Identifying and Teaching Essential Mathematical Skills—Items

Programming is an essential skill that electrical and electronics engineering students should possess. With the advances made in technology, even the simplest electrical devices are becoming more intelligent and connected. This emphasizes even more the need for programing skills for engineers. Traditionally, in electrical engineering curriculum introduction to programming is taught though without rigor. Computer programming is a challenging task since it requires abstract thinking, logic and mathematics skills. Novice students rapidly develop a disliking and avoid tasks/projects that involves programming. In order to overcome these issues and get students interested in programming, we took an evidence based approach for teaching computer programming. The method involves combining a number of proven best practices in teaching, together with a reflective tool for the instructor when planning and delivering the course. We experimented with novice students who are taking the basic computer programming for the first time. Our experiments demonstrate that an evidence based teaching approach is highly effective. This paper describes the methods used and our observations on the outcome.

In this chapter, the four-factor model of mathematics skills development in children aged 5–8 years is introduced with the aim of describing the most essential skills for later math learning. The early signs of mathematical learning difficulties are also discussed. Additionally, initial findings from a study on the role of parents’ education and values toward mathematics in children’s mathematics skills and interest, from kindergarten to the first grade, are presented. Our results highlight the complex interrelations between parent and child factors in the development of early mathematics skills. Regarding the ways in which adults could support their children’s learning of basic mathematics skills in non-school environments, two Finnish web services for teachers and parents (LukiMat, ThinkMath) will be briefly described.

This research aimed to identify the difficulties encountered by Junior Primary Teachers in assisting Junior Primary learners in the Omusati region of Namibia in enhancing their computational skills in Mathematics. Computational skills refer to the ability to perform basic arithmetic operations, addition, subtraction, multiplication, and division, swiftly and accurately using mental calculations, paper and pencil, or tools like calculators. The study employed a quantitative research method with a descriptive research design. The data were gathered through online questionnaires created with Google Forms, which were then analysed using descriptive statistics and linear regression tests via SPSS version 28 software. The population size of the study was all the junior primary teachers in Outapi circuit. The sample size of the study was 70 respondents selected through simple random sampling. The research was underpinned by Vygotsky’s social constructivist theory, which emphasizes a teaching methodology that fosters active engagement of learners in their educational processes. Findings revealed that language barriers, along with cultural and socioeconomic factors, pose significant challenges for Junior Primary Teachers in facilitating the development of computational skills in their learners. It is recommended that teachers incorporate hands-on activities as a teaching strategy, allowing learners to utilize manipulatives, which could enhance their ability to develop and acquire computation skills. These findings have significant implications for the teaching and learning process, particularly for JPTs who are tasked with ensuring learners acquire these essential skills.

Historians will undoubtedly refer to the period of American education that began in the 1970s as the back-to-basics era. This movement is unique in that its impetus was primarily based on the concerns of the lay public, which were effectively expressed by lawmakers and school board members. Professional educators responded to this thrust of public opinion by attempting to identify the essential basic skills that should be taught in Grades I through 12.

Effective teachers are those who are highly engaged and who have an essential role in promoting student motivation and achievement. Thus, this study was conducted to ascertain the engagement of Mathematics teachers and its relation to the learning motivation of students in a state college in the Philippines. It employed the mixed methods, specifically Creswell’s (2014) sequential explanatory approach, with the survey-questionnaire, interview, and focus group discussion as data collection techniques. The findings of the study revealed that teacher’s engagement in Mathematics in terms of “Body Language and Behaviors,” “Consistent Focus,” and “Individual Attention,” were “Very High” while “Rigorous Thinking,” “Meaningfulness of Work,” “Verbal Participation,” “Clarity of Teaching,” “Performance Orientation,” “Interest and Enthusiasm,” and “Confidence,” were only “High.” Meanwhile, students’ motivation to learn Mathematics as to “Relevance,” “Interest,” “Satisfaction,” and “Confidence” were also “High”. The test of hypothesis on significant correlation showed that there was a close association between teacher’s engagement in Mathematics and students’ motivation to learn Mathematics. There was also a corroboration between the quantitative data obtained from the survey and the qualitative data acquired during the interview and focus group discussion. The result further implied that teacher’s high engagement contributes positively to students’ willingness to learn essential concepts and skills in Mathematics.

Generalizing patterns is a fundamental mathematical skill with widespread applications. However, only 7.1% of students demonstrate high proficiency in generalizing patterns, indicating significant challenges in identifying and applying rules. This study explores the thinking processes of students who succeed and fail in generalizing linear patterns, analyzed through the lens of Holland's RIASEC personality model. Employing a qualitative phenomenological approach, data were collected through pattern generalization tests, RIASEC questionnaires, and interviews conducted with seven junior high school students in Bandung, selected based on communication skills and varied personality types. The findings reveal that students with investigative personalities are most successful, exhibiting critical thinking and problem-solving abilities aligned with pattern generalization tasks. In contrast, unsuccessful students predominantly rely on numerical data or recursive strategies without effectively connecting visual configurations. This research identifies three distinct thinking processes: focusing solely on numerical data, combining numerical data with operational adjustments, and refining generalizations using visual patterns. The study underscores the importance of leveraging visual aids and trial-and-error methods in teaching pattern generalization. Differentiated instruction, tailored to students’ cognitive and personality traits, is recommended to address diverse learning needs and enhance mathematics education quality. This study contributes to understanding the interplay between personality and cognitive strategies in mathematical problem-solving. It also emphasizes the necessity for inclusive teaching strategies that cater to varied student profiles to foster success in generalizing patterns and developing essential mathematical skills

Students with learning disabilities struggle to acquire essential mathematical concepts and skills, especially at the secondary level. One effective approach to improving secondary math performance supported by research is the concrete-to-representational-to-abstract (CRA) sequence of instruction. Although CRA is an evidenced-based instructional practice, it is somewhat complicated for teachers to implement in their day-to-day instruction.To better assist implementation of the CRA, an instructional approach with the mnemonic CRA-MATH was developed as a flexible roadmap to help math teachers better address student deficits using the CRA sequence of instruction. The purpose of this article is to describe the seven-step strategy used to guide curricular CRA modifications in secondary mathematics.

The integration of innovative digital tools offers a promising avenue to address traditional learning hurdles and enhance student engagement. This study aims to develop a mobile application to improve students' critical thinking and mathematical computational skills in the material of the multiplication rule of 5. The low level of both abilities and the limitations of innovative learning media. The use of the ADDIE development research method. The results of the study showed that the application was significantly successful in improving computational skills and critical thinking skills, which was empirically proven by increased test scores and active student involvement during the mathematics learning process. An important contribution in providing effective digital learning solutions for basic materials as a foundation in developing knowledge for students. Furthermore, this application serve as a scalable model for integrating technology to address fundamental learning gaps in mathematics across various educational settings. Its success suggests the potential for broader adoption of similar tools to foster essential cognitive skills from an early age.

Solving math puzzles is one of the most essential skills students should have in the 21st century. Despite this, Indonesian students' problem-solving ability still needs to improve. This research aims to analyze the effect of integrating computational thinking in geogebra-assisted measurement learning on mathematical problem-solving skills. This research uses a quantitative approach with an experimental type. The sample for this research consisted of 45 elementary school students using simple random sampling techniques. The methods used to collect data are observation and tests. The instrument used to collect data is test questions. The techniques used to analyze data are quantitative analysis and inferential statistics. The results showed that there was variation in the ability of the experimental and control groups to solve mathematical puzzles. The t-test results show an average difference between the pretest and post-test results in the control and experimental classes. There is a significant difference in problem-solving abilities between students who take part in learning using the computational thinking approach assisted by Geogebra and students who take part in learning without the computational thinking approach assisted by Geogebra. It was concluded that learning using a computational thinking approach assisted by Geogebra can improve problem-solving abilities.

Computational thinking (CT) is an essential mathematical skill for problem-solving and students’ future lives. It is integrated into the educational curricula of several countries, including Portugal. Therefore, pre-service teachers (PST) must possess didactic knowledge to effectively develop CT in students. The aim of this study encompassed three main objectives: translating and adapting the computational thinking scale into Portuguese (study 1), validating the scale (study 2), and assessing the perceived levels of CT competencies among PST in Portuguese university students while examining differences between undergraduate and master’s level PST (study 3). The sample consisted of study 1 with 43 participants and study 2 and study 3 with 382 participants. In study 1, temporal stability was assessed indicating strong stability. The internal consistency showed good homogeneity of the items. The exploratory factor analysis revealed consistency with the structure of the original scale. In conclusion, the Portuguese version of the CT scale demonstrates adequate psychometric properties, proving valid and reliable for assessing CT in university students. Additionally, significant differences were observed between undergraduate and master’s degree students, underscoring the importance of tailored training programs to meet the specific needs of undergraduate students.

A persistent challenge in education is the widespread difficulty students face in mastering mathematics. This challenge results in consistently low academic performance, hindering their ability to develop essential problem-solving skills and apply mathematical concepts in real-world contexts. Without effective interventions, these challenges continue to undermine student confidence, limit academic achievement, and contribute to long-term gaps in mathematical proficiency. To address this issue, the study examined the effectiveness of peer mentoring in improving the mathematical skills of Grade 11 students. The study employed a quantitative research approach and quasi-experimental research design to determine whether peer mentoring draws significant differences in the mathematical skills of students. The findings revealed that the experimental group showed significant improvement (M=-13.067, p<0.000), confirming the effectiveness of peer mentoring. In contrast, the control group showed no improvement (M=0.000, p<1.000), indicating traditional learning alone was insufficient. This implies the inclusion of intervention poses a significant effect on the mathematical skills of students. The study recommends integrating peer mentoring or other interventions in enhancing student’s performance in mathematics particularly in addressing poor mathematical performance of students in a class.

Advanced responder training priorities in Kenya: A Delphi study with implications for low- and middle- income countries.

Reasoning skill is one of the main components of mathematical competency (NCTM, 2014). Mathematics students use mainly two types of reasoning skills namely imitative reasoning and creative reasoning in solving mathematical tasks. The textbook tasks in our context are of routine types which are solvable using imitative reasoning. Most mathematics teachers use prescribed textbooks in lesson planning and teaching (Thomson & Fleming, 2004) which ultimately promotes imitative reasoning among the students as compared to creative reasoning. Moreover, many mathematics teachers still follow the traditional chalk-and-talk banking pedagogy which does not support the enhancement of creative thinking and reasoning skills. This literature-based research study has identified some of the ways to develop the creative thinking and reasoning skills of mathematics students through the intense study of the available research articles, thesis, and books in the field of mathematical thinking and creativity. This study has found the positive impact of productive struggle and adversity quotient on students’ creative thinking and reasoning skills. Likewise, problem-posing and problem-solving skills have been found to be essential skills for enhancing creativity. This study has also found modern student-centric teaching approaches like the ADI (Argument-Driven Inquiry) approach and the RME (Realistic Mathematics Education) approach beneficial in improving reasoning skills. This study also found CMR (Creative Mathematically Founded Reasoning) tasks to be helpful in increasing the creative reasoning skills of mathematics students.