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Running Head: PROBLEM SOLVING HIGHER ORDER THINKING ""
Teaching Problem Solving Skills in Math byEngaging Higher Order Thinking
By Chris AdamsMasters Research Project
St. Mary’s College of MarylandMasters of Arts in Teaching
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 G
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 T
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 ^
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 `
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 f
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Pretest Posttest Growth p-value
First Period (CM) 2.846 6.692 3.846 2.23E-05
Fourth Period (CM) 4.1 6.1 2 0.000298
Second Period 3.588 6.294 2.705 0.000104
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 "Q
Sixth Period 3.8235 6.176 2.352 0.000252
Certificate of Merit 3.606 6.333 2.72 7.92E-08
Standard 3.705 6.264 2.558 5.13E-08
All Classes 3.656 6.313 2.656 5.91E-13
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Item Analysis 1
Item1
Item2
Item3
Item4
Item5
Item6
Item7
Item8
Item9
Item10
Avg.
Pre-
Test
13% 20% 78% 51% 51% 23% 40% 33% 28% 48% 38%
Post-
Test
41% 58% 91% 79% 72% 63% 49% 50% 63% 87% 65%
Growth 28% 38% 13% 28% 21% 40% 9% 17% 35% 39% 27%
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 ""
R2& %) %-& %*/*(, )$ %-& *(%&'8&(%*)(: ; 9.1 .74& %) +)(%*(2& */64&/&(%*(, /0 .+%*)(
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Pretest Posttest Analysis 2
Pretest Posttest Growth p-value
First Period (CM) 3.07 8.40 5.33 3.62E-08
Fourth Period (CM) 2.84 9.42 6.58 2.41E-13
Both Classes 2.94 8.97 6.03 1.59E-19
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)2% %-& ,'&.%&1% +)//)( $.+%)': .(3 *%&/1 1&8&( %-')2,- %&( 6&'%.*( %) $.+%)'*(, %-&
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Item Analysis 2
Item
1
Item
2
Item
3
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4
Item
5
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6
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7
Item
8
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9
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10
Avg.
Pre-
Test
43% 25% 20% 25% 22% 42% 20% 34% 20% 25% 28%
Post-
Test
97% 83% 94% 97% 94% 91% 89% 91% 86% 70% 89%
Growth 54% 58% 74% 72% 72% 49% 69% 57% 66% 45% 61%
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.(19&'&3 .44 *%&/1 +)''&+%40
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 "G
#1 1&&( *( %-& %.74& .7)8&: $)' *%&/1 %-'&&: $)2': .(3 $*8& %-& 6&'+&(%.,& )$ 1%23&(%1
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*%&/1 )(&: %9): 1&8&(: &*,-%: .(3 (*(& .44 -.3 6&'+&(%.,&1 (&.' %-& .8&'.,&= ;% *1 +4&.' %-.%
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#44 $)2' +4.11&1 +)/64&%&3 %-'&& 6&'$)'/.(+& %.151 9-*+- 3&.4% 9*%- %-& 6')6&'%*&1
)$ &?6)(&(%1: 1+*&(%*$*+ ()%.%*)(: .(3 6)40()/*.41: '&16&+%*8&40= k21% .1 %-& &?%'. %*/&
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First Period Performance
First Period (CM) Exponent Properties Scientific Notation Polynomial Factoring
Average Percent 46.25 % 92.94 % 70.25 % 76.39 %
p-value 1.79929E-06 0.02 0.19
Table 6.
Fourth Period Performance
Fourth Period (CM) Exponent Properties Scientific Notation Polynomial Factoring
Average Percent 56.44 % 62.25 % 73.95 % 65.79 %
p-value 0.42 0.11 0.24
Table 7.
Second Period Performance
Second Period Exponent Properties Scientific Notation Polynomial
Average Percent 40.17 % 65.20 % 67.26 %
p-value 0.06 0.24Table 8.
Sixth Period Performance
Sixth Period Exponent Properties Scientific Notation Polynomial
Average Percent 18.68 % 69.33 % 75.87 %
p-value 1.94729E-06 0.06
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 "T
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1+)'&1 *(+'&.1&3 +)(%*(2)2140 $')/ %-& $*'1% %.15 %) %-& %-*'3H -)9&8&' %-& %9) OC +4.11&1
-.3 /*?&3 '&124%1= [*'1% 6&'*)3 3*3 9)'1& $')/ %-& 1&+)(3 %.15 %) %-& %-*'3 .(3 7&%%&' $')/
%-& %-*'3 %) %-& $)2'%- %.15: 9-*4& $)2'%- 6&'*)3 3*3 7&%%&' $')/ %-& 1&+)(3 %.15 %) %-& %-*'3.(3 9)'1& $')/ %-& %-*'3 %) %-& $)2'%-= >-&'& /.0 ()% -.8& 7&&( 3&$*(*%*8& ,')9%-
%-')2,-)2% %-& 6&'$)'/.(+& %.151: 72% *( .44 +.1&1 %-&'& 9.1 6)1*%*8& ,')9%- $')/ %-& $*'1%%.15 %) %-& $*(.4 %.15= >-& $)2' %.151 +.( 7& $)2(3 *( #66&(3*? O: R: \: .(3 [= ; +'&.%&3 .44
$)2' %.151 9*%- . $)+21 )( )6%*/*E*(, 1%23&(%1F 9)'5*(, /&/)'0=
B%23&(%1 R*16)1*%*)( %)9.'31 W')74&/ B)48*(,
#$%&' .(.40E*(, %-& '&124%1 $')/ %-& 12'8&0 %-.% 1%23&(%1 %))5 7&$)'& .(3 .$%&' %-&*/64&/&(%.%*)( )$ /0 .+%*)( 1%'.%&,0: ; $)2(3 %-.% %-&'& 9.1 () 6)1*%*8& )8&'.44 ,')9%- )(
.(0 )$ %-& &*,-% *%&/1 7&%9&&( %-& 6'&b12'8&0 .(3 6)1%b12'8&0 '&124%1= >-& 12'8&0 %-.% 9.1
.3/*(*1%&'&3 +.( 7& $)2(3 *( #66&(3*? V=
>-& *%&/1 )( %-.% 12'8&0 9&'& 1%'2+%2'&3 *( .( .%%&/6% %) ,.2,& -)9 9&44 /0 .+%*)(
1%'.%&,0 */6')8&3 1%23&(%F1 +)($*3&(+& *( %-&*' .7*4*%0 %) '&+),(*E& %-& /.%- (&&3&3 %)
1)48& 6')74&/1 .(3 %-&*' .7*4*%0 %) 21& %-& /.%- (&&3&3 %) 1)48& 6')74&/1: .1 9&44 .1 %-&
&?%&(% %) 9-*+- %-&0 8*&9 /.%- .1 . '&4&8.(% %))4 %-.% +.( 7& 21&3 %) 1)48& 6')74&/1 *( %-&
'&.4 9)'43= S&+.21& %-& 1%23&(%1 '&/.*(&3 .()(0/)21 %-')2,-)2% %-& 12'8&0*(, 6')+&11: ;
9.1 2(.74& %) /.%+- *(3*8*32.4 1%23&(%1F 6'&%&1% 9*%- %-&*' 6)1%%&1%=
>.74& f=
&'()"('#'"* ,-./$0 1*230('(
Class Pretest (out of 32) Posttest (out of 32) Growth p-value
First (CM) 22.38 17.06 -5.32 0.01
Fourth (CM) 23.43 24.26 0.83 0.32
Second 21.17 18.41 -2.75 0.07
Sixth 21.61 21.61 0.00 0.50
All 22.19 20.42 -1.78 0.04
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 "^
!"#$% >-&'& 9&'& ZT 1%23&(%1 9-) %))5 %-& 6'&b12'8&0 .(3 ZT 1%23&(%1 9-) %))5 %-& 6)1%b
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1+)'& )$ TG= ;%&/1 %-.% 9&'& 9)'3&3 (&,.%*8&40 J*%&/1 %-'&&: $)2': 1&8&(: .(3 &*,-%K: 9&'&
'&8&'1& 1+)'&3 %) &(12'& .( .++2'.%& 3&6*+%*)( )$ 1%23&(% '&16)(1&1=
#1 1&&( *( >.74& f: $)' $*'1% .(3 1&+)(3 6&'*)31: .(3 .44 $)2' +4.11&1 .1 . 9-)4&: %-&'&
9.1 . 1*,(*$*+.(% 3&+4*(& *( 1+)'&1 $')/ %-& 6'&%&1% %) %-& 6)1% %&1%= B*?%- 6&'*)3 -.3 ()
,')9%-: .(3 $)2'%- 6&'*)3F1 ,')9%- 9.1 ()% 1*,(*$*+.(%= >-*1 /&.(1 %-.% /0 1%'.%&,0 3*3
()% */6')8& 1%23&(% 3*16)1*%*)(: .(3: *( $.+%: /0 1%'.%&,0 .+%2.440 9)'1&(&3 1%23&(%1F
3*16)1*%*)( %)9.'31 6')74&/ 1)48*(,=
Interpretations
#+<2*1*%*)( .(3 N(3&'1%.(3*(, )$ %-& O)(%&(%
[')/ %-& $*(3*(,1 .7)8&: ; ./ +)($*3&(% %-.% ; 9.1 .74& %) .(19&' %-& $*'1% 6.'% )$ /0
'&1&.'+- <2&1%*)(= #15*(, 1%23&(%1 -*,-&' )'3&' <2&1%*)(1: -.8*(, 1%23&(%1 3&8&4)6 %-&*'
)9( 1%'.%&,*&1 $)' 1)48*(, 6')74&/1: .(3 '&<2*'*(, 1%23&(%1 %) 6')8& %-&*' '&124%1 3*3
*/6')8& %-&*' .+<2*1*%*)( .(3 2(3&'1%.(3*(, )$ %-& +)(%&(%= ])% )(40 9.1 %-&'& 1*,(*$*+.(%
,')9%- $)' 7)%- 1&%1 )$ 6'&%&1%1 .(3 6)1%%&1%1: 72% %-&'& 9.1 ,')9%- *( &.+- %)6*+ %-.% 9.1
+)8&'&3 )8&' %-& +)2'1& )$ %-& */64&/&(%.%*)(=
>-&'& 9.1 8&'0 4*%%4& 3*1%*(+%*)( 7&%9&&( %-& 6&'$)'/.(+&1 )$ OC 1%23&(%1
+)/6.'&3 %) B%.(3.'3 1%23&(%1: .1 7)%- ,')261 /.3& 1*/*4.' ,')9%- 9*%- %-& B%.(3.'3
+4.11&1 )2% .4/)1% )2% 6&'$)'/*(, %-&*' OC 6&&'1= >-*1 1266)'%1 /0 7&4*&$ %-.% .44 4&8&41 )$1%23&(%1 +.( 7&(&$*% $')/ 7&*(, &?6)1&3 %) +-.44&(,*(, .(3 3*$$*+24% <2&1%*)(1 .(3
6')74&/1= ;( +-.44&(,*(, 1%23&(%1 9*%- /.%&'*.4 %-.% &?+&&31 %-& &?6&+%.%*)(1 1&% $)'%- 70 .
1%.(3.'3*E&3 .11&11/&(%: ; 9.1 .74& %) )8&' 6'&6.'& %-&/ $)' %-& 6)1%%&1%= O)/6.'&3 %) %-&-*,-&' )'3&' <2&1%*)(1 .(3 %-& +-.44&(,*(, 6&'$)'/.(+& %.151: %-& *%&/1 )( %-& 6)1%%&1%
6')8&3 %) 7& 4&11 3*$$*+24% $)' /0 1%23&(%1=
Student Ability to Problem Solve#15*(, 1%23&(%1 -*,-&' )'3&' <2&1%*)(1: -.8*(, 1%23&(%1 3&8&4)6 %-&*' )9(
1%'.%&,*&1 $)' 1)48*(, 6')74&/1: .(3 '&<2*'*(, 1%23&(% %) 6')8& %-&*' '&124%1 3*3 */6')8&
%-&*' .7*4*%0 %) 6')74&/ 1)48&= >-& '&124%1 9&'& ()% 1*,(*$*+.(%: 72% %-&'& 9.1 .( )8&'.44
*(+'&.1& *( %-& 1%23&(%1F 6&'$)'/.(+& )( %-& %.151=
B)/& )$ %-.% ,')9%- +)243 7& .%%'*72%&3 %) %-& 1%23&(%1F $./*4*.'*%0 9*%- /0
&?6&+%.%*)(1 9*%- '&,.'31 %) %-& 4&8&4 )$ 3&%.*4 *( %-&*' .(19&'1= B%23&(%1 -.3 7&&(.11*,(&3 1*/*4.' 6&'$)'/.(+& %.151 &.'4*&' *( %-& 1+-))4 0&.': 72% %-)1& %.151 9&'& )(40
.3/*(*1%&'&3 .% %-& &(3 )$ &8&'0 <2.'%&'= >-)1& %.151 9&'& .41) /)'& 1%'2+%2'&3 9*%-/)'& +)/6)(&(%1= ;( 7)%- B%.(3.'3 +4.11&1 .(3 /0 $)2'%- 6&'*)3 +4.11: %-&'& 9.1+)(%*(2)21 ,')9%- %.5*(, 64.+& $')/ )(& 6&'$)'/.(+& %.15 %) .()%-&'= >-& 3&+4*(& *(
6&'$)'/.(+& %-.% 9.1 &?-*7*%&3 70 $*'1% .(3 $)2'%- 6&'*)3 *( %-& 4.1% +)264& )$ %.151 +)243
6&'-.61 7& .%%'*72%&3 %) . 3*$$&'&(+& *( 3*$$*+24%0 7&%9&&( %-& 6')74&/1=
>-& $*'1% %.15 6')8&3 %) 7& %-& /)1% 3*$$*+24%: .(3 *% 9.1 ()% *//&3*.%&40 +4&.' %)
1%23&(%1 9-.% 9.1 &?6&+%&3 )' -)9 9-.% %-&0 4&.'(&3 +)((&+%&3 %) %-*1 6')74&/= >-&
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 "c
1&+)(3 6')74&/ '&<2*'&3 %-& 1./& 7.1*+ )6&'.%*)(1 .1 %-& $*'1%: 72% %-& 6')74&/ 9.1 /)'&
1*/*4.' %) )%-&' 6')74&/1 %-.% %-&0 -.3 7&&( $.+&3 9*%-: &16&+*.440 %-)1& '&,.'3*(, '.%&1
9*%- /)(&0 )8&' . 6&'*)3 )$ %*/&= ; 9)243 &8.42.%& %-& %-*'3 .(3 $)2'%- %.151 %) 7& %-&
/)1% &$$&+%*8& *( +)((&+%*(, %-& /.%&'*.4 %) /)'& .2%-&(%*+ 6')74&/1= #1 %-&
*/64&/&(%.%*)( 6'),'&11&3: ; 3*3 7&+)/& 7&%%&' .% +'.$%*(, %-& 6')74&/1 J.1 1&&( *( %-&
3*$$&'&(+& *( 3*'&+%*)(1 $')/ %-& $*'1% %.15 %) %-& '&1% )$ %-& %.151K=
; %-*(5 %-.% %-& 21& )$ ,')261 *($42&(+&3 %-& 1%23&(%1F 6&'$)'/.(+& )( %-& 6')74&/1=
;( ,*8*(, 1%23&(%1 . +-)*+& *( %-&*' ,')261: ; )6&(&3 %-& 6)11*7*4*%0 %-.% *(&$$&+%*8& ,')261
+)243 &?*1%= R&16*%& /0 +)(1%.(% .%%&/6%1 %) 5&&6 ,')261 )( %.15: %-&'& 9&'& /24%*64&)++.1*)(1 9-&'& ,')26 /&/7&'1 9&'& ()% 7&*(, .1 6')32+%*8& .1 %-&0 +)243 -.8& 7&&(= ;%
*1 /0 7&4*&$ %-.% 1%23&(%1 3*3 ()% %.5& %-& 6')+&11 1&'*)2140 .(3 9)243 9.*% *( -)6&1 %-.% ;9)243 9.45 %-&/ %-')2,- %-& 6')+&11= B*(+& )9(&'1-*6 )$ %-& 6')74&/ 9.1 %-&*'1 .4)(&:
%-&0 3*3 ()% '&+&*8& %-& -&46 %-.% %-&0 -.3 +)/& %) &?6&+%: .(3 %-&*' 1+)'&1 '&$4&+%&3 %-&
4.+5 *(*%*.%*8& J'&124%*(, *( E&')1 )( . $&9 )++.1*)(1K=
>-.% 4.+5 )$ *(*%*.%*8& 1%'2+5 /& .1 .( .4.'/*(, 6')74&/= #1 (2/&')21 1%23&(%1 %)43
/&: ia)2F'& . 7.3 %&.+-&': 0)2F'& ()% -&46*(, 21=j >-*1 '&.+%*)( )++2''&3 9-&( 1%23&(%1
7&+./& $'21%'.%&3 9*%- %-& 6')74&/= ;% 1&&/1 %-.% %-&0 8*&9&3 %&.+-&'1 .1 %-& 1)4&
12664*&' )$ *($)'/.%*)( .(3 .(19&'1 *( %-& +4.11'))/= ;( ()% 6')8*3*(, %-&/ 9*%- %-&
3*'&1% .11*1%.(+& %-&0 1)2,-%: ; %'.(1$&''&3 /)'& )$ %-& )(21 %) %-& 1%23&(%1= ; %-*(5 %-.%
.()%-&' 6.'% )$ %-& *(*%*.%*8& 6')74&/ 1%&//&3 $')/ .( *(&$$&+%*8&(&11 %) &1%.74*1- %-.%
%-&1& 6')74&/1 9&'& 9)'%- 1)48*(,= ]) 3)27% .44 )$ %-& 6')74&/1 /.3& %-& 1%23&(%1 %-*(5
.7)2% /.%- *( . 3*$$&'&(% 9.0: 72% 1)/& )$ %-& 6')74&/1 /.0 ()% -.8& 7&&( .1 /&.(*(,$24
%) %-&/ .1 %-&0 1-)243 -.8& 7&&(=
Students Disposition towards Problem SolvingD&,.'3*(, %-& %-*'3 6.'% )$ /0 '&1&.'+- <2&1%*)(: .15*(, 1%23&(%1 -*,-&' )'3&'
<2&1%*)(1: '&<2*'*(, 1%23&(%1 %) 3&8&4)6 %-&*' )9( 1%'.%&,*&1 $)' 1)48*(, 6')74&/1: .(3
'&<2*'*(, 1%23&(%1 %) 6')8& %-&*' '&124%1 3*3 ()% */6')8& %-&*' 3*16)1*%*)( %)9.'31
6')74&/ 1)48*(,= ;( $.+%: /0 1%'.%&,0 6')8&3 %) 1*,(*$*+.(%40 9)'1&( %-& 3*16)1*%*)( )$ /0
1%23&(%1=
>-)1& '&124%1 '&$4&+% $*(3*(,1 $')/ @&.3&' .(3 C*334&%)( JGQQ^K 9-) 3*1+211&3
-)9 '&16)(1&1 *( %-& 7'.*( +.( $)'/ 1%23&(%1F .%%*%23&1 '&,.'3*(, 6')74&/ 1)48*(, %.151=
>-& 1%23&(%1 7&+./& $'21%'.%&3 &.'40 )( *( %-& 6')+&11: .(3 ; 7&4*&8& %-.% 9.1 %'*,,&'&3 %)
6'&8*)21 &?6&'*&(+&1 9*%- 3*$$*+24% .(3 1&&/*(,40 *(12'/)2(%.74& 6')74&/1 %-&0 $.+&3 *(
/.%-= # 1*,(*$*+.(% 6)'%*)( )$ /0 1%23&(%1 -.3 $.*4&3 %-& #4,&7'. AB#: .(3 7&*(, 64.+&3 *(;(%&'/&3*.%& #4,&7'. 12,,&1%1 %-.% %-& 1%23&(% 9.1 ()% 12++&11$24 &()2,- *( #4,&7'. %)
/)8& )(%) V&)/&%'0 )' #4,&7'. ;;= C.(0 1%23&(%1 -.8& ()% -.3 %-& /)1% 6)1*%*8&&?6&'*&(+&1 9*%- /.%-&/.%*+1= [)' %-.% '&.1)(: *% /.5&1 1&(1& %-.% %-&0 9)243 -.8& .
(&,.%*8& '&.+%*)( %) +-.44&(,*(, .(3 3*$$*+24% <2&1%*)(1 .(3 6')74&/1: .(3 .1 . '&124% .
3&+'&.1&3 3*16)1*%*)( %)9.'31 6')74&/ 1)48*(,=
>-*1 3)&1 ()% 12,,&1% %-.% 1%23&(%1 1-)243 ()% 7& %.15&3 %) .(19&' )' 1)48& %-)1&
3*$$*+24% <2&1%*)(1 .(3 6')74&/1: -)9&8&'= >-& */64&/&(%.%*)( %-)1& <2&1%*)(1 .(3
6')74&/1 1-)243 7& +)(32+*8& %) $)1%&'*(, . 1.$& .(3 6)1*%*8& &(8*')(/&(% $)' %-&
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 "d
1%23&(%1= >-& .71)42%& 9.0 %-.% 1%23&(%1 9*44 -.8& . 6)1*%*8& 3*16)1*%*)( %)9.'31 6')74&/
1)48*(, *1 $)' %-&/ %) -.8& 6)1*%*8& &?6&'*&(+&1 9*%- 1)48*(, /&.(*(,$24 6')74&/1=
ConclusionR2'*(, %-& 7&,*((*(, )$ /0 *(%&'(1-*6: ; ()%*+&3 %-.% /0 1%23&(%1 $)2(3 *% 3*$$*+24%
%) +'*%*+.440 %-*(5 )' 6')74&/ 1)48& &$$&+%*8&40= S0 .15*(, -*,-&' )'3&' <2&1%*)(1: '&<2*'*(,1%23&(%1 %) 3&8&4)6 %-&*' )9( /&%-)3 $)' 1)48*(, 6')74&/1: .(3 '&<2*'*(, %-&/ %) 6')8&
%-&*' '&124%1: ; 1)2,-% %) */6')8& /0 1%23&(%1F .7*4*%0 %) +'*%*+.440 %-*(5 .(3 6')74&/ 1)48&
9*%-*( %-& +)(%&(% %-&0 9&'& 4&.'(*(,= C0 1%'.%&,0 6')8&3 %) 7& 12++&11$24 *( */6')8*(,
1%23&(%1 2(3&'1%.(3*(, )$ %-& +)(%&(% .(3 .7*4*%0 %) 6')74&/ 1)48&=
>-*1 1%230 -.3 . $&9 4*/*%.%*)(1: *( %-.% ; 9.1 ()% %-& $244 %*/& %&.+-&': .(3 ; 9.1
)(40 .74& %) */64&/&(% /0 1%'.%&,0 $)' . 1-)'% 6&'*)3 )$ %*/&= ; .41) $)2(3 %-.% ; 9.14*/*%&3 *( /0 .7*4*%0 %) &$$&+%*8&40 +'.$% /&.(*(,$24 6')74&/1 .(3 %) &1%.74*1- '&4&8.(+& $)'
/0 1%23&(%1= R&16*%& %-&1& 4*/*%.%*)(1: ; ./ 1%*44 64&.1&3 9*%- -)9 %-*1 1%230 &(3&3: .(3-.8& $)2(3 %-.% %-& &/6-.1*1 )( +'*%*+.4 %-*(5*(,: 6')74&/ 1)48*(,: .(3 .15*(, -*,-&' )'3&'
<2&1%*)(1 9*44 '&/.*( .1 . 1%.64& *( /0 $2%2'& %&.+-*(,=
>-& $*(3*(,1 $')/ %-*1 1%230 12,,&1% %-.% 1%23&(%1 .% .44 4&8&41 .'& +.6.74& )$ 12++&11
*( .( &(8*')(/&(% %-.% *1 '*+- 9*%- -*,-&' )'3&' <2&1%*)(1 .(3 &(,.,*(, 6')74&/ 1)48*(,
)66)'%2(*%*&1= ;% *1 */6)'%.(% %-.% %-)1& )66)'%2(*%*&1 6')8*3& 1%23&(%1 9*%- 6)1*%*8&
6')74&/ 1)48*(, &?6&'*&(+&1: 1) %-.% 1%23&(%1 +.( 1&& %-.% 6')74&/ 1)48*(, *1 /&.(*(,$24=
\8&'0 1%23&(% 1-)243 7& 621-&3 %) %-*(5 .7)2% 3*$$*+24% .(3 */6)'%.(% <2&1%*)(1 .(3
6')74&/1 &8&'0 3.0: 7&+.21& &8&'0 1%23&(% 9*44 -.8& */6)'%.(% .(3 3*$$*+24% 6')74&/1 %)
1)48& 9-&( %-&0 4&.8& 1+-))4=
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Problem Solving Higher Order Thinking
Rising Tide Volume 5 "Z
+,-,&,.(,$
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O.1& $)' O)(+&6% C.61 .(3 g&&bR*.,'./1 *( C.%-&/.%*+1 W')74&/ B)48*(,=
1-(#.23'2* 42#5$62#'7( 8$275$.9 :;JGK: `b"Z=
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O-*((.66.(: C=: P O-.(34&': W= JGQ"QK= C.(.,*(, O),(*%*8& @).3 *( %-& C.%-&/.%*+1O4.11'))/= 1-(#.23'2* 42#5$62#'7( 8$275$.9 ::J"K: cb""=
3& @*/.: D= ]=: P >.44: R= JGQQ`K= W')+&32'.4 \/7)3*/&(% .(3 C.,*+ *( @*(&.' \<2.%*)(1=?@-72#'"*23 ,#-@'$( '* 42#5$62#'7(9 :A J"K: Tb"`=
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Properties of Exponents Performance Task
Task: With your group members solve the problem below. Discuss with
each other what needs to be solved, how to solve it, and what yoursolution means. These three elements must be present in your
answer in order to receive full credit.
Grading: This will be graded as a product grade. Do your best, and
work with your group members to solve the problem.
The Problem: The radius of the Sun is about 109 times greater thanthe Earth’s. How much greater is the Sun’s volume compared to theEarth’s?
Hint: Volume of a Sphere = ! !!
!!!
!
Appendix D
Scientific Notation Performance Task
The Task: With your group members solve the problem below. You willneed to figure out what the problem is (2), what needs to be done
to solve it (8), whether the math you use is correct (8), and what
your answer means in the context of the problem (2).
Grading: This will be a product grade. The bolded tasks above are eachworth five points. They all need to be clearly addressed in order toreceive full credit.
The Problem: The United States currently has over $15, 353, 220,000, 000 in debt. The country has a population of over 313, 000, 000people. If every person paid 20 dollars every month to pay off thedebt, how many years would it take for the debt to be paid off
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Problem Solving Higher Order Thinking
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(assuming no new debt is acquired)? Write your answer using scientificnotation.
Appendix E
Polynomial Performance Task
Task: With your group, you will solve the problem below. You will need
to clearly address; the information that the problem is giving you
(5pts), how you are going to use that information (5pts.), why your
math is correct (5pts), and what your solution means (5pts).
Grading: This will be graded as a product grade worth 20 points.
The four categories above must be clearly addressed in order to
receive full credit.
The Problem: You are designing a new can for your favorite sodacompany. The only specifications that the company has given you, is
that the can's height must be four times its diameter, and the volumeof the can must be 25 in3. What polynomial will represent the volume ofthe can that you design? Bonus (5pts): How would you find the height
of the can that you design?
Hint: Diameter = 2r
Volume of a Cylinder = !!!!
Appendix F
Factoring Performance Task
Task: With your group members you will work on solving the problem
below. In order to receive full credit, you will need to; identify theimportant information that you will need to solve the problem
(5pts.), explain how you will use that information to solve the
problem (5pts.), explain why your method for solving the problem is
correct (5pts.), and explain what your solution means (5pts.).
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Grading: This will be graded as a product grade, and all points aboveneed to be clearly addressed in order to receive all 20 points.
The Problem: You are the manager of a restaurant that has a buffet
line that has entrées and dessert items. You need to make sure thatbacteria will not grow on the food in your buffet, so that yourcustomers do not get food poisoning. Food poisoning is bad forbusiness.
The health inspector tells you that the quadratic,
B = T 2 + 150(T) – 1600, represents the number of bacteria cells, B,based on the temperature of the food, T. How hot or cold do you need
to keep your food, so that your buffet does not give someone foodpoisoning? Hint: To prevent food poisoning, the number of bacteriacells should be zero.
Appendix G
For each statement below circle the option that represents how strongly you agree or
disagree.
1) I feel confident in my ability to recognize the math needed to solve a real world problem.
Strongly Disagree Disagree No Opinion Agree Strongly Agree
2) I feel confident in my ability to use math to solve real world problems.
Strongly Disagree Disagree No Opinion Agree Strongly Agree
3) I do not feel confident in my ability to recognize the math needed to solve real world
problems.
Strongly Disagree Disagree No Opinion Agree Strongly Agree
4) I do not feel confident in my ability to use math to solve real world problems.
Strongly Disagree Disagree No Opinion Agree Strongly Agree
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Problem Solving Higher Order Thinking
5) I can use math to solve problems in my life.
Strongly Disagree Disagree No Opinion Agree Strongly Agree
6) Math is used in the real world to solve problems.
Strongly Disagree Disagree No Opinion Agree Strongly Agree
7) I cannot use math to solve problems in my life.
Strongly Disagree Disagree No Opinion Agree Strongly Agree
8) Math is not used in the real world to solve problems.
Strongly Disagree Disagree No Opinion Agree Strongly Agree