EFFECTS OF MATHEMATICAL REASONING SKILLS ON …

J.C. Adigwe. Review of Education Institute of Education Journal, University of Nigeria Nsukka. Vol. 23. No.1. 1-22

EFFECTS OF MATHEMATICAL REASONING SKILLS ON STUDENTS’ ACHIEVEMENT IN CHEMICAL STOICHIOMETRY

J.C. Adigwe

Cudimac, University of Nigeria Nsukka

Abstract This study was designed to (i) investigate whether there are significant relationships between achievement in chemical stoichiometry and mathematics skills (ii) identify those specific mathematics skills which have significant relationships to students’ achievement in chemical stoichiometry; (iii) whether there is significant relationship between improvement in mathematics achievement and achievement in chemical stoichiometry after remedial mathematics instruction, and (iv) compare mathematics capabilities and achievement in chemical stoichiometry of male and female students before and after remedial mathematics instruction. The sample consisted of four hundred subjects (100 male and 100 female) in each of experimental and control groups randomly taken from five senior secondary schools in Oshimili South LGA of Delta State, Nigeria. Two instruments were used: (i) a mathematics skill test consisting of 52 items with a re-test reliability coefficient of 0.87, and (ii) a chemistry achievement test consisting of 100 multiple-choice items on chemical stoichiometry. This test had a re-test reliability coefficient of 0.86. These two tests were administered on all the subjects in the two groups first as pretest and after remedial mathematics instructions as post-test. Three statistical tools were used in testing four hypotheses: (i). ANCOVA, using pre-test achievement scores of stoichiometry as covariate (ii) Multiple comparison, using scheffe’s critical ratios for pairs of achievement mean scores for pre-tests and post-test were made. (iii) Pearson’s correlation coefficient for significant relationships between achievement mathematics and chemistry achievement scores; and between chemistry achievement and each mathematics skill. The results of analyses indicated that (i) there was significant difference in achievement in stoichiometry as result of mathematics instruction (ii) there were significant relationships between entering mathematics skills and achievement in chemical stoichiometry; (iii) 26 mathematics skills correlated significantly with achievement in chemical stoichiometry (iv) there was significant gender difference in students’ achievement in mathematics and chemical


stoichiometry; (v) there were significant improvement in achievement in chemical stoichiometry after remediation. Introduction The study of chemistry at all educational levels requires the knowledge, thought-process and skills of mathematics. Mathematics has been found to be important in the study of science subjects because of its role in development of the scientific and technological processes (Denga, 1997; Ododo, 1997; Daniyan,1999; Eraikhuemen, 2002; Olalekan and Jerome,2006; Kurumeh, 2006; Popoola,2006; Kajuru’ and Kajuru’ 2010; Kankia, 2008 and 2010). The mathematics required in the study of science subjects, referred to as technical mathematics, is essential in the invention and development of technologies, and acquisition of reasoning processes/skills required in understanding of scientific concepts, principles and processes. Hence, mathematics is made a compulsory subject for students at both secondary and tertiary educational levels(Betiku,2001 ;Eraikhuemen,2002;Inekwe,2002;Kurumeh,2006; Adeleke,2007 and Enesi, 2007 ). A number of studies have drawn attention to inadequate mathematical skills of secondary school students in Nigeria. It is generally believed that mathematics is not being properly taught in

schools. This view is based on the fact that secondary school students perform poorly in mathematics examination (Shaaba,1995;Amazigbo,2000; Awoniyi, 2002; Eraikumen, 2002; Betiku, 2001; Popoola, 2006; Kurumeh, 2006; Iji, 2005; Popolla, 2006;Kankia,2010;kajuru’ and kauru’, 2010; Kajuru’ and Popoola.2010). Outside Nigeria a similar trend of poor achievement in mathematics has been observed (Perkin, 1979; Swan, 1990; McFarlane, 1994; Oliver, 1998; Swan and Philips, 1998) and Swatton and Taylor, 1994).The poor achievement indicates that students have learning difficulties in acquiring mathematics thought-processes and skills. The evidence from these studies seem to suggest that mathematics classrooms may not be providing students with adequate mathematics skills to enhance their performance in mathematics-based subjects in school. In the light of the above, it becomes necessary to investigate the extent to which the mathematical knowledge//skills of computation and applications have assisted secondary school students in the understanding of chemistry. Since some aspects of secondary


chemistry require solving quantitative chemical problems, to what extent have the students been capable to use their mathematical knowledge/skills to understand and achieve success in those mathematical areas of chemistry, like chemical stoichiometry, equilibrium, kinetics, entropy, electrochemistry, thermochemistry and nuclear chemistry etc. Attainment in the chemical contents and processes of these quantitative areas demand, not just that the learners acquire the mathematical skills of computation and application that are necessary in solving the problems, but in addition acquire the entire fundamental processes of mathematical reasoning relevant to the areas.

Since senior secondary school chemistry curriculum contains essentially chemical stoichiometry as the major mathematical aspect, the author decided to investigate the relationship between students’ achievement in chemical stoichiometry and relevant mathematical skills. Chemical stoichiometry generally involves determining quantitative relationships among reacting species in chemical reactions and the quantitative effects of the reaction conditions on the reacting species. Previous reports (Onwu and Ajuashi, 1987; Gambo and Wachanga, 2000; Offia and Egolum, 2006; Ibole,2007;

Mari,2008; WAEC,2008; Offia and Samuel,2008; Offia and Njelita,2010; Madichie and Isreal, 2010; Doka, 2010) found that students had poor performances in chemical stoichiometry and that it was a difficult topic for the students. Specifically, are the secondary school students capable of using the relevant mathematical concepts, principles and skills, and the accompanying mathematical reasoning processes to solve chemical stoichiometry problems? If there is a relationship between students’ achievement in mathematics and chemical stoichiometry, can remediation in mathematics lead to any improvement in students’ performances in chemical stoichiometry? Gender differences have been observed in mathematics (Agwagah,1993; Shaaba,1995; Awoniyi, 2002; Adeleke,2007; Alfa, 2007) and chemistry achievements of students (Adigwe,1993; Jimoh, 2004; Adeyegbe, 1985, 1993; and 2010). It is important to examine these gender differences to ascertain whether the gender differences in mathematical capabilities do in any way relate to gender differences in achievement in stoichiometry. It is equally important to identify those mathematics concepts/ skills that pose difficulties to students.


Purpose of study This study sought to: (i). determine whether there is

any relationship between the students’ achievements in stoichiometry and mathematics skills .

(ii). determine whether there is any improvement in students’ achievement in stoichiometry as a result of mathematics remediation.

(iii). determine whether there are any gender differences in students’ achievement in stoichiometry before after mathematics remediation.

(iv) identify the mathematical skills that pose learning difficulties to students.

Research Questions. (i) What relationship exists between students’ achievement in mathematics skills and chemical stoichiometry? (ii) What is the difference between students’ achievement mean-scores in chemical stoichiomety before and after mathematics remediation? (iii) What are the gender differences in students' achievement in chemical stoichiometry before and after mathematics remediation?

(vi) What mathematics skills were difficult for the students to perform?

Hypotheses The following hypotheses were tested.

(i). There is no significant relationship (P<0.01 between students’ achievements in stoichiometry and

mathematics skills. (ii). There is no significant

difference (P<0.01) between students’ achievement mean-scores in chemical stoichiometry before and after remedial mathematics instruction.

(iii). There are no significant gender differences (P<0.01) in students’ achievement mean-scores in chemical stoichiometry before and after remedial mathematics instruction.

(iv). There is no significant relationship (P<0.01)

between gain mean-scores in mathematics and chemical stoichiometry after

mathematics remediation. Method: Design This was a non-randomised control group pre-test and post-test design. This design was adopted because the


study examined the effects of remediation in mathematical skills and achievement in chemical stoichiometry. The experimental subjects[ES] and control subjects (CS) were pre-tested, and then post-tested after the mathematics remediation . Population and sample The population for this study is chemistry students in senior secondary class III. This population was chosen because they must have, at this final level of secondary school chemistry study, covered all aspects of chemical stoichiometry in the secondary chemistry curriculum/West African school certificate syllabus; and also covered the relevant mathematics topics. The experimental and control groups each comprised two hundred students (100 female and 100 male) drawn from five secondary schools in Oshimili-South Local Government Area of Delta State. On the whole there were four hundred subjects. They all offer mathematics and chemistry in the WAEC/NECO examinations. Instrument Two instruments were employed in the study: (1). Mathematics skills test (MST). This consisted of fifty–two (52) multiple-choice mathematics items.

The items were developed from six chemistry textbooks commonly used in teaching chemical stoichiometry in the local schools. Worked examples and practice exercises in the chemical stoichiometry topics in the textbooks were examined. The mathematics skills required in solving the stoichiometric problems in the practice exercises and worked examples were then extracted and constituted into mathematics problems. 26 items require the use of computation skills, while the remaining 26 items require the use of application skills. Thus, each mathematics skill had a computation item and an application item. The mathematics skills were found to fall under eight (8) mathematics topics as shown in appendix 1. Two examples of the items were: item 43; a student planned to use 5.38 grams of a substance in an experiment. The instructor advised him to get 2.5 times that much substance and to split it into four equal samples. How many grams would then be contained in each of these samples? Item 25: A substance is made up of zinc and copper. 42% of its mass is known to be due to its content. If a piece of the substance has a mass of 12 grams, how many grams of silver does the piece contain? The students were required to write all rough-work for each problem on the paper


provided, showing all the steps they used to obtain their answers. There was no time limit. The test had a retest reliability coefficient(KR-20) of 0.87 . (ii).Chemistry achievement test (CAT). This consisted of 100 multiple-choice items on chemical stoichiometry. It had a re-test reliability coefficient (KR-20) of 0.86. Two example of the items are: item 2: Concentrated Hydrogen Chloride acid is prepared by heating NaCI with concentrated H2SO4. How many kilograms of H2SO4, containing 90.0 percent H2SO4

by mass are required for the production of 1000kg of concentrated hydrogen chloride acid containing 42.0 per cent HCI by mass? [H= 1, S = 32, 0 = 16, CI = 35.50, N = 23] . Item 3 : 1.367 grams of a sample of an organic compound was burnt in a stream of air and it yielded 3.002 grams of CO2 and 1.640 grams of H20. If the original compound contained only C, H and O, what is its empirical formular? [C = 12, H = 1, 0 = 16]. Procedure All the subjects in the sample were pre-tested, first with the chemistry achievement test and then mathematics skills test. The experimental subjects were then taught the eight mathematics topics.

The teaching session was for eighteen (18) lessons spread over six weeks. A lesson lasted for forty (40) minutes. Assignments and lesson notes on the mathematics skills were given to the subjects. At the end of the mathematics instruction both the experimental and control subjects were post-tested with the mathematics. and then chemistry tests. Data Analyses (i) Pre-test and post-test mean and standard deviation scores of the groups were determined. The ANCOVA was analysed, using pre-test achievement scores on stoichiometry as covariate. (ii). Multiple comparison using

scheffe’s critical ratios for pairs of achievement mean-scores for pre-tests and post-test were made.

(iii). Pearson’s correlation coefficient was determined for relations between mathematics and stoichiometry achievements; and between achievement on stoichiometry and each mathematics skill.

Results Summary of results of the analyses are presented in the tables below:


Table I Achievement Mean and Standard deviation Scores of ES and CS in Mathematics and Stoichiometry Pre-test and Post-test. Tests ES CS n=200 n=200 Pre-tests X SD X SD Math (i) 34. 5.89 35.00 5.63 Chem (ii) 34.23 5.71 33.20 4.83 Post-tests Math (iii) 56.35 4.61 38.61 4.92 Chem.(iv) 63.31 4.53 39.10 4.91 N = 400

Table 2 Achievement Mean and Standard deviation Scores of ES / CS in Pre-tests and Post-test by Sex . Test Pre-tests Post-test Subjects Math Chem. Math Chem. Sex F M F M F M F M ES CS

X SD n=200 X SD n=200

33.00 5.03 31.00 4.38

35.42 5.07 39.00 4.21

38.10 4.81 32.01 4.10

41.35 4.51 34.40 4.82

52.94 4.87 35.00 4.31

59.75 4.50 42.62 4.53

60.03 4.79 36.01 4.93

66.59 4.31 42.20 4.81

N = 400; nm =nf = 100 in each group.

Table 3 Summary of ANCOVA Result. SOURCE SS DF MS F Pre-test Main effects Treatment Sex Interaction Sex X treatment Explained Residual Total

23476.10 18623.34 15291.25 1564.29 1354.09 10243.01 70552.08 72538.21 143090.31

1 2 1 1 1 1 4 391 399

23476.10 9311.67 15291.25 1564.29 1354.09 10243.01 17638.04 995.49

23.58* 9.35* 15.36* 7.57* 1.36 10.29* 17.72*

*P<0.01


Table 3 indicates that there were significant differences in the achievement mean-scores of experimental and control groups in chemistry pre-test and post-test ; and there were significant sex differences ( p<0.01) in achievement mean-scores of male and female

groups in chemistry pre-test and post-test. It also indicates significant treatment, main, and sex x treatment effects at ∞ = 0.01. Table 4: Multiple Comparison of Critical ratios for Pre-tests and Pro-test.

Tests i _______ ii 4.53* _______ _______ iii 64.39* 61.79* iv 103.59* 101.95* 33.32* i ii iii iv Table 4 presents the multiple comparisons of Scheff’s critical ratio. It indicates that the four mean-scores are significantly different at = 0.01.The significant value of t-statistic (t=101.95) for pre-test and post-test chemistry achievement mean-scores reveals that the students performed significantly higher in chemical stoichiometry after mathematics remediation. There was therefore, a significant improvement in the chemistry achievement of the students after mathematics instruction. Hypothesis I is therefore rejected.

Results in Tables 1, 2, 3 and 4 indicate significant differences (∞ = 0.01) in improvement in chemistry achievement after remedial instruction. The male students did attain significantly higher level of improvement in chemistry achievement than the female students. This observation seem to relate to the fact that the male group attained significantly higher levels of improvement in mathematics. Hypothesis II is therefore upheld.

Table 5

+ Relationships between students’ chemistry and mathematics achievements by Sex.


Sex Overall math skills Computation Application Skills skills F 0.59* 0.55* 0.58* (0.70*) (0.61*) (0.69*) M 0.60* 0.55* 0.61* ((0.72*) (0.71*) (0.73*) Total 0.58* (0.718) 0.53* (0.65*) 0.59* (0.70*) *p<0.01; (+r2 ); ( ) = correlation figures for post-test. Table 5 presents the relationship between students’ achievements in chemical stoichiometry and mathematics skills. It indicates that significant relationships (p<0.01) exist between the overall students’ achievement in stoichiometry and mathematics at pre-test and post-test levels, and at the two cognitive levels of computation and application skills. Also, there are significant relationships for the sexes at the two cognitive levels, and in both pre-test and post-test. It appears that the relationship became stronger after mathematics remediation [post-test] . Hypothesis iii is therefore rejected. Table 6 + Relationship between chemistry and each mathematics skills. Math Skills Female Male S/N Comp.

skills Appl. Skills

Comp. skills

Appl. Skills

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Multiplication and fraction Division of Decimal operation. Combined decimal operations. Rounding/sign figures. Finding percent of a number Computation of percent Drawing graphs / interpretation of graphs Positive negative integer operation Solving numerical equations Solving variable equations.

0.68 0.70 0.71 0.61 0.63 0.69 0.78 0.79 0.71 0.70

0.72 0.51 0.75 0.68 0.79 0.78 0.82 0.89 0.88 0.87

0.70 0.58 0.68 0.69 0.55 0.62 0.75 0.70 0.75 0.78

0.72 .69 0.79 0.70 0.66 0.61 0.81 0.78 0.80 0.83


11.

Solving ratio proportion problems.

0.69 0.72

0.78 0.89

12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26

Solving direct variation problems Solving indirect problems Squaring a number /square root Concept of positive powers of 10 Concept of negative powers of 10 Concept of positive exponents Concept of negative exponents. Multiplication with positive exponents Multiplication with negative exponents Division with positive exponents Division with negative exponents. Scientific notation conversions Multiplication with scientific notation Division with scientific notation Metric conversions.

0.65 0.68 *0.57 *0.69 0.63 0.58 *0.59 0.69 0.70 0.61 0.63 0.53 0.68 0.61 0.68

0.73 0.71 0.62 0.53 0.68 0.61 0.60 0.73 0.78 0.69 0.65 0.56 0.71 0.69 0.71

0.69 0.70 .59 *0.68 0.61 0.53 0.52 0.63 0.69 0.55 0.60 0.51 0.63 0.58 0.69

0.68 0.73 0.67 0.66 0.62 0.59 0.58 0.71 0.68 0.59 0.61 0.52 0.68 0.63 0.68

+ r2 P<0.01 ; *p<0.05 Table 6 indicates significance of the relationships between achievement in chemistry and each mathematics skills using the pre-test. It also indicates that almost all of the items correlated significantly with the chemistry achievement.


Table 7 Results of t-test and Correlational Analyses of Mathematics and Chemistry mean gain- scores. Math. Mean gain Chem. Mean gain Sex M F Overall Overall M F X 14.63 11.63 13.13 18.59 21.91 15.26 SD 4.51 3.75 4.12 4.80 5.53 4.01 t-values 16.33* 53.40* 27.37* +r2 F(0.63*) M(0.58*) overall (0.61*) *P<0.01; ( )= Correlation coefficients between mathematics mean gain scores and chemistry mean gain scores for overall sample and sex sub-samples. Table 7 indicates that there are significant correlations (p<0.01) between the overall mean-gain scores in chemistry and mathematics; and significant correlations (P<0.01) for each sex group. The t-values indicate significant differences among the mean gain scores in Mathematics and Chemistry for the sex sub-samples and overall sample. The improvement in chemistry achievement is therefore significantly related to the improvement in mathematics. Hypothesis 4 is therefore rejected.


Table 8 Percentage Correct on Mathematics Skills in Pre-test. S/No Math. Skills Comp. %

correct Appl. % correct

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11 .12. 13. 14. 15. 16. 17. 18. 19. 2 0. 21. 22. 23. 24. 25. 26.

Multiplication of fractions Division of Decimal Combined decimal operations Rounding/sign figures Finding percent of a number Computation of percent Use of graphs Positive-negative integer operations. Solving numerical equations Solving variables equations Solving ratio-proportion problems Solving direct variation problems Solving indirect variation problems Squaring / square root. Concept of positive powers of 10 Concept of negative powers of 10 Concept of positive exponents Concept of negative exponent Multiplication with positive exponents Multiplication with negative exponents Division with positive exponents Division with negative exponents Scientific notation conversion Multiplication with scientific notation Division with scientific notation Metric – metric conversions

64 62 48 50 64 54 31* 40 48 31* 42 62 41 86 51 38* 69 10* 58 38 52 29* 30* 39* 33* 54

61 52 31* 40 56 53 21* 27* 52 24* 26* 39* 12* 25* 30* 31* 66 6* 37* 42 40 24* 30* 46 22* 46

N=400 * skills that are extremely difficult.


Table 8 presents mathematics skills that students find difficult to execute in solving stoichiometry problems. These results indicate that there are variations in levels of difficulties experienced by students. Some skills could be executed at computational level and not at the application level. Summary of findings: (i). There is a significant

difference (at = 0.01 level) between students’achievement mean-scores in chemical stoichiometry before and after mathematics remediation.

(ii). There is significant sex difference at (at = 0.01 level) in students’ achievement mean-scores in chemical stoichiometry before and after mathematics remediation.

(iii). There is a significant relationship (at = 0.01 level) between students’ achievement in chemical stoichiometry and mathematics skills.

(iv). There is a significant relationship (at = 0.01 level) between the overall growth-mean scores of the students in chemistry and mathematics.

(v). There is a significant relationship (at = 0.01 level) between the growth-mean scores in chemistry and mathematics for each sex group.

Discussion The findings of this study seem to suggest that students’ achievements in chemical stoichiometry are influenced by the students’ mathematics capabilities. It is found that students’ achievement in mathematics had significant positive relationship with their achievement in chemical stoichiometry. These significant relationships exist for the overall experimental sample and for its sex subsamples. There are significant relationships between achievements in chemical stoichiometry and mathematics for each cognitive level (computation and applictation) and for each mathematics skill. There are significant relationships between improvement in chemical stoichiometry and improvement in mathematics for the overall sample and the sex subsamples. Significant differences were found between the female students’ achievement in mathematics and chemical stoichiometry pre-test; and between their achievements in the post-tests. Both mathematics and chemistry achievements significantly improved


after the remedial mathematics instruction. The trend was the same for the male students. Both groups had poor chemistry and mathematics achievements at the pre-test. The male group achieved significantly higher than the female group in mathematics and chemistry and had significantly higher improvement in both subjects. It was observed that high achievement in chemistry was accompanied by improvement in mathematics capabilities. The significant relationships of mathematics improvements to chemistry achievement, and to improvement in chemistry achievement tend to indicate that students who show most mathematics improvement had higher improvement in chemistry achievement. Majority of the relevant specific skills in mathematics test had significant relationships to chemistry achievement. However, items which had significant relationships to chemistry achievement for females did not match exactly those items for the males. This indicates a possible characteristic difference of the two groups. This gender characteristic seem to relate to sex differences in capabilities to apply mathematics skills. Application skills, and combinations of cognitive skills within the working-memory were very difficult for students to execute.

Since mathematics pre-test application total scores correlated higher than mathematics pre-test computation total scores to chemistry achievement, it seems that the capability to solve mathematics problems at a higher cognitive level has influence on chemistry achievement. It was found that mathematics application skills were significantly more related to chemistry achievement than computation skills. It is evident in this study that students do not posses all the mathematics skills needed for the study of chemical stoichiometry. Further analysis indicated that more than 50% of the students could not solve variable equations, indirect variation problems, multiply or divide using negative exponents or scientific notation in the mathematics pre-test. The mathematics capabilities of the students were therefore not as effective as might be desired for the study of chemical stoichiometry.These results support earlier arguments by Adeyegbe,( 1985,1993 and 2010) ; Offiah and Njelita( 2010 ); Offia and Egolum( 2006 ); Offia and Samuel( 2008) that the mathematical skills possessed by our senior secondary chemistry students cannot support the study of chemistry. Perkin, (1979); Ododo, (1997);Adigwe, (1993 and 1998)


;Popoola, (2006); Adeleke,(2007); and Offiah and Samuel,(2008) reported that the mathematical skills possessed by the senior secondary school students are grossly deficient for science studies. Considering the importance of mathematics competency for the study of science and technology (Oragwam,(1990); Daniyan,(1999); NPE,(1998); Eraikhumen,(2002);Awoniyi, (2007) stated that effective teaching and learning of mathematics should be vigorously pursued. As the bedrock of scientific and technological growth and development, no reasonable progress can be made in these areas without mathematics competencies (Swan, 1990; Swan and Philips, 1998; Swatton and Taylor; 1994 and Oliver, 1998). Unfortunately, our mathematics classrooms seem to deliver neither the mathematics foundations required for scientific and technological research in a modern society, nor does it provide the quantitative literacy necessary for a democratic society. The entire mathematics learned by the students seem substantially less than what they require for careers in science and technology; and the level of achievement seem, also, substantially low. It seems to imply that our mathematics curriculum is not what it ought to be and may not

even be close to what it ought to be. Or that our pedagogical approaches and its psychodynamics are not effective in inculcating functional mathematical knowledge and skills to our students. Summary and Conclusion This study examined relationship between mathematics skills and achievement in chemical stoichiometry. The entering mathematics skills possessed by the students significantly influenced their achievement in chemical stoichiometry. The male students had significantly better mathematics skills and chemical knowledge than the female students. Improvement in mathematics achievement of the students significantly improved attainment in chemical stoichiometry for both the experimental sample as a whole, and the sex sub-samples. There were significant sex differences in chemistry and mathematics improvement. In both subjects, the male students had signific antly higher level of improvement than the female group. Improvement in mathematics induced improvement in chemical stoichiometry. It implies that chemistry and mathematics classrooms have to collaborate. Mathematics education programmes should, in addition to their objectives, focus on functional


application of mathematics in chemical education. Recommendations (i) In as much as mathematics

skills significantly relate to achievement in chemical stoichiometry, diagnostic mathematics assessment should be done routinely in chemistry classes to determine the students mathematics status as an aid in counselling and remediation.

(ii) Chemistry and mathematics teachers should be advised of those mathematics skills that relate significantly to chemistry achievements and those skills in which students showed deficiencies for remedial programmes.

(iii) Guidance counselors should be made aware of relationship of mathematics capabilities to achievement in chemistry, and urged to consider individual student mathematics status during placement and Selection of subject for the senior secondary school certificate examination.

(iv) It is expected that the results of this study can be generalized to other chemistry topics that require

mathematics. Studies should be conducted in topics in other science subjects to determine whether similar trends exist in those areas.

(v) Finally, there have been numerous opinions on the relationship between mathematics ability and achievement in chemistry. This study has empirically established the fact that mathematics skills significantly relate to achievement in chemistry , specifically, chemical stoichiometry..

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APPENDIX 1 EXTRACTED MATHEMATICAL SKILLS (1). Whole Numbers Addition Subtraction Multiplication Division

Combined operations (2). Fractions Concept * Multiplication (3). Decimals Addition Subtraction Multiplication * Division * Combined operations * Rounding/significant figures (4). Algebra * Positive – negative integer

operation * Solving numerical equations * Solving variable equations * Solving ratio – proportion

problems * Solving indirect variation

problems. * Solving direct variation

problems.0 (5). Percent Concept Decimal – percent Conversion * Finding percent of a

number * Computation of percent (5). Graphing * Drawing / interpreting

graphs. * Skills tested in the items. (6). Exponent * Squaring a number/square

root


* Concept of positive integers of 10

* Concept of positive exponents

* Multiplication with positive exponents

* Multiplication with negative exponents

* Division with positive exponents

* Division with negative exponents

* Scientific notation conversions

* Multiplication with scientific notation

* Division with scientific notation.

(7). Measurement * metric-metric conversion

volume surface area.


EFFECTS OF MATHEMATICAL REASONING SKILLS ON …

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