Developing Conceptual Understanding of Algebraic Fractions in Grade 9 Learners
<p>Many Grade 9 learners in South Africa encounter considerable challenges with algebraic fractions, frequently relying on memorized procedures instead of developing the profound conceptual understanding essential for success in higher-level mathematics. This descriptive qualitative case study explores how learners develop meaning from algebraic fractions and evaluates the efficacy of targeted instructional strategies in redirecting learners’ attention from procedural fluency to conceptual comprehension. Anchored in a constructivist framework that incorporates theories of conceptual change and cognitive conflict, the study investigates how error analysis, reflective discussion, and guided exploration facilitate the reorganization of learners’ prior knowledge. The study was conducted in a South African high school with thirty-six Grade 9 learners and one mathematics teacher as participants. Data were collected through field notes, observations, learner tasks, and semi-structured interviews. The intervention had an emphasis on connecting symbolic manipulation with visual representations and verbal reasoning to enhance learners’ understanding of algebraic fractions within real-world problem contexts. The findings indicate that learners initially depended on superficial strategies like cross-multiplication; however, organized opportunities for contextualized problem-solving, error analysis, and collaborative discourse allowed most of them to develop more substantial conceptualizations of equivalence, the role of the denominator, and factorization. This research provides evidence of integrated instructional strategies based on conceptual change, constructivism, and metacognition. The study offers evidence-based recommendations for developing instruction that connects foundational fraction knowledge with algebraic reasoning, thereby supporting diverse learners’ critical thinking, engagement, and mathematical agency.</p>
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631
- 10.1016/s0959-4752(00)00037-2
- Apr 30, 2001
- Learning and Instruction
On the cognitive conflict as an instructional strategy for conceptual change: a critical appraisal
- Research Article
31
- 10.1080/09589236.2021.1881460
- Jan 29, 2021
- Journal of Gender Studies
Ending gender violence against girls in South African schools is an ongoing challenge. In this paper, we report on findings from focus groups and in-depth interviews that explore girls’ accounts of gender violence in a South African township high school. Our findings illuminate the normalization of violence instigated by boys against girls: such violence is highly sexualized and complex in its manifestations. Girls were sexually harassed, subjected to violence and sexual coercion by their male peers in different spaces at school. Beyond simplistic binary positions through which girls are constructed as merely victims, some girls in the study engaged in the problematic discourse of victim-blaming; girls who frequent school spaces dominated by boys and girls who use drugs, such as dagga, were often stigmatized and blamed for the violence they experienced. Furthermore, evidence of female-on-female violence (fights and humiliation) that occurred in the context of heterosexual competition came to light during the study. This kind of violence reinforced the subordination of girls in the broader hetero-patriarchal system. We conclude the paper by providing some recommendations towards addressing the complex manifestations of school-based violence against girls.
- Research Article
71
- 10.1187/cbe.10-06-0082
- Jan 1, 2010
- CBE Life Sciences Education
“I have to teach someone to make a peanut butter and jelly sandwich. How am I supposed to do that? What should I start with? How can this be so hard?” I have found that teaching anything to another person is rife with far more decisions and dilemmas than I could have ever imagined at first. Years ago, I had a college roommate who wanted to participate in a summer teaching program. For her interview, she had to develop a lesson plan to teach someone else how to make a peanut butter and jelly sandwich. Have you ever thought about teaching someone else how to make a peanut butter and jelly sandwich? She had asked for my input, and once we started to really consider the possibilities, our minds reeled. How would you start? What would you do first? Next? After that? Who was the learner anyway? And had they made a sandwich before? Were they allergic to peanuts? How old were they? Should we let them have a knife? Should we show them how first? Talk them through it? Let them have a go at it on their own? Should we first teach them the names of all the tools and things we were going to use? Should we ask them why they needed to learn how to make a peanut butter and jelly sandwich in the first place? What were the critical issues in teaching someone how to make a peanut butter and jelly sandwich? Much like in the “PBJ Dilemma” as we came to call it, there are many decisions to be made in designing effective learning experiences in undergraduate biology classes—and instructors are making these decisions constantly. It can seem overwhelming, yet the research literatures from cognitive science, psychology, and science education about how people learn suggest guidelines about constructing effective learning experiences (National Research Council [NRC], 1999 ). Much like the PBJ Dilemma, the order in which we decide to do things with students when we teach is critical, yet the order of things happening in a class session often goes undiscussed and unexamined. At first glance, the most pressing teaching dilemmas in our biology classrooms—student motivation, student retention of information, student understanding of difficult concepts—may seem unrelated to the order in which things are happening; however, what we do first, second, third, and so on can have many ramifications. For many instructors who have primarily learned from and used a lecture-based teaching approach, considerations of order have been primarily about the order of ideas. With the increasing use of active-learning strategies, class sessions are moving from having a single component—a lecture—to having many components over the course of even 50 minutes (e.g., a video clip, a pair discussion on a biology-based problem, a clicker question, a mini-lecture, and a final index card reflection). So, what is the optimal order for sequencing these elements to maximize student learning of biology?
- Research Article
199
- 10.1187/cbe.05-02-0068
- Jun 1, 2005
- Cell Biology Education
Underpinning science education reform movements in the last 20 years—at all levels and within all disciplines—is an explicit shift in the goals of science teaching from students simply creating a knowledge base of scientific facts to students developing deeper understandings of major concepts within a scientific discipline. For example, what use is a detailed working knowledge of the chemical reactions of the Krebs cycle without a deeper understanding of the relationship between these chemical reactions of cellular respiration and an organism’s need to harvest energy from food? This emphasis on conceptual understanding in science education reform has guided the development of standards and permeates all major science education reform policy docu
- Research Article
- 10.47348/sajmet/2024/i1a1
- Jan 1, 2024
- South African Journal of Maritime Education and Training
This study examines the benefits of teaching and learning maritime economics as a subject in South African high schools since official approval was given by the Minister of Basic Education in 2009. Initially piloted in 1995 at Simon’s Town School’s Lawhill Maritime Centre, offering maritime economics as a school subject has expanded to 34 high schools across four provinces, namely Eastern Cape, Gauteng, KwaZulu Natal, and Western Cape. Using a qualitative research methodology involving semi-structured interviews, the study reveals several significant benefits, including increased maritime career awareness, diversification of the previously white male-dominated maritime sector, enhanced critical thinking among youth, indirect contributions to economic growth and ensuring a steady supply of partially trained maritime professionals. The research confirms that maritime economics education supports South Africa’s mission to become a maritime nation, while aligning with Africa’s Integrated Marine Strategy (AIMS) 2050, Agenda 2063: The Africa We Want and the International Maritime Organization’s (IMO) mandate to ensure sufficient maritime professionals globally. The study concludes that offering maritime economics at the high school level creates exciting career opportunities, reduces youth unemployment and promotes general maritime awareness.
- Research Article
- 10.38140/ijsie.v2i2.1875
- Jul 31, 2025
- International Journal of Studies in Inclusive Education
Research has demonstrated that parents are critical in transforming cisnormative schooling cultures. However, South African literature has not explored how parents want gender diversity included in South African high schools. This study aims to give voice to parents of South African children of high school age and gauge their understanding of cisnormative schooling culture and how it can be challenged. To reach the objective, this study addressed the question: In what ways do both parents of trans and cis learners understand cisnormative schooling cultures in South African high schools? A qualitative research design was used to gather data through focus group interviews with nine parents with different occupations, such as police, teaching, religious preachers, among others, in a rural part of Free State province. Queer theory guided the study, and thematic analysis was used to identify themes that came out of the data collected. Findings suggest that parents acknowledge that a cisnormative schooling culture is a barrier to the promotion of gender diversity in South African high schools. Furthermore, findings reveal that infrastructure and school policies contribute to a delay in promoting an inclusive schooling environment for both trans learners and cis learners. This research recommends that future research studies should recruit parents from diverse demographics to capture different views on how queering cisnormative schooling culture can be achieved.Keywords: Cisnormative schooling, Gender diversity, High schools, Parental understanding, Queering
- Research Article
14
- 10.13189/ujer.2021.090509
- May 1, 2021
- Universal Journal of Educational Research
Technology is embraced as an integral part of modern society, and hence it is also important for education to integrate various aspects of technology into teaching and learning. The South African National Development Plan (NDP) also prescribes the inclusion of quality technology to enhance the classroom experiences of both teachers and learners. GeoGebra is one of the preferred mathematics software in South African high schools. This qualitative study explores the challenges of teachers in the integration of GeoGebra in the teaching of mathematics in South African high schools. Using interpretivism as a research paradigm, we listened to and recorded the views of teachers about challenges they experienced in the integration of GeoGebra. The data was elicited from four purposively selected teachers from the Bojanala District in the North West Province of South Africa by using unstructured interviews which were transcribed, coded and categorised into relevant themes. The selected teachers signed the consent forms as part of their willingness to participate voluntarily in the study. The study supports the view that teachers are pivotal factors in the integration of GeoGebra and hence the need to understand their challenges. The key finding revealed was that South African high schools were being robbed and vandalised of ICT equipment because of security issues. Further, each school owned only one data projector which stifles efforts to strengthen teachers' knowledge and skills in implementing the integration of GeoGebra into mathematics lessons. Consequently, this loss of equipment disadvantages teachers and learners concerning the integration of GeoGebra into mathematics lessons because learners did not have computers for exploring and experimenting, and teachers are becoming demotivated due to insufficient resources and a lack of modern skills to make mathematics lessons interesting and productive.
- Conference Article
12
- 10.1063/1.2177037
- Jan 1, 2006
- AIP conference proceedings
With proper context settings, instructors need to guide students to recognize explicitly cognitive conflicts among students’ existing understandings and new observations. To study this issue, we have developed an easy‐to‐use instrument, the in‐class Conflict and Anxiety Recognition Evaluation (iCARE), for monitoring the status of students’ cognitive conflicts and anxiety in the context of Physics by Inquiry (PBI) classes. Using iCARE, we investigate what types of cognitive conflict is constructive or destructive in conceptual change when college students are confronted with anomalous situations in a PBI class. In this research, we will present our results about the relationship between students’ prior knowledge and their conceptual change and the relationship between students’ types of cognitive conflicts and their conceptual change.
- Conference Article
- 10.1109/icacce.2016.8073750
- Nov 1, 2016
Less is known about reporting cyber threats in high schools because studies on cyber threats are focusing more on; how to prevent and mitigate negative behavior online, intervention and awareness programmers. Reporting cyber threats has been identified as a major problem amongst learners in the past few years. This paper, therefore, reviews some recent findings and discusses general concepts relevant to cyber threat reporting procedures and in the South African (SA) high schools context. The review is using the data that is currently available, for example; conference papers, journals, articles, books, online sources, dissertations, theses, educational and governmental documents and media publications. The literature survey has shown the short comings in the reporting of cyber threat incidents. As a result of this study, challenges have been highlighted and open issues indicated for further research. The results from this paper are not intended to be exhaustive as the research in this area is an on-going process. It should also be acknowledged that even the empirical research in this area is still evolving and therefore needs to be considered with a critical eye on operationalization and methodology. The intent of this research was to generate scholarly interest in the reporting of cyber threats incidents and therefore should be viewed simply as a platform on which further research efforts should be built.
- Conference Article
4
- 10.18260/1-2--22576
- Sep 4, 2020
The Effect of Inquiry-Based Activities and Prior Knowledge on Undergraduates’ Understanding of ReversibilityThis NSF funded (DUE 0717536) study investigates the role of prior knowledge and the use ofinquiry-based activities and their method of implementation to reduce misconceptions in five keyareas of thermodynamics (Entropy, Reversibility, Equilibrium and Steady State, Internal Energy,and Enthalpy), with a more detailed focus on reversibility. There is documented evidence ofproblems understanding heat, temperature, and energy concepts. Even after instruction,undergraduate engineering students have been found to still hold misconceptions aboutthermodynamic concepts. Previous research has shown that it is difficult to repair thesemisconceptions using a lecture-based pedagogy. One promising approach is the use of inquiry-based activities however; the way these activities are implemented can impact outcomes andprevious research has shown that faculty does not always implement activities as they areinstructed. The prior knowledge students bring to the classroom can also represent a challengewhen trying to alter these misconceptions. It would be anticipated from research that studentswith some prior knowledge from other engineering courses should have a better understanding ofthermodynamic concepts.A quasi-experimental design was used to analyze pre-post data from 26 different undergraduate,thermodynamics classes from multiple institutions, some who used a series of inquiry-basedactivities in each key concept area as part of their instruction and some who did not. Those usingthe inquiry-based activities were given a set of two activities along with worksheets andexplanatory materials for each of the five concept areas where misconceptions had previouslybeen identified, including reversibility. The Concept Inventory for EngineeringThermodynamics (CIET) and its Reversibility sub-test were used to measure conceptual change.Both have been found to have sufficiently high estimates of internal consistency reliability to beused for research purposes. Data was also collected on whether students had previously takenfluid dynamics and heat transfer courses. Finally, instructors were asked to indicate how theyhad implemented a packet of inquiry-based activities specifically designed to teach reversibility.Results showed that conceptual understanding of thermodynamics (five concept areas) asmeasured on the CIET was significantly higher for the inquiry-based activities groups than theno inquiry-based (control) groups, although the effect size was small. Post-test scores weresignificantly higher for students who had previously taken courses in fluid dynamics and heattransfer when compared to those who had not. There was a significant difference between theinquiry-based and control groups on students’ understanding of reversibility and theirunderstanding of this concept area was impacted by their having taken fluid dynamics and heattransfer. The way in which the professors implemented the reversibility activities was collectedand evaluated.
- Research Article
131
- 10.1023/b:rise.0000021001.77568.b3
- Mar 1, 2004
- Research in Science Education
In this study, we defined and quantified the degree of cognitive conflict induced by a discrepant event from a cognitive perspective. Based on the scheme developed, we investigated the relationship between cognitive conflict and conceptual change, and the influences of students' cognitive characteristics on conflict in learning the concept of density. Subjects were 171 seventh-grade girls from two city middle schools in Korea. Tests regarding logical thinking ability, field dependence/independence, and meaningful learning approach were administered. A preconception test and a test of responses to a discrepant event were also administered. Computer-assisted instruction was then provided to students as a conceptual change intervention. A conception test was administered as a posttest. In analysing students' responses to the discrepant event, seven types of responses were identified: Rejection, reinterpretation, exclusion, uncertainty, peripheral belief change, belief decrease, and belief change. These types were then ordered into four levels. The results indicated that there existed a significant correlation between cognitive conflict and conceptual change. t-test results revealed that there were statistically significant differences in the degree of cognitive conflict by the levels of students' logical thinking ability and field dependence/independence. Meaningful learning approach, however, was found to have no statistically significant effect on cognitive conflict. Educational implications are discussed.
- Research Article
- 10.5012/jkcs.2008.52.5.561
- Oct 20, 2008
- Journal of the Korean Chemical Society
In this study, we investigated the influences of students' cognitive characteristics on conceptual change processes which incorporate cognitive conflict strategy using discrepant events.In order to examine students' cognitive characteristics, the tests regarding logical thinking ability, field dependence-independence, and learning approach were administered to 517 seventh graders.A preconception test of density was also administered.Students' cognitive responses and situational interest to a discrepant event were then examined.After introducing an alternative hypothesis, students' cognitive responses and situational interest to the discrepant event were measured again.The students studied the concept of density individually with a researcher-made printed material.The tests of attention, effort, and conceptual understanding were administered after the intervention.The students (N=262) who had been found to possess the target misconception were selected from the subjects.The results revealed that logical thinking ability had larger direct effect on conceptual understanding than on cognitive conflict and situational interest.Field dependence-independence was found to have no substantial effects on conceptual change.Deep approach to learning, however, indirectly influenced conceptual understanding via situational interest and attention.
- Research Article
419
- 10.1002/tea.3660200804
- Jan 1, 1983
- Journal of Research in Science Teaching
One of the factors affecting students' learning in science is their existing knowledge prior to instruction. The students' prior knowledge provides an indication of the alternative conceptions as well as the scientific conceptions possessed by the students. This study is concerned primarily with students' alternative conceptions and with instructional strategies to effect the learning of scientific conceptions; i.e., to effect conceptual change from alternative to scientific conceptions. The conceptual change model used here suggests conditions under which alternative conceptions can be replaced by or differentiated into scientific conceptions and new conceptions can be integrated with existing conceptions. The instructional strategy and materials were developed for a particular student population, namely, black high school students in South Africa, using their previously identified prior knowledge (conceptions and alternative conceptions) and incorporate the principles for conceptual change. The conceptions involved were mass, volume, and density. An experimental group of students was taught these concepts using the special instructional strategy and materials. A control group was taught the same concepts using a traditional strategy and materials. Pre‐ and posttests were used to assess the conceptual change that occurred in the experimental and control groups. The results showed a significantly larger improvement in the acquisition of scientific conceptions as a result of the instructional strategy and materials which explicitly dealt with student alternative conceptions.
- Research Article
- 10.38140/ijspsy.v5i2.1749
- Jun 30, 2025
- International Journal of Studies in Psychology
It is important to note that transgender learners experienced gender discrimination, misgendering, and bullying at South African High Schools. Based on parental perspectives, this paper presents the strategies that can be used in South African high schools to promote gender diversity. This considers reconceptualisation of gender to enable parents to challenge the factors that act as barriers to the promotion of gender diversity and ensure that the schooling environment is an inclusive one for both trans and cis learners. This paper thus suggests a strategic step that can be used to queer religion and culture to promote gender diversity. This study provides strategies in a three-step guide that parents can use to transform South African high schools into more inclusive environments and to queer cisnormativity.
- Research Article
- 10.29303/jpm.v20i5.9598
- Aug 7, 2025
- Jurnal Pijar Mipa
Chemical literacy is a key component of scientific literacy, enabling individuals to understand, evaluate, and apply chemical concepts in real-life situations. This study investigates the relationship between students' prior knowledge and their chemical literacy on acid-base topics in senior high school. The study employed a quantitative descriptive method with a correlational approach, involving 99 eleventh-grade students from three accredited private schools in Padang City, Indonesia. Two validated instruments were used to collect data: the Structured Essay Diagnostic Test of Chemistry (SEDToC) to assess prior knowledge, and a discourse-based chemical literacy test. Data analysis included descriptive statistics and Spearman's Rank correlation. Results revealed a very weak and statistically insignificant positive correlation between prior knowledge and chemical literacy (rₛ = 0.1454; p > 0.05), with a coefficient of determination (r²) of 2.1%. Stoichiometry emerged as the subtopic with the highest level of understanding (41.68%), while chemical bonding was the lowest (3.05%). Although most students demonstrated procedural understanding, many struggled with contextual and discourse-based questions that required higher-order thinking. A high rate of misconceptions (36.59%) was also identified, which negatively affected students’ ability to reason and interpret chemical phenomena accurately. This study highlights that conceptual understanding alone is insufficient to support chemical literacy. The novelty of this research lies in its focus on chemical literacy as a multidimensional construct, beyond mere content mastery. The findings suggest that instructional strategies should not only strengthen prior knowledge but also integrate real-world contexts and promote critical thinking. Future research is recommended to explore other contributing factors such as motivation, metacognitive awareness, and teaching approaches that could better foster students’ chemical literacy. To support this, educators should design learning strategies that go beyond reinforcing prior knowledge and emphasise contextual, inquiry-based, and reflective approaches to develop students' comprehensive chemical literacy.