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158
Written and Oral Assessments of Intermediate Students’ Number Strategies: Possible Uses for a Written Assessment Tool
The Written Strategy Stage Assessment Tool
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Table 1
The Number of Items per Strategy Stage and Criteria for Achieving Each Stage
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159
Findings from the New Zealand Numeracy Development Projects 2009
Table 2
The Percentage Ethnic Make-up of the Year 7 and 8 Cohorts Included in This Study
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Table 3
Classes Showing the Number of Students Taking the Written and Oral Assessments
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160
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Analysis
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The Data
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Internal consistency
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]VYVahdcdiWZZcVhh^\cZYVhWZ^c\VihiV\Z*WZXVjhZi]Znb^hhZYVX]^Zk^c\i]ZhiV\Z*Xg^iZg^VWn
dcZ!i]Vi^h!i]ZnXdggZXianVchlZgZYdcani]gZZdjid[hZkZchigViZ\n^iZbhgVi]Zgi]Vc[djgdjid[
hZkZc!l]^X]ldjaY]VkZVX]^ZkZYi]ZhiV\ZXg^iZg^V#
D[i]Z.)nZVg,hijYZcihl]dXdjaYWZVhh^\cZYVhWZ^c\VihiV\Z,!(*VWdjidcZ"i]^gY]VYcdi
VX]^ZkZYi]ZXg^iZg^V[dgVhh^\c^c\hiV\Z+#D[i]ZhZ(*!&-VWdji]Va[]VYb^hhZYVX]^Zk^c\i]ZhiV\Z
+Xg^iZg^VWndcZ!WjiVaaVX]^ZkZYi]ZhiV\Z*Xg^iZg^V#D[i]ZgZbV^c^c\&,!&)]VYVX]^ZkZYi]ZhiV\Z
*Xg^iZg^V!l^i]dcani]gZZhijYZcihcdiVX]^Zk^c\i]ZXg^iZg^V[dgWdi]hiV\Zh+VcY*#
D[i]Z(&nZVg,hijYZcihVhh^\cZYVhWZ^c\VihiV\Z-!&,VWdji]Va[]VYcdiVX]^ZkZYi]ZXg^iZg^V
[dghiV\Z,VcYdcZhijYZcil]dbZii]ZhiV\Z-VcY,Xg^iZg^V]VYb^hhZYVX]^Zk^c\i]ZXg^iZg^V[dg
hiV\Z+WndcZ#D[i]Z&,cdiVX]^Zk^c\i]ZXg^iZg^V[dghiV\Z,!ildVWdjidcZ"iZci]]VYb^hhZY
Yd^c\hdWndcZVcYi]ZhZildeajh[djgdi]ZghVX]^ZkZYi]ZXg^iZg^V[dghiV\Z+#D[i]ZgZbV^c^c\
&&!Z^\]i]VYVX]^ZkZYi]ZhiV\Z*Xg^iZg^V!l^i]dcani]gZZhijYZcihcdiVX]^Zk^c\i]ZXg^iZg^V[dgWdi]
hiV\Zh+VcY*#
161
Findings from the New Zealand Numeracy Development Projects 2009
D[i]Z,%nZVg-hijYZcihVhh^\cZYVhWZ^c\VihiV\Z+!dcani]gZZ]VYcdiWZZcVhh^\cZYVhWZ^c\
Vi hiV\Z *# I]ZhZ i]gZZ ]VY dcan _jhi VX]^ZkZY i]Z hiV\Z + Xg^iZg^V [djg XdggZXi dji d[ i]Z hZkZc
higViZ\nfjZhi^dchVcYVaai]gZZb^hhZYVX]^Zk^c\i]ZhiV\Z*Xg^iZg^VWnilddcanildXdggZXidji
d[hZkZc#
D[i]Z&)&nZVg-hijYZcihVhh^\cZYVhWZ^c\VihiV\Z,!',VWdjidcZ"Ä[i]]VYcdiVX]^ZkZYi]ZXg^iZg^V
[dghiV\Z+#D[i]ZhZ',!&'VWdji]Va[]VYb^hhZYi]ZhiV\Z+Xg^iZg^VWndcZ!'+]VYVX]^ZkZYi]Z
hiV\Z*Xg^iZg^V!VcYdcZhijYZcib^hhZYWdi]i]ZhiV\Z+VcY*Xg^iZg^VWndcZ#
D[i]Z(%nZVg-hijYZcihVhh^\cZYVhWZ^c\VihiV\Z-!c^cZVWdjidcZ"i]^gY]VYcdiVX]^ZkZYi]Z
Xg^iZg^V[dghiV\Z,#D[i]ZhZc^cZ!ildVWdjidcZ"Ä[i]]VYcdiVX]^ZkZYi]ZXg^iZg^V[dghiV\Z,Wn
dcZ!l^i]dcZhijYZciVX]^Zk^c\Wdi]i]ZhiV\Z+VcY*Xg^iZg^VVcYi]Zdi]ZgVX]^Zk^c\cZ^i]Zgi]Z
hiV\Z+dg*Xg^iZg^V#D[i]ZhZkZcgZbV^c^c\hijYZcih!ildVX]^ZkZYhiV\Z+![djghiV\Z*!VcYdcZ
i]ZhiV\Z&·)Xg^iZg^V#
I]ZVhh^\cbZcid[hiV\Zh*VcY+^h]^\]anXdch^hiZciVXgdhhWdi]nZVg\gdjeh#=dlZkZg!i]ZgZ^haZhh
Xdch^hiZcXn[dghiV\Zh,VcY-!l^i]i]Zegdedgi^dcd[hijYZcihb^hh^c\i]ZegZk^djhhiV\ZXg^iZg^VWn
dcZWZ^c\]^\]Zgi]Vc[dgi]Zdi]ZghiV\ZhVcY]^\]Zg[dghiV\Z,i]Vc[dghiV\Z-[dgZmVbeaZ!¹VWdji
]Va[ºid¹VWdjidcZ"iZci]º[dgi]ZnZVg,Xd]dgiVcY¹VWdji]Va[ºid¹VWdjidcZ"Ä[i]º[dgi]ZnZVg-
Xd]dgi#>cVYY^i^dc!egdedgi^dcVaan[ZlZgnZVg-hijYZcih[V^aZYidVX]^ZkZegZk^djhhiV\ZhXg^iZg^V
ViWdi]hiV\Z,VcYhiV\Z-/[dgi]ZnZVg-hiV\Z-hijYZcih!dcanVWdjidcZ"i]^gY]VYcdiVX]^ZkZY
i]ZhiV\Z,Xg^iZg^VXdbeVgZYl^i]VWdjiV]Va[[dgnZVg,!VcY[dgi]ZnZVg-hiV\Z,hijYZcih!dcan
VWdjidcZ"Ä[i]]VYcdiVX]^ZkZYi]ZhiV\Z+Xg^iZg^VXdbeVgZYl^i]VWdjidcZ"i]^gY[dgnZVg,#I]jh
i]Z\gZViZhiaZkZad[^cXdch^hiZcXn^h^ci]ZhiV\Z,Xjgg^XjajbaZkZa)Vhh^\cZYhiV\Zh[dgWdi]nZVg
\gdjeh#
I]^hYViV^hWgdVYanh^b^aVgidi]ZegZk^djhjhZd[i]ZLHH6I^cadl"YZX^aZhZXdcYVgnZck^gdcbZcih
AdbVh=j\]Zh!'%%.#I]^hhj\\Zhihi]Vii]ZLHH6I^haVg\Zan^ciZgcVaanXdch^hiZci^cVhh^\c^c\
hiV\Zh[dg^ciZgbZY^ViZ"V\ZhijYZcih!ZmXZeiVihiV\Zh,VcY-!l]ZgZV\gZViZgaZkZad[kVg^Vi^dclVh
Zk^YZci#=dlZkZg!i]Zb^hh^c\d[bjai^eaZhiV\Zh!VhYZhXg^WZY]ZgZ[dghijYZcihVhh^\cZYhiV\Zh,
VcY-!lVhdcanb^c^bVaanZk^YZci^cegZk^djhjhZhd[i]ZLHH6I#6ahd!i]Zegdedgi^dcd[hijYZcih
l]db^hhZYVX]^Zk^c\VcZVga^ZghiV\ZWjidcanb^hh^c\WndcZl]ZcVhh^\cZYVaViZghiV\ZlVh
bjX]]^\]Zgi]Vc^cegZk^djhYViVhZih#
8dbbZci/ <^kZc i]Z YZkZadebZci d[ LHH6I VcY ^ih ig^Vaa^c\ ^c adl"YZX^aZ hX]ddah i]Vi lZgZ
^beaZbZci^c\C9E"ineZegd\gVbbZh!hX]ddaZck^gdcbZcih^cl]^X]lg^iiZciZhihlZgZi]Zcdgb!
VcYi]ZgZWZ^c\cdgZedgiZYaVc\jV\Z^hhjZhl^i]i]ZLHH6I!i]ZXVjhZd[i]ZhZVcdbVadjhgZhjaih
^hjcXZgiV^c#I]ZLHH6I\VkZbdgZXdch^hiZcigZhjaih^cdi]ZgVeeVgZcianh^b^aVgZck^gdcbZcih!hd
i]ZgZbVnWZeVgi^XjaVghX]ddadgiZVX]^c\[VXidghi]Vib^\]i]ZaeZmeaV^ci]ZhZgZhjaih#
IdZmeadgZi]^h[jgi]Zg!VcZmVb^cVi^dcd[i]ZgZhedchZhid^iZbh[dghijYZcihl]d]VYb^hhZYhiV\Zh
lVhXdcYjXiZY#I]ZgZlVhcdXaZVgeViiZgcidi]ZgZhedchZh[dgi]ZhZhijYZcih#;dgZmVbeaZ!i]ZgZ
lZgZ&,nZVg,hijYZcihl]dlZgZVhh^\cZYhiV\Z-Wjib^hhZYZVga^ZghiV\Zh#D[i]ZhiV\Z-higViZ\n
^iZbh!ildYZVa^c\l^i]eZgXZciV\ZhXjgg^XjajbaZkZa)bViZg^ValZgZVchlZgZYXdggZXianWnbdhi
d[i]ZhijYZcih!i]gZZdi]Zg^iZbhWnVWdji]Va[i]ZhijYZcih!VcYi]Zh^c\aZ^iZbdc[gVXi^dchWndcan
dcZhijYZci#I]ZildeZgXZciV\Z^iZbhXdjaY]VkZWZZcVeegdVX]ZYjh^c\Va\dg^i]b^XbZi]dYh!
l]^aZi]Z[gVXi^dc^iZb!¹Ldg`dji*h^mi^Zi]hd[i]gZZi]djhVcYh^m]jcYgZYº!lVhaZhhVbZcVWaZid
hjX]VcVeegdVX]#D[i]ZhiV\Z,higViZ\n^iZbh!i]Z^iZbl^i]i]ZbdhiXdggZXigZhedchZhiZclVh
dc[VXidgh!i]ZcZmic^cZdcbjai^ea^XVi^dc.-m*!l]^aZi]ZgZhi]VYdcanV[ZlXdggZXigZhedchZh!
l^i]i]Zild[gVXi^dc^iZbh!¹Ldg`dji*h^mi]hd[)'ºVcY¹DcVcjbWZga^cZ! ) a^ZhWZilZZcl]^X]
,
ildcjbWZgh4º!]Vk^c\i]ZaZVhicjbWZgd[XdggZXigZhedchZh#6eVgi[gdbhdbZ^iZbh]Vk^c\bdgZ
162
Written and Oral Assessments of Intermediate Students’ Number Strategies: Possible Uses for a Written Assessment Tool
XdggZXigZhedchZhi]Vcdi]Zgh!i]ZgZlVhcdXaZVgeViiZgcVhidl]ni]^h\gdjed[hijYZcih]VYi]Z
hVbZ^iZbhXdggZXidg^cXdggZXi#I]ZVeeVgZcijcYZghiVcY^c\d[eZgXZciV\ZhigViZ\^ZhVadc\h^YZV
aVX`d[jcYZghiVcY^c\d[[gVXi^dchigViZ\^Zhhj\\ZhihVedhh^WaZXaVhhgddb[dXjhdcXZgiV^cXdciZci
Xjgg^XjajbaZkZa)VcYVeegdVX]ZhVa\dg^i]bhgVi]Zgi]VcVC9E[dXjhd[ldg`^c\[gdbl]Vi
hijYZcihjcYZghiVcY#
Comparison between oral and written assessments
I]ZgZlVhXdch^YZgVWaZkVg^Vi^dcWZilZZci]ZhiV\ZhVhh^\cZYid^cY^k^YjVahhZZIVWaZ)!l^i]i]Z
LHH6I"Vhh^\cZYhiV\ZhkVgn^c\Xdch^YZgVWan!Wnjeidi]gZZhiV\Zh^cVhbVaacjbWZgd[XVhZh#I]^h
kVg^Vi^dclVh\gZViZgi]Vc^cegZk^djhhijY^Zh!l]ZgZ^ilVha^b^iZYidh^c\aZ"hiV\ZkVg^Vi^dcAdbVh
=j\]Zh!'%%.#;dgZmVbeaZ!]Va[d[i]Z&)hijYZcihVhh^\cZYhiV\Zh&·)dci]ZdgVaVhhZhhbZci
lZgZVhh^\cZY]^\]ZghiV\Zhdci]ZLHH6I/ÄkZhiV\Z*h!dcZhiV\Z+!VcYdcZhiV\Z,#
Table 4
Comparison of Stages Assigned to Year 7 Students by the WSSAT and the Oral Assessment
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8dbbZci/I]Z\gZViZgaZkZad[kVg^Vi^dcWZilZZci]ZdgVa"VcYLHH6I"Vhh^\cZYhiV\ZhZk^YZci^ci]^h
hijYngV^hZhi]Z^hhjZd[l]Zi]Zgi]ZjhZd[i]Z]^\]ZhihiV\ZXg^iZg^VVX]^ZkZYidVhh^\cVhiV\Zl^i]
i]ZLHH6IcZZYhidWZgZXdch^YZgZY#L]ZgZi]ZhiV\ZVhh^\cZY]VhZVga^ZghiV\ZXg^iZg^VcdiVX]^ZkZY
WnbdgZi]VcdcZ!eVgi^XjaVganl]ZgZi]^h^hXdbW^cZYl^i]adlaZkZahd[`cdlaZY\Z!VcdgVaX]ZX`dg
i]ZjhZd[di]ZgVhhZhhbZciYViVbVnWZcZXZhhVgnidVhh^\cVhiV\Z#I]^hbVnVahdWZcZXZhhVgnl]Zc
i]ZiZVX]ZghjheZXihi]Vii]ZLHH6I"Vhh^\cZYhiV\ZYdZhcdigZÅZXii]ZhijYZci¼hhiV\Z#I]Z[dgbVi
d[i]ZVchlZgh]ZZiVcYbVg`gZXdgY^c\VaadlhVcdgVaX]ZX`d[heZX^ÄXhigViZ\^Zhdg`cdlaZY\Zid
WZXVgg^ZYdjigZaVi^kZanZVh^an#I]jh![dgi]ZhbVaacjbWZgd[hijYZcih^cVXaVhha^`ZanidWZ^ci]^h
h^ijVi^dc!VcdgVaX]ZX`^c\egdXZhhh]djaYcdiWZdkZgani^bZ"Xdchjb^c\[dgi]ZiZVX]Zg#
Comparison with numeracy expectations
I]ZVhh^\c^c\d[hiV\Zh[gdbi]ZLHH6I\VkZg^hZidgZVhdcVWanh^b^aVg¹W^bdYVaºY^hig^Wji^dch!l^i]
gZaVi^kZan]^\]ZgaZkZahd[hiV\Z*hVcY,h[dgWdi]nZVg\gdjeh#I]ZgZ^hVh]^[iid]^\]ZgaZkZahZk^YZci
^ci]ZnZVg-YViVVhldjaYWZZmeZXiZY!Vai]dj\]l^i]a^iiaZX]Vc\Z^ci]ZeZgXZciV\Zd[hiV\Z-hhZZ
IVWaZ*#I]ZdkZgVaanZVg-LHH6IhiV\ZY^hig^Wji^dc^hXdch^hiZcil^i]i]ZnZVg,Y^hig^Wji^dc/Vh
hijYZcihegd\gZhh[gdbhiV\Zh&·)idhiV\Z*![gdb*id+!VcYhddc!i]ZeZgXZciV\Zd[ZVga^ZghiV\Zh
gZYjXZhVcYi]Vid[]^\]ZghiV\Zh^cXgZVhZh#=dlZkZg!WZXVjhZd[i]Z\gZViZgXdbeaZm^ind[Wdi]hiV\Zh
,VcY-!i]Z\gdli]^chiV\ZVXfj^h^i^dc^hjhjVaanhadlZgi]Vc[dgZVga^ZghiV\Zh#DkZgi]ZXdjghZd[
dcZnZVg!bdgZhijYZcihl^aabdkZ^cidhiV\Z,i]Vci]ZcjbWZgl]dl^aabdkZje[gdb^i#I]jhi]Z
h^oZd[i]Z^cXgZVhZ^ci]ZhiV\Z,h¼eZgXZciV\Z[gdbnZVg,id-^haVg\Zgi]Vcb^\]iWZZmeZXiZY#
163
Findings from the New Zealand Numeracy Development Projects 2009
8dbbZci/I]ZC9Ee]^adhde]nVcYCjbWZg;gVbZldg`egdbdiZVhZfjZci^VaYZkZadebZciVgdjcY
Wdi]`cdlaZY\ZVcYhigViZ\nVXfj^h^i^dc!l]^X]^bea^ZhVbdgZZkZcanhegZVYY^hig^Wji^dcgVi]Zgi]Vc
VW^bdYVaY^hig^Wji^dc#I]jhi]Z]^\]ZgeZgXZciV\Zhd[hiV\Z,hXdbeVgZYl^i]hiV\Z+h[dgWdi]nZVg
\gdjehVcYi]Z^cXgZVhZ^ceZgXZciV\Zd[hiV\Zh,h[gdbnZVg,id-'(id(+VeeZVghVcdbVadjh#
I]^hbVnWZV[jcXi^dcd[i]ZlVni]ZLHH6IVhh^\cZYhiV\Zh[dgnZVg,VcY-\gdjeh!VcY$dgi]ZgZ
bVnWZeVgi^XjaVghX]ddadgiZVX]^c\[VXidghi]Vib^\]i]ZaeZmeaV^ci]ZhZgZhjaih#
Table 5
The Percentage of Stages Assigned to Year 7 and 8 Students by the WSSAT
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VcYdgVahVbeaZLHH6IY^hig^Wji^dch]'2&%#&!Y#[#2)!e2%#%)!^cY^XVi^c\i]Vii]ZhVbeaZ^h
[V^gangZegZhZciVi^kZd[i]ZXd]dgihZZIVWaZ+#L]^aZi]ZdgVahiV\ZYViVY^hig^Wji^dc[dgi]ZhVbeaZ
h]dlhVY^hig^Wji^dcbdgZh^b^aVgidi]Vid[i]ZcjbZgVXnZmeZXiVi^dch!l^i]hiV\Zh+VcY,h]dl^c\
eZgXZciV\Zhi]VilZgZh^b^aVgidVai]dj\]adlZgi]Vci]ZZmeZXiVi^dcheZgXZciV\ZhVcYl^i]]^\]Zg
eZgXZciV\Zh^chiV\Zh&·)VcY*!i]ZgZ^hV]^\]anh^\c^ÄXVciY^[[ZgZcXZWZilZZci]Zild]'2(%#.!
Y#[#2)!e1%#%%&#HjX]VY^hig^Wji^dcXdjaYlZaaWZZmeZXiZY[gdbVadlZgYZX^aZhX]ddal]Zc
XdbeVgZYl^i]cVi^dcVaYViV#I]ZgZ^hVahdVh^\c^ÄXVciY^[[ZgZcXZWZilZZcdgVaanVhh^\cZYhiV\Zhd[
i]ZdgVahVbeaZhVcYi]ZLHH6I"Vhh^\cZYhiV\Zh]'2&(#(!Y#[#2)!e1%#%&!l^i]i]ZbV^cY^[[ZgZcXZ
dXXjgg^c\[dghiV\Zh+VcY,!l]ZgZi]ZeZgXZciV\Zd[dgVahiV\Z+h^h\gZViZgVcYi]Vid[dgVahiV\Z,h
^hadlZgi]Vci]ZLHH6IeZgXZciV\Zh#
8dbbZci/I]ZdgVaYViVXdaaZXi^dcegdXZhhjcYZgiV`Zc^ci]^hhijYnlVhgZegZhZciVi^kZd[i]ZdgVa
egdXZhhZhjhZY^ci]ZC9EVhhZhhbZcihi]VijcYZge^ci]ZZmeZXiVi^dch!VcYi]ZdgVa^ciZgk^ZlZglVh
VcZmeZgi^cC9EVcY^cXdcYjXi^c\C9EdgVa^ciZgk^Zlh#I]jh!i]ZhiV\ZhVhh^\cZYWni]ZdgVaYViV
VgZa^`ZanidWZVcVXXjgViZgZegZhZciVi^dcd[i]ZhVbeaZ¼hY^hig^Wji^dc#I]^hhj\\Zhihi]VihdbZd[
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ViZVga^ZghiV\Zh#
Table 6
The Percentage of Stages Assigned to Year 7 Students for Each Assessment Tool and Numeracy
Expectations Data for Year 7 Students (End of Year)
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164
Written and Oral Assessments of Intermediate Students’ Number Strategies: Possible Uses for a Written Assessment Tool
I]ZhX]ddaXd]dgiYViVl^i]^ihW^bdYVaY^hig^Wji^dcViWdi]nZVgh,VcY-hZZiVWaZh+VcY,^h
h^\c^ÄXVcianY^[[ZgZciidi]ZcjbZgVXnZmeZXiVi^dch]'2&(,#)!Y#[#2)!e1%#%%&VcY]'2&)-#,!Y#[#
2)!e1%#%%&!gZheZXi^kZan#6ii]Z^ciZgbZY^ViZaZkZanZVgh,VcY-!i]ZZmeZXiVi^dchYViV^cY^XViZh
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Table 7
The Percentage of Stages Assigned to Year 8 Students by WSSAT and Numeracy Expectations Data for
Year 8 Students (End of Year)
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165
Findings from the New Zealand Numeracy Development Projects 2009
Table 8
Classes, Showing the Numeracy Expectations Percentages and the Percentage of Year 7 Students
Assigned a Particular Stage by the WSSAT for the Non-Composite Classes
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166
Written and Oral Assessments of Intermediate Students’ Number Strategies: Possible Uses for a Written Assessment Tool
Table 9
Classes, Showing the Numeracy Expectations Percentages and the Percentage of Year 8 Students
Assigned a Particular Stage by the WSSAT for the Non-Composite Classes
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168