24. Mathematics Education Research
Paper
Improving the Process of Preparing 10th Grade Students for External Summative Assessment in Mathematics by Implementing Problem-based Learning Technologies.
Zhadyra Nurym, Gulzada Rakhimova, Aliya Sissaliyeva, Ingkar Sabyrova
NIS, Kazakhstan
Presenting Author: Nurym, Zhadyra;
Rakhimova, Gulzada
Introduction:
In contemporary education, considerable emphasis is placed on the implementation of pedagogical techniques that promote effective teaching through active engagement of students with educational content. Among these approaches, problem-based learning (PBL) stands out as a method that fosters the development of creative thinking, autonomy, and problem-solving abilities among students, while also facilitating the application of acquired knowledge in practical contexts. This study aims to investigate the influence of employing problem-based learning methods in preparing 10th grade students for an external summative assessment in the domain of mathematics.
Theoretical Basis of the Study
Summative assessment serves as a means of evaluating the educational accomplishments of students upon completion of specific sections or cross-cutting topics within the curriculum. It also encompasses the assessment conducted over a designated educational period, such as a quarter, as well as external assessments. These assessments entail the allocation of points and grades, while providing valuable insights on student progress to teachers, parents, and students themselves.
External summative assessments are carried out upon the culmination of particular levels of education, encompassing primary, basic, and secondary education. The benchmarks utilized in these exams adhere to international standards, such as the Cambridge Primary (grade 5), IGCSE (grade 10), AS-level, and A-level (grades 11-12). External summative assessment exams feature multiple components, including closed and open-ended questions that require both concise and detailed responses.
Upon the completion of external summative assessments, students in 12th grade receive an NIS Grade 12 Certificate. This certificate holds recognition by esteemed universities in Kazakhstan, as well as by leading international organizations. [1]
The issue we encountered revolved around our school's performance in mathematics during external summative assessments, as we ranked last within the Nazarbayev Intellectual School network. Notably, there existed a disparity between internal assessments and external assessments. The aim of this action research was to enhance the quality of mathematics outcome measures among 10th grade students. The study pursued the following research question: How does the integration of problem-based learning impact students' effective preparation for external summative assessments in mathematics?
Problem-Based Learning (PBL) technology has been utilized in higher education since the mid-20th century, serving as an interactive learning method. Initially employed by universities in the United States and Canada during the 1950s, PBL later proliferated across European universities during the 1960s. The introduction of this technique initially occurred in the Faculty of Medicine at Case Western Reserve University. Recognizing the contemporary context characterized by an information and technological "explosion," which entails rapidly evolving requirements for future professionals, PBL emerged as the training model best aligned with this situation. [2]
The traditional approach to higher education emphasizes the passive transfer and rote memorization of existing knowledge. Students grapple with the monotonous task of memorizing vast amounts of information that, in their estimation, may not always directly pertain to their forthcoming professional endeavors. Consequently, apathy, detachment, and occasionally disillusionment arise. Frequently, students tend to forget a substantial portion of the material they have learned once an assessment has been completed. Moreover, the retained information often proves challenging to apply when attempting to solve problems across related subject areas, especially within the realm of real-world professional application. [3]
The foundation of PBL rests upon a constructivist approach, which has garnered opposition from critics of this teaching method. In line with the constructivist trend, which emphasizes student participation in the construction of new knowledge through the reevaluation of experiences, PBL brings about significant changes in the learning process itself. It assumes an active and socially-oriented character, thereby embracing a more interactive format.[4]
Methodology, Methods, Research Instruments or Sources UsedThe study involved the participation of all 10th grade students at NIS in Aktau during the academic year 2022-2023. A purposive sampling technique was used to recruit 129 participants for the research sample.
To establish a control group, 88 participants were selected from the 10th grade students at NIS Aktau during the academic year 2021-2022.
The experimental class consisted of 10th grade students at NIS Aktau in 2022-2023, while the control class consisted of 10th grade students at NIS Aktau in 2021-2022. The experimental class received training using drill methods with PBL, whereas the control class received training using drill methods without PBL.
Data collection methods included tests to measure problem-solving skills and questionnaires to gather student responses during PBL training.
Within the framework of problem-based learning (PBL), practice-oriented case assignments served as the primary teaching tool, which students studied in practical classes.
The Vocational Education and Training (VET) was implemented through the following main stages:
1. Teachers provided students with descriptions of exam problems that required solving and evaluating their work against a mark scheme.
2. Students familiarized themselves with the case, analyzed it, and identified key problems requiring solutions.
3. Students worked independently or in groups to solve the problems. They conducted research, gathered information, performed analyses, and developed solutions [5].
4. In subsequent practical classes, students presented their work results, engaged in discussions, and collectively arrived at the most optimal solution.
5. Additional mathematics lessons were organized outside of regular school hours.
The questionnaire comprised 6 questions aimed at identifying factors including:
- Motivation to learn
- Perception of teaching methods
- Level of satisfaction with training
The data collection methods also included midterm mock exams to measure problem-solving skills.
A quantitative approach was employed to compare students' final scores and identify patterns and regularities.
1. Systematization and analysis of the obtained data:
• The collected data on students' regular exam preparation activities were processed and analyzed, taking into account their academic performance.
• Data on the use of various pedagogical methods and technologies were summarized and analyzed to identify their impact on students' success.
2. Cross-analysis of the data:
• Furthermore, the obtained results of data analysis for each factor (regular activities, method and technology usage, individualized approach, parental involvement) were cross-compared and analyzed together to identify common patterns and interrelationships between these factors.
Conclusions, Expected Outcomes or FindingsResearch findings
The examination of the questionnaires revealed that students in the experimental group exhibited a higher level of motivation towards their learning compared to students in the control group. Additionally, they demonstrated a greater acceptance of Problem-Based Learning (PBL) teaching methods and expressed higher satisfaction with their training.
In relation to the study on the preparation for external summative assessment, several factors influencing student achievement were identified:
1. Regular exam preparation sessions were found to positively impact student performance.
2. The utilization of diverse pedagogical methods and technologies proved to be effective in preparing students for exams.
3. Adopting an individualized approach that considers students' unique characteristics and needs also contributed to successful outcomes in external assessments.
4. Involving parents in the exam preparation process also yielded positive outcomes in terms of academic performance.
Based on the collected data, it can be concluded that the effective organization of student preparation for external summative assessment is a crucial component of academic success. It is recommended to further investigate and implement contemporary methods and technologies to enhance student performance in future endeavors.
The research results demonstrated that the experimental group, which received training using PBL methods, achieved higher outcomes compared to the control group that underwent drill-based instruction without the integration of PBL.
The average score for the experimental group was 52.2%, while the control group achieved an average of 41.97%. This difference was found to be statistically significant. Consequently, our school's ranking within the NIS network improved from 15th place to 10th place.
Furthermore, the results of the experimental group surpassed those of previous years. For instance, in 2019, the average was 49%, in 2021 it was 39.65%, and in 2022 it was 41.97%. These findings indicate that the implementation of PBL can enhance students' problem-solving skills.
ReferencesReferences
1.Educational program AEO “Nazarbayev Intellectual Schools” – NIS-Programme URL:
https://www.nis.edu.kz/storage/app/media/NIS-Programme/NIS-Programme_RU.pdf
2. The Aalborg PBL-model – Progress, Diversity and Challenges. Aalborg : Aalborg Univer- sity Press, 2006. 13 p.
3. Newman M.J. Problem Based Learning: an Introduction and Overview of the Key Features of the Approach // Journal of Veterinary Medical Education. 2005. No 32 (1). Р. 12–20.
4. Dolmans D., Schmidt H. What directs self-directed learning in a problem based curriculum// Problem Based Learning: a Research Perspective on Learning Interactions.Mahwah, NJ : Lawrence Erlbaum, 2000. Р. 251–262.
5. Barrows H. Generic Problem-Based Learning Essentials. 2004. URL: http://www.pbli.org/pbl/generic_pbl.htm.
6. Savin-Baden M. Facilitating Problem Based Learning: Illuminating Perspectives.Buckingham : Society for Research in Higher Education / Open University Press, 2003.
24. Mathematics Education Research
Paper
Levelling up Problem-solving Skills through Strategy Video Gaming and Reflection: An Intervention Study with Malaysian Form 4 Secondary School Students.
Siti Nadiah Binti Mohammad Johari
University of Cambridge, United Kingdom
Presenting Author: Binti Mohammad Johari, Siti Nadiah
In its recent Education Blueprint, the Malaysian Ministry of Education has emphasised the imperative to enhance national critical thinking skills. This call-to-action stems from the alarming low rankings in the PISA Problem-Solving Test, and mathematics test and reports from employers highlighting pervasive skill gaps. This research aims to explore a potential tool for developing problem-solving skills: Strategy Video Games (SVGs).
The integration of play in education systems is a growing trend in various nations, including China, the USA, and Denmark, recognising its significance in pedagogy (Mardell, Solis & Bray, 2019). Play, as highlighted by Prince (2017), is instrumental in children's learning and the development of problem-solving skills and fluid reasoning. Given the acknowledged benefits of play and the recognition of video games as a manifestation of play, thus, proposing the use of SVGs is not an outrageous idea to improve cognition. Digital games, specifically SVGs, not only enrich the learning experience but also foster skill development, enhance memorisation, and deepen understanding in STEM fields (Ishak, Din & Hasran, 2021). This approach aligns with the current digital landscape where today's youth spend significant time in the digital world, and SVG skills inherently mirror those demanded by the problem-solving process. However, despite this potential, there is limited empirical evidence linking SVGs to problem-solving skill improvement.
Most research to date on gaming and PS focuses exclusively on self-reported measures. For example, Adachi and Willoughby's (2013) previous study sought to investigate the correlation between strategy video gameplay frequency and adolescents' self-reported problem-solving skills. Their findings suggested a positive relationship: a higher video gameplay frequency was associated with higher self-reported problem-solving skills. The only study that has searched for such links using non-self-reports struggled to find an effect. In this project, Emihovich (2017) explored the impact of two distinct types of video gameplay, namely strategy role-playing video games (World of WarCraft) and brain-training video games (CogniFit), on undergraduates' problem-solving skills. However, the study found no significant effects on problem-solving. Nonetheless, Emihovic, Rogue and Mason (2020) noted that results could be different by prompting participants to actively recognise the strategies during gaming sessions. Therefore, by adding reflection sessions as a medium to transfer learnt problem-solving skills from SVGs to real-life situations could yield different outcomes. Research on metacognition and mindset suggests that combining SVGs with student reflection could further enhance skill development.
The utilisation of reflection sessions in problem-solving proves to be a valuable tool in education. Reflection, as defined by Bjuland (2004), involves the conscious consideration of personal experiences, aligning with Dewey (1933), Inhelder and Piaget (1958), Hiebert (1992), and Wistedt (1994) in the context of forming interactions between ideas and action. In education, reflection is the process of thoughtful examination and evaluation of one's experiences, thoughts, and actions to gain insight and make informed decisions for future practice (Chang, 2019). It plays a pivotal role in transforming experiences into the development of new skills, attitudes, knowledge, and capabilities (Gribbin, Aftab, Young, & Park, 2016).
Thus, this study hypothesises that strategy video gaming may affect both (1) externally assessed and (2) self-reported problem-solving skills when reflection sessions are employed. In response, this study investigated the relationship between SVG and two dependent variables: (1) externally assessed problem-solving skills (2) self-reported problem-solving skills. To test the power of student reflection on problem-solving development, it further assessed whether changes in these variables differed with or without engagement in reflection sessions.
RQ 1: Does playing SVGs affect (1) externally-assessed problem-solving skill assessment scores?
RQ1a: Do these effects change with the inclusion of reflection sessions?
RQ 2: Does playing SVGs affect the (2) self-reported problem-solving skill assessment scores?
RQ2a: Do these effects change with the inclusion of reflection sessions?
Methodology, Methods, Research Instruments or Sources UsedParticipants of the study were about 404 Form 4 pupils (15- to 16-year-olds) from nine (9) participating Malaysian National secondary schools. Participants were split equally across one control and two treatment groups. Using a randomised controlled trial (RCT) approach, participants were stratified into two groups based on gender (male and female) before they were randomised equally into the 3 groups (in control or intervention conditions).
To test the power of reflection, this research compared pre- and post-test scores of 3 groups: a control group ("A") that received no treatment; a group ("B") that played SVGs; and a group ("C") that played SVGs and engaged in supplemental of reflection sessions. Through this experimental design, we were able to monitor the possible effect (if any) of both playing SVGs and reflection on the development of self-perception of problem-solving skills and examined actual problem-solving skills.
Two instruments were used to measure the 2 variables of interest during pre-intervention and post-intervention. The external assessment measure employed in this study is the publicly accessible isomorphic test designed by the OECD for the 2003 iteration of the PISA Problem-Solving Test. To adapt it for this research, the test was divided into two sets, resulting in two distinct PISA Problem-Solving Tests. To assess students' self-reported problem-solving skills, the study employed the Problem-Solving Inventory (PSI) created by Heppner and Petersen (2011). This inventory comprises 32 items and utilises a 6-point Likert scale to gauge an individual's self-evaluation of their problem-solving competence, focusing on their perceived competency rather than their demonstrated abilities.
The intervention protocol involved gaming phases and reflection sessions. A gaming phase includes three (3) weeks of gaming session aimed at yielding about 5 hours of gaming duration. Within the 3 weeks, there were three reflection sessions (before, during and after reflection sessions) conducted. Before-reflection sessions was done before gaming sessions starts (in the first week), and in the second week, during-reflection session was done as a group discussion. After-reflection sessions was done at the end of each gaming phases. Before- and after-reflection sessions were done online individually. There were 4 intervention phases all together, each using four different strategy video games.
The analysis of the data used a quantitative technique, multiple regression, to assess the relationships between SVGs, reflection sessions, and outcome variables of interest. Ultimately, it attempts to cover gaps from previous studies and provide a guide to utilise SVGs in a school context.
Conclusions, Expected Outcomes or FindingsDue to COVID restriction policies, dosage, adherence, and participants' responsiveness, the quality of intervention delivery varied significantly. Nonetheless, the findings yielded interesting insight into the hypotheses.
There is some evidence that SVGs together with reflection sessions have the potential ability to affect actual Problem-solving skills.
RQ 1: Based on the statistical analysis, we can reject the null hypothesis and accept there is a significant difference in PISA Pre-post-test score difference means among the 3 groups, with a consideration that it is a positively weak model (R-squared =0.0248). Group C difference is significant at p=0.025. The post-hoc Tukey test revealed significant differences between Group C and Group B (p = 0.041), and near significant between Group C and Group A (p = 0.064).
All groups' mean score showed decline in PISA Problem-Solving score performance, but Group C performed slightly better by having the least amount of decline. Group B did not perform any differently than Group A .
RQ 2: Similarly, regression analysis showed that Group C is significantly different than the other groups, with a p value of = 0.018 with a weak model (R-squared =0.0271). Tukey's post hoc test revealed that Group C is significantly different than Group A (p = 0.054). However, Group B is not statistically significantly different from Group A and C.
Both findings in RQ 1 and 2 above may indicate that SVGs without the supplement of reflection session do not help in improving or developing Problem-Solving skills, as seen in PISA problem-solving scores.
In conclusion, these findings suggest that there is potential to utilise SVGs in developing competent problem-solvers, provided that SVGs are paired with reflection sessions to aid in transferring learnt problem-solving skills into real-life situations. However, there is a need to further delve into the findings, especially exploring the measurement of fidelity to ensure these results are not a result of positive placebo effect.
ReferencesAdachi, P. J. C., & Willoughby, T. (2013). More Than Just Fun and Games: The Longitudinal Relationships Between Strategic Video Games, Self-Reported Problem-Solving Skills, and Academic Grades. Journal of Youth and Adolescence, 42(7), 1041–1052. https://doi.org/10.1007/s10964-013-9913-9
Bjuland, R. (2004). Student teachers' reflections on their learning process through collaborative Problem-Solving in geometry. Educational Studies in Mathematics, 55 (1–3), 199–225. https://doi.org/10.1023/B:EDUC.0000017690.90763.c1
Chang, B. (2019). Reflection in Learning. Online Learning, 23(1). https://doi.org/10.24059/olj.v23i1.1447
Dewey, J. (1933). Why have progressive schools? Current History (1916-1940), 38(4), 441–448.
Emihovich, B. (2017). IMPROVING UNDERGRADUATES' PROBLEM-SOLVING SKILLS THROUGH VIDEO GAMEPLAY.
Emihovich, B., Roque, N., & Mason, J. (2020). Can Video Gameplay Improve Undergraduates' Problem-Solving Skills?. International Journal of Game-Based Learning (IJGBL), 10(2), 1-18.
Gribbin, J., Aftab, M., Young, R., & Park, S. (2016). Double-loop reflective Practise as an approach to understanding knowledge and experience. DRS 2016 International Conference: Future-Focused Thinking. 8, pp. 3181-3198. Design Research Society.
Heppner, P. P., & Petersen, C. H. (2011). Problem-Solving Inventory [Data set]. American Psychological Association. https://doi.org/10.1037/t04336-000
Hiebert, J. (1992). Reflection and communication: Cognitive considerations in school mathematics reform. International Journal of Educational Research, 17(5), 439–456.
Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence: An essay on the construction of formal operational structures (Vol. 22). Psychology Press.
Ishak, S. A., Din, R., & Hasran, U. A. (2021). Defining digital game-based learning for science, technology, engineering, and mathematics: a new perspective on design and developmental research. Journal of medical Internet research, 23(2), e20537.
Mardell, B., Lynneth Solis, S., & Bray, O. (2019). The state of play in school: Defining and promoting playful learning in formal education settings. International Journal of Play, 8(3), 232-236.
Prince, P. (2017). From play to Problem-Solving to Common Core: The development of fluid reasoning. Applied Neuropsychology: Child, 6(3), 224-227.
Programme for International Student Assessment. (2004). PISA Problem Solving for Tomorrow's World: First Measures of Cross-Curricular Competencies from PISA 2003. OECD.
Wistedt, I. (1994). Reflection, communication, and learning mathematics: A case study. Learning and Instruction, 4(2), 123–138.
24. Mathematics Education Research
Paper
Effect of Flipped Classroom Learning Approach on Mathematics Achievement and Interest Among Secondary School Students
Bakyt Alzhanova
NIS, Kazakhstan
Presenting Author: Alzhanova, Bakyt
The flipped classroom is a teaching technique that has gained worldwide currency during recent years. In a flipped approach, the information-transmission element of students’ learning is moved out of the classroom; instead, students view recorded lectures in their own study time ahead of the live session. This frees the class time for activities (such as discussion and problem-solving) in which students can apply their knowledge and potentially gives the teacher a better opportunity to detect their misconceptions.
According to the State Education Policy (Republic of Kazakhstan), mathematics is one of the fundamental subjects that all students must study up to higher education. Mathematics receives a lot of attention in the school curriculum from primary to secondary school, reflecting the importance of the subject in modern society. It is particularly disappointing that students consistently perform poorly in mathematics in internal and external examinations, despite the relative importance of the subject.
The purpose of this study, which was conducted at the Nazarbayev Intellectual School of Physics and Mathematics in the city of Aktobe, was to determine the effect of the “flipped classroom” approach on mathematics achievement and interest of students. Given this, a quasi-experimental design was used, specifically non-equivalent pretest-posttest control group design. The study’s participants were a sample of 56 learners selected from two classes purposively. Each two SS 1 classes, divided into experimental and control groups via balloting.
The following research questions guided the study.
1. What are the mean achievement scores of students who received mathematics instruction using flipped classroom approach and their peers in the control group?
2. What are the mean achievement scores of male and female students who received flipped classroom approaches?
3. What are the mean interest scores of students who received mathematics instruction using flipped classroom approach and their peers in the control group?
4. What are the mean interest scores of male and female students who received flipped classroom approach?
The following hypotheses guided the study.
1. Difference exists between the mean achievement scores of students who received mathematics instruction using flipped classroom approach and their peers in the control group.
2. Difference exists between the mean achievement scores of male and female students who received mathematics instruction using flipped classroom approach.
3. Difference exists between the mean interest scores of students who received mathematics instruction using flipped classroom approach and their peers in the control group.
4. Difference exists between the mean interest scores of male and female students who received mathematics instruction using flipped classroom approach.
Data were gathered through the instrumentality of the Mathematics Achievement Test (MAT) and Mathematics Interest Inventory (MII), which have reliability scores of 0.88 and 0.79, respectively. Prior to and following a six-week course of treatment, each group completed a pretest and posttest. SPSS, a statistical tool for social sciences, was applied to analyse the acquired data. The mean and standard deviation were utilised to report the study’s questions, and analysis of covariance (ANCOVA) was utilised to evaluate the hypotheses at a 0.05 significance level. Results established that learners taught mathematics utilising flipped classroom approach had higher mathematics achievement and interest scores than their peers taught using the conventional approach. Results also revealed that the achievement and interest scores of male and female learners who received mathematics instruction using flipped classroom approach were the same. Considering the findings, recommendations were given, among others, that mathematics teachers should use the flipped classroom approach to assist learners in boosting their achievement and interest in mathematics, especially in geometry.
Methodology, Methods, Research Instruments or Sources UsedThis quasi-experimental research study design used a non-equivalent control group for the pretest and posttests. The design was employed rather than randomly allo¬cating students to groups because it is impractical to do so in quasi-experimental research. A sample of 56 pupils (27 males and 29 females) was selected from two classes purposively.
The research instruments were Mathematics Achievement results. Test (MAT) and Mathematics Interest Inventory (MII). The researchers created 20 multiple-choice questions on the MAT, which served as the study's primary instrument. The MAT items were created using a test design to ensure adequate coverage of the subject matter of interest and to maintain consistent distribution across different levels of the cognitive domain. However, the MII was adapted from the mathematical calculations of Snow (2011). interest reserve. The MII consists of 20 items and uses a 4-point Likert scale with the following response options: strongly agree (4), agree (3), disagree (2), and strongly disagree (1). I developed two lesson plans/notes for the experimental and control groups. Also checked MAT, MII and lesson plans/notes. Both MAT and MII have been pilot tested. The reliability coefficient for the MAT was determined to be 0.88 using the Kuder-Richardson formula 20. However, the internal consistency of the MII was calculated using Cronbach's alpha and the reliability coefficient was found to be 0.79.
The treatment ran for four weeks. The fifth week saw the administration of the posttest. The posttest items are the same as the pretest items; however, they were rearranged to give them a new look and avoid memory effects. The posttest results were noted and utilised to present information on learners’ mathematics achievement and interest by gender and treatment group. The SPSS software version 28 was used to analyse the collected data. The mean (−X) and standard deviation (SD) were used to answer the study’s research questions, and analysis of covariance (ANCOVA) was utilised to test the hypotheses at a significance level of 0.05. The reason for the choice of ANCOVA was to establish equality of baseline pre-test data before the commencement of the treatment. ANCOVA helped to establish the covariates between the pre-test and post-test.
Conclusions, Expected Outcomes or FindingsThe findings revealed that students who received mathematics instruction using flipped classroom approach had their interest increased in the mathematics concept compared to their counterparts who received the same concept using the conventional method. Accordingly, a further test of hypothesis three established that learners in the experimental group held increased interest levels in the mathematics concept than their peers in the control group. Thus, it concluded that the flipped classroom approach successfully enhanced learners’ interest in the mathematics concept taught. The increased interest could have been caused by the students’ interpersonal interaction with video resources and materials in the flipped classroom environment.
Moreover, the study’s findings indicated that male learners exhibited more interest in mathematics than females when the flipped classroom approach was utilised. Consequently, further analysis by testing hypothesis four divulged no significant difference between the interest scores of male and female learners who received mathematics instruction utilising the flipped classroom strategy. The outcome of the no significant difference could be that both male and female learners showed the same degrees of interest and engagement in learning the mathematics concept.
The flipped classroom approach significantly enhanced learners’ achievement and interest in the mathematics concept taught. This was seen in the mean achievement and interest scores of students in the experimental group, which were higher than their counterparts in the control group. Again, the achievement and interest scores of male and female learners who received mathematics instruction using flipped classroom approach were the same. This means that learners of both sexes that utilised the flipped classroom approach benefited equally from the treatment. The study also explains to mathematics education specialists how the flipped classroom approach can help learners enhance their achievement and interest levels in mathematics, particularly geometry.
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