How prior knowledge, learning, teaching and assessment affect students' achievements in Mathematics
Abstract
In this study we investigate how prior knowledge, the comprehensive learning approach, problembased teaching and assessment influence students’ basiclearning skills in Mathematics at the university level. To do so, we employed a quasiexperimental research design and a structured questionnaire. Two experimental groups and two control groups of students were involved. We found a negligible correlation between prior knowledge and basiclearning skills but a positive correlation between prior knowledge and the comprehensive learning approach. On the other hand, we found practically no correlation between prior knowledge and assessment. We also found that problembased teaching correlated positively and that the traditional approach correlated negatively with prior knowledge. Moreover, prior knowledge, problembased teaching, the comprehensive learning approach and assessment explained 50% of the variance in the levels of basiclearning skills.
Keywords
prior knowledge, comprehensive learning approach, problembasedinstruction, assessment impact, student's basic knowledge conceived in mathematics
Resumen
El objeto de este estudio es investigar la influencia del conocimiento previo del alumnado, el enfoque de aprendizaje integral, la enseñanza basada en problemas y el impacto de la evaluación en el aprendizaje básico del estudiante de matemáticas a nivel universitario. La investigación plantea un diseño de investigación cuasi experimental y un cuestionario estructurado. En él participaron dos grupos experimentales y dos grupos de control. Los resultados muestran que existe una correlación no significativa entre el conocimiento previo y la habilidad de aprendizaje básico; también plantea que un enfoque de aprendizaje integral se correlaciona positivamente con el conocimiento previo, mientras que con la evaluación casi no existe correlación, si bien existe una correlación positiva con la enseñanza basada en problemas. El enfoque tradicional se correlaciona negativamente con el conocimiento previo. Otros resultados que se obtienen es que el conocimiento previo, la enseñanza basada en problemas, el enfoque de aprendizaje integral y el impacto de la evaluación explican el 50% de la variación en los niveles de habilidades de aprendizaje básico.
Palabras clave
conocimientos previos, enfoque de aprendizaje integral, aprendizaje basado en problemas, evaluación de impacto, conocimientos previos del estudiante en matemáticas
Resum
El propòsit d'aquest estudi és investigar la influència del coneixement previ de l'alumnat, l'enfocament d'aprenentatge integral, l'ensenyament basat en problemes i l'impacte de l'avaluació en l'aprenentatge bàsic de l'estudiant de matemàtiques a nivell universitari. La investigació planteja un disseny quasiexperimental i un qüestionari estructurat. Hi van participar dos grups experimentals i dos grups de control. Els resultats mostren que hi ha una correlació no significativa entre el coneixement previ i l'habilitat d'aprenentatge bàsic. L'estudi també va revelar que un enfocament d'aprenentatge integral es correlaciona positivament amb el coneixement previ, mentre que amb l'avaluació gairebé no hi ha correlació. D’altra banda, s'observa que hi ha correlació positiva amb l'ensenyament basat en problemes. L'enfocament tradicional es correlaciona negativament amb el coneixement previ. La investigació també planteja que el coneixement previ, l'ensenyament basat en problemes, l'enfocament d'aprenentatge integral i l'impacte de l'avaluació expliquen el 50% de la variació en els nivells d'habilitats d'aprenentatge bàsic.
Paraules clau
conexements previs, enfocament d'aprenentatge integral, aprenentatge basat en problemes, avaluació d'impacte, coneixements previs de l'alumnat en matemàtiques
Practitioner notes
What is already known about the topic

Mathematics proficiency has always been a challenge for lecturers and students at university. Many researchers have investigated the factors related to students’ achievements in mathematics, such as mathematics preferences, teachers’ knowledge and teacher’s behavior, as well as students’ thinking and learning, and cognitive complexity.
What this paper adds

The researcher examined and revealed that a comprehensive learning approach correlates positively with knowledge conceived, as well as half of the variance of basiclearning skill levels is explained by prior knowledge, problembased teaching, comprehensive learning approach, and assessment impact. The researcher also found that problem based teaching is making a significant positive contribution, meanwhile, the traditional approach is making a significant but negative contribution to the prediction of basiclearning skill.
Implications of this research and / or paper

While students’ achievements in mathematics has proven to be the most challenging experience for students, as well as the lecturers, mathematics departments might pretest prior knowledge of students to strengthen their work to increase their academic success in mathematics, as well as might promote the comprehensive learning approach, and. problembased teaching. There is a need to investigate the influence of other variables on basiclearning skill in mathematics.
Introduction
The prior mathematics knowledge, comprehension learning approach, as well as problembased teaching used by teacher and assessment impact, are supposed to be the important variables that influence knowledge conceived in mathematics. The main aim of the study was to investigate the impact of prior knowledge, comprehensive learning approach, problembased teaching and assessment impact on student's basiclearning skill in mathematics. Learning is to be student‐initiated and that ample time for self‐study should be available (Evensen & HmeloSilver, 2000; HmeloSilver, 2004; Schmidt, 1983; Schmidt, 1993). Experiential learning should be triggered by a problem, understood as an unclear situation or phenomenon in need of an explanation (Dewey, 1934). Problem‐based instruction has been deemed one of the most innovative pedagogies to better benefit student learning (, 2019), and includes a process of inquiry, learning to learn, or cognitive constructivist approach (Schmidt, Molen, Wilkel, & Wijnen, 2009). Therefore, problem‐based instruction including the use of problems as the starting point for learning, students collaborating in small groups, and flexible guidance of a tutor (Schmidt, Rotgans, & Yew, 2019). Experiential learning, problem‐based teaching, as well as other approaches are some of the characteristics of teaching and learning in mathematics. (Solbrekke & Helstad, 2016) pointed out that teaching in higher education encompasses engaging students in their formation; meanwhile, (Hourigan & O’Donoghue, 2007) indicated that the ability of students to tertiary level mathematics education lies in the nature of entrants’ pretertiary mathematical experiences. (Kajander & Lovric, 2005) pointed out that the transition between secondary and tertiary education in mathematics is a complex phenomenon; meanwhile, (Harwell et al., 2009) provide evidence that curricula do not prepare students to enroll in difficult university mathematics courses. (Edwards, Sandoval, & McNamara, 2015) revealed that more than 60% of students are required to complete one mathematics class before enrolling in college. On average across OECD countries, 28% of students are able to solve only straightforward collaborative mathematics problems, and 8% of students are top performers, meaning that they can maintain an awareness of group dynamics, ensure team members act in accordance with their agreedupon roles, and resolve disagreements and conflicts while identifying efficient pathways and monitoring progress towards a solution (OECD, 2019). The conceptual definitions of the main variables selected to use in the study are explained as follows. Prior knowledge means grade in math in the previous academic year. Comprehensive learning approach indicates including information from different sources as class teaching, reading material, practical, etc. by students. Problembased teaching stands for supporting the students to learn a lot in every lesson by the lecturer. Assessment impact means trying to learn from mistakes and study better next time if the students don’t do well in an exam. And finally, basiclearning skill signifies to be able to learn the basic concepts taught in the math course subject.
Theoretical framework and Literature review
The fundamental factors in the educative process are an immature, undeveloped being; and certain social aims, meanings, values incarnate in the matured experience of the adult. The educative process is the due interaction of these forces. Abandon the notion of subject matter as something fixed and readymade in itself, outside due child's experience; cease thinking of the child’s experience as also something hard and fast; see it as something fluent, embryonic, vital; and we realize that the child and the curriculum are simply two limits which define a single process. The present standpoint of the child and the facts and truths of studies define instruction (Dewey, 1902, 182189). Constructivism theory must be used as a basis of the theoretical framework. Constructivism is an instruction paradigm posits that learning is an active, constructive process, and where the learner is an information constructor, and actively construct or create their subjective representations of objective reality (David, 2015). New information is linked to prior knowledge, thus mental representations are subjective, and students would engage in realworld, practical workshops in which they would demonstrate their knowledge through creativity and collaboration (Creighton & Dewey, 1916). Each student has a base level of knowledge, but they can increase it by practicing what they know well and adding onto it, and the social interaction between the student, teacher and other students reinforces their increase of knowledge (Vygotsky, 1980). In this context constructivism is served as a fundamental basis of problembased teaching, as well as comprehensive learning approach and learning skills and competencies.
Conceptual framework
Constructivism is grounded in the concept that learners construct their understanding through experiences and interpretations (Dewey, 1934). This construction of knowledge comes initially from the prior knowledge, experiences, attitudes, and interests that individuals bring to learning that transpires when individuals apply these factors to new experiences and situations (Howe & Berv, 2000). According to (Howe et al., 2000), constructivist paradigm requires active participation in the classroom, where learners participate in generating understanding (Brooks & Brooks, 1993). The framework for the study, as shown in Figure 1, is based on constructivism, and was also developed from an extensive review of existing evidence about the relationship between main variables. The review began with a search for relevant empirical research through ERIC, EBSCO, and Sage, using the keywords prior knowledge, comprehensive learning approach, problembased teaching, assessment impact, and student's basiclearning skill. The results of the study were interpreted in terms of constructivism theory, and research conducted in the field.
Literature review
Relationship between prior mathematical knowledge and basiclearning skill
Prior mathematical knowledge in secondary education is thought to be one of the most important premises to obtain good grades in mathematics in the university studies. Many authors have done a lot of research to investigate the association between prior knowledge in mathematics and basiclearning skill in university studies.
Prior knowledge had a positive influence on new learning (Lin & Liou, 2019; Reinholz & Gillingham, 2017). The high preference for mathematics have a much greater influence on the process of acquiring knowledge in mathematics (Lambić & Lipkovski, 2012; Mutodi & Ngirande, 2014). (James, Montelle, & Williams, 2008) found that the secondary school qualifications in mathematics influence their results in the core firstyear mathematics, meanwhile (Kizito, Munyakazi, & Basuayi, 2016) found that students' perceptions of their workload emerged as the factor having the greatest impact on student's performance, and (Richardson, Abraham, & Bond, 2012) revealed that the academic selfefficacy, grade goal, and effort regulation generated mediumsized correlations with GPA. The higher levels of mathematical knowledge (Hill, Schilling, & Ball, 2004; Schlomer, 2017) showed a greater focus on student mathematical thinking, meanwhile, limited mathematics thinking impact a smooth transition into mathematics programs (Hourigan & Leavy, 2017). (Flitcroft & Woods, 2018) revealed that teacher behaviors to students' academic performance have both positive and negative impacts, according to their positive or negative attitude, and (King & Cattlin, 2015) found that there are significant negative impacts associated with students’ pass rates with large numbers of students enrolling in degrees. Hence, there is evidence of positive relationship between prior knowledge, mathematics preferences, qualification, workload, higher levels of mathematical knowledge, as well as teacher behaviors and mathematics learning. (Fernández & Figueiras, 2014) found that teachers' knowledge impacts the continuity of mathematics, but (Hilby, Stripling, & Stephens, 2014) revealed that there is no relationship between mathematics ability of teachers. Teachers applying metacognitive skills in assisting their learners, and academic servicelearning experience influence a shift away toward selfefficacy for teaching by the students (Hollingsworth & KnightMcKenna, 2018; Tachie & Molepo, 2019). (Remillard, 2005) indicated that use of mathematics curriculum materials is an increasingly widespread practice to regulate mathematics teaching, and (Krain, 2016) confirm that casebased materials led students to gain a better understanding of theoretical concepts. (Steele, Johnson, Otten, HerbelEisenmann, & Carver, 2015) found that student thinking influence mathematics learning, meanwhile deepened teachers' knowledge influence mathematical knowledge for students (Kaur, 2017), and colleagues’ critical review provided progress of mathematics teachers (Kortjass, 2019). (McLeskey & Waldron, 2004) indicated that knowledgeforpractice, knowledgeinpractice, and knowledgeof practice of teacher learning (CochranSmith & Lytle, 1999) influence academic progress of students, and (Baumert et al., 2017) revealed a substantial positive effect of pedagogical content knowledge on students’ learning gains. Thus, it is evidenced that teachers' knowledge, metacognitive skills, curriculum materials student thinking, colleagues’ critical review, as well as pedagogical content knowledge impact students’ learning in mathematics. In conclusion, the investigation of the relationship between mathematical knowledge and basiclearning skill, as resulted in previous research, is important. Therefore, based on the above literature review it is hypothesized that:
H # 1: The higher mathematical knowledge scores are associated with higher basiclearning skill scores
Relationship between comprehensive learning approach and basiclearning skill
The comprehensive learning approach is assumed to be one of the important variables that impact basiclearning skill in mathematics at the university. A lot of research is carried out to investigate the association between comprehensive learning approach in mathematics and basiclearning skill at university. (Karagiannopoulou & Christodoulides, 2005) found that the learning is a stronger predictor of academic achievement, and (Jenkins, 2017) indicated that problembased learning impacts positively the students’ proficient level in mathematics. (Wyse & Soneral, 2018) revealed that the cognitive complexity is a contributor of the learning process, and (Gilstrap, 2019) reports a strong correlation between the standards for learners and the approaches to learning. (Crawford & Wang, 2015) revealed an increasingly significant performance by prior academic performance, and (Johnson, Johnson, & Johnson, 2017) found that comprehensive learning impact student achievements. (Yildirim, 2017) pointed out that flipped classroom increases the learning, and (Rimbey, 2013) revealed significant differences in classroom practice as a result of the treatment using the learning mathematics for teaching. Thus, it is evidenced that problembased learning, cognitive complexity, standards for learners, prior academic performance, comprehensive learning, flipped classroom correlate positively with basiclearning skill. (Tsouccas & MeletiouMavrotheris, 2019) indicated a positive impact of utilizing mobile apps as an instructional tool, and (Holmes & Hwang, 2016) showed that the students benefited greatly from the problem based learning in mathematics. (White & Nitkin, 2014) demonstrate the positive impact of the program on students learning, meanwhile (Alkhateeb, 2003) found that surface learning and deep learning approach accounting for 34.6% of variance to learning mathematics. (Barakat, 2005) showed that differences in the teaching methods yielded no statistically significant differences in skills, but (Schaub & Baker, 1991) revealed that instructional methods yield higher mean classroom knowledge. (Kogan & Laursen, 2014) pointed out that the impact of inquirybased learning on students' grades is sizable and persistent. Hence, there is evidence that mobile apps, the program, deep learning approach, instructional methods, and inquirybased learning influence basiclearning skill. In conclusion, the investigation of the relationship between a comprehensive learning approach and basiclearning skill, as resulted by previous research, indicates the scientific and practical importance. Therefore, based on the above research it is hypothesized that:
H # 2: The higher comprehensive learning approach scores are associated with higher basiclearning skill scores
Relationship between problembased teaching and basiclearning skill
Problembased teaching used by math teachers is supposed to be one of the most important variables that impact basiclearning skill in mathematics. A lot of research has been done to investigate the association between problembased teaching in mathematics and basiclearning skill at university.
Collaborative problemsolving performance is positively related to performance in the core PISA subjects (science, reading and mathematics), but the relationship is weaker than that observed among those other domains (OECD, 2019). The mathematics teaching predicted achievement, quality of the learning, and learning experience (Giles, Byrd, & Bendolph, 2016; Huntley, 2013; Karagiannopoulou et al., 2005; Serra, Bikfalvi, Masó, Carrasco, & Garcia, 2017). From the other point of view, (Toetenel & Rienties, 2016) found no positive correlation between learning design and student outcomes. Virtual manipulatives displayed considerable growth in students’ learning, and better performance in mathematics (Demir, 2018; Lee & Chen, 2014); but (Wilder & Berry, 2016) indicated that the traditional approach to instruction was equally effective in improving student mathematics knowledge. Students who received e problembased learning instruction (Baele, 2017) selfreported significantly greater engagement than those who received traditional instruction, and facetoface courses (Derr, 2017). Therefore, as above work evidenced, the collaborative problemsolving performance, mathematics teaching, virtual manipulatives, e problembased learning instruction correlate positively with basiclearning skill.
(Maciejewski, 2016) pointed out that how a student conceives the nature of a subject affects their learning outcome, and (Kelly, 2002) found that an equitable classroom climate in mathematics influence students' formation with knowledge. Teachers’ mathematical knowledge, a computerized instructional management system, and simulated teaching environment explained significant gains in math achievement (Hill, Blazar, & Lynch, 2015; Hill et al., 2004; Ma et al., 2016; Ysseldyke et al., 2003). (Kearns & Fuchs, 2018) found that cognitively focused instruction accelerated lowachieving students' academic progress, but (Chung, 2004) revealed that students from both constructivist and traditionalist approach improved their skills. (Burns, 2005) indicated that solving mathematics problems often requires searching for new approaches, and there is a significant improvement in mathematics’ achievement influenced by the learning style approach (AlBalhan & Soliman, 2019; Burns, 2005). Hence, it is evidenced the positive association between conceives the nature of a subject, teachers’ mathematical knowledge, computerized instructional management system, simulated teaching environment, cognitively focused instruction, and basiclearning skill. In conclusion, the investigation of the relationship between problembased teaching and basiclearning skill, as resulted in previous research, is important. Therefore, based on the previous research it is hypothesized that:
H # 3: The higher problembased teaching scores are associated with higher basiclearning skill scores
Relationship between assessment impact and basiclearning skill
Knowledge assessment of students is one of the important variables that are related to basiclearning skill in mathematics. A lot of research is carried out to investigate the association between assessment impact in mathematics and basiclearning skill in the university studies.
Assessment methods and matriculation examination score were the predictors of students’ progress (Karagiannopoulou et al., 2005; Kizito et al., 2016). (Duzhin & Gustafsson, 2018) found that online homework with immediate feedback was found to be even more effective than clickers, as well as (Abushammala, 2019) indicates that the use of multiple inclass activities and digital technology are important to enhance students' performance. (Lees & Anderson, 2015) pointed out that formative assessment may improve student performance, and (Brosvic, Dihoff, Epstein, & Cook, 2006) revealed that feedback facilitates the acquisition of mathematics knowledge. Mathematics teachers' judgments and information literacy assessment were highly predictive of students' performance (Chen, 2006; Pinto & FernándezPascual, 2017). Thus, assessment methods, matriculation examination score, online homework with immediate feedback, multiple inclass activities, digital technology, formative assessment, mathematics teachers' judgments, as well as information literacy assessment are associated with basiclearning skill.
Assessment support the advancement of teaching and learning (Cao, Jung, & Lee, 2005; Pinto et al., 2017). (Prevost, Vergara, UrbanLurain, & Campa, 2018) found the relationship between the assessment and the teaching and learning, and (Pomplun & Omar, 2000) found that invariance of a mathematics assessment was supported for factor loadings and intercepts. Assessing student learning support academic progress (Poskitt, 2014), although, students from different countries show the different academic ability of mathematics achievement (Randel, Stevenson, & Witruk, 2000). Thus, as above work evidenced, assessment support, assessment, as well as invariance of a mathematics assessment influence basiclearning skill. In conclusion, the investigation of the relationship between assessment impact and basiclearning skill, as resulted by literature review, indicates the research and practical importance. Therefore, it is hypothesized that:
H # 4: The higher assessment impact scores are associated with higher basiclearning skill scores.
Relationship between p rior knowledge, comprehensive learning approach , problembased teaching, assessment impact , and student's basiclearning skill in mathematics
Many researchers have done a lot of work to investigate the impact of prior knowledge, comprehensive learning approach, problembased teaching, and assessment impact on basiclearning skill in mathematics. Approaches to instruction and curriculum design, formative assessment data and feedback to students (Gersten et al., 2009), as well as prior knowledge (Fries, DeCaro, & Ramirez, 2019) have their impact on students’ learning. But, from the other point of view (Gruendler, 2018) found that none of the previous grades had a significant impact on the students' actual earned grade. A positive effect of pedagogical knowledge on students’ learning gains was mediated by the provision of cognitive activation and individual learning support (Baumert et al., 2017), as well as by teachers’ mathematical knowledge (Hill et al., 2015). (Gearing & Hart, 2019) revealed that problembased lessons increased the students’s ability, and (Hakyolu & OganBekiroglu, 2016) found a positive relationship between knowledge of students and arguments during a scientific argumentation. Ongoing professional development for teachers are positively associated with student achievement (Fox, 2014; Visser, Juan, & Hannan, 2019), but (Benken, Ramirez, Li, & Wetendorf, 2015) reported that merely the number of years of mathematics in high school does not necessarily imply that students are prepared for the level of rigor expected in postsecondary institutions. Hence, it is evidenced that approaches to instruction and curriculum design, formative assessment data, feedback to students, prior knowledge, pedagogical knowledge, individual learning support, teachers’ mathematical knowledge, problembased lessons, ongoing professional development for teachers impact student's basiclearning skill in mathematics. (Garet et al., 2016) revealed that math content knowledge and instructional practice were generally not correlated with student math achievement, but (Lampinen & McClelland, 2018) pointed out that pedagogical materials affect learning. Projectbased learning instruction, as well as diagnostic assessment information, influenced student achievement in mathematics (Han, Capraro, & Capraro, 2015; Linsell et al., 2012). (Nguyen, 2016) found that students with math preference in high school, as well as teaching approach influence the academic outcome (Nguyen, 2016; Santagata & Yeh, 2014), and teaching techniques influence students’ achievement (Kilion, 2016; Rimbey, 2013). Thus, there is evidence that pedagogical materials, projectbased learning instruction, diagnostic assessment information, students with math preference in high school, teaching techniques influence student's basiclearning skill in mathematics. In conclusion, the investigation of the relationship between prior mathematics knowledge, comprehensive learning approach, problembased teaching used by the teacher, assessment impact, and knowledge conceived in mathematics, as confirmed by previous research, is important. Therefore, based on the above previous research it is hypothesized that:
H # 5: The higher prior knowledge, comprehensive learning approach, problembased teaching, and higher assessment impact scores predict higher basiclearning skill scores
Methodology
Method and design
The quantitative approach was the method used in the research. A quasiexperimental research design was used. Quasiexperimental designs do not include the use of random assignment. Researchers who employ these designs rely instead on other techniques to control, or at least reduce threats to internal validity (Fraenkel, Wallen, & Hyun, ). Four groups of respondents, two experimental groups, and two control groups of students were involved. Four groups of respondents were non equivalent. Experimental and control groups of students were selected using existed students’ groups in economic and information technology and innovation faculties of the university.
Design
In the quasiexperimental research design, the matchingonly design was used in the study. The matchingonly design differs from random assignment with matching only in the fact that random assignment is not used. The researcher still matches the subjects in the experimental and control groups on certain variables, but he has no assurance that they are equivalent on others. When several groups are available for a method study and the groups can be randomly assigned to different treatments, this design offers an alternative to random assignment of subjects. After the groups have been randomly assigned to the different treatments, the individuals receiving one treatment are matched with individuals receiving the other treatments (Fraenkel et al., ) . The design is shown in the following Figure, Figure 2.
Teaching method was selected to be used as a manipulated variable: traditional vs problem based teaching, controlling the moderator, mediator and extraneous variables: teaching, curriculum, climate, class management, and technology as a teaching tool. The lecturers of the two experimental groups of students, or the lecturers from economic faculty were trained primarily using four modules with some of the main knowledge and skills in problembased teaching. Meanwhile, the lectures of the two control groups of students, or lecturers from faculty of information technology and innovation were not trained on this topic. This is the reason why the experimental and control group of respondents were chosen from different faculties.
Sample and data collection
Two experimental and two control groups of freshman and sophomore students as a nonrandom sample were selected to be investigated in the research. The two experimental groups of students: finance bank, business administration (N=135) were selected in the economic faculty of the university. Meanwhile, the two control groups of students: economical informatics, and information technology (N= 121) were selected in information technology and innovation faculty of the university. The four groups of respondents, except the fact that are from different faculties, they were taught the same syllabus of mathematics curriculum. Relating to classification at university, 81 respondents from experimental groups (60%) were freshman, and 54 respondents (40%) were the sophomore students. Meanwhile, 56 respondents from control groups (46.3%) were freshman, and 65 respondents (53.7%) were the sophomore students. Two experimental groups sample of respondents is composed by 18 females (13.3%), and 117 (86.7%) males; meanwhile two control groups sample of respondents is composed by 32 females (26.4%), and 89 (73.6%) males. Relating to the choice of career, 90 respondents (66.7%) from experimental groups studied in the first choice, 27 (20%) in the second choice, 9 respondents (6.7%) in the third choice, and 9 respondents (6.7%) in the fourth choice. Meanwhile, 40 respondents (33.1%) from control groups studied in the first choice, 32 (26.4%) in the second choice, 24 respondents (19.8%) in the third choice, and 25 respondents (20.7%) in the fourth choice.
A structured questionnaire was used to gather the primary data from the students in the 2018 2019 academic year. The questionnaire is based on CEVEAPEU questionnaire an instrument to assess the learning strategies of university students (Gargallo, SuárezRodríguez, & PérezPérez, 2009), and is modified, piloted and validated by the author. The questionnaire’ source is constructed by five dimensions: (1) demographic data of respondents, (2) parents’ level of education, (3) grades obtained in the previous academic year, and (4) learning strategies at university (88) items. Meanwhile, the questionnaire used in the research is also compounded by five dimensions, but it has less items (37) than the source.
Alfa Cronbach values of questionnaire scales vary from .83 to .91 confirming a very good value of reliability, as following Table 1.
N0 
Variables 
Alpha Cronbach value 
Evaluation 

1 
Prior knowledge 
.89 
Good 
2 
Comprehensive learning approach 
.91 
Excellent 
3 
Problembased teaching 
.88 
Good 
4 
Assessment impact 
.85 
Good 
5 
Basiclearning skill 
.83 
Good 
Analysis
Central tendency values, as well as frequency values, were used to describe the prior mathematics knowledge, comprehensive learning approach, problembased teaching, assessment impact, and knowledge conceived in mathematics for both, experimental and control groups. Pearson productmoment correlation coefficient was used to assess the relationship between prior mathematics knowledge, comprehensive learning approach, problembased teaching, assessment impact, and knowledge conceived in mathematics. Linear multivariate regression was used to assess the ability of one control measure to predict knowledge conceived in mathematics by prior knowledge, comprehensive learning approach, problembased teaching, and assessment impact. Preliminary assumption testing was conducted to check for normality, linearity, outliers, homogeneity of variancecovariance matrices, and multicollinearity, with no violations noted.
Results
Descriptive statistics
Frequencies and central tendency values of prior knowledge, comprehensive learning approach, problembased teaching, assessment impact, and basiclearning skill variables for experimental and control group of respondents are shown below. The statistical tables with frequencies and central tendency values of main variables are shown in the annexes. The more detailed frequencies of main variables according to gender and study program as crosstabs tables are shown in the annexes too.
Prior knowledge
Prior knowledge’ frequencies indicates that most of the respondents (46.7%) of the experimental groups and 40.5% of the control groups passed in the previous academic year; 33.3% of the experimental groups and 39.7% of the control groups achieved good results; meanwhile 20% of the experimental groups and 19.8% of the control groups achieved high results. Central tendency values for experimental groups (M= 2.733, SD = .774), as well as for control groups (M= 4.00, SD = .897), indicate the same tendency for values as measured by frequencies. Hence, there are small differences of prior knowledge (pass: 6.2%; good: 6.4%; high: 0.2%) between the experimental and control groups of students. Therefore, there are small differences of prior knowledge between the experimental and control groups of students.
Prior knowledge vs current knowledge (preposttest)
Comparing prior knowledge from previous academic year with current knowledge of experimental group has resulted that: (1) 5.93 % more students fail; (2) 2.96% more students pass, (3) 4.44% less students achieved good; (4) 4.44% less students achieved outstanding results in mathematics. Comparing prior knowledge from previous academic year with current knowledge of control group scores has shown that: (1) 9.09 % more students fail; (2) 6.61% more students pass, (3) 8.27% less students achieved good; (4) 7.43% less students achieved outstanding results. Hence, there is a difference between experimental and control group of students, especially in fail and outstanding levels achieved in mathematics.
Comprehensive learning approach
Comprehensive learning approach’ frequencies indicates that most of the respondents (53.4%) of experimental groups and 47.1% of control groups include full information from class reading material, practical, etc. during learning; 13.3% of the experimental groups and 26.4% of the control groups include a little; meanwhile 33.3% of the experimental groups and 26.4% of the control groups are undecided. Central tendency values for experimental groups (M= 3.46, SD = .808), as well as for control groups (M= 2.79, SD = .751) indicate the same tendency for values as measured by frequencies. Therefore, there are small differences of comprehensive learning approach (fully include: 6.3%; a little include: 13.1%; undecided: 6.9%) between the experimental and control groups of students.
Problembased teaching
Problembased teaching’ frequencies indicates that most of the respondents (66.7%) of the experimental groups and 19.8% of control groups have acquired fully support by lecturers in every lesson during teaching; 6.7% of the experimental groups, and 60.4% of the control groups a little support; meanwhile 26.7% of the experimental groups and 19.8% of the control groups are undecided. Central tendency values for experimental groups (M= 3.86, SD = .887), as well as for control groups (M= 3.27, SD = .930), indicate the same tendency for values as measured by frequencies. Hence, there are substantial differences of problembased teaching (fully support: 46.9%; a little support: 53.7%; undecided: 6.9%) between the students to whom problembased teaching is used compared to the students to whom the traditional approach is used.
Assessment impact
Assessment impact’ frequencies indicates that most of the respondents (73.3%) of experimental groups and 66.9% of control groups have fully learned from mistakes and study better next time if they don’t do well in an exam; 6.7% of the experimental groups and 6.6% of the control groups have a little learning; meanwhile 20.0% of the experimental groups and 26.4% of the control groups are undecided. Central tendency values for experimental groups (M= 2.73, SD = .774), as well as for control groups (M= 3.40, SD = 1.311), indicate the same tendency for values as measured by frequencies. Therefore, there are small differences of assessment impact (fully learned: 6.4%; a little learned: 0.1%; undecided: 6.4%) between the experimental and control groups of students.
Basiclearning skill
Basiclearning skill’ frequencies indicates that most of the respondents (53.4%) of experimental groups and 53.7% of control groups are fully able to learn the basic concepts taught in the math course; 6.7% of the experimental groups and 6.6% of the control groups are a little able; meanwhile 26.7% of the experimental groups and 26.4% of the control groups are undecided. Central tendency values for experimental groups (M= 4.00, SD = .897), as well as for control groups (M= 3.80, SD = .832), indicate the same tendency for values as measured by frequencies. Hence, there are small differences of basiclearning skill (fully able: 0.3%; a little able: 0.1%; undecided: 0.3%) between the students to whom problembased teaching is used compared to the students to whom the traditional approach is used.
Inferential statistics
Test of hypothesis

Basiclearning skill 
Prior knowledge 
Comprehensive learning approach 
Problembased teaching 
Assessment impact 

Basiclearning skill 
1.000 
.008 
.417 
.319 
.029 
Prior knowledge 
.008 
1.000 



Comprehensive learning approach 
.417 

1.000 


Problembased teaching 
.319 


1.000 

Assessment impact 
.029 



1.000 

Basiclearning skill 
Prior knowledge 
Comprehensive learning approach 
Problembased teaching 
Assessment impact 

Basiclearning skill 
1.000 
.003 
.443 
.048 
.106 
Prior knowledge 
.003 
1.000 



Comprehensive learning approach 
.443 

1.000 


Problembased teaching 
.048 


1.000 

Assessment impact 
.106 



1.000 
Table 2 and Table 3 shows Pearson correlations outputs of the relationships between variables
H # 1: As shown in Table 2 and Table 3, there is a negligible correlation between prior knowledge and basiclearning skill variables, r^{2} = .008, n = 135, p > .005 for experimental groups, as well as for control groups, r^{2} = .003, n = 121, p > .005. Furthermore, there is not a statistically significant relationship between prior knowledge and basiclearning skill by students, thus a random chance could explain the result.
H # 2: As shown in Table 2 and Table 3, there is a significant positive correlation between comprehensive learning approach and basiclearning skill variables, r^{2} = .417, n = 135, p < .005 for experimental groups as well as for control groups: r^{2} = .443, n = 121, p < .005. Hence, high scores of comprehensive learning approach are associated with high scores of knowledge conceived.
H # 3: As shown in Table 2 and Table 3 , there is a significant positive correlation between problembased teaching and basiclearning skill variables, r^{2} = .319, n = 135, p < .005 for experimental groups, meanwhile there is a low negative correlation between these variables for control groups: r^{2} = .048, n = 121, p < .005. Therefore, high scores of problembased learning teaching’ strategies are associated with high scores of knowledge conceived. Meanwhile, high scores of traditional learning problembased teaching are associated with low scores of knowledge conceived.
H # 4: As shown inTable 2 and Table 3, there is almost a negligible correlation between assessment impact and basiclearning skill variables, r^{2}= .029, n = 135, p < .005 for experimental groups as well as for control groups: r^{2} = .106, n = 121, p < .005. Hence, it is expected that the scores of assessment impact are not likely to associate with the scores of basiclearning skill.
Model Summary 


Experimental groups^{b} 






Change Statistics 


Model 
R 
R Square 
Adjusted R Square 
Std. Error of the Estimate 
R Square Change 
F Change 
df1 
df2 
Sig. F Change 
DurbinWatson 
1 
.713^{a} 
.508 
.493 
.93370 
.508 
33.570 
4 
130 
.000 
1.802 
Control groups^{b} 






Change Statistics 


Model 
R 
R Square 
Adjusted R Square 
Std. Error of the Estimate 
R Square Change 
F Change 
df1 
df2 
Sig. F Change 
DurbinWatson 
1 
.748^{a} 
.559 
.544 
.79902 
.559 
36.786 
4 
116 
.000 
1.768 
H # 5: As shown in Table 4, the total variance of basiclearning skill levels explained by prior knowledge, problembased teaching, comprehensive learning approach and assessment impact (the model) is 50.8%, F (4, .933), p < .005 for experimental groups, and 54.4%, F (4, .799), p < .005 for control groups. The model reaches statistical significance (Sig. = .000; this means p <.0005). The F value, that is the ratio of the mean regression sum of squares an estimate of population variance that accounts for the degrees of freedom indicates that null hypothesis is false (regression coefficients are different from zero).
Coefficients Experimental Groups 





Model 1 

Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 
95% Confidence Interval for B 
Correlations 
Collinearity Statistics 


B 
Std.Error 
Beta 
Lower Bound 
Upper Bound 
Zeroorder 
Partial 
Part 
Tolerance 
VIF 


(Constant) 
1.016 
.544 

1.869 
.064 
.060 
2.092 






Prior Knowledge 
.261 
.107 
.154 
2.430 
.006 
.473 
.048 
.093 
.208 
.149 
.943 
1.061 

Comprehensive learning approach 
1.067 
.162 
.658 
6.571 
.000 
.746 
1.389 
.646 
.499 
.404 
.377 
2.651 

Problembased teaching 
320 
.136 
.217 
2.351 
.002 
.051 
.590 
.565 
.202 
.145 
.445 
2.246 

Assessment impact 
.460 
.111 
.315 
4.153 
.000 
.680 
.241 
.171 
.342 
 
.657 
1.523 
Coefficients_Control groupsª 

Model 1 

Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 
95.0% Confidence Interval for B 
Correlations 
Collinearity Statistics 


B 
Std.Error 
Beta 
Lower Bound 
Upper Bound 
Zeroorder 
Partial 
Part 
Tolerance 
VIF 


(Constant) 
.150 
.478 

.313 
.755 
1.097 
.798 






Prior Knowledge 
.181 
.098 
.115 
1.852 
.006 
.013 
.375 
.055 
.169 
.114 
.982 
1.018 

Comprehensive learning approach 
.800 
.083 
.629 
9.640 
.000 
.635 
.964 
.666 
.667 
.594 
.892 
1.121 

Traditional approach 
.314 
.062 
.320 
5.047 
.000 
.437 
.191 
.221 
.424 
.311 
.943 
1.060 

Assessment impact 
.276 
.095 
.194 
2.909 
.004 
.088 
.464 
.326 
.261 
.179 
.852 
1.174 
For experimental groups, beta value for prior knowledge is.154, for comprehensive learning approach, is .658, for problembased teaching is .217, and for assessment impact is .315. The largest beta standardized coefficient is .658, which is for comprehensive learning approach.
For control groups, beta value for prior knowledge is.115, for comprehensive learning approach is .629, for the traditional approach is .320, for assessment impact, is .194. The largest beta standardized coefficient is .629, which is for comprehensive learning approach.
Discussion and implications
According to frequencies as well as the central tendency values, there are small differences of prior knowledge between the experimental and control groups of students. Thus, the students to whom the problembasedlearning approach is used reported higher levels of prior knowledge compared to the students to whom the traditional approach is used. Comparing prior knowledge from previous academic year with current knowledge scores it is found that there is a difference between experimental and control group of students, especially in fail and outstanding levels achieved in mathematics. Therefore, faculties, as well as mathematics departments might pretest prior knowledge of students to strengthen their work to increase their academic success in mathematics.
Frequencies as well as the central tendency values indicate that there are small differences of comprehensive learning approach between the students to whom problembasedlearning approach is used compared to the students to whom traditional approach is used. Hence, faculties, as well as mathematics departments might promote the comprehensive learning approach.
Frequencies as well as the central tendency values indicate that there are bigger differences of problembased teaching between or the students to whom problembasedlearning approach is used compared to the students to whom traditional approach is used. Hence, faculties, as well as mathematics departments might promote and use more problembased teaching.
According to frequencies as well as the central tendency values there are small differences of assessment impact between the students to whom problembasedlearning approach is used, compared to the students to whom the traditional approach is used.
Therefore, faculties, as well as mathematics departments might use assessment to increase its impact on students' learning to learn from mistakes and study better next time if they don't do well in an exam.
Frequencies, as well as the central tendency values, indicate that there are small differences of basiclearning skill between the students to whom problembasedlearning approach is used, compared to the students to whom traditional approach is used. Hence, faculties, as well as mathematics departments might support the students to be able to learn the basic concepts taught in the math course.
Pearson correlation outputs indicate that there is a negligible correlation between prior knowledge and basiclearning skill variables (r^{2} = .008) for experimental groups as well as for control groups (r^{2} = .003). Furthermore, there is not a statistically significant relationship between prior knowledge and basiclearning skill by students, thus a random chance could explain the result. The value of correlation indicates that other variables might be important in variance prediction of basiclearning skill scores. So, future researchers may do more work to investigate the influence of other variables on basiclearning skill. The result was not consistent with some previously reported works, who argued that prior knowledge influence basiclearning skill scores (James et al., 2008; Lambić et al., 2012; Lin et al., 2019; Mutodi et al., 2014; Reinholz et al., 2017; Richardson et al., 2012). Meanwhile other authors (Fernández et al., 2014; Flitcroft et al., 2018; Hill et al., 2004; Hollingsworth et al., 2018; Kizito et al., 2016; Remillard, 2005; Schlomer, 2017; Tachie et al., 2019) revealed the other variables that impact basiclearning skill scores in mathematics, including students’ workload, teachers’ knowledge, curriculum, and pedagogy. In conclusion, H # 1: The higher prior knowledge scores are associated with higher basiclearning skill scores, is been rejected.
Pearson correlation outputs indicate that there is a significant positive correlation between comprehensive learning approach and basiclearning skill variables (r^{2} = .417) for the experimental groups as well as for control groups (r^{2} = .443). Therefore, high scores of comprehensive learning approach are associated with high scores of basiclearning skill. The value of r^{2} indicates that other variables might be important in variance prediction of basiclearning skill scores. So, future researchers may do more research to investigate the influence of other variables on basiclearning skill. The result was consistent with some previously reported works, who argued that comprehensive learning approach influence basiclearning skill scores (Alkhateeb, 2003; Gilstrap, 2019; Hill et al., 2015; Holmes et al., 2016; Jenkins, 2017; Johnson et al., 2017; Karagiannopoulou et al., 2005; Kogan et al., 2014; Ma et al., 2016; Rimbey, 2013; Tsouccas et al., 2019; Wyse et al., 2018; Yildirim, 2017). In conclusion, H # 2: The higher comprehensive learning approach scores are associated with higher basiclearning skill scores, is been supported.
Pearson correlation outputs indicate that there is a significant positive correlation between problembased teaching and basiclearning skill variables (r^{2} = .319) for the experimental groups, meanwhile, there is a low negative correlation between traditional approach and basiclearning skill for the control groups (r^{2} = .048). Hence, high scores of problembased learning teaching’ strategies are associated with high scores of basiclearning skill. Meanwhile, high scores of traditional teaching are associated with low scores of basiclearning skill. The value of correlation indicates that other variables might be important in variance prediction of basiclearning skill scores. So, future researchers may do more work to investigate the influence of other variables on basiclearning skill. The result was consistent with some previously reported works, who argued that problembased teaching influence basiclearning skill scores (Baele, 2017; Demir, 2018; Derr, 2017; Giles et al., 2016; Hill et al., 2015; Huntley, 2013; Karagiannopoulou et al., 2005; Lee et al., 2014; Ma et al., 2016; Maciejewski, 2016; Serra et al., 2017; Ysseldyke et al., 2003). The result was not consistent with a few previously reported works, who argued that problembased teaching does not influence basiclearning skill scores (Chung, 2004; Toetenel et al., 2016; Wilder et al., 2016). In conclusion, H # 3: The higher problembased teaching scores are associated with higher basiclearning skill scores, is been supported.
Pearson correlation outputs indicate that there is a negligible correlation between assessment impact and basiclearning skill variables (r^{2}= .029) for the experimental groups as well as for control groups (r^{2} = .106). Therefore, it is expected that the scores of assessment impact are not associated with thw scores of basiclearning skill. The value of r^{2} indicates that other variables might be important in variance prediction of basiclearning skill scores. So, future researchers may do more research to investigate the influence of other variables on basiclearning skill. The result was not consistent with some previously reported works, who argued that assessment impact influence basiclearning skill scores (Abushammala, 2019; Brosvic et al., 2006; Chen, 2006; Karagiannopoulou et al., 2005; Kizito et al., 2016; Lee et al., 2014; Lees et al., 2015; Pinto et al., 2017; Prevost et al., 2018). In conclusion, H # 4: The higher assessment impact scores are associated with higher basiclearning skill scores, is been rejected.
Regression outputs indicate that the total variance of basiclearning skill levels explained by prior knowledge, problembased teaching, comprehensive learning approach and assessment impact (the model) is 50.8% for the experimental groups and 54.4% for the control groups. The model reaches statistical significance (Sig. = .000).
Problembased teaching beta value in the experimental groups means that 21.7% of the variance on basiclearning skill is explained by problembased teaching. Hence, problem based learning or manipulated variable is making a significant contribution to the prediction of basiclearning skill dependent variable in the experimental groups.
Traditional approach beta value in the control groups is negative and means that 32.0% of the variance on basiclearning skill dependent variable is explained by the traditional approach. Therefore, traditional teaching independent non manipulated variable is making a significant but negative contribution to the prediction of the basiclearning skill dependent variable in the control groups.
Meanwhile, beta values for prior knowledge and assessment impact in the experimental groups are negatives and are explained 15.4% and 31.5% of the variance on the dependent variable. The largest beta standardized coefficient is .658, which is for comprehensive learning approach. This means that this variable makes the strongest unique contribution to explaining the dependent variable.
Beta value in the control groups for prior knowledge explain 11.5%, and beta value for assessment impact is negative and explain 19.4% of the variance on the dependent variable. The largest beta standardized coefficient is .629, which is for comprehensive learning approach. This means that this variable makes the strongest unique contribution to explaining the dependent variable.
Therefore, problem based teaching is making a significant positive contribution, meanwhile, the traditional approach is making a significant but negative contribution to the prediction of basiclearning skill. The result was consistent with some previously reported works, who argued that higher prior knowledge, comprehensive learning approach, problembased teaching, and higher assessment impact scores predict higher basiclearning skill scores (Baumert et al., 2017; Fries et al., 2019; Gearing et al., 2019; Gersten et al., 2009; Hakyolu et al., 2016; Han et al., 2015; Hill et al., 2015; Kilion, 2016; Lampinen et al., 2018; Linsell et al., 2012; Nguyen, 2016; Rimbey, 2013; Santagata et al., 2014). In conclusion, H # 5: The higher prior knowledge, comprehensive learning approach, problembased teaching, and higher assessment impact scores predict higher basiclearning skill scores, is been supported.
The results of this study supported by other researchers about the basiclearning skill in mathematics have important implications for future research on academic achievements. Such research should investigate various variables and their relation to basiclearning skill. Results of this study about basiclearning skill also have important implications for practice. The important programs or other interventions should be designed to develop and to support students to obtain better results in mathematics.
Conclusions
Several limitations of the study should be acknowledged as part of the conclusion. First, the measurement of prior knowledge, comprehensive learning approach, problembased teaching, assessment impact, and basiclearning skill variables is made through using of self reported instrument. Second, the study included four independent variables, since it is known that basiclearning skill is influenced by other variables as well. The prior assumption was that prior knowledge, comprehensive learning approach, problembased teaching, and assessment impact student's basiclearning skill.
The results showed that there are small differences of prior knowledge between the students to whom the problembased teaching approach is used compared to the students to whom the traditional approach is used. The study confirmed that there are small differences of comprehensive learning approach and assessment impact between the students to whom the problembased teaching approach is used compared to the students to whom the traditional approach is used. The results showed that there are substantial differences of problembased teaching between the students to whom problembased teaching is used compared to the students to whom the traditional approach is used. The results showed that there are small differences of basiclearning skill between the students to whom problembased teaching is used compared to the students to whom the traditional approach is used.
It is found that there is a negligible correlation between prior knowledge and basiclearning skill, and there is not a statistically significant relationship between them. It is found that a comprehensive learning approach correlate positively with knowledge conceived, meanwhile, assessment almost does not correlate. Thus, higher scores of learning approach are associated with higher scores of basiclearning skill. It is found that problembased teaching correlates positively with basiclearning skill, meanwhile traditional approach correlates negatively with basiclearning skill Thus, higher scores of problembased teaching are associated with high scores of basiclearning skill, meanwhile higher scores of traditional approach are associated with lower scores of basiclearning skill.
The study found that 50% of the variance of basiclearning skill levels is explained by prior knowledge, problembased teaching, comprehensive learning approach, and assessment impact. It is found that problembased teaching explains 21.7% of the variance of basiclearning skill, prior knowledge 15.4%, comprehensive learning approach 65.8%, and assessment impact 31.5%. The other variance may be explained by hidden or unknown variables. The study confirmed that the comprehensive learning approach makes the strongest unique contribution to explaining basiclearning skill in mathematics. Problembased teaching is making a significant positive contribution, meanwhile, the traditional approach is making a significant but negative contribution to the prediction of basiclearning skill in mathematics.