Research_ Teaching Hots Adams

8/11/2019 Research_ Teaching Hots Adams

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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

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Rising Tide Volume 5 c

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Rising Tide Volume 5 d

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Rising Tide Volume 5 Z

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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




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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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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6)40()/*.41 +)/64&%&40=

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Item Analysis 2

Item

1

Item

2

Item

3

Item

4

Item

5

Item

6

Item

7

Item

8

Item

9

Item

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




Rising Tide Volume 5 "G

#1 1&&( *( %-& %.74& .7)8&: $)' *%&/1 %-'&&: $)2': .(3 $*8& %-& 6&'+&(%.,& )$ 1%23&(%1

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B%23&(% #7*4*%0 %) W')74&/ B)48&

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)$ &?6)(&(%1: 1+*&(%*$*+ ()%.%*)(: .(3 6)40()/*.41: '&16&+%*8&40= k21% .1 %-& &?%'. %*/&

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.74& %) .3/*(*1%&' .( .33*%*)(.4 %.15 %) %-)1& +4.11&1 '&4.%&3 %) $.+%)'*(,= >-& '&124%1 $)'

&.+- +.( 7& $)2(3 *( %.74&1 c: d: Z: .(3 `=

>.74& c=

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




Rising Tide Volume 5 "T

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>.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




Rising Tide Volume 5 "^

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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&/= >-&




Rising Tide Volume 5 "c

1&+)(3 6')74&/ '&<2*'&3 %-& 1./& 7.1*+ )6&'.%*)(1 .1 %-& $*'1%: 72% %-& 6')74&/ 9.1 /)'&

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9*%- /)(&0 )8&' . 6&'*)3 )$ %*/&= ; 9)243 &8.42.%& %-& %-*'3 .(3 $)2'%- %.151 %) 7& %-&

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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&&(= ;%

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4.+5 *(*%*.%*8& J'&124%*(, *( E&')1 )( . $&9 )++.1*)(1K=

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7&+./& $'21%'.%&3 9*%- %-& 6')74&/= ;% 1&&/1 %-.% %-&0 8*&9&3 %&.+-&'1 .1 %-& 1)4&

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%) %-&/ .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

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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&/

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%) +'*%*+.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&

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9*%-*( %-& +)(%&(% %-&0 9&'& 4&.'(*(,= C0 1%'.%&,0 6')8&3 %) 7& 12++&11$24 *( */6')8*(,

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Rising Tide Volume 5 "Z

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Rising Tide Volume 5 "`

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Rising Tide Volume 5 "f

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Rising Tide Volume 5 GQ

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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




Rising Tide Volume 5 G"

(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.).




Rising Tide Volume 5 GG

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.


3) I do not feel confident in my ability to recognize the math needed to solve real world

problems.


4) I do not feel confident in my ability to use math to solve real world problems.





5) I can use math to solve problems in my life.


6) Math is used in the real world to solve problems.


7) I cannot use math to solve problems in my life.


8) Math is not used in the real world to solve problems.


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