KARTET Paper 2 cheat sheet

Piaget's stages and their markers: sensorimotor (0-2, object permanence), preoperational (2-7, egocentrism, irreversibility, no conservation), concrete operational (7-11, conservation, seriation, classification, reversibility), formal operational (11+, abstract and hypothetical-deductive reasoning).

Vygotsky: ZPD is the gap between what a learner does alone and what the learner does with adult or peer support; scaffolding is temporary, graded support withdrawn as competence grows; private speech becomes inner speech.

Kohlberg's three levels, two stages each: preconventional (punishment-obedience, instrumental exchange), conventional (good boy-good girl, law and order), postconventional (social contract, universal ethical principle); moral reasoning, not behaviour, defines the stage.

Constructivist classroom decision rule: start from the learner's existing schema, pose a cognitive conflict, allow peer discussion, and treat errors as diagnostic data rather than as failure.

Intelligence theories to match with items: Spearman's g factor, Thurstone's primary abilities, Gardner's multiple intelligences, Sternberg's triarchic theory (componential, experiential, contextual), Guilford's structure of intellect.

Motivation: intrinsic motivation sustains learning without external reward; extrinsic motivation uses rewards and punishment; Maslow's hierarchy places physiological and safety needs below belonging, esteem and self-actualisation; attributing success to effort supports mastery.

Inclusion and law: RTE Act 2009 guarantees free and compulsory education for ages 6-14, bars capitation fees and screening, reserves 25% of entry seats for disadvantaged groups; the RPwD Act 2016 lists 21 specified disabilities.

Assessment decisions: formative assessment is ongoing and feedback-oriented; summative assessment certifies achievement; diagnostic assessment locates specific learning gaps; item difficulty index p = number correct / number attempted.

Specific learning disabilities: dyslexia affects accurate and fluent word reading, dysgraphia affects handwriting and written expression, dyscalculia affects number sense and computation, dyspraxia affects motor coordination; these are not caused by low intelligence.

Natural order of language skills is listening, speaking, reading, writing; receptive skills are established before productive skills, so oral work precedes reading and writing in early teaching.

Krashen's monitor model: acquisition is subconscious and meaning-focused while learning is conscious rule study; the input hypothesis requires comprehensible input slightly beyond current level (i + 1); the affective filter blocks intake under anxiety or low motivation.

Theoretical anchors: Chomsky's language acquisition device and universal grammar; Skinner's behaviourist imitation-reinforcement chain; Piaget's cognitive readiness; Vygotsky's social interaction and mediation.

Method-to-feature matching: grammar-translation uses deductive rules and the first language; the direct method avoids translation; the structural-situational approach drills graded patterns; communicative language teaching organises teaching around functions and real use.

Linguistic units: phoneme is the smallest sound unit that distinguishes meaning, morpheme the smallest meaningful unit, free morphemes stand alone while bound morphemes attach (prefix, suffix), syntax governs sentence structure, semantics meaning, pragmatics use in context.

Reading types and purpose: skimming for the gist, scanning for a specific detail, intensive reading for close analysis, extensive reading for fluency and pleasure; a cloze test measures contextual and syntactic prediction.

Writing as a process: prewriting, drafting, revising, editing, publishing; assessment criteria should separate content and organisation from grammar, spelling and mechanics.

Errors versus mistakes: an error reflects an underlying rule the learner has not yet acquired and calls for remedial teaching; a mistake is a performance slip the learner can self-correct.

Multilingual classrooms: the home language is a cognitive resource, not an obstacle; planned code-switching and translation bridges support concept formation when the target language is still developing.

Second-language learning differs from first-language acquisition: the learner already has a full linguistic system, so transfer from Language I can accelerate comprehension or produce interference errors.

Contrastive analysis predicts difficulty by comparing the two systems; where Language I and Language II differ, negative transfer or interference is more likely, especially in word order, articles, prepositions and tense.

Comprehension levels to test separately: literal (stated information), inferential (implied meaning), evaluative or critical (judgement about the text), and appreciative (response to style and effect).

Grammar teaching choice: inductive (examples first, rule discovered by learners) suits younger and mixed-ability classes; deductive (rule stated first, then practice) is faster for adult and examination-oriented learners.

Teaching aids and infrastructure: flashcards and charts for vocabulary, audio recordings and the language laboratory for listening and pronunciation, realia and role play for speaking; each aid must serve a stated objective.

Micro-teaching cycle: teach a small skill to a small peer group for a short time, receive feedback, re-plan and re-teach; it isolates one teaching skill at a time and builds fluency in questioning, explaining, reinforcement and stimulus variation.

Vocabulary teaching: present words in context, teach collocation and word families rather than isolated lists, and recycle new items at spaced intervals to move them into long-term memory.

Evaluation in Language II: objective items test recognition, short-answer and composition tasks test production; oral testing requires a rubric with criteria such as fluency, accuracy, pronunciation and interaction.

Lesson planning (Herbartian five steps): preparation, presentation, comparison and association, generalisation, application; behavioural objectives should name observable performance, condition and criterion.

Number relations: HCF × LCM = product of the two numbers; divisibility tests work by digit sum (3, 9), last two digits (4), last three digits (8) and alternating digit sum (11).

Percentage and commercial arithmetic: profit% = profit/CP × 100, loss% = loss/CP × 100, discount is computed on marked price, and successive changes are not additive but multiplicative.

Interest formulas: simple interest = P × R × T / 100; compound interest = P(1 + R/100)^T − P, with half-yearly compounding using R/2 and 2T.

Algebraic identities: (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b², a² − b² = (a + b)(a − b), (a + b)³ = a³ + b³ + 3ab(a + b); the sum of the first n natural numbers is n(n + 1)/2.

Mensuration: triangle ½ × base × height, circle πr², trapezium ½(a + b)h, cylinder πr²h, sphere (4/3)πr³; sum of interior angles of an n-sided polygon is (n − 2) × 180°; Pythagoras applies to right triangles only, with common triplets 3-4-5 and 5-12-13.

Statistics and probability: mean = sum of observations / number of observations, median is the middle value of ordered data, mode is the most frequent value; probability of an event = favourable outcomes / total equally likely outcomes and always lies between 0 and 1.

Motion and force: speed = distance/time, acceleration = change in velocity/time, Newton's second law F = ma, work = force × displacement, power = work/time; sound needs a material medium while light does not.

Electricity and light: Ohm's law V = IR, resistances add in series and add reciprocally in parallel, plane-mirror image is virtual, same size and laterally inverted; frequency determines pitch, amplitude determines loudness.

Matter and life processes: acids turn blue litmus red and bases turn red litmus blue, neutralisation gives salt and water; photosynthesis is 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ in chloroplasts; mitochondria release energy, and Rhizobium, Lactobacillus and yeast are used in nitrogen fixation, curd making and fermentation respectively.