Turn Speaker Inform ation
1. R T hank you for allow ing m e to carry out this interview w ith you. W e are going to view together one o f your lessons I captured. I w ish to understand b etter w h at you w ere doing and w h y you w ere doing it.
2. G No problem
3. RG [P lays the vid eo a n d to g e th e r th ey w a tc h a n d liste n]
4. R W h y is it im portant for them to know th e com position of num bers, like you w an t them to break up 36, you w an ted them to understand the m ake, w hat 36 is m ade of. W h y is it im portant th at th ey should have that
understanding?
5. G It is very im portant because otherw ise th ey see 36 as a th ree and a six, and 36 actually is not a three and a six but a th irty and a six.
6. R O kay. W hen y o u ... W hen th ey are learn in g about n um bers, like w hen th ey learn in g to identify num bers say at G rade 1, are t h e y . . , before th ey get into realization th at 36 is a 30 and a 6 are th ey allow ed all to lik e...do y o u . Can you allow them to like identify 36 as a th ree and six so th at they can be able to p ick up 36 n um ber from a n um ber line, a th ree and six? 7. G T hey are not going to see it as a three and a six. Three and a six m eans they
d on ’t actually know w h at th at n um ber is actually m ade out of. T hey ju st gonna see it as 3 otherw ise if th ey see it as 3 tens there is a d ifference but a lot o f children ju st see it as 3 and a 6 w hich m akes nine. T hey d on ’t refer to it as tens.
8. R O kay.
9. G Y ou see w hat you are actually doing is part o f strategies that children need in building up and breaking down num bers so now you are actually breaking down th e num bers to see w h at th ey actually com posed of.
10. R [N ods h e r head]
11. G It is very im portant. A n oth er th ing th at w e are actually doing w hen w e are breaking down those num bers and building up num bers is that you can actually say to them put your finger under 3. W hat is that? They have got to be able to identify that 3 as either th ree tens or it’s a 30. I t’s not ju st the three. A 3 is 3 ones or 3 units.
12. R O kay. O ne m ore thing! A nd I asked this before and I w ill ask it again. I realize th at all your lessons you start them w ith counting, th ey count on, th ey count backw ards, w h y are you putting so m uch em phasis on counting?
13. G B ecause counting is th e basis o f m athem atics [silence]
14. R E xplain th at further
15. G W ell the th ing is you w an t children to ... C ounting is not ju st a com ponent of ju st rote count, spit out of you r m outh and it m eans
absolutely n othing, w hich is w h at lot of teachers actually do th ey th ink it’s ju st count, count, count. T hey d on ’t even know if children are actually counting the right n um ber on th e right w ord or w hatever, or if you d id n ’t give th e counting apparatus on the floor or things like that. W hat you w ant to do is to use th e counting skills in your calculations.
16. R O k a y . . So w hy?
17. G . a n d also w ith counting, w h at com es b efore, w h at com es after, if you look at the C A PS docum ent, everything th at I am actually doing I ’m taking, I build all th ose th ings, reading th eir num bers, counting, breaking, building up and breaking down n um bers, doubling and halving. All those problem solving th ey ’re all built into m y lessons. I d on ’t ju st say “right! T oday I am doing p roblem -solving, tom orrow I am ju st going to count”. A ll these build in. I am giving them w h at w e call conceptual know ledge, basis o f m athem atical know ledge. I am building up th eir netw ork in logical m athem atical know ledge.
18. R Okay.
19. G Yeah.
20. R W h y do you use counters? You see, you d on ’t ju st do counting like “okay
[clapping h a n d s like to p u t o rd e r in class] okay boys sit down boys lets count! O ne, tw o, th re e...” Y ou actually go to y o u r. . [ P o i n t i n g to the b ea d strin g ]
21. G Y es, th e abacus .
22. R . abacus and you w ill be pulling o u t .
23. G It m ust be one to one, it m ust be a uttering the correct w ord o n . 24. G R [In unison] the correct num ber.
25. G Yes.
26. R So w hat is the, w h at is the im portance o f using the abacus?
27. G L ike I can use th e num bers set, I can use the n um ber grid, I can use anything as long as th ey are actually uttering th e w ord to th e correct num ber.
28. R O kay, so th e abacus is helping them to realize th at this n um ber m eans this quantity?
29. G A nd also if you look at th e abacus right now [ p o in tin g to the a b a c u s] I can already see w e are on 32 [sile n ce]. H ow can I see w e are on 32? B ecause it’s 10, 20, 30 and 2 [pointing to the b ea d s on the abacus]
30. R [L ooking a t the a b a c u s a n d s m ilin g ] yes, so it m akes it easy for them to identify num bers. O kay [p la y in g the video, w a tc h in g a n d listening].
31. G The reason w h y you also b reak is because you w an t to keep them focussed.
32. S O kay.
33. G Y ou are w orkin g w ith the w h ole group .
34. R Um
35. G . and y o u ’re going to get day dream ers.
36. R O kay.
37. G So instead o f ju st counting and being boring you need to th row in these other things to keep them focused.
39. G A n d th e other reason w h y you deal w ith th e w hole group is th at w eak kids can learn from th e stronger children.
40. R So im portant th at som etim es put them together and t h e y ...
41. G .... I always starts w ith w hat I call m ental m aths at th e beginning of m y lesson.
42. R Okay.
43. G The w h ole class.
44. R [Nodding]
45. G A t th e m om ent it takes th e round-about 10 to 15 m inutes. At th e m om ent it takes a little bit longer but there is quite a lot o f conceptual know ledge th at I need to get through to them to discover through m y m ental m athem atics and learn in g from each other.
46. R O kay [p la y in g the v id e o on ce m ore] it ’s not very loud.
47. G [ L e a n in g fo r w a r d to listen] Yeah!
48. S W hen do th ey learn about tens and units?
49. G C om ing up now.
50. S C om ing up now!
51. G W e are doing revision up to n i n e . . . A nd then o f course I am building in all m y things then w e start breaking up tens, but they have already done up to 19. The m inim um requirem ents in G rade one is th e w ork up to 19. So th ey know th a t’s if 15 is a 10 and a 5, 19 is 10 and 9. T hey have already picked th at up. It is 10 and 9 ones.
52. S O k, so it’s like w hen you stopped them at 40 you asked th em , “Ah how m any tens in 40?”
53. G T hey have been counting in tens in G rade one.
54. S O kay, so you expect them to know ?
55. G W ell! T h at’s w h at I am lookin g for. I am still doing a lot o f...
56. S A ssessm ent
57. G N ot assessm ent but baseline, to see actually w h at know ledge th ey have. 58. S O kay, so it’s like as you do you r counting, it’s ju st having them understand
counting but you also get to understand them better is you ask them questions.
59. G [Nodding]]
60. S O kay.
61. G I m ean you could actually see th at w ith the bottom group, the w eek ones, som e o f th ose children th ey can ’t count.
62. S Y eah, th ey can ’t!
64. S So is it ideal for you to say you have realized, like th is...W h at’s th e nam e o f the group?
65. G M y B row n Group
66. S Y our Brow n G roup, they still need an lot of learning to count, can it be a deal for you to sit them on th e m at and you start counting using that the n um ber line w ith them counting
67. G [N odding] Yeah! This is w hy I do use th e num ber grid.
68. S O kay.
69. G E ach child has a num ber grid.
70. S [N odding] O kay.
71. G Y eah, and I can actually do w h at th ey call point counting. There are lots of different w ays o f actually counting.
72. S Um
73. G T here are five principles o f counting th at govern m eaningful counting.
74. S O kay?
75. G I am not even going to those, but then it’s a lecture th at I w ill do. You can go and study that the five principles o f counting. A nd this one i s . It is not one of th e principles but you get rote counting w hich is ju st spitting out, it ’s ju st rote, th ey d on ’t som etim es even know . You m ay th ink th e child, you r child is being clever, a four year old child or th ree year old can be counting up to 19 or 20 all w h atever but th e th ing is if you give them counters, th e go “one, tw o, three, four, five, six” [pulling im a g in a ry co u n ters in a w a y th a t is n o t co rre sp o n d in g w ith the c o u n tin g o f num bers] but th ey have lots only five counters or w hatever. W h ere th ey point count th ey literally p oint, this is w h at w e call one to one correspondence. Say th e w ord and m ove it, say th e n um ber and m ove it, say th e num ber, m ove it [m o v in g the im a g in a ry co u n ters]
76. S O kay [playing the video]
77. G Y ou see th at is one to one correspondence, [P o inting to the screen] there, so th ey are saying as I am m oving [m oving the im a g in a ry b ids w ith h is fin g e r s ] .
T hey are saying th e n um ber I can stop them and say “w h at have w e counted to ? ” 10, 20, 30, 40, 50 w h atever [p o inting to the b e a d strin g on the screen] You can see it, 10, 20,30, 40, 50, 55.
78. GS [w a tching the video]
79. S H m m I enjoyed this part o f you r lesson. [Smiling]
80. [silence as the tw o w a tch the video]
81. G Y ou can hear it, w e also w an t them to hear the num ber.
82. S H m m . Can you ju st tell m e about th e illustration, W hy did you do it?
[P o inting the im a g in a ry f l o o d ca rd s f r o m the m o u th a s sh o w n in the video]
W h y use th ose cards? H ow does it help them ?
83. G B reak up num bers w e use flood cards. Fantastic! You can ’t actually do edition o f tw o digits num bers any kind of edition or subtraction w ithout them .
84. S O kay.
85. G Y eah you know w h at? W hen a child does addition o f num bers tw o digits and one digit num bers th ey actually pull them apart horizontally.
86. S H m m .
87. G T here is no vertical m aths. W e don ’t do vertical m aths. W e do everything horizontally.
88. S O kay.
89. G So if I have 36+42, th ey pull th e num ber o f parts [pulling h e r h a n d s apart]
and then the social know ledge th at I give th em , okay say go from the biggest to the sm allest. So th ey go a 40 and a 30 w h atever w hatever w hatever. 40 count on 30 m akes 70. H ow do you know ? 10, 20, 30, 40, 50, 60, 70. Y ou see how counting is com ing in? 40 and 30 m akes 7 0 ...Plus a 2 plus a 4 w hatever.
90. S [S ilen ce ]
91. G So everything is horizontal.
92. S O kay, like w hen you did this, this illustration. B efore you did the
illustration you asked w hat is, w h at is 55 m ade of? O r som ething alm ost like that and one learn er gave you th e answ er a 50 and a 5 but you w ent on to illustrate how it b ecom es a 50 and a 5 w h y did you do that?
93. G F or a bottom group to realize, for your other children w h o h aven ’t got that.
94. S O kay.
95. G So you actually show ing them u sing th e flood cards.
96. O kay.
97. G So th ey can actually see it, pulling th e num bers apart [pulling a p a r t im a g in a ry ^ flo o d c a rd s]
98. S So you are tryin g to go w ith the w h ole class.
99. G [Nodding]
100. S Y ou realize you have the, the top ones are w ith you but you also keep in m ind y o u .
101. G Y ou have to!
102. S O kay [nodding]
103. G It is very easy to teach a clever child, your teach in g ability lays w ith the bottom group, that is w here you r teach in g ability lays [nodding] it’s very easy to teach a top child
104. S O kay [nodding] but to pull along the bottom ones is w h at teaching is all about.
105. G [A d d re sse s the ch ild ren w h o w ere c o m in g b a c k to the c la ssro o m ]
106. S [P la y in g the v id e o ]
107. G W h at am I actually doing here is the revision o f grade one w ork because th ey should be able to count up to 100
109. G [N odding] H m m .
110. S In grade 1?
111. G [N odding] H m m .
112. S A n d in grade 2?
113. G 200.
114. GS [W atching the video]
115. S W h at does that m ean, “close M r.80’s h ou se” ?
116. G Y ou see th e th ing is like Sam u th ey battle. T hey really b attle to com e, to com e out o f one ten and go into th e next one if the accounting backw ard.
117. S O kay?
118. G So now w hat you are w an tin g them to do, w h at I have discovered th at over th e years is you start at the top [raising her hands above her head] so can 79, 78, 77, 76, 75,74, 73, 72, 71 [sta g g erin g h e r h a n d s d o w n w a rd s on each count] Close M r 70 ’s house. [P ulling h a n d s a p a r t in a w a y o f c lo sin g a n d s p e a k in g so ftly] w e are now finished w ith M r. 70s house. O therw ise w hat th ey w ill do is th ey w ill go to 70 again or th ey w ill go to 80 instead of going to 69.
119. S O kay, so th at ‘h ou se’ help them realize now w e have noth in g to do w ith the 70s, w e going to the ...
120. G W e are finished w ith the 70s w e are now falling into th e 60s house and you fall in at the top [raising h e r h a n d s a b o v e h e r head] then you count
backw ards [sta g g erin g h e r h a n d s dow n w a rd s] it’s som ething I have learnt over th e years.
121. S A n d it’s quite interesting.
122. G It works! It’s definitely does help them actually realizing w e have finished th e 70s
123. S A n d it also helps all o f them to be w ith you because all of them have to be w orkin g [raising h a n d s a b o ve the h e a d a n d sta g g e rin g them d o w n like th ey do w h e n co u n tin g b a ckw a rd ].
124. G Oh yes, [also r a isin g hands] you see that is actually getting th e children, w ith the boys th e boys have to m ove to learn.
125. S O kay.
126. G T hat is w h y you often see m e doing th at counting in 2s, get up, get down, it ’s to get them focused again. It’s to get them m oving then back to your next bit of w ork.
127. S O kay [n o d d in g a n d p la y in g the vid eo again].
128. GS [L iste n in g a n d w a tc h in g ]
129. S So is there any possibility th at th ey can, let m e use th e w ord sing, sing this close M r w h atever th e bottom group w ith ou t und erstan din g w h at is happening.
130. G H opefu lly th ey do understand because I have also show n them . W e did a house and w e had all those num bers th at are part o f seventy. So now , I m ean there are only nine num bers that are part of seventy and only nine
num bers that are part of eighty, see w h at I m ean, so w hen u are finished w ith those w h ere do u go from there?
131. S W h at do u m ean there are only nine num bers th at are part o f eighty? 132. G 81, 82, 83, 84, 85, 86, 87, 88, 89 you then go to 90.
133. S O kay.
134. G A n d all th e num bers in ninety are 91 to 99 basically there are only nine ones then you go to tens then you get ten and nine ones then you go to tw enty.
135. S So basically does it m ean if a child as w ell understood counting back from 10 to 0 it becom es easy for them to count from any num ber com ing down? 136. G N ot necessarily com ing from nine to zero, not at all, not necessarily from
nine, um , it’s very easy and also parrot fashion w hen th ey do it that w ay, 9, 8, 7, 6, 5, 4, 3, 2, 1 then they blast off. I d on ’t know , get all these w eird things com ing in, um , no it’s w hen you get to the bigger num bers that it b ecom es difficult for them to actually finish. T hey w ill go like 71, 60 or 71, 80 th ey w o n ’t say 70 finish th at ten.
137. S O kay [nodding] C lose M r seventy’s house.
138. G Y ah but now you w ill actually see initially w e w ere closing but now I just do [show s h a n d sig n a l] th ey d on ’t do close M r seven ty’s house anym ore th e y ’re now counting ju st backw ards 79-70 w e ’re not saying “Close M r seventy’s h ou se” anym ore.
139. S N ow th ey understand that sign [show ing sign] w e are closing, okay.
140. G Yah.
141. S O kay so w ith tim e w ill you still have to do th e actions or you can get to a stage w ere you ju st go dow n, go dow n, go down w ith having t o .
142. G Y ah eventually you w ill actually see by th e end o f the year I am not doing h a lf as m uch counting.
143. S [nodding]
144. G I t’s only at th e beginning of the year that I do an enorm ous am ount of counting.
145. S O kay.
146. G Y ah tow ards th e end o f th e year I a m uch further th ey know how to use th eir counting skills in th eir calculations so I am not doing h a lf of this m uch counting.
147. S O kay.
148. GS [W atch video]
149. S T here is that b oy [pointing a t video] w hen w e started ju st now w ho w as u sing his fingers to [show ing w h a t b o y w a s doing] w h a t’s is im portant for them to be able to use th eir fingers in counting. I have realised even w hen you are doing counting w ith them at tim es you say ‘’use your fingers, use you r fin gers’’ w h a t’s . .
150. G . w ell our fingers are part o f a resource.
152. G Y ah I m ean you r fingers can be ones, th ey can be tw os, th ey can be fives, th ey can be one hundreds, anything ...
153. S M m m .
154. G C hildren need to learn, th ey need concrete in order to do m aths, you can ’t ju st tell them som ething. T h at’s th e basis as w ell is u got to discover things u sing concrete apparatus. [w iggling h e r fingers] this is concrete
155. S M m m . O kay but w h y don ’t u ask them to use th e num ber line? Like they look at th e n um ber line or th ey look at the fingers on th e board but they use th eir own fingers. Is there any special th ing about th eir own fingers?
156. G I t’s part o f them .
157. S I t’s part o f them .
158. G M m m . I t’s m uch b etter for them to use th eir own finger th at to get up and w alk around to go use your n um ber grid, th ey can, but y o u ’ re going to have lots of children w alk in g around w hereas fingers are on you r hands th e w hole tim e.
159. S O kay.
160. GS [W atch v id e o ]
161. G H ow m uch m ore I have to go?
162. S O k m aybe I w an ted to understand about this part [pointing at the video]
163. G Q uickly let’s do.
164. S O kay.
165. GS [W a tch v id eo ]
166. G T hey need to realise th at counting backw ards you are tak ing away one every tim e.
167. S O kay.
168. G So you are tryin g to, through counting, you are trying to let them realise th at counting is a strategy. F orw ard, addition and backw ards is taking away.
169. S O k so th a t’s w h at you w an ted them to realise t o . ?
170. G So I am tak ing away one each t i m e .
171. S E ach tim e you counting back u sing one you are tak ing aw ay one! 172. G A n d if I am counting back in tw os I am rem oving two.
173. S [S ilen ce ]
174. G So u see how counting helps you w ith addition and subtraction.
175. S O kay.
176. G Yah.
177. S So you r counting, you use it for building skills for addition and subtraction?
178. G [N o dding in agreem ent]
179. S O kay.
180. G T here you see tak ing aw ay one. [referring to the video]
181. SG [W atch the v id e o ]
182. G T here w e go! [referring to the video]
183. S [Silence]
184. G Y ou see 10, 20 is 2 tens and 30 is 3. 185. SG [W a tch v id eo ]
186. G L ook at this one! [P o inting to screen] H e’s not listening at all!
187. S [Laughing]
188. G O kay now you are going ask m e w h y th at ...
189. S M m m [sm ilin g ]
190. G A lright can I w rite here? [ p o in tin g a t the p a p e r in f r o n t o f the researcher]
191. S Y a you can w rite at th e back. [giving h e r a s h e e t o f paper]
192. G Patterns, m aths is also about patterns, okay, so I w ent, I have, [a ddresses a s t a f f m e m b er]
193. S [L o o ks a t the p a g e ]
194. G I t’s a pattern [c o n tin u e s to w rite on p a g e the m u ltip le s o f tw o u p to ten in a row , then u p to tw en ty u n d e rn e a th su ch th a t the 2s a re in the sa m e c o lu m n a n d the 4 s,6 se tc fo rm a p a ttern ) all th e tw o, here [pointing a t h e r th u m b ].
195. S O kay.
196. G It d oesn ’t m atter I can start 22, 24, 26, 28, [p o inting a t a ll h e r fin g e r s s ta r tin g w ith thum b] 30, 32. This is a 2, a 4, a 6, a 8. I only need five fingers to count in tw os.
197. S O kay.
198. G Y a go it’s all about patterns. [ h a n d in g p a p e r b a c k to Sam u]
199. S So you m ake them realise th e patterns?
200. G I m ake them aw are of patterns all the tim e. The sam e th ing if you see w ith m y counting in 10s, I said is w e w ent down w h at could w e actually see, the 6 w as all the sam e w hat w as changing w as th e 10 w as going to 20 because