As per educational and training policy of Ethiopia (1994), numeracy, literacy, home science, health services, agriculture and civics are the focus of basic education where as research oriented education which enables to solve problem, which makes professional leader, and which fulfils societal needs is the focus of higher education. According to Ethiopian Education Development Road Map (2017–30), the curriculum should suggest teaching of science technology and math subjects corresponding to each grade level in order to bring higher order thinking skills. The growth and transformation plan - GTP2 (2016, p.189) of Ethiopia also suggests that number of students in higher education should be increased and the number of higher institutions should also be increased, and to improve the achievements of preparatory school students in mathematics and science subjects, the university should work in collaboration to schools.

Numeracy, literacy and problem solving skills can be enabled in mathematics and the emphasis in improving achievement in mathematics and science needs further detail including checking students’ mathematics self-beliefs and other motivational variables on their mathematics achievement. Thus, this study will be much more important to give the emphasis on Mathematics Learning Motivation to fulfill the GTP2 Objectives. GTP 2 also suggests to use trained and skilled man power which can empower technology transformation; the 70:30, that is 70% Natural and computational science and 30% Social Science, University students admission policy of Ethiopia should be supported by encouraging activities such as activities which bring good attitudes on primary and secondary students on math and science.

This 70: 30 program makes the enrollment natural and computational science students in University to be massive than that of Social Science students. There are many researches on mathematics learning which suggests valid mathematics instruments and specific points where students need help ( Gersten et al., 2005). But Mathematics curriculum does not include research results concerning the best practices beliefs that children can learn mathematics and the curriculum revision do not incorporate classroom performance ( Clements, 2004b). As it has been seen from EGMA (2009) report, there were differences in skill levels among students in early grade level throughout the countries. This implies there will be differences in level of motivation or self-beliefs in learning mathematics among students and thus in the higher grade level also it is not expected that all the 70% of students enrolled to be science learners in Universities of Ethiopia are high achievers in mathematics and highly motivated to learn mathematics. Thus the need to check the impact of self-beliefs on their mathematics achievement is unquestionable. Thus examining students’ level mathematics achievement in relation to their mathematics self-beliefs in tandem with the spirit of the recently introduced Ethiopian Education Development Road Map.

Despite all these factors, little is known about students’ mathematics achievement in relation to the motivation variables such as self-beliefs, expectancy values and achievement goal in the case University students of Ethiopia hence, the need for this study. Thus this study is aimed at identifying the relationship of mathematics achievement of university students with these motivational constructs in Ethiopian context.

H ₀₁: Self-beliefs has no significant effect on mathematics achievement in the case of university students in Ethiopia.

H ₀₂: Expectancy Values has no significant effect on mathematics achievement in the case of university students in Ethiopia.

H ₀₃: Achievement goal has no significant effect on mathematics achievement in the case of university students in Ethiopia.

The study was conducted following the approval of PhD dissertation proposal and obtaining written ethical clearance with Reference number: መትት/17/2014 and date October 19/2021 from School of Teacher Education, Hawassa University and each participants gave written informed consent.

This is study is conducted on undergraduate university students in Ethiopia in 2023. The interview was to pilot test the instruments validity. Interview was taken place at Bongo University and at Bong Education College. 9 experts, three from the field of psychology, three from the field of measurement and evaluation, and three from the field mathematics were participated in experts’ review of the MLM items and the MAT items. Also 5 respondent students from Bonga University were participated in cognitive interview. These, 5 participants, were discussed on MLM items as well as MAT items being in group and identified those items with ambiguity meanings. (see appendix 1 and 3).

Considerable effort has made to control the cofounding variables which might result in research bias. In this regard, sufficient and representative sample size was considered, appropriate statistical data analysis tool was employed, and appropriate research design, sampling technique were used. Possible psychometric tests were also made to have valid d gathering tools.

The primary data were collected by using self-developed- questionnaires, Mathematics achievement test and interviews.

Independent variables:

Dependent variable:

Academic achievement: is a measurable variable which can be measured in terms of achievement test or achievement results obtained from students’ current grade report. That is, students reported their commutative grade point average (CGPA), which was considered to be their academic achievement. Students were also administered Mathematics Achievement Test (MAT) which indicated their mathematics achievement.

The population of the study was undergraduate University students of Ethiopia. The reason to consider the undergraduate student is that most undergraduate students were taking mathematics as a common course and these students were believed to provide relevant data. The study sample was 400 randomly undergraduate university students who attend mathematics course as a common course from Addis Ababa University, from Hawassa University and from Jimma University. Purposive sampling technique was used to select the three universities, while stratified random sampling technique was used to select participants from each University and each College and each Department. Students were approached in person to take part in the study. The reason for inclusion of the three Universities were the homogeneous nature of students enrolled in Ethiopian public Universities, their being first generation Universities, the plenty of experiences of these Universities, and their being budget saving and convenient for the researcher for collecting relevant data.

The reason to have only 400 respondents is as follows:

As per the Chaokromthong & Sintao (2021) Sample size estimation by means of Yamane and Cochran and Krejcie and Morgan and green formulas, n = N 1 + ε 2 N , and as N becomes very large (goes to infinity), this formula for the significance level being 0.05 is 400 (that is, lim N → ∞ N 1 + ε 2 N = 400;for ε = 0.05). Thus for large (infinite) population, a sample size 400 is sufficient, provided that the sample selection technique is correct. Moreover, Israel (1992) and Singh and Masuku (2014) confirmed that for 95% confidence interval, and for the large size of population more than 100, 000, the sample size n = 400 is sufficient. Hence, the researcher took 400 samples from the large population of undergraduate University students in Ethiopia.

Undergraduate students in Addis Ababa, Hawassa and Jimma Universities were the respondents of this study. The first tool was the experts’ interview concerning items of Mathematics Learning Motivation(MLM);

Nine experts, three from the psychology field, three from the measurement and evaluation field and three from the mathematics fields were made to fill the content validation form. The Experts were chosen according to their field of study from Bonga Eduction College and from Bonga University, Ethiopia.

The experts review has been taken place at Bonga University and at Bonga College. Each expert was made to put expert judgment on the domain on the degree of relevant each item to the measured domains based on the definition and relevant terminologies provided to them. 5 students selected from Bonga University were also interviewed to think aloud all the question in their group and answer Which item do they think is(are) confusing or misleading about the survey question. (see Appendix 3).

The MLM items were adapted from different related surveys and then re-developed in university students’ context in Ethiopia. The MLM is a self-report Likert-type scale which was adapted and contextualized from Butler (2016). At first stage 160- items based on different motivation theories was adapted and only 51 items which was validated by experts review and cognitive interview of group debriefing was retained for data collection. (see Appendix 3)

The Mathematics Achievement Test (MAT) was developed by the authors and pilot tested. The items consists of all freshman mathematics contents which is given as common course for first year University students. Primarily 31 items was developed and pilot tested on 150(male= 86, Female=64) University students in Bonga University. The item is analysis by using Item response Theory. The item difficulty and discrimination indices were verified. The item characteristic curve and test information curve were employed. Finally only 25 items which fulfill these psychometric properties were retained for further data collection. (Appendix 1)

Students were selected based on stratified sampling techniques. The strata were based on the colleges of students. Students who took basics mathematics during the freshman course were randomly selected from appropriate Colleges of the three universities, namely Addis Ababa, Jima and Hawassa Universities. The randomization process is in such a way that once the Universities and the colleges of students are selected purposively, participant selection was randomly from each college by not bothering on inclusion all students in each department and in each class and section of students. Accordingly, the College of Natural Science, the College of Education, the College of Engineering, and the College of Health science were the strata from which sample was randomly selected. The questionnaire distributed in paper form. The researcher distributed the questionnaire and administered the test. In average one week of time were spent the questionnaire to be filled and the test to be administered in one University. Participants first filled MLM questioner and then they took MAT as the same time after completion of responding to the questionnaire. In average one and half hour was given to each participant to respond on the questionnaire and administer the test.

The standardized MAT was administered to undergraduate students taking the mathematics course to tap students’ mathematics achievement. In addition, students’ current cumulative GPA (Grade Point Average) was also tapped as along with the demographic characteristics of respondents.

For pilot test of MAT, the data was analyzed by using experts’ review, cognitive interview, item characteristic curve (ICC), test information curve, difficulty and discrimination indices by means of the application of IRT. The 9 experts: 3 experts from the measurement and evaluation field, 3 experts from the psychology field, and 3 experts from the mathematics field were participated on experts’ were also reviewed of the MAT items. The results of experts review reveal that all the 31 items have good face validity; 5 students were participated in cognitive interview of type group debriefing. The results of cognitive interview revealed that all the 31 items match with the intended meaning to measure the construct; the item discrimination indices and item difficulty indices by using the application of IRT results to suppressed 5 items from the list. Thus 25 items were retained for further data collection tool. The ICC and the test information indicted all the 25 items were considerably acceptable. Accordingly, 25 items were retained for the main data collection.

Three phases (item development, scale development, and scale evaluation) with nine steps of item development and validation was employed in this study.

The first phase was the Item development concerned with the initial set of questions for an eventual scale, which consists of (i) identification of the domain(s) and item generation, and (ii) consideration of content validity. The second phase was scale development that is converting or modifying individual items into a harmonious and measuring construct, consists of (iii) pre-testing questions, (iv) sampling and survey administration, (v) item reduction, and (vi) extraction of latent variables. The final stage is the scale evaluation, which contains: (vii) tests for dimensionality, (vii) tests for reliability, and (ix) tests for validity. For these, the Structural equation modeling and Explanatory analysis (EFA) was employed. Item Response Theory (IRT) and Latent Construct Theory (LCT) were used. The software SPSS 23, and STATA 15 were used for data analysis.

We observe from Table 4 that all items significantly contributed to their corresponding self-beliefs construct.

Table 5 indicates that all the expectancy value items have significant and positive contribution to the construct.

It was also depicted in Table 6 that all the achievement goal items are significantly contributed to the achievement goal factor.

The modification indices has to be made on item 25 and 26, on item 81 and 82 , and on item 56 and 57. Applying modification indices or drawing covariance between the listed items decreases the degree of freedom with value more than 100. Thus the modification indices were applied on these three pairs of items (see Appendix 2 in the Extended data and Figure 2).

Figure 2 indicates the full-fledged model and from this model we get the measurement and structural model statistic together.

As depicted in Table 8, the two predictors, namely the expectancy value ( β =.0000355, p=.664 >.05) and Achievement Goal ( β =.0199, p=.780 >.05), are positively related with math achievement and but they are not significant estimators of mathematics achievement whereas the self-belief ( β =4080, p=.000 <.05) is positively related with mathematics achievement and significant estimator of math achievement.

The implication was that as self-belief related mathematics leaning motivation has significant effect on students’ mathematics achievement:

The result is supported by former researches of House (2006) who stated that a number of significant relationships between self-beliefs and mathematics achievement; Stankov & Lee (2017) who states that Self-beliefs affect cognitive performance either as impediments (anxiety) or facilitators (good calibration of self-efficacy and confidence) and it also related with the researches of Pitsia, Biggart, & Karakolidis (2017) revealing that students' mathematics self-efficacy, anxiety, self-concept, motivation, attitudes were statistically significantly predict achievement in math.