often incorrectly thought deflected magnetic field magnetic field created internal motions core produces magnetosphere protects earth 's atmosphere solar wind earth billion years old ref name age earth ref would lost atmosphere protective magnetosphere earth 's magnetic field electromagnet magnet created electric current earth solid iron inner core surrounded


fluid outer core convects ref name oldroyd core therefore earth electromagnet motion fluid convection sustains earth 's magnetic field ref name oldroyd core ref ref name dynamo ref magnetic field also important birds insects use navigate long distances using magnetized iron crystals found skin important function earth 's magnetic field protecting organisms high energy protons deflected along electrons solar wind organisms directly exposed particles would lethal consistency magnetic field remain


constant must attractive magnetic field motion magnetic field changes every aspect well indicates force proportional velocity moving charge magnetic flux density generally measured teslas another unit sometimes used gauss g g equivalent sup sup mg image first example anti parallel currents cause repel second example parallel currents cause attraction lorentz force law force


exerted magnetic field object defined lorentz law chem mathbf f q mathbf e mathbf v times mathbf b chem '''''f''''' force ''q'' object 's electric charge '''''e''''' electric field '''''v''''' object 's velocity '''''b''''' magnetic field strength electromagnetic force holds atoms molecules together fact scale forces electric attraction repulsion electric charges dominant three fundamental forces considered negligible determiners atomic molecular structure lorentz force


law named dutch physicist hendrik antoon lorentz first formulate equation lorentz theorized atoms might consist charged particles suggested oscillations charged particles source light website wwwrpiedu ref methodology methodologies vary depending nature subjects studied studies typically fall one three categories observational experimental theoretical earth scientists often conduct sophisticated computer analysis visit interesting location study earth phenomena eg antarctica hot spot island chains foundational idea earth science notion


retrieved november ref correspond rocks water air life also included cryosphere corresponding ice distinct portion hydrosphere pedosphere corresponding soil active intermixed sphere earth science breakup atmosphere atmospheric chemistry geography climatology meteorology hydrometeorology paleoclimatology biosphere biogeochemistry biogeography ecology landscape ecology geoarchaeology geomicrobiology paleontology palynology micropaleontology hydrosphere hydrology hydrogeology limnology freshwater science oceanography marine science chemical oceanography physical oceanography biological oceanography marine biology geological oceanography marine geology paleoceanography lithosphere geosphere geology economic geology engineering geology environmental geology


terms list geoscience organizations list russian earth scientists list unsolved problems geoscience ''making north america'' pbs film nanogeoscience national association geoscience teachers science tourism structure earth references sources url access registration url https archiveorg details americanheritage unse reading allaby dictionary earth sciences oxford university press korvin g fractal models earth sciences elsvier tarbuck e j lutgens f k tasa earth science prentice hall external links http epodusraedu earth science picture day service universities space research association sponsored


nasa goddard space flight center http tierraredirises geoethics planetary protection geoethics planetary space exploration https geologybuzz earth science geology buzz earth science physical sciences planetary science science related lists


set social changes proposed climate change mitigation '''social change''' involves alteration social order society may include changes social institutions social behaviours social relations definition social change may refer notion social progress sociocultural evolution philosophical idea society moves forward evolutionary means may refer paradigmatic change socio economic structure instance transition feudalism capitalism hypothetical future transition form post capitalism '''social development''' refers people develop social emotional skills across


lifespan particular attention childhood adolescence healthy social development allows us form positive relationships family friends teachers people lives accordingly may also refer social revolution socialist revolution presented marxism social movements women 's suffrage civil rights movement social change may driven cultural religious economic scientific technological forces prominent theories change comes two sources one source random unique factors climate weather presence specific groups people another


source systematic factors example successful development generally requirements stable flexible government enough free available resources diverse social organization society whole social change usually combination systematic factors along random unique factors many theories attempt explain social change one view suggests theory change include elements structural aspects change like population shifts processes mechanisms social change directions change '''hegelian''' classic hegelian dialectic model change based


interaction opposing forces starting point momentary stasis ''thesis'' countered ''antithesis ''first yields conflict subsequently results new ''synthesis'' '''marxist''' marxism presents dialectical materialist concept history seeing humankind 's history fundamental struggle social classes '''kuhnian''' philosopher science thomas kuhn argues ''the structure scientific revolutions'' respect copernican revolution people likely continue utilizing apparently unworkable paradigm better paradigm commonly accepted kuhnian approach study societies provided critical juncture approach


social order change '''heraclitan''' greek philosopher heraclitus used metaphor river speak change thus stepping rivers staying waters flow dk b heraclitus seems suggesting later interpretations notwithstanding order river remain river change must constantly taking place thus one may think heraclitan model parallel living organism order remain alive must constantly change contemporary application approach shown social change theory seed scale


types change social changes vary according speed scope impetus research various types social change focuses social organizations corporations different manifestations change include fabian change gradual reformist incremental amelioration manner fabian society radical change improvements root branch style political radicalism revolutionary change abrupt radical drastic change implications violence starting afresh perhaps popular political bogeyman transformational change new age version radical change


thus difficult define continuous change open ended change change allegedly sake change top change reliance leadership bottom change reliance huddled masses current examples global demographic shifts one obvious changes currently occurring change relative global population distribution countries recent decades developing countries become larger proportion world population increasing population developed countries declined total world population


developed world changes distinct men 's work women 's work gender equal patterns economically important since mid th century men women considered great contributors social change worldwide see also accelerating change activism alternative movement comparative historical research constitutional economics critical juncture theory culture change decadence global social change research project globalization historical sociology industrialisation lifestyle sociology modernization theory reform movement reformism revolution secularization social conservatism social degeneration social development theory social movement social progress social relation social revolution social transformation societal collapse societal transformation sociocultural evolution


references reading eisenstadt sn https booksgoogleconz books tradition change modernityhtmlid wz zaaaamaaj redir esc ''tradition change modernity'' krieger publishing giddens anthony ''sociology'' cambridge polity press haralambos michael holborn martin ''sociology themes perspectives'' london harpercollins harper cl ''exploring social change'' new jersey engelwood cliffs polanyi karl ''the great transformation'' new york farrar rinehart tilly charles misreading rereading nineteenth century social change pp nbsp ''social structures network approach'' eds barry wellman sd berkowitz cambridge cambridge university press tilly charles ''social movements '' boulder co paradigm publishers vago steven ''social change'' th ed upper saddle river


nj prentice hall external links http gsociologyicaaporg understanding world today reports global social political economic demographic technological change http digitalcollectionslibrarygsuedu cdm landingpage collection schange social change collection georgia state university social movements


logic developed arthur prior jaakko hintikka saul kripke mid twentieth century semantics formulas assigned truth values relative ''possible world'' formula 's truth value one possible world depend truth values formulas ''accessible'' possible worlds particular possibility amounts truth ' 'some'' accessible possible world necessity amounts truth ''every'' accessible possible world modal logic often referred logic necessity possibility applications continue play major role philosophy language epistemology metaphysics

Humanities
Philosophy
Logic
Mathematical logic
Modal logic


point often called ''possible world'' formula contains modal operator truth value depend true accessible worlds thus relational semantics interprets formulas modal logic using models defined follows ' 'relational model'' tuple math mathfrak langle w r v rangle math math w math set possible worlds math r math binary relation math w math math v math valuation function assigns truth value pair atomic


formula world ie math v w times f math math f math set atomic formulae set math w math often called ''universe'' binary relation math r math called accessibility relation controls worlds see sake determining true example math w r u math means world math u math accessible world math w math say state affairs known math u math live possibility math w math finally function math v math known valuation


function determines atomic formulas true worlds recursively define truth formula world model math mathfrak math math mathfrak w models p math iff math v w p math math mathfrak w models neg p math iff math w models p math math mathfrak w models p wedge q math iff math w models p math math w models q math math mathfrak w models box p math iff every element math u math math w math math w r u math math u models p math math mathfrak w models diamond p math iff element math u math math w math holds math w r u math math u


models p math according semantics formula ''necessary'' respect world math w math holds every world accessible math w math ''possible'' holds world accessible math w math possibility thereby depends upon accessibility relation math r math allows us express relative nature possibility example might say given laws physics possible humans travel faster speed light given circumstances could possible using accessibility


relation translate scenario follows worlds accessible world case humans travel faster speed light one accessible worlds ''another'' world accessible ''those'' worlds accessible humans travel faster speed light frames completeness choice accessibility relation alone sometimes sufficient guarantee truth falsity formula instance consider model math mathfrak math whose accessibility relation reflexive


''w r w'' every ''w'' ''g'' '' 'symmetric''' ''w r u'' implies ''u r w'' ''w'' ''u'' ''g'' '''transitive''' ''w r u'' ''u r q'' together imply ''w r q'' ''w'' ''u'' ''q'' ''g'' '' 'serial''' every ''w'' ''g'' ''u'' ''g'' ''w r u'' '''euclidean''' every ''u'' ''t'' ''w'' ''w r u'' ''w r t'' implies ''u r t'' symmetry also implies ''t r u'' logics stem frame conditions


worlds see worlds ''w'' ''ie'' ''r'' total relation gives corresponding ''modal graph'' total complete ''ie'' edges relations added example modal logic based frame conditions math w models diamond p math element ''u'' ''g'' holds math u models p math ''w r u'' consider frames based total relation say math w models diamond p math element ''u'' ''g'' holds


math u models p math drop accessibility clause latter stipulation total frames trivially true ''w'' ''u'' ''w r u'' note case frames still consist multiple parts fully connected among still disconnected logical systems also defined axiomatically shown next section example axioms math p implies box diamond p math math box p implies box box p math math box


p implies p math corresponding ' 'symmetry'' ''transitivity'' ' 'reflexivity'' respectively hold whereas least one axioms hold weaker logics topological semantics modal logic also interpreted using topological structures instance ''interior semantics'' interprets formulas modal logic follows ''topological model'' tuple math chi langle x tau v rangle math math langle x tau rangle math topological space math v math valuation function maps atomic formula subset math x math basic interior semantics interprets formulas


modal logic follows math chi x models p math iff math x v p math math chi x models neg phi math iff math chi x models phi math math chi x models phi land chi math iff math chi x models phi math math chi x models chi math math chi x models box phi math iff math u tau math math x u math also math chi models phi math math u math topological approaches subsume relational ones allowing non normal modal logics


extra structure provide also allows transparent way modeling certain concepts evidence justification one one 's beliefs topological semantics widely used recent work formal epistemology antecedents earlier work david lewis angelika kratzer 's logics counterfactuals axiomatic systems first formalizations modal logic axiomatic numerous variations different properties proposed since c lewis began working area hughes cresswell example describe normal non normal modal logics zeman describes


matter sort computational deductive system one wishes model many modal logics known collectively normal modal logics include following rule axiom '''n''' '''necessitation rule''' ''p'' theorem system invoking '''n''' ''p'' likewise theorem '''k''' '''distribution axiom''' weakest normal modal logic named '''k''' honor saul kripke simply propositional calculus augmented rule '''n''' axiom '''k''' ''k'' weak fails determine whether proposition necessary contingently necessary


theorem ''k'' ''p'' true ''p'' true ie necessary truths necessarily necessary perplexities deemed forced artificial defect ''k'' great one case different answers questions yield different systems modal logic adding axioms ''k'' gives rise well known modal systems one cannot prove ''k'' ''p'' necessary ''p'' true axiom '''t''' remedies defect '''t''' '''reflexivity axiom''' ''p'' necessary ''p'' case '''t''' holds


modal logics zeman describes exceptions ''s sup sup '' well known elementary axioms ''' ''' math box p box box p math '''b''' math p box diamond p math '''d''' math box p diamond p math ''' ''' math diamond p box diamond p math yield systems axioms bold systems italics ''k'' '''k''' '''n''' ''t'' ''k'' '''t''' ''s '' ''t'' ''' ''' ''s '' ''t'' ''' ''' ''d'' ''k'' '''d''' ''k'' ''s '' form nested hierarchy systems making


core normal modal logic specific rules sets rules may appropriate specific systems example deontic logic math box p diamond p math ought ''p'' permitted ''p'' seems appropriate probably include math p box diamond p math fact commit appeal nature fallacy ie state natural also good saying ''p'' case ''p'' ought permitted commonly employed system ''s '' simply makes


modal truths necessary example ''p'' possible necessary ''p'' possible also ''p'' necessary necessary ''p'' necessary systems modal logic formulated part ''s '' describe every kind modality interest structural proof theory sequent calculi systems natural deduction developed several modal logics proven hard combine generality features expected good structural proof theories purity proof theory introduce extra logical notions labels


analyticity logical rules support clean notion analytic proof complex calculi applied modal logic achieve generality decision methods analytic tableaux provide popular decision method modal logics modal logics philosophy alethic logic modalities necessity possibility called ''alethic'' modalities also sometimes called ' 'special'' modalities latin ' 'species'' modal logic first developed deal concepts afterward extended others reason perhaps familiarity simplicity necessity possibility often casually treated


''the'' subject matter modal logic moreover easier make sense relativizing necessity eg legal physical nomological epistemic make sense relativizing notions classical modal logic proposition said '''possible''' ''not necessarily false'' regardless whether actually true actually false '''necessary''' ''not possibly false'' ie true necessarily true '''contingent''' ''not necessarily false'' ''not necessarily true'' ie possible necessarily true '''impossible''' ''not possibly true'' ie false


necessarily false classical modal logic therefore notion either possibility necessity may taken basic notions defined terms manner de morgan duality intuitionistic modal logic treats possibility necessity perfectly symmetric example suppose walking convenience store pass friedrich 's house observe lights way back observe turned somebody something turned lights ''necessary'' friedrich turned lights friedrich 's roommate max turned


lights burglar named adolf broke friedrich 's house turned lights ''contingent'' statements ''possible'' ''impossible'' socrates dead two thousand years turned lights course analogy apply alethic modality ''truly'' rigorous fashion would axiomatically make statements human beings cannot rise dead socrates human immortal vampire take hallucinogenic drugs caused us


falsely believe lights ''ad infinitum'' absolute certainty truth falsehood exists sense logically constructed abstract concepts impossible draw triangle four sides bachelors unmarried difficulty concept something possible true meaning terms may made comprehensible thinking multiple possible worlds sense leibniz alternate universes something necessary true possible worlds something possible true least one possible world possible


world semantics formalized kripke semantics physical possibility something physically nomically possible permitted laws physics example current theory thought allow atom atomic number even atoms existence contrast logically possible accelerate beyond speed light ref name feinberg see also feinberg 's later paper phys rev ref modern science stipulates physically possible material particles information metaphysical possibility philosophers debate objects


properties independent dictated scientific laws example might metaphysically necessary advocate physicalism thought thinking beings bodies experience passage time saul kripke argued every person necessarily parents anyone different parents would person metaphysical possibility thought restricting bare logical possibility ie fewer things metaphysically possible logically possible however exact relation logical possibility physical possibility matter


dispute philosophers also disagree whether metaphysical truths necessary merely definition whether reflect underlying deep facts world something else entirely epistemic logic '''epistemic modalities''' greek ''episteme'' knowledge deal ''certainty'' sentences operator translated x knows operator translated x knows may true ordinary speech metaphysical epistemic modalities often expressed similar words following contrasts may help person jones might reasonably say ''both''


''not'' possible bigfoot exists quite certain ''and'' sure 's ''possible'' bigfoots could exist jones means given available information question remaining whether bigfoot exists epistemic claim makes ''metaphysical'' claim ''possible for'' bigfoot exist ''even though not'' physical biological reason large featherless bipedal creatures thick hair could exist forests north america regardless whether similarly


possible person reading sentence fourteen feet tall named chad ''metaphysically'' true person would somehow prevented account height name ''alethically'' true unless match description ''epistemically'' true 's known fourteen foot tall human beings never existed direction jones might say ''possible'' goldbach 's conjecture true also ''possible'' false ''also'' ''is'' true necessarily true possibly false


jones means ''epistemically possible'' true false knows goldbach 's conjecture proven either true false ''is'' proof heretofore undiscovered would show ''logically'' possible goldbach 's conjecture false could set numbers violated logical possibility form ''alethic'' possibility makes claim whether possible ie logically speaking mathematical truth false makes claim whether possible


jones knows ie speaking certitude mathematical claim specifically either true false jones contradict worthwhile observe jones necessarily correct possible epistemically goldbach 's conjecture true unprovable epistemic possibilities also bear actual world way metaphysical possibilities metaphysical possibilities bear ways world ''might been'' epistemic possibilities bear way world ''may be'' know suppose example want know whether


take umbrella leave tell ''possible that'' raining outside sense epistemic possibility would weigh whether take umbrella tell ''possible for'' rain outside sense ''metaphysical possibility'' better bit modal enlightenment features epistemic modal logic debate example ''x'' knows ''p'' ''x'' know knows ''p''


say ''p'' ''p'' axiom systems answer question unclear least one axiom generally included epistemic modal logic minimally true normal modal logics see section axiomatic systems '''k''' ''distribution axiom'' math box p q box p box q math questioned whether epistemic alethic modalities considered distinct criticism states real difference truth world alethic


truth individual 's mind epistemic investigation found single language alethic epistemic modalities formally distinguished means grammatical mood temporal logic temporal logic approach semantics expressions tense expressions qualifications expressions ' ' true times tensed expressions 'john happy' true sometimes temporal logic tense constructions treated terms modalities standard method formalizing talk


time use ''two'' pairs operators one past one future p mean 'it presently case p' example '''f'''''p'' sometimes case ''p'' '''g'''''p'' always case ''p'' '''p'''''p'' sometime case ''p'' '''h'''''p'' always case ''p'' least three modal logics develop example stipulate math diamond p math ''p'' case time ''t''


past true necessary'' seems reasonable say possibly rain tomorrow possibly wo n't hand since ca n't change past true rained yesterday probably n't true may rained yesterday seems past fixed necessary way future sometimes referred accidental necessity past fixed everything future eventually past seems plausible say future events


necessary similarly problem future contingents considers semantics assertions future either propositions 'there sea battle tomorrow' 'there sea battle tomorrow' true considering thesis led aristotle reject principle bivalence assertions concerning future additional binary operators also relevant temporal logics ''qv'' linear temporal logic versions temporal logic used computer science model computer operations prove theorems one version ''p'' means future time


one naturally leads slightly different axioms deontic logic likewise talk morality obligation norms generally seems modal structure difference must may looks lot like difference necessary possible logics called ' 'deontic'' greek duty deontic logics commonly lack axiom '''t''' semantically corresponding reflexivity accessibility relation kripke semantics symbols math box phi phi math interpreting obligatory '''t''' informally says every obligation true


example obligatory kill others ie killing morally forbidden '''t''' implies people actually kill others consequent obviously false instead using kripke semantics say though world realize obligations worlds accessible ie '''t''' holds worlds worlds called idealized worlds ''p'' obligatory respect world idealized worlds accessible world ''p'' holds though one first interpretations formal semantics recently come


criticism one principle often least traditionally accepted deontic principle ''d'' math box phi diamond phi math corresponds seriality extendability unboundedness accessibility relation embodiment kantian idea ought implies clearly interpreted various senses eg moral alethic sense intuitive problems deontic logic try formalize ethics standard modal logic run problems suppose proposition ''k'' stolen money another ''q'' stolen small


amount money suppose want express thought stolen money ought small amount money two likely candidates math k box q math math box k q math ''k'' together entail ''q'' says ought case stolen small amount money surely n't right ought stolen anything n't work either right representation stolen money


ought small amount right representation stolen money ought large amount math box k k land lnot q math suppose seems reasonable ought steal anything math box lnot k math deduce math box k k land lnot q math via math box lnot k box k k land lnot k math math box k land lnot k k land lnot q math contrapositive math q k math sentence follows


hypothesis course logic shows sentence ca n't right right use natural language telling someone steal certainly imply steal large amounts money engage theft doxastic logic ''doxastic logic'' concerns logic belief set agents term doxastic derived ancient greek ' 'doxa'' means belief typically doxastic logic uses often written b mean believed relativized particular agent


believed metaphysical questions common interpretation modal logic one considers logically possible worlds statement true possible worlds necessary truth statement happens true world true possible worlds contingent truth statement true possible world necessarily called possible truth possible worlds idiom maintain bigfoot 's existence possible actual one says possible


actual world significantly different statements neither commit us existence possible world david lewis hand made notorious biting bullet asserting merely possible worlds real distinguishes world ''actual'' simply indeed world ''this'' world position major tenet modal realism philosophers decline endorse version modal realism considering ontologically extravagant prefer seek various ways paraphrase away ontological


commitments robert adams holds 'possible worlds' better thought 'world stories' consistent sets propositions thus possible rolled state affairs described coherently computer scientists generally pick highly specific interpretation modal operators specialized particular sort computation analysed place worlds may possible next states computer possible future states computer applications modal logics begun used areas humanities literature


poetry art history history basic ideas modal logic date back antiquity aristotle developed modal syllogistic book ''prior analytics'' chs theophrastus attempted improve also passages aristotle 's work famous sea battle argument ''de interpretatione'' seen anticipations connection modal logic potentiality time hellenistic period logicians diodorus cronus philo dialectician stoic chrysippus developed modal system accounted interdefinability possibility necessity accepted axiom '''t''' see


much acknowledgment c lewis founded modern modal logic series scholarly articles beginning implication algebra logic lewis led invent modal logic specifically strict implication grounds classical logic grants paradoxes material implication principle falsehood implies proposition work culminated book ''symbolic logic'' c h langford introduced five systems ''s '' ''s '' lewis modal logic received little attention several decades nicholas rescher argued bertrand russell rejected


however jan dejnozka argued view stating modal system dejnozka calls mdl described russell 's works although russell believe concept modality come confusing propositions propositional functions wrote ''the analysis matter'' arthur norman prior warned ruth barcan marcus prepare well debates concerning quantified modal logic willard van orman quine due biases modal logic ruth c barcan later ruth barcan marcus developed first axiomatic systems quantified modal logic first second order extensions lewis' ''s ''


''s '' ''s '' contemporary era modal semantics began saul kripke year old harvard university undergraduate introduced standard kripke semantics modal logics commonly referred possible worlds semantics kripke n prior previously corresponded length kripke semantics basically simple proofs eased using semantic tableaux analytic tableaux explained e w beth n prior created modern temporal logic closely related modal logic adding modal operators f p meaning eventually previously vaughan pratt introduced dynamic logic


amir pnueli proposed using temporal logic formalise behaviour continually operating concurrent programs flavors temporal logic include propositional dynamic logic pdl propositional linear temporal logic pltl linear temporal logic ltl computation tree logic ctl hennessy milner logic ''t'' mathematical structure modal logic namely boolean algebras augmented unary operations often called modal algebras began emerge j c c mckinsey 's proof ''s '' ''s '' decidable reached full flower work alfred tarski student bjarni j nsson j nsson tarski work revealed


''s '' ''s '' models interior algebra proper extension boolean algebra originally designed capture properties interior closure operators topology texts modal logic typically little mention connections study boolean algebras topology thorough survey history formal modal logic associated mathematics see robert goldblatt see also accessibility relation conceptual necessity counterpart theory david kellogg lewis ''de dicto'' ' 'de re'' description logic doxastic logic dynamic logic enthymeme free choice inference hybrid logic interior algebra interpretability


methods beth evert w https booksgooglecom booksid ie fbgaaqbaj printsec frontcover v onepage q f false formal methods introduction symbolic logic study effective operations arithmetic logic reidel semantic tableaux proof methods blackburn p van benthem j wolter frank eds '' http wwwcsclivacuk frank mlhandbook handbook modal logic '' north holland blackburn patrick de rijke maarten venema yde ''modal logic'' cambridge university press chagrov aleksandr zakharyaschev michael ''modal logic'' oxford university press chellas b f '' https booksgooglecom booksid yupixwv j cc printsec frontcover v onepage q f false modal logic introduction '' cambridge university press cresswell j modal logic goble lou ed ''the blackwell guide philosophical logic''


basil blackwell fitting melvin mendelsohn r l ''first order modal logic'' kluwer james garson ''modal logic philosophers'' cambridge university press thorough introduction modal logic coverage various derivation systems distinctive approach use diagrams aiding comprehension girle rod ''modal logics philosophy'' acumen uk proof refutation trees good introduction varied interpretations modal logic http wwwmcsvuwacnz rob goldblatt robert logics time computation nd ed csli lecture notes university chicago press ''mathematics modality'' csli


lecture notes university chicago press http wwwmcsvuwacnz rob papers modalhistpdf mathematical modal logic view evolution gabbay woods john eds ''handbook history logic vol '' elsevier bv gor rajeev tableau methods modal temporal logics d'agostino gabbay haehnle r posegga j eds ''handbook tableau methods'' kluwer hughes g e cresswell j ''a new introduction modal logic'' routledge j nsson b tarski boolean algebra operators ii ''american journal mathematics '' '' ''


history logic britannica online reading ruth barcan marcus ''modalities'' oxford university press gabbay kurucz f wolter zakharyaschev ''many dimensional modal logics theory applications'' elsevier studies logic foundations mathematics volume covers many varieties modal logics eg temporal epistemic dynamic description spatial unified perspective emphasis computer science aspects eg decidability complexity andrea borghini https wwwgooglecom books edition critical introduction metaphysi ifw cwaaqbajhl en gbpv bsq modal logic ''a critical introduction metaphysics modality'' new york bloomsbury external links internet encyclopedia philosophy http wwwieputmedu modal lo modal logic contemporary view johan


modal logic http teachinglogicimagfr tableauxs prover tableaux prover logic http wwwlabrifr perso moot talks topologynotespdf remarks logic topology richard moot exposits topological semantics modal logic http wwwiritfr lotrec lotrec generic prover modal logics irit toulouse university logic philosophical logic mathematical logic semantics


lifespan participate things want need therapeutic use everyday activities occupations common occupational therapy interventions include helping children disabilities participate fully school social situations injury rehabilitation providing supports older adults experiencing physical cognitive changes typically occupational therapists university educated professionals must pass licensing exam practice occupational therapists often work closely professionals physical therapy speech language pathology audiology nursing social work psychology medicine assistive technology history early history earliest evidence using occupations method therapy

Applied science
Medicine and health
Occupational therapy


found ancient times c bce greek physician asclepiades treated patients mental illness humanely using therapeutic baths massage exercise music later roman celsus prescribed music travel conversation exercise patients however medieval times use interventions people mental illness rare nonexistent ref name quiroga quiroga virginia phd http www aotaorg shop aota prodviewaspxtype sku occupational therapy first years bethesda maryland american occupational therapy association inc ref th century europe revolutionaries philippe pinel johann christian reil reformed hospital system instead use


focused creating structure balance work rest leisure although habit training initially developed treat individuals mental health conditions basic tenets apparent modern treatment models utilized across wide scope client populations slagle opened first occupational therapy training program henry b favill school occupations hull house chicago slagle went serve aota president secretary aota created eleanor clarke slagle lectureship award honor year award recognizes member aota


association aota founded profession occupational therapy officially named william rush dunton one founders nspot visionary figure first decades profession struggled cumbersomeness term occupational therapy lacked exactness meaning possessed scientific terms titles work cure ergo therapy ergo greek root work creative occupations discussed substitutes ultimately none possessed broad meaning practice occupational therapy demanded order capture many forms


guidelines accreditation procedures ref name colman ref early twentieth century time rising incidence disability related industrial accidents tuberculosis world war mental illness brought increasing social awareness issues involved entry united states world war also crucial event history profession time occupational therapy concerned primarily treatment people mental illness however us involvement great war escalating numbers injured disabled soldiers presented daunting challenge


command military enlisted assistance nspot recruit train reconstruction aides help rehabilitation wounded war entry world war ii ensuing skyrocketing demand occupational therapists treat injured war field occupational therapy underwent dramatic growth change occupational therapists needed skilled use constructive activities crafts also increasingly use activities daily living ref name struggle keep people profession


post war years emphasis shifted altruistic war time mentality financial professional personal satisfaction comes therapist make profession appealing practice standardized curriculum entry exit criteria established american occupational therapy association advocated steady employment decent wages fair working conditions via methods occupational therapy sought obtained medical legitimacy ref name quiroga time establishing standards education laying foundation profession organization eleanor clarke slagle proposed


month course training standards adopted educational standards expanded total training time months place requirements professional entry par professions first textbook published united states occupational therapy edited helen willard clare spackman profession continued grow redefine profession also began assess potential use trained assistants attempt address ongoing shortage qualified therapists


educational standards occupational therapy assistants implemented ref name time ongoing change growth profession struggled incorporate new knowledge cope recent rapid growth profession previous decades new developments areas neurobehavioral research led new conceptualizations new treatment approaches possibly groundbreaking sensory integrative approach developed jean ayres ref name profession continued grow expand scope settings practice occupational science study


occupation created tool providing evidence based research support advance practice occupational therapy well offer basic science study topics surrounding occupation ref name yerxa yerxa e clark f jackson j pierce zemke r introduction occupational science foundation occupational therapy st century haworth press ref said occupational science continues largely theory driven present day application clinical practice frequently questioned addition occupational therapy practitioner 's roles expanded include political advocacy


grassroots base higher legislation example pl titled patient protection affordable care act habilitation clause passed large part due aota 's political efforts noted aota 's centennial website aota furthermore occupational therapy practitioners striving personally professionally toward concepts occupational justice human rights issues local global impacts world federation occupational therapist 's resource centre many position statements occupational therapy 's roles regarding participation human rights issues us news world


report ranked occupational therapy list ' best jobs' philosophical underpinnings philosophy occupational therapy evolved history profession philosophy articulated founders owed much ideals romanticism ref name hocking ref pragmatism ref name breines ref humanism collectively considered fundamental ideologies past century ref name yerxa ref ref name mccoll ref ref name chapparo ref one widely cited early papers philosophy occupational therapy presented adolf meyer psychiatrist emigrated united states switzerland late th century invited


present views gathering new occupational therapy society time dr meyer one leading psychiatrists united states head new psychiatry department phipps clinic johns hopkins university baltimore maryland ref name meyer meyer philosophy occupation therapy archives occupational therapy ref ref name christiansen ref william rush dunton supporter national society promotion occupational therapy american occupational therapy association sought promote ideas occupation basic human need occupation therapeutic


statements came basic assumptions occupational therapy include occupation positive effect health well occupation creates structure organizes time occupation brings meaning life culturally personally occupations individual people value different occupations ref name townsend ref assumptions developed time basis values underpin codes ethics issued national associations relevance occupation health well remains central theme criticism medicine multitude disabled world war ii veterans resulted emergence


reductionistic philosophy approach led developments technical knowledge occupational performance clinicians became increasingly disillusioned considered beliefs ref name turner turner history philosophy occupational therapy turner foster johnson eds occupational therapy physical dysfunction principles skills practice th edition edinburgh churchill livingstone ref ref name punwar punwar aj philosophy occupational therapy occupational therapy principles practice nd ed williams wilkins baltimore ref result client centeredness occupation emerged dominant themes profession ref name douglas ref ref name whiteford ref ref name polatajko ref past century


underlying philosophy occupational therapy evolved diversion illness treatment enablement meaningful occupation ref name townsend three commonly mentioned philosophical precepts occupational therapy occupation necessary health theories based holism central components people occupations activities environments activities take place however dissenting voices mocellin particular advocated abandoning notion health occupation proclaimed obsolete modern world well questioned appropriateness advocating holism


practice rarely supports ref name mocellin ref ref name mocellin ref ref name mocellin ref values formulated american occupational therapy association critiqued therapist centric reflect modern reality multicultural practice ref name kielhofner kielhofner g conceptual foundations occupational therapy nd ed philadelphia fa davis ref ref name hocking whiteford hocking c whiteford g multiculturalism occupational therapy time reflection core values australian occupational therapy journal ref recent times occupational therapy practitioners challenged think broadly potential scope profession expanded include working groups experiencing occupational injustice


consistency among therapists occupational therapy practice framework otpf core competency occupational therapy united states otpf framework divided two sections domain process domain includes environment client factors individual 's motivation health status status performing occupational tasks domain looks contextual picture help occupational therapist understand diagnose treat patient process actions taken therapist implement plan strategy treat patient ref name canadian model client centered enablement cmce


embraces occupational enablement core competency occupational therapy ref name townsend canadian practice process framework cppf ref name townsend core process occupational enablement canada canadian practice process framework cppf ref name townsend eight action points three contextual element set stage evaluate agree objective plan implement plan monitor modify evaluate outcome central element process model focus identifying client therapists strengths resources prior developing outcomes action plan occupations according american occupational therapy association 's aota occupational therapy


practice framework domain process rd edition otpf occupation defined type meaningful activity one engages order occupy one 's time ref name ref occupations goal directed task oriented purposeful culturally relevant role specific individually tailored community oriented depending one 's values beliefs context environment following examples occupations activities daily living adls ref name doiorg american occupational therapy association occupational therapy practice framework domain process american journal occupational therapy suppl http doiorg ajot ref otpf defines adls daily activities required take care one 's


self body instrumental one 's health well social participation examples adl 's include bathing showering toileting toilet hygiene dressing swallowing eating feeding functional mobility personal hygiene grooming sexual activity instrumental activities daily living iadls ref name doiorg otpf defines iadls daily activities support daily life within home community often require complex interactions used adls examples iadls include care others care pets child rearing communication management driving community mobility financial management health management maintenance home establishment managements meal preparation


name doiorg employment interests pursuits otpf cites mosey pg individual selects work opportunities likes dislikes possible limitations assets employment seeking acquisition otpf defines aspect work opportunity one advocate oneself along completing submitting reviewing application materials preparation involved interviews act participating interview well following interview lastly act participating job performance otpf defines aspect work individual carries job examples given


way person carries job requirements ie work skills work patterns time management interactions relationships coworkers managers customers supervision production initiation etc retirement preparation adjustment otpf defines aspect work individual adjusts new role includes vocational interests opportunities opportunity individuals develop enhance interests skills volunteer exploration otpf defines aspect work opportunity individual discover community causes organizations opportunities participate without pay meets personal interests


skills location play ref name doiorg play exploration otpf defines aspect work opportunity individual discover community causes organizations opportunities participate without pay meets personal interests skills location play participation otpf defines aspect play individual 's participation selected method play individual able balance play occupations area also addresses person gathers necessary components play uses equipment appropriately leisure ref name doiorg leisure exploration otpf identifies aspect leisure


individual 's identification interests skills opportunities activities appropriate leisure participation otpf identifies aspect leisure individuals activity planning participating leisure activities appropriate capacity maintain balance leisure occupation well using equipment necessary appropriately social participation ref name doiorg community otpf defines aspect social participation successful interaction engagement activities group ie neighborhood workplace school religious spiritual group family otpf cites mosey p nbsp defines aspect social participation


successful interaction within familial role peer friend otpf defines aspect social participation distinctive levels interaction closeness include engagement desired sexual activity practice settings according salary workforce survey american occupational therapy association occupational therapists work wide variety practice settings including hospitals schools long term care facilities skilled nursing facilities free standing outpatient home health academia early intervention mental health community recently trend ots moving towards working


hospital setting long term care facilities skilled nursing facilities setting comprising ot workforce canadian institute health information cihi found nearly half occupational therapists worked hospitals worked community worked professional practice areas practice broad spectrum ot practice makes difficult categorize areas practice especially considering differing health care systems globally section categorization american occupational therapy association used children youth platform swing tire used occupational


therapy children occupational therapists work infants toddlers children youth families variety settings including schools clinics homes hospitals community assessment person 's ability engage daily meaningful occupations initial step occupational therapy ot intervention involves evaluating young person 's occupational performance areas feeding playing socializing daily living skills attending school occupational therapists take consideration strengths weaknesses child 's underlying skills may physical cognitive emotional nature well context environmental demands play


environment possible child required individualized family service plan ifsp focuses family 's goals child 's possible ot serve family 's service coordinator facilitate team process creating ifsp eligible child objectives occupational therapist addresses children youth may take variety forms ref name aotaorg ref ref name case smith ref example providing splinting caregiver education hospital burn unit facilitating handwriting development providing intervention develop fine motor writing readiness skills school aged children providing individualized treatment


sensory processing difficulties teaching coping skills child generalized anxiety disorder consulting teachers counselors social workers parents caregivers person works children regarding modifications accommodations supports variety areas sensory processing motor planning visual processing sequencing transitions schools etc instructing caregivers regard mealtime intervention children autism feeding difficulties united states pediatric occupational therapists work school setting related service children individual education plan iep ref name case smith every student receives special


education related services public school system required law iep individualized plan designed specific student us department education related services developmental corrective supportive services required assist child disability benefit special education include variety professions speech language pathology audiology services interpreting services psychological services physical occupational therapy related service occupational therapists work children varying disabilities address skills needed access


special education program support academic achievement social participation throughout school day aota nd b occupational therapists help children fulfill role students prepare transition post secondary education career community integration aota nd b occupational therapists specific knowledge increase participation school routines throughout day including modification school environment allow physical access children disabilities provide assistive technology support student success helping plan instructional activities implementation classroom support needs students significant challenges helping determine


methods alternate assessment learning helping students develop skills necessary transition post high school employment independent living education aota settings homes hospitals community important environments occupational therapists work children teens promote independence meaningful daily activities ref name case smith outpatient clinics offer growing ot intervention referred sensory integration treatment therapy provided experienced knowledgeable pediatric occupational therapists originally developed jean ayres occupational therapist ref name case smith sensory integration therapy evidence based practice enables


health wellness according american occupational therapy association 's aota ''occupational therapy practice framework'' rd edition domain occupational therapy described achieving health well participation life engagement occupation occupational therapy practitioners distinct value ability utilize daily occupations achieve optimal health well examining individual 's roles routines environment occupations occupational therapists identify barriers achieving overall health well participation ref name factsheet american occupational therapy association https wwwaotaorg media corporate files aboutot professionals whatisot hw facts factsheet healthpromotionpdf role occupational therapy health promotion fact sheet retrieved august ref


occupational therapy practitioners intervene primary secondary tertiary levels intervention promote health wellness addressed practice settings prevent disease injuries adapt healthy lifestyle practices chronic diseases two occupational therapy programs emerged targeting health wellness lifestyle redesign program real diabetes program occupational therapy interventions health wellness vary setting ref name factsheet school occupational therapy practitioners target school wide advocacy health wellness including bullying prevention backpack awareness recess promotion school lunches pe inclusion


also heavily work students learning disabilities autism spectrum study conducted switzerland showed large majority occupational therapists collaborate schools half providing direct services within mainstream school settings results also show services mainly provided children medical diagnoses focusing school environment rather child 's disability outpatient occupational therapy practitioners conduct treatment sessions group interventions address leisure health literacy education modified physical activity stress anger management healthy meal preparation medication management acute care occupational therapy practitioners


conduct treatment sessions group interventions promote hospital wide programs targeting self care activities neurocognitive assessment intervention pain management techniques physical activity mobility leisure social engagement stress management diet lifestyle recommendations medication management community based occupational therapy practitioners develop implement community wide programs assist prevention diseases encourage healthy lifestyles conducting education classes prevention facilitating gardening offering ergonomic assessments offering pleasurable leisure physical activity programs mental health occupational therapy profession believes health individual fostered active engagement one 's occupations aota


early detection screenings intensive intervention bazyk downing occupational therapy practitioners work directly clients provide professional development staff work collaboration team members families instance occupational therapists specifically skilled understanding relationship demands task person 's abilities knowledge practitioners able devise intervention plan facilitate successful participation meaningful occupations occupational therapy services focus engagement occupation support participation areas related school education work play leisure adls instrumental adls bazyk


downing occupational therapy utilizes public health approach mental health emphasizes promotion mental health well prevention intervention mental illness model highlights distinct value occupational therapists mental health promotion prevention intensive interventions across lifespan miles et al three major levels service tier intensive interventions intensive interventions provided individuals identified mental emotional behavioral disorders limit daily functioning interpersonal relationships feelings emotional well ability cope challenges daily


life occupational therapy practitioners committed recovery model focuses enabling persons mental health challenges client centered process live meaningful life community reach potential champagne gray focus intensive interventions direct individual group consultation engagement occupation foster recovery reclaiming mental health resulting optimal levels community participation daily functioning quality life functional assessment intervention skills training accommodations compensatory strategies brown identification implementation healthy habits rituals routines support wellness tier targeted services targeted


services designed prevent mental health problems persons risk developing mental health challenges emotional experiences eg trauma abuse situational stressors eg physical disability bullying social isolation obesity genetic factors eg family history mental illness occupational therapy practitioners committed early identification intervention mental health challenges settings focus targeted services small groups consultation accommodations education engagement occupations promote mental health diminish early symptoms small therapeutic groups olson environmental modifications enhance participation eg create sensory friendly


classrooms home work environments tier universal services universal services provided individuals without mental health behavioral problems including disabilities illnesses barry jenkins occupational therapy services focus mental health promotion prevention encouraging participation health promoting occupations eg enjoyable activities healthy eating exercise adequate sleep fostering self regulation coping strategies eg mindfulness yoga promoting mental health literacy eg knowing take care one 's mental health experiencing symptoms associated ill mental health occupational therapy practitioners develop universal programs


embed strategies promote mental health well variety settings schools workplace focus universal services individual group school wide employee organizational level universal programs help individuals successfully participate occupations promote positive mental health bazyk educational coaching strategies wide range relevant stakeholders focusing mental health promotion prevention development coping strategies resilience environmental modifications supports foster participation health promoting occupations productive aging occupational therapists work older adults maintain independence participate meaningful activities live fulfilling lives


examples areas occupational therapists address older adults driving aging place low vision dementia alzheimer 's disease ad addressing driving driver evaluations administered determine drivers safe behind wheel enable independence older adults home occupational therapists perform falls risk assessments assess clients functioning homes recommend specific home modifications addressing low vision occupational therapists modify tasks environment working individuals ad occupational therapists focus maintaining quality life ensuring safety promoting independence geriatrics productive aging occupational therapists address


aspects aging health promotion treatment various disease processes goal occupational therapy older adults ensure older adults maintain independence reduce health care costs associated hospitalization institutionalization community occupational therapists assess older adults ability drive safe found individual safe drive occupational therapist assist finding alternate transit options occupational therapists also work older adults home part home care


home occupational therapist work things fall prevention maximizing independence activities daily living ensuring safety able stay home long person wants occupational therapist also recommend home modifications ensure safety home many older adults suffer chronic conditions diabetes arthritis cardiopulmonary conditions occupational therapists help manage conditions offering education energy conservation strategies coping strategies occupational therapists work older adults homes also work older adults


hospitals nursing homes post acute rehabilitation nursing homes role occupational therapist work clients caregivers education safe care modifying environment positioning needs enhancing iadl skills name post acute rehabilitation occupational therapists work clients get back home prior level function hospitalization illness accident occupational therapists also play unique role dementia therapist may assist modifying environment ensure safety disease progresses along caregiver education prevent


burnout occupational therapists also play role palliative hospice care goal stage life ensure roles occupations individual finds meaningful continue meaningful person longer able perform activities occupational therapist offer new ways complete tasks taking consideration environment along psychosocial physical needs occupational therapists work older adults traditional settings also work senior centre 's alfs visual impairment visual impairment one top


disabilities among american adults occupational therapists work professions optometrists ophthalmologists certified low vision therapists maximize independence persons visual impairment using remaining vision efficiently possible aota 's promotional goal living life fullest speaks people learning want particularly promoting participation meaningful activities regardless visual impairment populations may benefit occupational therapy includes older adults persons traumatic brain injury adults potential return driving children


visual impairments visual impairments addressed occupational therapists may characterized types including low vision neurological visual impairment example neurological impairment cortical visual impairment cvi defined abnormal inefficient vision resulting problem disorder affecting parts brain provide sight following section discuss role occupational therapy working visually impaired occupational therapy older adults low vision includes task analysis environmental evaluation modification tasks environment needed many occupational therapy practitioners


work closely optometrists ophthalmologists address visual deficits acuity visual field eye movement people traumatic brain injury including providing education compensatory strategies complete daily tasks safely efficiently adults stable visual impairment may benefit occupational therapy provision driving assessment evaluation potential return driving lastly occupational therapy practitioners enable children visual impairments complete self care tasks participate classroom activities using compensatory strategies adult rehabilitation occupational therapists address need rehabilitation following injury


impairment planning treatment occupational therapists address physical cognitive psychosocial environmental needs involved adult populations across variety settings occupational therapy adult rehabilitation may take variety forms working adults autism day rehabilitation programs promote successful relationships community participation instruction social skills increasing quality life individual cancer engaging occupations meaningful providing anxiety stress reduction methods suggesting fatigue management strategies ref name radomski ref coaching individuals hand amputations put take


myoelectrically controlled limb well training functional use limb ref name radomski pressure sore prevention sensation loss spinal cord injuries using implementing new technology speech text software nintendo wii video games communicating via telehealth methods service delivery model clients live rural areas working adults stroke regain activities daily living assistive technology occupational therapy practitioners occupational therapists ots uniquely poised educate recommend promote use assistive technology improve


quality life clients ots able understand unique needs individual regards occupational performance strong background activity analysis focus helping clients achieve goals thus use varied diverse assistive technology strongly supported within occupational therapy practice models travel occupational therapy rising need occupational therapy practitioners us many facilities opting travel occupational therapy practitioners willing travel often state work temporarily facility assignments range weeks


months typically last weeks length travel therapists work many different settings highest need therapists home health skilled nursing facility settings educational requirements needed travel occupational therapy practitioner however may different state licensure guidelines practice acts must followed according zip recruiter july national average salary full time travel therapist range across united states commonly travel occupational therapists enter industry


family social context contribute global health advocating individuals disabilities participate meaningful activities global level occupation therapists involved world health organization non governmental organizations community groups policymaking influence health well individuals disabilities worldwide occupational therapy practitioners role occupational justice align perceptions procedural social justice advocate inherent need meaningful occupation promotes society well quality life among people relevant context


recommended clinicians consider occupational justice everyday practice promote intention helping people participate tasks want need occupational injustice contrast occupational injustice relates conditions wherein people deprived excluded denied opportunities meaningful ref name pmid ref types occupational injustices examples within ot practice include ref name trimboli ref occupational deprivation exclusion meaningful occupations due external factors beyond person 's control example person difficulties functional mobility may find challenging reintegrate


community due transportation barriers occupational apartheid exclusion person chosen occupations due personal characteristics age gender race nationality socioeconomic status example seen children developmental disabilities low socioeconomic backgrounds whose families would opt therapy due financial constraints occupational marginalization relates implicit norms behavior societal expectations prevents person engaging chosen occupation example child physical impairments may offered table top leisure activities instead sports extracurricular activity due


cognitive mental health spiritual types clients may seen community based settings role ot also may vary advocate consultant direct care provider program designer adjunctive services therapeutic leader ref name scaffa e education worldwide range qualifications required practice occupational therapist occupational therapy assistant depending country expected level practice degree options include associate degree bachelor 's degree entry level master 's degree post professional master 's degree entry level doctorate otd post professional doctorate otd doctor clinical science ot cscd doctor


philosophy occupational therapy phd combined otd phd degrees occupational therapist occupational therapy assistant roles exist internationally currently united states dual points entry exist ot ota programs ot entry level master 's entry level doctorate ota associate degree bachelor 's degree world federation occupational therapists wfot minimum standards education ots revised educational programs around world need meet minimum standards standards subsumed supplemented academic standards


occupations include following generic models generic models overarching title given collation compatible knowledge research theories form conceptual practice generally defined aspects influence perceptions decisions practice person environment occupation performance model peop originally published charles christiansen carolyn baum describes individual 's performance based four elements including environment person performance occupation model focuses interplay components interaction works inhibit promote successful engagement occupation occupation focused practice models


occupational therapy intervention process model otipm anne fisher others occupational performance process model oppm model human occupation moho gary kielhofner others moho first published explains people select organise undertake occupations within environment model supported evidence generated thirty years successfully applied throughout world canadian model occupational performance engagement cmop e occupational performances model australia opm chris chapparo judy ranka opm conceptualized current form launched opm illustrates complexity occupational performance


scope occupational therapy practice provides framework occupational therapy education kawa river model michael iwama biopsychosocial models engel 's biopsychosocial model takes account disease illness impacted social environmental psychological body functions biopsychosocial model unique takes client 's subjective experience client provider relationship factors wellness model also factors cultural diversity many countries different societal norms beliefs multifactorial multi dimensional model understand cause disease also person centered approach


provider participatory reflective role models incorporate biology body brain psychology mind social relational attachment elements influencing human health include interpersonal neurobiology ipnb polyvagal theory pvt dynamic maturational model attachment adaptation dmm latter two particular provide detail source mechanism function somatic symptoms kasia kozlowska describes uses models better connect clients understand complex human illness includes occupational therapists part team address functional somatic symptoms ref name ref research indicates children


functional neurological disorders fnd utilize higher challenging dmm self protective attachment strategies cope family environments impact functional somatic symptoms ref name pamela meredith colleagues exploring relationship attachment system psychological neurobiological systems implications occupational therapists improve approach techniques found correlations attachment adult sensory processing distress pain perception ref name literature review meredith identified number ways occupational therapists effectively apply attachment perspective sometimes uniquely frames reference frames


reference additional knowledge base occupational therapist develop treatment assessment patient client group though conceptual models listed allow therapist conceptualise occupational roles patient often important use reference embed clinical reasoning therefore many occupational therapists use additional frames reference assess develop therapy goals patients service users biomechanical frame reference biomechanical frame reference primarily concerned motion occupation used individuals experience


limitations movement inadequate muscle strength loss endurance occupations frame reference originally compiled occupational therapists therapists translate occupational therapy perspective avoid risk movement exercise becoming main focus rehabilitative compensatory neurofunctional gordon muir giles clark wilson dynamic systems theory client centered frame reference frame reference developed work carl rogers views client center therapeutic activity client 's needs goals direct delivery occupational therapy process cognitive behavioural frame


reference ecology human performance model recovery model sensory integration sensory integration framework commonly implemented clinical community school based occupational therapy practice frequently used children developmental delays developmental disabilities autism spectrum disorder dyspraxia core features sensory integration treatment include providing opportunities client experience integrate feedback using multiple sensory systems providing therapeutic challenges client 's skills integrating client 's interests therapy organizing environment support client 's engagement facilitating physically safe emotionally supportive environment modifying


activities support client 's strengths weaknesses creating sensory opportunities within context play develop intrinsic motivation sensory integration traditionally implemented pediatric practice emerging evidence benefits sensory integration strategies adults ref name meredith p j bailey k j strong j rappel g adult attachment sensory processing distress healthy adults american journal occupational therapy https dxdoiorg ajot ref icf international classification functioning disability health icf framework measure health ability illustrating components


impact one 's function relates closely occupational therapy practice framework stated profession 's core beliefs positive relationship occupation health view people occupational beings ref name aota american occupational therapy association occupational therapy practice framework domain process nd ed american journal occupational therapy ref icf built nd edition practice framework activities participation examples icf overlap areas occupation performance skills performance patterns framework icf also includes contextual factors environmental personal


along icf order ensure correct communication specific concepts ref name stamm ref icf might lack certain categories describe occupational therapists need communicate clients colleagues also may possible exactly match connotations icf categories occupational therapy terms icf assessment specialized occupational therapy terminology replaced icf terminology ref name haglund ref icf overarching framework current therapy practices global occupational therapy occupational therapy practiced around world translated practice many


different cultures environments construct occupation shared throughout profession regardless country culture context occupation active participation occupation seen human right asserted strong influence health well ref name ref profession grows lot people travelling across countries work occupational therapists better work opportunities context every occupational therapist required adapt new culture foreign understanding cultures communities crucial occupational therapy ethos


effective occupational therapy practice includes acknowledging values social perspectives client families harnessing culture understanding important client truly faster way towards independence world federation occupational therapists international voice profession membership network occupational therapists worldwide wfot supports international practice occupational therapy collaboration across countries wfot currently includes member country organizations occupational therapy practitioners approved educational programs profession celebrates world occupational therapy day th october annually


increase visibility awareness profession promoting profession 's development work local national international platform ref name ref wfot close collaboration world health organization since working together programmes aim improve world health ref name wfot supports vision healthy people alignment united nations sustainable development goals focuses ending poverty fighting inequality injustice tackling climate change promoting health ref name occupational therapy major player enabling individuals communities engage chosen necessary occupations