Appendix for Chapter 3: B

Appendix for Chapter 3: B
Chart of Incidents

TUTOR ITEMS

CODE

CONTENT

T.PHIL.TEACH.

T views on mathematics teaching as expressed directly or indirectly during tutorial: hysteron-proteron structure of mathematics lessons p1 p7, p25, takes responsibility for student difficulty, p11 display of vulnerability, p21,p28 list of test - example - apply.

T.FORM.INSTR.PART.

Particular instances that illustrate form of instruction: adjusts pace of teaching to individual needs p1, asks them to remember things from past terms p2 and p14, effective use of 'reverse' questions p6 - twice recognising theorems trick p11, 13, 17, 19, nice twist of student suggestion p11 and p13, optimism p13 and p23, connections - coherence pl4 constructs from what they know p14 -twice and p21, co-ordinates p14 and p21, informal proving p18, 22, 23, trial-and-error p23, on fear of delta-epsilon and on what these mean p17 and p26, identifies source of misunderstanding p26, explaining compactness p27.

T.FORM.INSTR.GEN.

Gets carried away in monologue pl,9,2l,26 artificial dialectics p5, 17,23, improvises all alone p11,19,26 time constraints hurry up distress p12, 18, brief, dense explanations p17, 25, resorts to visualisation p22, closed questioning p7, 25, appreciates strong memory p27.

T.BEH.ARB.STU.

Arbitrary treatment of students' responses: ignores them and goes on her own way p2,3,13,14,15,17,18 gives logically incomplete answers-equal intervals query p3 and 15-twice, leaves student originality 'unexploited' p3, 16.

T.BEH.ARB.MATH.

Use of tricks or arguments that appear 'out of the blue'

T.BEH.AFF.RESP.

Affective response to students: humour, neutral in mistakes, makes fun of weaknesses (topical or memory) p2,8, irony p13,wrong solution joke p18, snaps answer to reserve contempt p24.

T.BEH.AFF.EMIT.

Affectively formative pieces of advice: 'do on with what you start' p14, setting good example p15, injecting confidence p15, compliments students p18, demystification of theorem p23.

T.SLOG.MATH.

,Metamathematical slogans: 'Analysis is about taking limits' p3, proving from first principles p19, 'get the feel of the function' p22.

T.SLOG.RECIPE.

Rules of thumb: diagonalisation and eigenvalues p3, 6, checking 1-1 p10, proving uniqueness p14, events in probability p19, list of tests on convergence p21, 23, how to remember the integral test p21, outlines use of theorem p22, uses of the integral test p23, on additive sigmas p25.

T.LANG.USE.AMB.

Ambiguous use of language: 'lot more work for me' p4, 'straightforward proof' p21.

T.LANG.USE.COLL.

'Use of coloquialisms: to serve individual needs p4, to describe

technique ('bare hands' ,'naive' , 'sophisticated' pl, 14, 'alternative', 'polished proof' p14, 'solve this without trouble' p10, 'start from scratch' p19, 'sandwiched' p21, 'stick it to a rectangle' p22, 'nasty' p24, 'things from g(x) . . . ' p26.

T.EX.

Discussion of exam conventions: 'short answers' p6, 'looks like one you can make' p7,on ambiguity p8, negotiating marks p15, exam proof proper p16, on Give/Findp18. 'theorem that comes up every year' p25, 'stating precisely known theorems' p25, uneven measures of rigour p25

T.META.TEACH.

Improved handling of double sigma's p17,improved on f: Rⁿ ® R p18, problem on notation p22.

T.REGRESSION.

On f: Rⁿ ® R p18, unnecessary conservatism p21, spoils nice handling p21,anti-constructivism p23.

STUDENT ITEMS

CODE

CONTENT

S. ORIG MATH.

Original, peculiar or brilliant not necessarily 'correct' - ideas of students: triangles suggested instead of rectangles in the definition of the Riemann integral p3. trapezia suggested instead of rectangles in the definition of the Riemann integral p4. leap to S f(x_i)f_i p9, f is injective hence d_n is unique p11, on infinity in sigma p14.

S.LANG .USE

Students' use of language: integral as the 'other way around' of differentiation, asking for 'clear' proof p22.

S.DIFF TOP.

Students' topical difficulties.' (f'=O Þ f(x)=?) and (f'=1Þ f(x)=?) and f(x+1)=f(x)+1

p6, vector space of field p7. f: Rⁿ ® R f(x) looks like? p7, speciality of f pl0. on free variable p12. on the greatest lower boundary p14. conditioning in Probability Theory p15, factorising xⁿ-yⁿ p15 on absolute value p17, on the remainder in the Taylor series p18, on rankA where A is a matrix being the maximum number p18, on the integral test p21, a_n® f (x) p21. on delta-epsilon definitions p26, on set-familv union and compactness p26, f=c and two values in order to find c p25, 2.

S.DIFF. LOG.

Students'. Logical difficulties: applying theorems without checking conditions p7.22,23,27, use of induction dangerous p14, if ? is true for all n>k then it is true for all n p17, resort to memorv p20,26.

S.DIFF. SYMB.

Students' symbolic difficulties: i-j notation p9, A-2 instead of A-2I confusion where A is a matrix, x- and x+ confused p13, double sigmas p17, switching from n to k notation p17.

S.EX.

Discussion of exam conventions: interpretation of exam cuestion p7confusion p10, use of part i in part ii in exam question p12. Question sloppily worded p12, on expected length of answers p19, ambiguity in the formulation of an exam question p19.

S.BEH . AFF .RESP.

Students' response to tutor's mathematical or other behaviour from an affective point of view: 'nasty trick' p10'. tacit acceptance of the tutor's arbitrary unjustified answers p15, coldness p17, dead zone p19, 23, student frustration coming from the tutor's failure to answer question.

S . INTUITION

lim=l p11, 14. d_n decreasing pl4. definition of Accumulation point p22.

S.METAMATH.

Students ' metamathematical queries: 'how legitimate is to feel a limit and then prove it?' p16., they like slogans p23. expectations higher from problems requiring long calculations p24.juxtapose with; frustration from simple relations found in p12,they don't do the simple thing p25.

MISCELLANEOUS ITEMS

BEAUTY

Instances of fruitful interaction: on the definition of the Riemann integral p4, co-operation p9.

BR-REG

Breaking the rules of minimal-participant observation p10.

SURPR-MATH.

Unnecessary complex formulation of a problem p12, different approach to to integral of l/xlogx

T-PERC.

On infinity p19.

COMM-OBS

Comments on way of observation p23. 26.

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