Investigating the Relationship of Grades to Performance scores from the Arizona

Investigating the Relationship of Grades to Performance scores from the
Arizona's Instrument to Measure Standards (AIMS)

July 30, 2003

A statistical investigation was conducted to determine if there is a relationship between students’ final academic grades and students’ academic performances on the 2001/2002 Arizona’s Instrument to Measure Standards (AIMS). The AIMS is designed to measure student performance relative to state learning standards. Curriculum in schools is designed around the state learning standards. Therefore,final grades, which describe how well a student has learned the state standards, should be positively related to students’ performance on AIMS.

Eighth and 10^th grader students enrolled in TUSD during the 2001/2002 school having a valid academic grade in the areas of Mathematics, English, or Language Arts and a valid math performance score, reading performance score, or writing performance score on the 01/02 AIMS test were included in this investigation (See Tables 1 and 2 for demographic information by academic subgroups).

AIMS scores are categorized in four performance levels(from best to worst): Exceeds the Standard, Meets the Standard, Approaches the Standard and Falls Far Below the Standard. The goal is for all students to meet the standard. For this investigation, students’ performance outcomes were categorized into a pass/no pass variable. A student was deemed to have passed the AIMS if they achieved a Meets the Standard or Exceeds the Standard. Consequently, students who Approached the Standard or Fell Below the Standard were placed into the No Pass category. Using this schema, 21.6% (793) of the 8^th graders and 35.8% (891) of the 10^th graders passed the math portion, 49.7% of the 8^th graders and 59.5% of the 10^th graders passed the reading portion, and 39.2% of the 8^th graders and 59.5% of the 10^th graders passed the writing portion (see Tables 3-5).

Table 1:Demographic information on TUSD 8^th and 10^th Grade Students (Math Subgroup)

AIMS Status	Ethnicity										Total by Grade
	White/Anglo		African American		Hispanic		Native American		Asian American
	F	M	F	M	F	M	F	M	F	M
8^th Grade	915	777	139	129	771	721	70	58	39	45	3664
	25.0	21.2	3.8	3.5	21.0	19.7	1.9	1.6	1.1	1.2
8^th Totals	1692		268		1492		128		84
	46.2		7.3		40.7		3.5		2.3
10^th grade	638	622	79	54	476	456	32	33	44	53	2487
	25.7	25.0	3.2	2.2	19.1	18.3	1.3	1.3	1.8	2.1
10^th Totals	1260		133		932		65		97
	50.7		5.3		37.5		2.6		3.9

Note. Percents are in italics and represent a percent of the Grade Total

Table 2:Demographic information on TUSD 8^th and 10^th Grade Students (Reading/Writing Subgroup)

AIMS Status	Ethnicity										Total by Grade
	White/Anglo		African American		Hispanic		Native American		Asian American
	F	M	F	M	F	M	F	M	F	M
8^th Grade	925	804	142	133	826	766	73	59	39	45
	24.3	21.1	3.7	3.5	21.7	20.1	1.9	1.5	1.0	1.2
8^th Totals	1729		275		1592		132		84		3812
	45.4		7.2		41.8		3.5		2.2
10^th grade	649	622	80	59	496	462	31	33	45	56
	25.6	24.6	3.2	2.3	19.6	18.2	1.2	1.3	1.8	2.2
10^th Totals	1271		139		958		64		101		2533
	50.2		5.5		37.8		2.5		4.0

Note. Percents are in italics and represent a percent of the Grade Total

Table 3: Final Math Grades by AIMS Math Performance (Pass/No Pass)

AIMS Status	Final Math Grade					Totals
	A	B	C	D	F
8^th Grade						3664
Pass	324	250	154	56	9	793
	8.8	6.8	4.2	1.5	0.2	21.6
No Pass	349	745	773	628	376	2871
	9.5	20.3	21.1	17.1	10.2	78.4
10^th Grade						2487
Pass	344	273	177	70	27	891
	13.8	10.9	7.1	2.8	1.1	35.8
No Pass	157	267	361	378	433	1596
	6.3	10.7	14.5	15.2	17.4	64.2

Note. Percents are in italics and represent a percent of the Grade Total

Table 4:Final Reading Grades by AIMS Reading Performance (Pass/No Pass)

AIMS Status	Final Reading Grade					Totals
	A	B	C	D	F
8^th Grade
Pass	787	556	326	149	83	1901
	20.6	14.6	8.6	3.9	2.2	49.7
No Pass	263	440	482	333	296	1784
	6.9	11.5	12.6	8.7	7.8	46.8
10^th Grade
Pass	550	507	264	116	70	1507
	21.7	20.0	10.4	4.6	2.8	59.5
No Pass	96	171	191	173	154	785
	3.8	6.8	7.5	6.8	6.1	31.0

Note. Percents are in italics and represent a percent of the Grade Total

Table 5:Final Writing Grades by AIMS Writing Performance (Pass/No Pass)

AIMS Status

Final Writing Grade

Totals

A

B

C

D

F

8^th Grade

Pass

693

453

217

81

49

1493

18.2

11.9

5.7

2.1

1.3

39.2

No Pass

335

531

556

354

266

2042

8.8

13.9

14.6

9.3

7.0

53.6

10^th Grade

Pass

550

504

285

115

52

1506

21.7

19.9

11.3

4.5

2.1

59.5

No Pass

78

150

139

147

132

646

3.1

5.9

5.5

5.8

5.2

25.5

Note. Percents are in italics and represent a percent of the Grade Total

A Pearson bivariate Correlation Coefficient was used (SPSS Version 11.5) to determine the relationship between students’ final academic grades and related academic AIMS performance outcome. See Table 6 for correlations.

Table 6 Correlations between Final Academic Grade and AIMS Performance Outcomes

Academic Area	Performance Outcome (Pass/ No Pass)	Percent of AIMS outcome Explained by Obtained Academic Final Grade
8^th Grade Math	.336**	11.3
10^th Grade Math	.467**	21.8
8^th Grade Reading	.349**	12.2
10^th Grade Reading	.387**	15.0
8^th Grade Writing	.373**	13.9
10^th Grade Writing	.394**	15.5

Note. **.correlation is significant at the 0.01 level (2 tailed)

For all three academic areas, it was found that academic grades were positively correlated with AIMS performance outcomes; implying that the higher one’s grade in an academic course, the more likely one is to pass the corresponding academic portion on the AIMS test. However, in all academic areas only a relatively small percentage of the AIMS performance outcome variance is explained by a students’ final grade. For example, 21.8% of the variance in 10^th graders’ AIMS math performance status is explained by the final math grade. This finding suggests that nearly 78% of students’ performance is unexplained for and leaves ample room for speculations.

AIMS is harder than curriculum offered in schools.

Since math correlation is higher in 10^th grade than in 8^th, 9^th and 10^th graders may be exposed to more AIMS related skills during academic year than 8^th graders.

District curriculum many not be aligned with state standards.

If district curriculum is aligned with state standards, teachers may not be teaching appropriately.

If teachers are using a curriculum that is aligned with state standards, AIMS may not be aligned with state standards.

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AIMS Status	Final Writing Grade					Totals
	A	B	C	D	F
8^th Grade
Pass	693	453	217	81	49	1493
	18.2	11.9	5.7	2.1	1.3	39.2
No Pass	335	531	556	354	266	2042
	8.8	13.9	14.6	9.3	7.0	53.6
10^th Grade
Pass	550	504	285	115	52	1506
	21.7	19.9	11.3	4.5	2.1	59.5
No Pass	78	150	139	147	132	646
	3.1	5.9	5.5	5.8	5.2	25.5