This study has conducted analyses to examine the issue of whether any gender and location differences exist in students’ mathematics achievement using Item Response Theory and test statistics method. Performance comparisons among males and females, and students from urban and rural schools were made for sample of 482 7TH graders in Mongolia.
According to the first objective of the study there was no significant gender difference in mathematics achievement among Mongolian 8th graders. However, it had small difference favoring boys. This finding supports the findings of several previous studies which carried out by Fierros, (1999), Zhang and Manon (2000) and Johnson (2000) and Erickan, McCreith, and Lapointe, (2005). Interestingly, Examining differences by content area reveals males scored higher on average than females in all mathematics content areas (algebra, arithmetic, proportionality and probability and statistics) with the exception of geometry in which female students scored higher. This finding is exactly parallel to the study carried out by Catherine T.Amelink (2009).
Hence, we may conclude that girls have better geometric ability than boys.
To the second objective, research has also found there is a statistically significant difference in math achievement between students from rural and urban schools. This is parallel to the findings of Lindberg and Wilson (1985), and Raul Ramos and his colleagues (2012) and Jennifer Lawless (2009) which say that students from small rural schools performed worse than those attending large urban schools. This might be caused of several reasons as follow. Firstly, it is due to the distance and environment problem. Five rural schools were sampled in this study 3 of those are located over 1000 km far away from the urban area. Some evidence say that the support from the state and federal recourse come to the rural schools slowly. Therefore children from rural area still need to do house chores and help out on the farm and take care of the domestic animals. Moreover, rural schools have lack of classroom equipments and latest trend in technology compare to urban schools. For example: Students from urban schools have greater access to many resources and therefore have opportunities that
are not as easily accessible to rural students (Jennifer Lawless). Secondly, rural schools might be short of qualified teachers.
Surprisingly, in some rural schools, one teacher provides 2-3 different classes at the same time which means rural schools have lack of number of professional teachers for particular subjects.
To the third objective, Mongolian math items had higher item difficulty index versus TIMSS mathematics items for 8TH grade. However, the hardest item was found among TIMSS items. Furthermore, Mongolian students haven’t been experienced in PISA or TIMSS yet. So, it could be a signal that claims Mongolia should participate in TIMMS or PISA to evaluate its national curriculum on several particular subjects comparing other participating countries’ experience.
According to the item analysis results from the five content categories that measured students’ levels of mathematics knowledge. While 77.7% of students answered the statistics and probability items correctly, only 54.4% answered the geometry items correctly and 63.8% answered the proportionality items correctly.
Moreover only 52.8% answered the algebra items correctly and 64.3% answered the arithmetic items correctly. Furthermore 45.8% or 221 of students answered less than 18 items correctly and, only one student answered all 30 items correctly. According to frequency table (Table) 38.1% or 184 of students answered 18-23 items correctly and while 13.7% or 28 of students answered 24-26 items correctly. Therefore, mean mathematics ability of the 7th graders is -0.021 which is very low, while all students’
ability was found between 2.665 and -2.043. Hence, we conclude in any case, the low correct response rates, particularly to the geometry and algebra items, indicated that many 7th graders lack knowledge of basic mathematics concept.
Based on these findings, several future paths of research are opened up. Firstly, present study supports a hypothesis that girls may perform on geometry better than boys. So this result encourages us to investigate what factors could possibly be strong predictor of girls’ knowledge of geometry which makes them perform better than boys.
Secondly, however, such studies will require larger database regarding the information needed to capture the characteristics of the areas in which the students are resident.
This kind of data would enable us to investigate which geographical location or environment can have an impact on student’s educational outcomes and what standard
demographic characteristics such as gender, ethnicity, and family background could possibly be strong predictor of mathematics ability. In this respect, it is important to develop new ways to assess the impact of mathematical education on the young.
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Appendix “A”
Table 9: Test reliability
Test information Number of items Number of students Reliability
Mathematics 30 482 0.779
Table 10: Each item’s reliability
Item Reliability Item Reliability
1 0.777 16 0.775
2 0.779 17 0.784
3 0.773 18 0.774
4 0.789 19 0.768
5 0.780 20 0.772
6 0.782 21 0.768
7 0.772 22 0.780
8 0.775 23 0.786
9 0.767 24 0.768
10 0.769 25 0.767
11 0.768 26 0.768
12 0.771 27 0.765
13 0.774 28 0.770
14 0.773 29 0.774
15 0.765 30 0.771
Table 11: Score frequency
Appendix “B”
№
Item 1
Two groups of tourists each have 60 people. If of the first group and of the second group board buses to travel to a museum, how many more people in the first group board buses than in the second group?
A. 2 B. 4 C. 5 D. 45 IRT
parameters
a b c PIRT
0.679 0.199 0.320 0.628
Options analysis
Options Total
Number of students
57 104 305 15 482
Percentage
11.82% 21.57% 63.27% 3.11% 100.00%
Figure 3
№
Item 2
In a discuss-throwing competition, the winning throw was 61. 60 m. The second –place throw was 59.72 m. How much longer was the winning throw than the second-place throw?
A. 1.18 m B. 1. 88 m C. 1. 98 m D. 2.18 m
IRT parameters
a b c PIRT
0.447 -2.585 0.283 0.898
Options analysis
Options Total
Number of
students 16 433 24 9 482
Percentage
3.31% 89.83% 4.97% 1.86% 100.00%
Figure 4
№
Item 3
In a bag of cards are green are yellow are white and are blue. If someone takes a card from the bag without looking, which color is it most likely to be?
A. White B. Blue C. Green D. Yellow IRT
parameters
a b c PIRT
0.729 -0.393 0.343 0.733
Options analysis
Options Total
Number of
students 355 15 17 94 482
Percentage 73.65% 3.11% 3.52% 19.50% 100.00%
Figure 5
№
Item 4 1. What is the size of angle ACD?
A. 44 B. 126 C. 136 D. 150 IRT
parameters
a b c PIRT
0.685 2.972 0.347 0.377
Options analysis
Options Total
Number of students
251 28 182 19 482
Percentage 52.07% 5.80% 3.77% 3.94% 100.00%
Figure 6
№
Item 5
Which of the following are most likely to be the coordinates of point P?
A. (8, 12) B. (8, 8) C. (12, 8) D. (12, 12) IRT
parameters
a b c PIRT
0.379 0.960 0.322 0.566
Option analysis
Options Total
Number of students
274 29 155 24 482
Percentage 57.1% 6.01% 32.15% 4.97% 100.00%
Figure 7
№
Item 6 The table represents a relation between x and y.
x y
1 1
2 ?
4 7
7 14
What is the missing number in the table?
A. 2 B. 3 C. 4 D. 5 IRT
parameters
a b c PIRT
0.954 1.840 0.285 0.353
Option analysis
Options Total
Number of
students 109 174 157 42 482
Percentage 22.61% 36.1% 32.57% 8.71% 100.00%
Figure 8
№
Item 7
The length of a rectangle is 6 cm, and its perimeter is 16 cm. What is the area of the rectangle in square centimeters?
A. 12 B. 22 C. 24 D. 48 IRT
parameters
a b c PIRT
0.863 -1.104 0.236 0.823
Option analysis
Options Total
Number of
students 395 39 25 22 482
Percentage 81.95% 8.09% 5.18% 4.56% 100.00%
Figure 9
№
Item 8 >7 is equivalent to
A. x< B. x> C. x>14 D. x<14 IRT
parameters
a b c PIRT
0.840 0.840 0.380 0.559
Option analysis
Options Total
Number of
students 52 104 274 52 482
Percentage 10.78% 21.57% 56.84% 10.78% 100.00%
Figure 10
№
Item 9
Last year there were 1172 students at Beaton High School. This year there are 15 percent more students than last year. Approximately how many students are at Beaton High School this year?
A. 1800 B. 1600 C. 1500 D. 1400 IRT
parameters
a b c PIRT
0.814 -0.279 0.184 0.650
Option analysis
Options Total
Number of
students 68 66 36 312 482
Percentage 14.10% 13.69% 7.46% 64.73% 100.00%
Figure 11
№
Item 10 The table shows a relation between x and y.
x 2 3 4 5
y 7 10 13 16
Which of these equations express this relation?
A. y=x+5 B. y= (x+1) C. y=x-5 D. y=3x+1
IRT parameters
a b c PIRT
0.836 0.228 0.228 0.575
Option analysis
Options Total
Number of
students 91 67 44 280 482
Percentage 18.87% 13.90% 9.12% 58.09% 100.00%
Figure 12
№
Item 11
A class has 28 students. The ratio of girls to boy is 4:3. How many girls are in the class?
A. 13 B. 14 C. 15 D. 16 IRT
parameters
a b c PIRT
0.960 0.305 0.275 0.567
Option analysis
Options Total
Number of
students 77 70 59 279 482
Percentage 15.97% 14.52% 12.24% 57.88% 100.00%
Figure 13
№
Item 12
A newspaper reported that about 18200 trees had been planted in the park. The number was rounded to the nearest hundred. Which of these could have been the actual number of trees planted?
A. 18043 B. 18189 C. 18289 D. 18328 IRT
parameters
a b c PIRT
0.852 -0.432 0.301 0.728
Option analysis
Options Total
Number of
students 60 352 46 23 482
Percentage 12.44% 73.02% 9.54% 4.77% 100.00%
Figure 14
№
Item 13
“n” is a number. When n is multiplied by 7, and 6 is then added, the result is 41. Which of these equations represents this relation?
A. 7n+6=41 B. 7n x 6=41 C. 7+(6n)=41 D. 7(n+6)=41 IRT
parameters
a b c PIRT
0.690 -1.070 0.287 0.810
Option analysis
Options Total
Number of students
389 42 34 17 482
Percentage 80.70% 8.71% 7.05% 3.52% 100.00%
Figure 15
№
Item 14
A drawer contains 28 pens; some white, some blue, some red, and some gray.
If the probability of selecting a blue pen is , how many blue pens are in the drawer?
A. 4 B. 6 C. 8 D. 10 IRT
parameters
a b c PIRT
0.659 -1.200 0.287 0.822
Option analysis
Options Total
Number of
students 28 42 396 16 482
Percentage 5.80% 8.71% 82.15% 3.31% 100.00%
Figure 16
№
Item 15
Which of these expressions is equivalent to y3?
A. y+y+y B. y x y x y C. 3y D. y2+y IRT
parameters
a b c PIRT
1.139 -0.724 0.172 0.758
Option analysis
Options Total
Number of
students 58 363 32 29 482
Percentage 12.03% 75.31% 6.63% 6.01% 100.00%
Figure 17
№
Item 16 Please simplify the expression.
5(a+2)+(a+2)
A. 6a+12 B. 10+5a C. 6(a+2) D. a2+5a+12 IRT
parameters
a b c PIRT
1.029 1.681 0.116 0.210
Option analysis
Options Total
Number of
students 249 72 103 58 482
Percentage 51.65% 14.93% 21.36% 12.03% 100.00%
Figure 18
№
Item 17 Please simplify the expression.
2x (x+1)-4x(2-x)
A. 6x2-6x B. x2 C. 6x(x-1) D. 6x IRT
parameters
a b c PIRT
1.709 2.044 0.155 0.180
Option analysis
Options Total
Number of
students 336 43 89 14 482
Percentage 69.70% 8.92% 18.46% 2.90% 100.00%
Figure 19
№
Item 18 Please find the correct.
c4 x □ = c12
A. c3 B. c8 C. c48 D. c412 IRT
parameters
a b c PIRT
0.626 -0.189 0.304 0.680
Option analysis
Options Total
Number of
students 122 329 20 11 482
Percentage 25.41% 68.25% 4.14% 2.28% 100.00%
Figure 20
№
Item 19 Please quadrate using a suitable formula.
(x+5)2
A. 2x +10 B. x+25 C. x2+25 D. x2+10x+25 IRT
parameters
a b c PIRT
1.007 0.080 0.219 0.591
Option analysis
Options Total
Number of
students 61 37 99 285 482
Percentage 12.65% 7.67% 20.53% 58.28% 100.00%
Figure 21
№
Item 20 Please simplify the fraction.
ab + a2 a2
A. ab B. C. ab +a4 D. a3b+a2 IRT
parameters
a b c PIRT
1.428 1.208 0.181 0.306
Option analysis
Options Total
Number of
students 246 150 59 27 482
Percentage 51.03% 31.12% 12.24% 5.60% 100.00%
Figure 22
№
Item 21
Two photographers took 657 photos in total. One photographer took 63 more photos than another. How many photos did each photographer take?
A. 360 and 297 B. 345 and 408 C. 247 and 410 D. 307 and 350 IRT
parameters
a b c PIRT
1.051 -0.335 0.250 0.697
Option analysis
Options Total
Number of
students 336 76 53 17 482
Percentage 69.70% 15.76% 10.99% 35.26% 100.00%
Figure 23
№
Item 22 Please find c.
A. c=5 B. c=25 C. c=31 D. c=√527 IRT
parameters
a b c PIRT
0.463 1.878 0.256 0.410
Option analysis
Options Total
Number of
students 49 199 188 46 482
Percentage 10.16% 41.28% 39.00% 9.54% 100.00%
Figure 24
№
Item 23 Please compute the inequality.
% x>-1
A. x>
-% B. x>9 C. x> - 9 D. x< 9 IRT
parameters
a b c PIRT
1.279 2.243 0.395 0.414
Option analysis
Options Total
Number of
students 153 85 205 39 482
Percentage 31.74% 17.63% 42.53% 8.09% 100.00%
Figure 25
№
Item 24
What value of “x” makes the following equation true?
& = 9
A. 1 B. 5 C. 12 D. 24 IRT
parameters
a b c PIRT
1.461 -0.696 0.300 0.802
Option analysis
Options Total
Number of
students 34 42 387 19 482
Percentage 7.05% 8.71% 80.29% 3.94% 100.00%
Figure 26
№
Item 25
Please find equivalent of following expression: 9a2+6ab+b2 A. (9a+b)2 B. (3a2+b2)2 C. (3a+b)2 D. (3a+b)(3a-b) IRT
parameters
a b c PIRT
1.021 -0.307 0.219 0.677
Option analysis
Options Total
Number of
students 68 38 326 50 482
Percentage 14.10% 7.88% 67.63% 10.37% 100.00%
Figure 27
№
Item 26 What is 30 % of 185=?
A. 5.55 B. 55.5 C. 555 D. 5.55.
IRT parameters
a b c PIRT
1.636 -0.313 0.297 0.721
Option analysis
Options Total
Number of
students 69 349 37 27 482
Percentage 14.31% 72.40% 7.67% 5.60% 100.00%
Figure 28
№
Item 27 Please calculate following expression.
4( :)(= ?
A. ) B. 7 C. ( ) D. 12 IRT
parameters
a b c PIRT
2.177 -0.449 0.261 0.744
Option analysis
Options Total
Number of
students 57 360 53 12 482
Percentage 11.82% 74.68% 10.99% 2.48% 100.00%
Figure 29
№
Item 28
A bakery made 350 cupcakes. They sold 280 of those cupcakes. What percentage of the cupcakes did they sell?
A. 20% B. 70% C. 80% D. 125%
IRT parameters
a b c PIRT
0.750 -0.449 0.216 0.693
Option analysis
Options Total
Number of
students 34 96 333 19 482
Percentage 7.05% 19.91% 69.08% 3.94% 100.00%
Figure 30
№
Item 29 Please find the largest one.
A. B. 0.21 C. D.
IRT parameters
a b c PIRT
0.800 1.913 0.133 0.229
Option analysis
Options Total
Number of
students 238 88 110 46 482
Percentage 49.37% 18.25% 22.82% 9.54% 100.00%
Figure 31
№
Item 30 Please find the correct one.
A. 23 x 27=221
C. 23 x 27=210 B. 23 x 27=410
D. 23 x 27=237 IRT
parameters
a b c PIRT
0.687 0.106 0.189 0.573
Option analysis
Options Total
Number of
students 64 135 276 7 482
Percentage 13.27% 28.00% 57.26% 1.45% 100.00%
Figure 32