Rita T. D e n n y Graduate school of Education Universiy of Pennsylvania Philadelphia, 19104
The Mathematics
Skill Test
(MAST) for Chemistry
D o high school students of chemistry have the necessary mathematics competency to perform chemistry calculations? An analysis was made of chemistry texts copyrighted 1960 to 1970. This analysis showed ten mathematics skills were used by all texts as a basis for solving chemistry problems
Table 1. Correlotions of Mathematics Skill Test Scores with 1 9 6 9 ACS-NSTA High School Chemistry Test Scores
Scores of
ACS test scorea
ACS calculations subscorea
(1) computation; (2) use of parentheses; (3) signed number usage; (4) use and manipulation of fractions; (5) use of decimals; (6) use of exponents, manipulation of numbers with exponents and logarithm equivalence; (7) use of percentage; (8) manipulation of one-variable equations; (9) use of ratio and proportion; (10) producing and interpreting z,y graphs.
To ascertain the presence of these skills in the chemistry student, the Mathematics Skill Test (MAST) was composed and validated. Items applying the ten mathematics skills in three operationally defined levels of difficulty were composed. A 5-member jury of experts having master's competency in mathematics and science teaching experience was chosen to validate both the skills that were used in each item and the level of difficulty. Eighty percent agreement of the judges was the criterion for accepting an item. The 91-item test resulting from this validation comprised the experimental form of MAST (MAST-long form). It was administered in March, 1970, in a 90-min double class period, to 128 first-year chemistry students in seven high schools of the Philadelphia Public School System. The test results were subjected to a comprehensive item-analysis. Discrimination indexes, difficulty indexes, and application of skills were the criteria used to select the sixty best items for the revised form of MAST (MAST-short form). MAST is an untimed power test designed to indicate the student's understanding of a basic concept or skill; it is not an achievement test for mathematics. There are 14 items judged to be Level I ; 32 items illustrate Level 11; and Level I11 has 14 items. I n May, 1970, the 60-item MAST test was given in a 45-min class period to 276 first-year chemistry students in six high schools of the Philadelphia Public School System. A mean score of 24.83 was achieved with a standard deviation of 16.36 and a standard error of measurement of 0.78. Overall test reliability was 0.967 (covariance) and 0.963 (Kuder-Richardson #20). Subtest reliabilities for each skill and each level (Kuder-Richardson #20) varied between 0.879 and 0.964. Each subtest varied in length. Because of a desire to compare subtest reliabilities, alpha coefficients were computed for each subtest, based on an equivalent 80-item length. Results ranged between 0.970 and 0.992. Work supported by the ACS-duPont Small Grants Program.
Table 2.
Sample Student MAST Result
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Smith, J.
MAST Total Level I Level I1 Level I11 52.75 11.75 28.50 10.50 max. score 60.00 14.00 32.00 14.00
Skill # l Skill #2 Skill #3 Skill #4 Skill #b 41.25 7.00 3.75 18.25 20.75 mzxseore 46.00 8.00 6.00 23.00 23.00 Skill +6 Skill #7 Skill #8 Skill #9 Skill #10 5.50 4.75 5.00 15.75 5.00 9.00 7.00 6.00 maxscore 18.00 6.00
In order to establish concurrent validity of MAST with chemistry achievement, 285 students took the 1969 ACS-NSTA High School Chemistry Test. The 242 students common to both MAST and ACS testi n g ~formed the sample for correlating MAST achievement. The 80-item ACS test, designed to be given in two 40-min class periods, has 47 items which use one or more mathematics skills. These items were used to form a chemistry-calculations subscore. Product-moment correlations between MAST and ACS scores ranged between 0.633 and 0.823 (r = 0.181; p = 0.01; df = 200) (refer to Table I). The correlation values are all of a similar magnitude, indicating an equivalence of skill importance. Further support is lent to this conclusion in analyzing the individual student results. There was no instance of high student achievement on some skills and not on all skills. There was no instance of a student's having high ACS achievement (above the mean), overall or calculations, and low MAST achievement, although there were several instances of average t o high MAST achievement with low ACS achievement. The data supports the need for proficiency in all ten skills, but does not suggest a minimum MAST score as a cut-off point for probable ACS achievement. Volume 48, Number 7 2, December 7 971
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In demonstrating that these ten mathematics skills are necessary for chemistry calculation success, the question now emerges of how to insure that the students have the necessary mathematics competency before the start of chemistry instruction. No claim is made that the desired mathematics background is the only prerequisite for chemistry success. It is one prerequisite of many. The Mathematics Skill Test is a reliable and valid test which can be used by chem-
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Journol of Chemical Education
istry personnel to determine individual student preparedness, prior to the student's encountering chemistry difficulties (refer to Table 2). Do not assume the student has this needed preknowledge for chemistry success after he has completed certain mathematics courses of instruction. I t is suggested that MAST be used as a means for discerning the student's needs, thus providing a firm empirical basis for future chemistry instruction.
