8. appendix viii - quantitative reasoning - findings and actions

8/2/2019 8. Appendix VIII - Quantitative Reasoning - Findings and Actions

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Appendix VIII: Quantitative Reasoning: Findings and Actions

First Level Mathematics Courses- 16% of the students achieved the expected performance level of 15 or more

correct answers (70%) in the Campus General Logical Mathematical Reasoning Test (CG-LMRT).Approximately 50% of the students achieved a performance level of 12 or more correct answers (55%). These

low results could be due to:

End of semester administration two weeks prior to finals;

Test results did not count towards their course grade;

Some students did not received on time the learning objectives in which they were going to be tested;

Some students were not aware that they were going to be tested.

A closer examination of the results revealed that students performed better on the higher order cognitive test

items (Evaluation area) than on the lower order cognitive test items (Computing area). These outcomes suggestthat some students could not adequately represent the mathematic information provided in order to arrive to a

correct answer or that calculation errors resulted in wrong answers. A detailed scheme of the CG-LMRTresults is presented in this Appendix. Findings were discussed with the Department of Mathematics

Chairperson and with faculty members in a departmental meeting. It was agreed to implement a series of out ofclass tutoring sessions to students enrolled in MATE 3105, MATE 3001, MATE 3036, MATE 3041, and

MATE 3042 courses in order to strengthen their logical mathematical reasoning skills, which are currentlyunderway. Also, during the second semester of 2011-2012, course modifications and tutors training will be

address in order to strengthen student learning.



University of Puerto Rico

Rio Piedras Campus

Dean of Academic Affairs

Office of Evaluation of Student Learning

Campus General Logical Mathematical Reasoning Test (CG-LMRT) Results - May 2011

Item Area of competenceSpecific competency

(learning outcome)

Expert’s

Delta

Difficulty

Index

Equivalent

Delta

Discrimination

IndexComments

1 Computing Basic operations (fractions) 7 0.52 13 0.44Medium difficu

high discriminat

2 Representation Apply measurement concepts 8 0.48 13 0.41Medium difficu

high discriminat

3 Representation Probability 8 0.85 9 0.19Low difficulty, v

low discriminat

4 Computing Equations 9 0.49 13 0.51Medium difficu

high discriminat

5 Representation Graph interpretation 8 0.87 8 0.26Low difficulty,

discriminatio

6 Representation Graph interpretation 13 0.68 11 0.55 Low difficulty, hdiscrimination

7 Evaluation Analyze evidences 9 0.72 11 0.26Low difficulty,

discrimination

8 Computing Proportions 10 0.45 13 0.58Medium difficu

high discriminat

9 Computing

Use quantitative competencies to

analyze and solve everyday

situations

10 0.35 14 0.47High difficulty, h

discrimination




(learning outcome)

Expert’s

Delta

Difficulty

Index

Equivalent

Delta

Discrimination

IndexComments

10 Representation Geometry 10 0.60 12 0.46Medium difficu

high discriminat

11 Computing Percentage 9 0.72 11 0.47Low difficulty, h

discrimination

12 ComputingUse statistics principles to

describe situations12 0.46 13 0.44

Medium difficu

high discriminat

13 Computing Percentage 9 0.43 14 0.46Medium difficu

high discriminat

14 EvaluationAnalyze information presented

on a graph12 0.12 18 0.09

High difficulty, v

low discriminat

15 Representation Graphically represent functions 13 0.37 14 0.46Low difficulty, h

discrimination

16 Evaluation

Understand the relation between

quantitative information and its

different representations15 0.11 18 0.20

High difficulty,

discrimination

17 Evaluation



different representations

14 0.74 11 0.46Low difficulty, h

discrimination

18 Evaluation




Medium difficu

high discriminat

19 Evaluation




Low difficulty, h

discrimination

20 Evaluation Analyze evidence 13 0.46 13 0.43Medium difficu

high discriminat




(learning outcome)

Expert’s

Delta

Difficulty

Index

Equivalent

Delta

Discrimination

IndexComments

21 ComputingUse statistics principles to

describe situations13 0.26 15 0.34

High difficulty, g

discrimination

22 Evaluation



different representations

12 0.76 10 0.34Low difficulty, g

discrimination

Global test delta: 12.5 – Medium difficulty test Internal consistency index (reliability – Cronbach’s alpha): 0.719

Global test difficulty index: 0.54

Item difficulty Item discrimination

College Board’s

Delta indexDifficulty

Percentage of students that

answered correctly

Number of items

in the testIndex Discrimination

Number of item

the test

6 - 8 Very low 95 - 90 0 ≥ 0.40 High 15

9 - 11 low 85 - 70 8 0.39 - 0.30 Good 2

12 - 14 Medium 60 - 40 9 0.29 - 0.20 Low - Can be revised 3 Check difficu

instructions,

alternative15 - 19 High 30 - 5 5 ≤ 0.19

Very low - does not

discriminate2

Negative

Does not discriminate

and should beeliminated.

0

Notes:

The CG-LMRT was administered from May 16th

to the 20th

, 2011 to 521 students out of a total of 806 enrolled in 34 sections of MATE,

ESGE and EDFU courses that comply with the Campus General Logical-Mathematical Reasoning requirement. A total of 65% of the

students enrolled these courses’ sections participated in this assessment.

The item difficulty appreciation by experts (delta) of the College Board was established prior to the administration of the CBA-LMRT.

An equivalent delta index was calculated using item difficulty statistics to establish a degree of agreement between experts’ item

difficulty appreciation and test results.

The item difficulty index indicates the proportion of students that answered each item correctly.

Descriptive Statistics of the Campus General Logical Mathematical Reasoning Test (CG-LMRT) Administration Results -

May 2011



Distribution of Student’s Total Score in the Campus General Logical Mathematical Reasoning Test (CG-LMRT) AdministrationResults – May, 2011



Expected outcome: 70% of the students enrolled in MATE, ESGE and EDFU courses that comply with the Campus General Logical-

Mathematical Reasoning requirement. will obtain a score of 15 points or higher.

Findings: As presented on the table, 77.1% of the students achieved a score of 14 or lower. Therefore, only 22.9% of the students obtained ascore of 15 points or higher. The goal was not met.

Median score: 12



Student’s Item Alternatives Selection Distribution in the Campus General Logical Mathematical

Reasoning Test (CG-LMRT) Administration Results – May, 2011

Item 1

Frequency PercentValid

PercentCumulative

Percent

Valid

5 1.0 1.0 1.0

A 30 5.8 5.8 6.7

B 14 2.7 2.7 9.4

C 192 36.9 36.9 46.3

D 266 51.1 51.1 97.3

E 14 2.7 2.7 100.0

Total 521 100.0 100.0

Item 1 Frequenc

yPercent

Valid

Percent

Cumulative

Percent

Valid

Incorrect 250 48.0 48.4 48.4

Correct 266 51.1 51.6 100.0

Total 516 99.0 100.0

Missing System 5 1.0Total 521 100.0

Item 2


Percent

Cumulative

Percent

Valid

15 2.9 2.9 2.9

A 12 2.3 2.3 5.2

B 119 22.8 22.8 28.0

C 242 46.4 46.4 74.5

D 42 8.1 8.1 82.5

E 91 17.5 17.5 100.0Total 521 100.0 100.0

Item 2

Frequency

PercentValid

PercentCumulative

Percent

Valid Incorrect 264 50.7 52.2 52.2



Correct 242 46.4 47.8 100.0

Total 506 97.1 100.0


Item 3


Percent

Cumulative

Percent

Valid

4 .8 .8 .8

A 437 83.9 83.9 84.6

B 38 7.3 7.3 91.9

C 32 6.1 6.1 98.1

D 10 1.9 1.9 100.0

Total 521 100.0 100.0

Item 3

Frequency

PercentValid

PercentCumulative

Percent

Valid

Incorrect 80 15.4 15.5 15.5

Correct 437 83.9 84.5 100.0

Total 517 99.2 100.0Missing System 4 .8

Total 521 100.0

Item 4


PercentCumulative

Percent

Valid

28 5.4 5.4 5.4

A 50 9.6 9.6 15.0

B 52 10.0 10.0 25.0

C 83 15.9 15.9 40.9

D 67 12.9 12.9 53.7

E 241 46.3 46.3 100.0

Total 521 100.0 100.0

Item 4

Frequency

PercentValid

PercentCumulative

Percent



Valid

Incorrect 252 48.4 51.1 51.1

Correct 241 46.3 48.9 100.0

Total 493 94.6 100.0Missing System 28 5.4

Total 521 100.0

Item 5


PercentCumulative

Percent

Valid

2 .4 .4 .4A 9 1.7 1.7 2.1

B 25 4.8 4.8 6.9

C 449 86.2 86.2 93.1

D 26 5.0 5.0 98.1

E 10 1.9 1.9 100.0

Total 521 100.0 100.0

Item 5

Frequency

Percent ValidPercent

CumulativePercent

Valid

Incorrect 70 13.4 13.5 13.5

Correct 449 86.2 86.5 100.0

Total 519 99.6 100.0Missing System 2 .4

Total 521 100.0

Item 6


Percent

Cumulative

Percent

Valid

11 2.1 2.1 2.1

A 102 19.6 19.6 21.7

B 24 4.6 4.6 26.3

C 17 3.3 3.3 29.6



Valid

11 2.1 2.1 2.1

A 85 16.3 16.3 18.4

B 50 9.6 9.6 28.0

C 48 9.2 9.2 37.2

D 230 44.1 44.1 81.4

E 97 18.6 18.6 100.0

Total 521 100.0 100.0

Item 8

Frequency

PercentValid

PercentCumulative

Percent

Valid

Incorrect 280 53.7 54.9 54.9

Correct 230 44.1 45.1 100.0


Total 521 100.0

Item 9


Percent

Cumulative

Percent

Valid

10 1.9 1.9 1.9

A 77 14.8 14.8 16.7

B 149 28.6 28.6 45.3

C 42 8.1 8.1 53.4

D 179 34.4 34.4 87.7

E 64 12.3 12.3 100.0

Total 521 100.0 100.0

Item 9

Frequency

PercentValid

PercentCumulative

Percent

Valid

Incorrect 332 63.7 65.0 65.0

Correct 179 34.4 35.0 100.0




Item 9

Frequency

PercentValid

PercentCumulative

Percent

Valid

Incorrect 332 63.7 65.0 65.0

Correct 179 34.4 35.0 100.0

Total 511 98.1 100.0


Item 10


Percent

Cumulative

Percent

Valid

7 1.3 1.3 1.3

A 52 10.0 10.0 11.3B 310 59.5 59.5 70.8

C 68 13.1 13.1 83.9

D 66 12.7 12.7 96.5

E 18 3.5 3.5 100.0

Total 521 100.0 100.0

Item 10

Frequency

PercentValid

PercentCumulative

Percent

ValidIncorrect 204 39.2 39.7 39.7Correct 310 59.5 60.3 100.0


Total 521 100.0

Item 11


Percent

Cumulative

Percent

Valid

4 .8 .8 .8

A 9 1.7 1.7 2.5

B 31 6.0 6.0 8.4



C 371 71.2 71.2 79.7

D 100 19.2 19.2 98.8

E 6 1.2 1.2 100.0

Total 521 100.0 100.0

Item 11

Frequenc

yPercent

Valid

Percent

Cumulative

Percent

Valid

Incorrect 146 28.0 28.2 28.2

Correct 371 71.2 71.8 100.0

Total 517 99.2 100.0

Missing System 4 .8Total 521 100.0

Item 12


PercentCumulative

Percent

Valid

11 2.1 2.1 2.1

A 65 12.5 12.5 14.6

B 76 14.6 14.6 29.2

C 78 15.0 15.0 44.1

D 233 44.7 44.7 88.9

E 58 11.1 11.1 100.0

Total 521 100.0 100.0

Item 12

Frequenc

yPercent

Valid

Percent

Cumulative

Percent

Valid

Incorrect 277 53.2 54.3 54.3

Correct 233 44.7 45.7 100.0

Total 510 97.9 100.0




Item 13


PercentCumulative

Percent

Valid

8 1.5 1.5 1.5

A 77 14.8 14.8 16.3

B 219 42.0 42.0 58.3

C 42 8.1 8.1 66.4

D 157 30.1 30.1 96.5

E 18 3.5 3.5 100.0

Total 521 100.0 100.0

Item 13

Frequenc

yPercent

Valid

Percent

Cumulative

Percent

Valid

Incorrect 294 56.4 57.3 57.3

Correct 219 42.0 42.7 100.0

Total 513 98.5 100.0


Item 14


PercentCumulative

Percent

Valid

10 1.9 1.9 1.9A 12 2.3 2.3 4.2

B 156 29.9 29.9 34.2

C 59 11.3 11.3 45.5

D 31 6.0 6.0 51.4

E 253 48.6 48.6 100.0

Total 521 100.0 100.0

Item 14

Frequenc

yPercent

Valid

Percent

Cumulative

Percent

Valid

Incorrect 452 86.8 88.5 88.5

Correct 59 11.3 11.5 100.0

Total 511 98.1 100.0




Item 15


Percent

Cumulative

Percent

Valid

26 5.0 5.0 5.0

A 69 13.2 13.2 18.2

B 184 35.3 35.3 53.6

C 98 18.8 18.8 72.4

D 90 17.3 17.3 89.6

E 54 10.4 10.4 100.0

Total 521 100.0 100.0

Item 15

Frequency

PercentValid

PercentCumulative

Percent

Valid

Incorrect 311 59.7 62.8 62.8

Correct 184 35.3 37.2 100.0


Total 521 100.0

Item 16


Percent

Cumulative

Percent

Valid

24 4.6 4.6 4.6

A 218 41.8 41.8 46.4

B 100 19.2 19.2 65.6

C 24 4.6 4.6 70.2

D 54 10.4 10.4 80.6

E 101 19.4 19.4 100.0

Total 521 100.0 100.0

Item 16

Frequency

PercentValid

PercentCumulative

Percent

Valid Incorrect 443 85.0 89.1 89.1



Correct 54 10.4 10.9 100.0

Total 497 95.4 100.0


Item 17


Percent

Cumulative

Percent

Valid

12 2.3 2.3 2.3

A 5 1.0 1.0 3.3

B 66 12.7 12.7 15.9

C 37 7.1 7.1 23.0

D 378 72.6 72.6 95.6

E 23 4.4 4.4 100.0

Total 521 100.0 100.0

Item 17

Frequency

PercentValid

PercentCumulative

Percent

Valid

Incorrect 131 25.1 25.7 25.7

Correct 378 72.6 74.3 100.0


Total 521 100.0

Item 18

Frequency Percent ValidPercent

CumulativePercent

Valid

14 2.7 2.7 2.7

A 183 35.1 35.1 37.8

B 297 57.0 57.0 94.8

C 11 2.1 2.1 96.9

D 6 1.2 1.2 98.1

E 10 1.9 1.9 100.0



Item 18


PercentCumulative

Percent

Valid

14 2.7 2.7 2.7

A 183 35.1 35.1 37.8

B 297 57.0 57.0 94.8

C 11 2.1 2.1 96.9

D 6 1.2 1.2 98.1

E 10 1.9 1.9 100.0

Total 521 100.0 100.0

Item 18

Frequenc

yPercent

Valid

Percent

Cumulative

Percent

Valid

Incorrect 210 40.3 41.4 41.4

Correct 297 57.0 58.6 100.0

Total 507 97.3 100.0


Item 19


Percent

Cumulative

Percent

Valid

14 2.7 2.7 2.7

A 20 3.8 3.8 6.5

B 8 1.5 1.5 8.1

C 22 4.2 4.2 12.3

D 55 10.6 10.6 22.8

E 402 77.2 77.2 100.0

Total 521 100.0 100.0

Item 19

Frequency

PercentValid

PercentCumulative

Percent

Valid

Incorrect 105 20.2 20.7 20.7

Correct 402 77.2 79.3 100.0

Total 507 97.3 100.0




Item 20


Percent

Cumulative

Percent

Valid

30 5.8 5.8 5.8

A 48 9.2 9.2 15.0

B 224 43.0 43.0 58.0

C 51 9.8 9.8 67.8

D 55 10.6 10.6 78.3

E 113 21.7 21.7 100.0

Total 521 100.0 100.0

Item 20

Frequency

PercentValid

PercentCumulative

Percent

Valid

Incorrect 267 51.2 54.4 54.4

Correct 224 43.0 45.6 100.0


Total 521 100.0

Item 21


PercentCumulative

Percent

Valid

28 5.4 5.4 5.4* 1 .2 .2 5.6

A 138 26.5 26.5 32.1

B 113 21.7 21.7 53.7

C 63 12.1 12.1 65.8

D 130 25.0 25.0 90.8

E 48 9.2 9.2 100.0

Total 521 100.0 100.0



Item 21

Frequenc

yPercent

Valid

Percent

Cumulative

Percent

Valid

Incorrect

362 69.5 73.6 73.6

Correct 130 25.0 26.4 100.0Total 492 94.4 100.0

Missing System 29 5.6

Total 521 100.0

Item 22


Percent

Cumulative

Percent

Valid

23 4.4 4.4 4.4

A 11 2.1 2.1 6.5

B 62 11.9 11.9 18.4

C 16 3.1 3.1 21.5

D 31 6.0 6.0 27.4

E 378 72.6 72.6 100.0

Total 521 100.0 100.0

Item 22

Frequency Percent ValidPercent CumulativePercent

Valid

Incorrect 120 23.0 24.1 24.1

Correct 378 72.6 75.9 100.0


Total 521 100.0

Index of Internal Consistency (reliability – Cronbach’s alpha) of the Campus General Logical

Mathematical Reasoning Test (CG-LMRT) – May, 2011

Case Processing Summary



N %

Cases Valid 415 79.7

Excludeda

106 20.3

Total 521 100.0

a. Listwise deletion based on allvariables in the procedure.

Reliability Statistics

Cronbach'sAlpha

Cronbach's

Alpha Basedon

StandardizedItems

N of Items

.719 .713 22

8. appendix viii - quantitative reasoning - findings and actions

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