Developing Mathematics Achievement and Inductive Reasoning: A Proposed Technique According to Brain Compatible Learning Theory

The aim of the study was to find the role of technology in teaching and learning mathematics in public secondary schools of Rwanda. It has three specific objectives: To assess the level of using technology in teaching and learning mathematics in public secondary school in Rwanda, to examine the levels of students learning achievement due to use of Technology in mathematics subject in public secondary school of Rwanda and to analyze the influence of technology on students ‘mathematical academic achievement in mathematics in public secondary schools in Rwanda. This research would benefit the Rwandan government, educational planners, policymakers, teachers, students and future researchers. The study took Quantitative method to collect the data, descriptive research design was used, target population were 854, sample size was 272 which include 4 teachers and 268 students from three secondary schools, Questionnaire was used as the data collection tools. Statistical Package for Social Sciences or SPSS version 21 used to analyze the data, which was then displayed in the form of tables, the findings of my studies Teachers on the level of using technology in teaching and learning mathematics for teachers 25% were strong disagree that the they have not been using technology tools for teaching mathematics at all, 25% were disagree that the I have not been using technology tools for teaching mathematics at all, the students on the levels of students learning achievement due to the use of Technology in mathematics subject, 41% were agree that Technology enhanced student engagement in the learning process in classroom and 53% were strong agree that Technology enhanced student engagement in the learning process in classroom, teachers on the levels of students learning achievement due to the use of Technology in mathematics subject in public secondary school,75% were strong agree that Teachers can effectively integrate technology tools, 50% were agree that Technology into their mathematics instruction to support diverse learners, teachers on the influence of technology on students ‘mathematical academic achievement in mathematics, 75% were strong agree that the integration of technology impact students’ engagement and motivation in learning mathematics, 50% were agree that the accessibility of technology resources both inside and outside the classroom influence students’ proficiency in mathematical concepts and skills and students on the influence of technology on students ‘mathematical academic achievement in mathematics, 23% were agree that the integration of technology impact students’ engagement and motivation in learning mathematics and 55% were strong agree that the integration of technology impact students’ engagement and motivation in learning mathematics, as conclusion teachers and students was used to form a conclusion about how to address the second research questions on What is the levels of students learning achievement due to the use of Technology in mathematics subject ’’it were conclude that the Technology enhanced student engagement in the learning process in classroom and teachers and students was used , Teachers should recognize the transformation potential of technology in enhancing mathematics education and The Ministry recommends providing ongoing professional development for teachers to ensure they are proficient in using technology to enhance mathematics instruction.

In his song “Still Crazy after All These Years,” Paul Simon (1974) writes, “I seem to lean on old familiar ways.” Shipley's article “Algebra in the Elementary Schools,” written in 1912, offers the opportunity for us to reflect on what we have accomplished, what we have learned, and what remains hazy even 100 years later with respect to teaching and learning mathematics. Do we still lean on old familiar ways of teaching algebra? This article has many messages that are relevant to us today in thinking about algebra and about teaching and learning mathematics in general. In addition, it raises the following questions: How does Shipley's conception of algebra compare with our conception of it today? What broader issues does he address that are still prevalent today? How far have we come in our implementation of his ideas? What aspects of teaching and learning mathematics in elementary school remain hazy after all these years?

To achieve a successful mathematics education through the implementation of the school mathematics curriculum, the teacher’s beliefs emanating from their experiences (including learning theories) with their environment should be a considerable factor. This is to ensure that all learning situation in mathematics classroom generate understanding among the individuals involve for it to be meaningful. In this paper my goal is to highlight on some issues which are of great importance to mathematics education as a field of study. The issues in focus are; theory and practice, the role of theory in mathematics education research, some widely used learning theories in mathematics education, theories of models and modelling and their impact on mathematics research, teaching and learning, the aims of teaching and learning mathematics, and the status of mathematics education as knowledge field.

The home environment refers to the physical, emotional, and psychological atmosphere in which a child grows up. The home environment plays a vital role in shaping a student’s performance in mathematics. National Policy on Education (NPE, 1986) has envisaged that, “Mathematics should be visualized as the vehicle of communication to train a child to think, to reason, to articulate and to analyses logically. It should be treated as a concomitant to any subject involving analysis and synthesis. Different types of problem solving are critical to the discussion of problem solving and student achievement because of the potentially different impact on student achievement. The present study aimed to find out the relationship between achievement in mathematics and problem solving ability of high school students. A sample of 434 high school students was selected for data collection. Achievement Test in Mathematics constructed and validated by the investigators and Home Environment Scale constructed and validated by the investigators. Descriptive and differential analysis for further analysis and interpretation. Findings of the study revealed that High School students’ level of Achievement in Mathematics is average. High School students’ level of Problem Solving Ability is average. There is no significance difference between male and female High school students in their Achievement in Mathematics and Home environment. There is a significance difference between rural and urban High school students in their Achievement in Mathematics. There exist a positive and significant relationship between achievement in mathematics and Home Environment among high school students.

Abstract: The purpose of this research was to determine the effect of learning models on mathematics achievement viewed from student attitude toward mathematics. The learning models compared were Team Assisted Individualization (TAI) based Assessment for Learning (AfL), TAI, and conventional learning model. The research was quasi experimental. The population of this research was all students of grade VIII State Junior High School of the District Karanganyar, academic year 2013/2014. The samples in this research were SMPN 1 Tasikmadu, SMPN 2 Jaten, and SMPN 2 Colomadu taken by stratified cluster random sampling. Instruments used to collect data were mathematics achievement instrument test and questionnaires students toward mathematics instrument. Data analysis technique used hypothesis test with two-way analysis of variance with unbalanced cells. From the results of the analysis, can be concluded that: 1) the learning achievement in mathematics of the students who were learning mathematics with cooperative learning model TAI Based AfL were better than the ones who were learning mathematics with cooperative learning model TAI and conventional learning model, however the students who were learning mathematics with cooperative learning model TAI were better than the ones who were learning mathematics with conventional learning model, 2) the learning achievement in mathematics of the students with the high attitude toward mathematics were better than the ones with the medium and low attitude toward mathematics, however the students with the medium attitude toward mathematics were better than the ones with the low attitude toward mathematics, 3) in the cooperative learning model TAI Based AfL, the learning achievement in mathematics of the students with ones who have the high attitude toward mathematics were better than the students with the low attitude toward mathematics, and students with the medium attitude toward mathematics were as good as the ones who have low attitude toward mathematics as well. In the cooperative learning model TAI and conventional learning model, the students with the high, medium, and low attitude toward mathematics had the same achievement in learning mathematics, 4) in the students with the high attitude toward mathematics, the learning achievement of the students who were learning mathematics with ones who have cooperative learning model TAI Based AfL were better than the students were learning mathematics with cooperative learning model TAI, the students who were learning mathematics with cooperative learning model TAI had the same achievement in learning mathematics with conventional learning model, and the students who were learning mathematics with cooperative learning model TAI Based AfL had the same achievement in learning mathematics with cooperative learning model TAI. The students with the medium and low attitude toward mathematics had the same achievement in learning mathematics among the ones who were given the cooperative learning model TAI Based AfL, TAI, and conventional learning model. Keywords: Team Assisted Individualization (TAI), Assessment for learning (AfL), students attitude toward mathematics, achievement learning mathematics.

Teaching Secondary and Middle School Mathematics combines the latest developments in research, standards, and technology with a vibrant writing style to help teachers prepare for the excitement and challenges of teaching secondary and middle school mathematics today. In the fully revised fifth edition, scholar and mathematics educator Daniel Brahier invites teachers to investigate the nature of the mathematics curriculum and reflect on research-based "best practices" as they define and sharpen their own personal teaching styles. The fifth edition has been updated and expanded with a particular emphasis on the continued impact of the Common Core State Standards for Mathematics and NCTM’s just-released Principles to Actions, as well as increased attention to teaching with technology, classroom management, and differentiated instruction. Features include: A full new Chapter 7 on selection and use of specific tools and technology combined with "Spotlight on Technology" features throughout clearly illustrate the practical aspects of how technology can be used for teaching or professional development. Foundational Chapters 1 and 2 on the practices and principles of mathematics education have been revised to build directly on Common Core State Standards for Mathematics and Principles to Actions, with additional references to both documents throughout all chapters. A new Chapter 4 focuses on the use of standards in writing objectives and organizing lesson plan resources while an updated Chapter 5 details each step of the lesson planning process. A fully revised Chapter 12 provides new information on teaching diverse populations and outlines specific details and suggestions for classroom management for mathematics teachers. Classroom Dialogues" features draws on the author’s 35-year experience as an educator to present real-world teacher-student conversations about specific mathematical problems or ideas "How Would You React?" features prepares future teachers for real-life scenarios by engaging them in common classroom situations and offering tried-and-true solutions. With more than 60 practical, classroom-tested teaching ideas, sample lesson and activities, Teaching Secondary and Middle School Mathematics combines the best of theory and practice to provide clear descriptions of what it takes to be an effective teacher of mathematics.

This study investigated the predictive potency of teachers’ assessment practices on secondary school students’ academic achievement in Mathematics in the Nsukka Education Zone, Enugu State, Nigeria. A correlational survey research design was adopted. A sample size of 342 Senor Secondary Two (SS II) Mathematics students in Nsukka education zone was used for the study. Teachers’ Assessment Practice Questionnaire (TAPQ) and Mathematics Achievement Test (MAT) were used for data collection. Reliability coefficients of 0.93 and 0.91 were obtained for TAPQ and MAT respectively. Linear regression analysis was used to answer research questions 1-5 while research questions 6-7 was answered using multiple regression analysis. Regression t-test was used to test hypotheses 1-5, while hypotheses 6 was tested using regression ANOVA. All hypotheses were tested at 0.05 level of significance. The findings revealed that formative assessment predicted 38.4%, diagnostic assessment predicted 37.1%, peer-assessment predicted 32%, and self-assessment predicted 26.4% of the variation in students’ academic achievement. Summative assessment accounted for 5.2% of the variance. Importantly, the combined effect of all assessment practices jointly predicted 65.7% of students’ achievement, indicating a significant and substantial influence of teachers’ assessment practices on Mathematics achievement. The study concludes that assessment practices, particularly when used in combination, play a critical role in enhancing students’ understanding, engagement, and learning outcomes in Mathematics. The study recommends that teachers adopt an integrated approach to assessment by combining formative, summative, diagnostic, self-, and peer-assessment strategies, and that educational authority provide professional development and policy support to strengthen the effective implementation of these practices. The findings highlight the importance of diverse and continuous assessment strategies as tools for improving academic achievement in secondary school Mathematics.

Objectives. This study examined the impact of socio-economic status (SES)—specifically parental education, municipal quality of life, and settlement size—on Czech grade-school students’ performance in four cognitive domains (inductive reasoning, quantitative reasoning, associative memory, spatial skills), on their term-end grades in Czech, mathematics, and English, and on the likelihood of being labeled as exceptionally gifted via formal counseling-center diagnoses versus test-based screening.Sample and settings. A convenience sample of 11332 Czech primary-school children (grades 1–6; M_age = 10.32, SD = 1.05; 48.3 % girls) was tested during the 2022–2023 school year. Assessments were administered in supervised computer-room sessions using the web-based, game-based Invenio diagnostic system. Parents completed an online SES questionnaire and provided students’ most recent grades and information about officially assigned labels.Hypotheses. H1: Parental education and the overall quality of life in the school’s district predict children’s scores in inductive reasoning, quantitative reasoning, associative memory, and spatial skills tests. H2: Parental education is associated with children’s school grades, independent of their measured cognitive abilities. H3: Parental education and the overall quality of life in the school’s district predict the likelihood of children being formally labeled as high-ability learners.Statistical analyses. Pearson correlation coefficients quantified associations among SES indicators and each cognitive domain. Multiple linear regressions estimated the unique effects of parental education, municipal quality, and settlement size on IQ-standardized test scores. Logistic regressions predicted (a) the odds of achieving top grades (grade 1) in each subject and (b) the odds of formal versus screening-based gifted identification.Results. Parental education emerged as the strongest SES predictor of cognitive performance (β = .24 for inductive/quantitative reasoning; β = .21 for spatial skills; β = .12 for associative memory) and of top grades (OR = 1.62–1.77), whereas cognitive abilities yielded only modest grade effects (OR = 1.01–1.04). Spatial skills and associative memory were least sensitive to SES. Formal gifted identification odds increased approximately 2.48-fold per parental-education level (p < .001), while screening-based identification showed reduced SES bias (ORs = 1.34–2.03 across domains).Limitations. The non-representative, consent-based sample may have introduced selection bias; reliance on teacher-assigned grades lacked standardization across schools; SES was indexed by parental education and regional indicators, lacking further details of family background; municipal quality of life was tied to school location rather than each child’s home; and potential school-level influences (e.g., resource availability, teaching quality) were not examined.

This study examined social Networking and Students’ Academic achievement in Senior Secondary Schools in Ikom Education Zone, Cross River State, Nigeria. The Independence variables examine were: use of Facebook and YouTube while the dependent variable was students’ academic achievement in Mathematics. To achieve the purpose of the study, two research questions and two hypotheses were formulated to guide the study. Literature was reviewed based on the variables. The research design adopted was survey research design. One hundred and sixty-five (165) SS II students who offered Mathematics in public secondary schools were randomly selected for the study. The instruments used for data collection was a 20 – items questionnaire titled “Social Networking and Students’ Academic Achievement Questionnaire (SNASAAQ), and achievement test in Mathematics constructed by the researchers, Independent t-test was used as statistical tool for data analysis. Each of the hypotheses was tested at .05 level of significance. The findings of the study revealed that the use of Facebook and YouTube significantly influenced students’ academic achievement by SS II students in Mathematics. Based on the findings, it was recommended among other things that government/school proprietors should provide in-service training for Mathematics teachers to enhance achievement especially on use of social networking.

Teaching and learning mathematics through problem-based learning is highly promoted all around the world. This student-centered approach highlights the fact that students are sense makers. In this regard, the contexts presented in the problems given to students should serve the purpose of learning by providing meaning to construct. On the other hand, the contexts should also serve the purpose of teaching mathematics by designing meaningful problems for students and guiding them in the learning process of making sense of mathematics within a meaningful context. This book chapter discusses three different uses of contexts to enhance problem-based learning when teaching mathematics: for designing mathematical tasks, for interpreting or situating students’ thinking, and for developing citizenship competencies. In order to illustrate the three different uses, two learning situations will be presented and analyzed using these lenses: the culture present in contexts, the mathematical knowledge targeted, and critical thinking as part of citizenship competencies.

With the framework of the cognitive load theory, researchers have shown students in an experimental condition learned mathematics with worked-out examples significantly outperformed those learning mathematics in the control condition. The current consists of two experimental studies with 66 fifth grade students as participants. In Study 1, participants were divided into an experimental and a control condition, learning mathematics with the worked-out example instruction and traditional instruction, respectively. The result shows an aptitude-treatment interaction, that is, the worked-out example method was more beneficial for students for students with lower prior achievement, while the traditional method was more beneficial for students with higher prior achievement in mathematics. In Study 2, students were assigned to three conditions to learn mathematics, a condition with worked-out examples presented with PowerPoint, a condition with worked-out examples presented with hard copies, and a condition with traditional instruction. The results indicated that the students who received instruction with the worked-out example presented via PowerPoint gained significantly higher grades in a posttest of the mathematical achievement test than those who received the traditional instruction.

Purpose:
 The purpose of the study is to investigate how the "flipped" classroom impacts Primary 3 Mathematics students' learning and achievement. 
 Methodology:
 In this study, mathematics instruction in Primary 3 was recontextualised using the Flipped Classroom methodology. Using pre- and post-test methodology, a quasi-experimental research design was used with 81 lower essential school students from two private primary schools. Data collection utilised three designed instruments: the Mathematics Achievement Test (MAT), Traditional Flipped Classroom Instructional Guide (TFCIG), and Control Group Instructional Guide (CGIG). The test-retest reliability of MAT was established at 0.75. The study explored the potential benefits of the flipped classroom model in improving pupils' mathematics achievement and interest within the three primary classes. Two hypotheses were formulated and analysed using descriptive statistics for demographics and Analysis of Covariance (ANCOVA) at a 0.05 significance level.
 
 
 
 Findings:
 The findings shed light on the success of using a flipped model to recontextualise math classes at the Primary 3 level in Mathematics in Ilorin South Local Government Area of Kwara State, Nigeria. The findings indicate a significant positive effect of traditional flipped classroom instructional strategy on pupils' academic achievement in Mathematics. However, there was no significant interaction effect between treatment and gender. The conclusion is that the traditional flipped classroom instructional strategy improves pupils' academic achievement, irrespective of gender. This study found a statistically significant effect size for the flipped classroom instructional strategy.
 Unique Contributions to theory, policy and practice:
 This research contribution is twofold. Firstly, the study advances our understanding of the advantages, difficulties, and prospective improvements of flipped learning in Mathematics classes in Primary schools. Secondly, this study helps teachers understand how to integrate the flipped classroom within the learning and teaching system.
 
 The study recommends that school teachers or educators undergo training to implement traditional flipped classroom instructional strategies in math classes effectively.

Role of inductive reasoning, gender, learning satisfaction, and educational and career preference in predicting scientific competency in high school

Purpose: Underperformance of secondary school students in Mathematics is a great concern to all stakeholders in education sector. Efforts have been made by many researchers to arrest this situation, but it seems unresolved. Therefore, this study examined discipline and professional development as prognosticators of student’s academic achievement in mathematics. The study was led by four hypotheses and relevant literatures were reviewed.
 Methodology: Survey research design was used, and the population comprised all secondary schools in South-West Nigeria. Multistage sampling technique was employed: Simple random sampling technique was used to select three (3) out of the six (6) states in South-West, five (5) Local Government Area (LGA) from each state and from each LGA ten (10) schools and 10 students from each school was selected. In all 3 states, 15 LGA, 150 schools and 1500 students were used. Also, purposive sampling method was used to select two (2) teachers of Mathematics from each school. Thus, a total of three hundred (300) teachers of Mathematics were used for the study. Data collection was done by using Discipline and Professional Development Questionnaire (DPDQ) and Mathematics Achievement Test(MAT) with reliability coefficients of 0.82 and 0.86 respectively and content and face validity of the instruments was established by expert in test construction.
 Findings: The findings clearly revealed discipline and professional development as prognosticators of secondary school students’achievement in mathematics. It can be concluded that the two predictor variables are effective in improving students’academic achievement in Mathematics.
 Unique contribution to theory, practice and policy: This investigation has generated baseline data about the importance of discipline and professional development in schools. It was recommended that eenlightenment programmes should be organized on what should constitute the disciplinary measures to take in schools to improve students’ achievement in Mathematics. When correcting misbehaviour educators should focus on strategies for developing self-discipline and for preventing misbehaviour. There should be regular training and re-training programmes for teachers in schools so as to provide a basis for their own personal improvement with regards to knowledge in their areas of study and, by extension, improvement on the performances of their students. A relevant theory is the Glasser Theory of Classroom Management is based on the principles that the classroom environment and curriculum should create a safe place for learning by meeting the needs for belonging, power, fun and freedom (William 2009) . Glasser also stressed helping the students achieve success by teaching them to make appropriate behavioural choices. According to Glasser, behaviour is a matter of choice. A student's behaviour stems from the choices he or she makes. It's the teacher's responsibility to help the students make good choices, which would result in good behaviour.The Glasser Theory states that teachers should stress student responsibility, establish rules that lead to success, accept no excuses, call for value judgments, suggest suitable alternatives, invoke responsible consequences, be persistent, and carry out continual review. The benefit Glasser believed that students will have is that they will be provided with a choice in deciding the curriculum and classroom rules. This will help the students take ownership of the learning process, leading to increased enthusiasm, confidence and participation.
 Teachers employing the Glasser Theory may need to deviate from the classical classroom structure in order to achieve success. Glasser favours having the students work together in small groups. This fosters a sense of belonging, motivates the students to work for the group, and reduces theirdependence on the teacher. When divided into smaller groups, stronger students will help the weaker students, improving relationships and classroom harmony.The Glasser Theory alone won't eliminate all classroom behavioural problems however. Glasser suggests that the teacher organizes the classroom the best way possible to meet students' needs and then intervene with the supplied strategies to improve behaviour (William, 2009). Even when the theory is followed, Glasser concedes up to 25 percent of students may remain unproductive. This theory therefore cannot be the best for this study. Kohn’s theory of classroom management emphasises curiosity and cooperation above all else. This is true throughout Kohn’s discussions on standards, standardized testing, homework, and classroom management. Kohn believes that the students’ curiosity should govern what is taught inside the classroom

The aim of this research was to find out the influence of learning model implementation toward student’s achievement in mathematics. This research was using quasi-experimental research. The population of the research was all of 7th grade students in Karanganyar. Sample was taken using stratified cluster random sampling technique. The data collection has been conducted based on students’ mathematics achievement test. The results from the data analysis showed that the learning mathematics by using Numbered Head Together (NHT) learning model with scientific approach improved student’s achievement in mathematics rather than direct learning model particularly in learning object of quadrilateral. Implementation of NHT learning model with scientific approach could be used by the teachers in teaching and learning, particularly in learning object of quadrilateral.