Mathematical Tasks Research Articles

Introducing the ProInterest model

This study introduces the ProInterest model, a novel framework designed to foster long-term student engagement in mathematics. ProInterest model identifies features that trigger initial interest and subsequently sustain student interest towards mathematics activities. We explore the interplay between these features based on a focused narrative review and demonstrate their application through a case analysis of two mathematics tasks that look different on the surface, yet can be identified to share common features fostering interest when looked through the lense of the ProInterest model. We also apply the model to tasks generated by experts and AI. We show that applying the model to identify features that can trigger and maintain student interest towards a task, one can reveal shortcomings in typical mathematics tasks: humour and creativity are typically missing, and even tasks aimed to be tailored to appeal to students may utilise unimaginative layout and structure. This research bridges a critical gap in the knowledge of interest promoting mathematics tasks by providing a practical tool for educators and instructional designers to create engaging mathematics experiences.

Analysis of the computerized activities included in Palestinian Mathematics textbooks

Purpose– The study aimed to analyze the standards of computerized activities included in mathematics textbooks based on international standards and indicators. Design/methodology/approach–The researcher developed a tool (content analysis) to analyze these activities and verified its validity and reliability. This tool was then applied to a sample of mathematics textbooks. Findings –The results revealed a significant gap between the expected standards and indicators and the actual standards and indicators found in the mathematics textbooks. Originality/value – It is crucial to consider fundamental international standards in utilizing computer software in mathematics textbooks, including the design of mathematical tasks, posing mathematical questions, facilitating and simplifying mathematical discussions, and assessing student learning. Based on these findings, the researcher recommended a reassessment of the development of computerized activities in mathematics textbooks.

GPS: Artificial Intelligence Image Processing

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners' growth as problem solvers across their years of school mathematics.

Open mathematical tasks conceived, designed, and reflected upon by preservice elementary teachers

Open mathematical tasks conceived, designed, and reflected upon by preservice elementary teachers

Are Mathematics and Writing Skills Related? Evidence from Meta-Analysis

Writing and mathematics are essential in academic achievement. In the present study, we investigated whether writing skills and mathematics skills are related and if so, whether their relation is moderated by participants’ grade level (a proxy for developmental phase), subskills of mathematics and writing skills, and assessment characteristics (normed and standardized nature of mathematics and writing tasks, and reliability of mathematics and writing measures), using a meta-analysis. A total of 211 studies (k = 564, N = 1,207,983) met inclusion criteria. Overall, mathematics and writing were moderately related (r = .48). The overall magnitude of their relation differed as a function of grade level such that the relation was stronger for students in primary grade levels compared to those in university and above. When explored by higher order and lower order writing and mathematics skills and grade levels, lower order writing and mathematics (.59) and higher order writing and mathematics (.48) had substantial relations in primary grades, whereas higher order writing and mathematics were weakly related in adulthood (.25). The relation also differed by the reliability of mathematics tasks such that the magnitude was stronger for mathematics tasks with higher reliability. For writing, the relation was stronger for writing tasks that were normed and standardized compared to those that were not. These results confirm not only a mathematics–writing relation but also factors that influence this relation. Future work is warranted to investigate mechanisms of the relation and potential practical implications.

USING ARTIFICIAL INTELLIGENCE IN MATHEMATICS TEACHING

In modern education, there is a growing need for innovative teaching approaches, particularly in the context of using artificial intelligence. The relevance of the issue under consideration lies in exploring the potential of ChatGPT for automating the creation of mathematical problems, which can significantly reduce the workload of teachers. The aim of the research is to assess the potential of ChatGPT in generating high-quality math problems across various topics in the school curriculum. To achieve this goal, methods of theoretical analysis of scientific literature and an empirical experiment were applied, during which ChatGPT was used to create tasks on proportionality, combinatorics, algebra, and geometry. The research results demonstrate that ChatGPT can effectively generate both simple and complex mathematical problems, opening new opportunities for automating teachers' preparatory work. This allows teachers to automate part of the preparation process and focus on more creative aspects of teaching. However, certain limitations are identified, such as the dependence of task quality on the clarity of queries and the presence of errors in complex calculations. Overall, the research emphasizes that artificial intelligence can become a valuable tool for math teachers, but its use requires an understanding of its capabilities and limitations. Further research may include researching the impact of using ChatGPT on the student motivation and academic achievements, developing of methods for assessing the quality of ChatGPT-generated tasks, integrating ChatGPT with other learning tools (e.g. learning management systems), exploring the possibility of using ChatGPT to create more complex mathematical tasks that require a creative approach.

Communicative AI Agents in Mathematical Task Design: A Qualitative Study of GPT Network Acting as a Multi-professional Team

Communicative AI Agents in Mathematical Task Design: A Qualitative Study of GPT Network Acting as a Multi-professional Team

Differences in Mathematical and Verbal Achievement Between Girls and Boys: The Heuristic Potential of the Structural Typing Approach in Large‐Scale Studies

ABSTRACTThe results of total testing from the years 2015–2022 on the mathematical and verbal achievement of Lithuanian pupils (N ≈ 250,000) are presented. These are the standardised tests from grades 4 to 12. The K‐Means method has discovered six types of achievement. The highest achievement type is dominated by girls (61.1%) who perform well on both mathematical and verbal tasks. The lowest achievement type is dominated by boys (57.4%) who solve both mathematical and verbal tasks extremely poorly. Each of these types makes up 1/5 of the population, and the gap between the means of their groups is about 2.5 standard deviations. The remaining four types of achievement are in the 20th to 80th percentile and make up about 60% of the population. Differences in means within the same type between mathematic and verbal achievement average 0.85 standard deviations or span one quartile. Gender differences are clearly visible in this subgroup: boys solve mathematical tasks better and verbal tasks worse; girls solve verbal tasks better and mathematical tasks worse. Big data may form a mixed distribution. It is appropriate to first discover the basic types of achievement and only then look for gender‐specific differences. Such a type‐building approach is heuristically superior to the conventional approach of working only with the mixed dataset.

Secured Fog-Body-Torrent : A Hybrid Symmetric Cryptography with Multi-layer Feed Forward Networks Tuned Chaotic Maps for Physiological Data Transmission in Fog-BAN Environment

Recently, the Wireless Body Area Networks (WBAN) have become a promising and practical option in the tele-care medicine information system that aids for the better clinical monitoring and diagnosis. The trend of using Internet of Things (IoT) has propelled the WBAN technology to new dimension in terms of its network characteristics and efficient data transmission. However, these networks demand the strong authentication protocol to enhance the confidentiality, integrity, recoverability and dependability against the emerging cyber-physical attacks owing to the exposure of the IoT ecosystem and the confidentiality of biometric data. Hence this study proposes the Fog based WBAN infrastructure which incorporates the hybrid symmetric cryptography schemes with the chaotic maps and feed forward networks to achieve the physiological data info security without consuming the characteristics of power hungry WBAN devices. In the proposed model, scroll chaotic maps are iterated to produce the high dynamic keys streams for the real time applications and feed-forward layers are leveraged to align the complex input-output associations of cipher data for subsequent mathematical tasks. The feed forward layers are constructed which relies on the principle of Adaptive Extreme Learning Machines (AELM) thereby increasing randomness in the cipher keys thereby increasing its defensive nature against the different cyber-physical attacks and ensuring the high secured encrypted-decrypted data communication between the users and fog nodes. The real time analysis is conducted during live scenarios. BAN-IoT test beds interfaced with the heterogeneous healthcare sensors and various security metrics are analysed and compared with the various residing cryptographic algorithms. Results demonstrates that the recommended methodology has exhibited the high randomness characteristics and low computational overhead compared with the other traditional BAN oriented cryptography protocol schemes

Assessing Difficulty Levels of Mathematical Tasks through Subjective and Behavioral Criteria

Assessing Difficulty Levels of Mathematical Tasks through Subjective and Behavioral Criteria

Utilizing Trust to Examine Pre-Service Teachers’ Challenges When Learning to Implement Mathematics Tasks

ABSTRACT Implementing challenging mathematics tasks in elementary classrooms is a foundational teaching practice that is known to be difficult for teachers. Yet, little is known about the challenges pre-service teachers (PSTs) experience as they work to develop this practice. Additionally, the importance of trusting relationships in schools is well established, though research has not examined how issues of trust might influence PSTs’ development of specific pedagogical practices. This cross-institutional study examined written reflections highlighting challenges experienced by 77 PSTs from seven teacher preparation programs. Findings elucidate six distinct challenges, three of which align with necessary features of trusting relationships (teacher control with vulnerability, perceptions of student ability with competence, and concerns about student feelings/experiences with benevolence). Based on these findings, we offer recommendations for mathematics teacher educators to consider as they prepare PSTs to implement challenging tasks, including ways to support PSTs’ vulnerability, perceptions of students’ competence, and benevolence during methods courses and field placements.

Mathematical tasks: a review of classification systems

Mathematical tasks: a review of classification systems

Educational robotics and primary school mathematics teaching: An analysis of pre-service teachers didactic-mathematical knowledge

The scarcity of studies dedicated to the integration of educational robotics (ER) in teaching mathematical content, and the discomfort of teachers when integrating ER in their teaching practices make it pertinent to understand the development of the didactic knowledge of mathematics necessary to integrate ER in mathematics teaching practices during initial teacher training. This qualitative and interpretive study identifies the knowledge of the didactic dimension from the didactic-mathematical knowledge conceptual framework that is mobilized by pre-service teachers (PST) during the implementation of mathematical tasks that integrate ER during the practicum. Through content analysis of the data collected on the PST’s performance, we mapped the occurrence and co-occurrence based on the components of the didactic suitability criteria. From the results, we highlight: (i) the existence of a relationship between the mathematical knowledge needed to teach, knowledge of the mathematics curriculum, and knowledge of ER and how its integration in the teaching process can influence the learning process and (ii) the positive contribution of the implementation in the practicum of mathematical tasks that promote robot manipulation/programming at the same time as the exploration of the mathematical content for the development of the participants’ didactic knowledge of mathematics. A practical implication of our results is that these features should be part of future work dedicated to integrating ER in mathematics teaching practices of PST, aiming to assess their value in initial teacher training programs.

GPS: Counting Goldfish Crackers: Three-Act Math Tasks

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

중등수학교사의 수학적 신념에 따른 수업목표 이해 및 과제 선별

The purpose of this study is to determine how secondary school mathematics teachers interpret the geometry unit lesson objectives in relation to the characteristics of teachers' mathematical beliefs and what main tasks they present during specific classes with the interpreted lesson objectives. For this purpose, a survey was conducted targeting secondary mathematics teachers regarding mathematical beliefs, teaching goals, and task selection. As a result of the study, no evidence was obtained that there was a difference in mathematical beliefs depending on the teaching goals understood by teachers. In general, teachers were found to select class goals that correspond to knowledge and understanding, and only in some units did specific mathematical beliefs appear to influence teachers' interpretation of class goals. Second, there was no significant difference in the level of cognitive demand of tasks teachers wanted to present in class depending on the class goals. However, in certain units, it was found that there was a difference in the ratio of cognitive demand levels. The findings provide important implications for better understanding of teachers' behaviors focusing on cognitive demands of tasks and mathematical beliefs.

Some New Algebraic Method Developments in the Characterization of Matrix Equalities

Algebraic expressions and equalities can be constructed arbitrarily in a given algebraic framework according to the operational rules provided, and thus it is a prominent and necessary task in mathematics and applications to construct, classify, and characterize various simple general algebraic expressions and equalities. As an update to this prominent topic in matrix algebra, this article reviews and improves upon the well-known block matrix methodology and matrix rank methodology in the construction and characterization of matrix equalities. We present a collection of fundamental and useful formulas for calculating the ranks of a wide range of block matrices and then derive from these rank formulas various valuable consequences. In particular, we present several groups of equivalent conditions in the characterizations of the Hermitian matrix, the skew-Hermitian matrix, the normal matrix, etc.

An examination of the cognitive demand levels posed by problems in the middle grades mathematics textbooks

This research investigated the cognitive demand levels of mathematics tasks within the middle school mathematics textbooks endorsed by the Ministry of National Education for the academic year of the 2023-2024. To achieve this, a qualitative research method was utilized, and document analysis was performed. In this direction, the textbooks were analyzed using descriptive analysis. The tasks within the textbooks were examined through the lens of Smith and Stein’s (1998) theoretical framework. The findings indicate that the majority of mathematics tasks in middle school mathematics textbooks exhibit a low level of cognitive demand. It was found that over 80% of the tasks fell into the categories of memorization and procedures without connections levels. It has been revealed that tasks at the levels of procedures with connections and doing mathematics, which are high cognitive demand levels, are uncommon. This shows that textbooks do not sufficiently support the potential of students to develop mathematical thinking and problem-solving skills. Based on these results, various suggestions have been made for textbooks. The most important of these suggestions include ensuring that students are cognitively exposed to higher level tasks and increasing the number of tasks that will improve their mathematical thinking skills. Thus, it will be possible for students to have a more effective learning process by deepening their mathematical understanding.

The professional practice of designing tasks: how do pre-service early childhood teachers promote mathematical processes in early algebra?

AbstractSpanish educational curriculum adopts a mathematical process-based approach, which encompasses problem solving, reasoning and proof, communication, connections and representation. A fundamental role in the integration of these processes in mathematics teaching is played by teachers’ professional practice of designing tasks. According to this, our aim is to analyze the ways in which pre-service early childhood teachers understand the mathematical processes in the professional practice of designing early algebra tasks and to identify how they intend to promote these processes through the tasks. Content analysis techniques were used to examine the designed tasks. To illustrate the data analysis and results, six tasks are presented. As a result, pre-service early childhood teachers associate problem solving with challenges and questions. They understand problems as unfamiliar situations but ignore the relationships between students and tasks. Moreover, they do not encourage exploration of phases of problem solving and tend to use strategies more suitable for routine tasks. Communication is identified in all the tasks designed, encouraging interaction and discussion. However, only one task explicitly promotes mathematical language. For reasoning and proof, pre-service teachers begin to use questions to elicit explanations and justifications, but do not encourage verification strategies and various modes of reasoning. The process of connections is only present in one task, reflecting the fragmented nature of mathematics teaching. We conclude that the professional practice of designing mathematical tasks is a powerful in teacher education. However, training programs should place greater emphasis on the meaningful use of mathematical processes.

Investigating preservice secondary mathematics teachers' skills in posing realistic mathematics tasks

Mathematics tasks situated in realistic situations play a central role in developing and applying mathematical knowledge. However, mathematics educators face difficulties in designing realistic mathematics tasks. This study was conducted to gain deeper insights into the characteristics of mathematical problems that underprepared preservice secondary mathematics teachers pose. This study examined 32 preservice secondary mathematics teachers' problem-posing skills based on three problem-posing situations: structured problem-posing, semi-structured problem-posing, and free problem-posing. As the context of the participants, they did not have learning experiences in designing realistic mathematics tasks. In evaluating the preservice teachers' works, the researchers used several evaluation criteria, namely the compatibility of the problem with the mathematical principles, plausibility and sufficiency of information, the problem text, level of context authenticity, cognitive demand, and the correctness of the solution. The results revealed that most preservice teachers posed problems with the first-order level of context use and low cognitive demand. Additionally, many of them encountered difficulties when attempting to solve the problem. The findings of this study were expected to serve as a basis for developing a curriculum for pedagogic and mathematics courses in teacher education.

Evaluation and Time Constraint: Impact of Time Processing on Mathematical Performance

This study investigated the impact of a temporal assessment context on children’s mathematical performance and anxiety. Children aged 7- to 9-years-old were given mathematics tasks under three different assessment conditions: no time constraint (NoT), time constraint with an invisible timer (IT), and time constraint with visible timer (VT). Results showed that children performed worse under the time constraint condition when the timer was not visible to them. This supports the resource-based theory of time perception, which suggests that the processing of temporal information is a demanding cognitive task that consumes limited attention resources. Of greater interest, the use of a visible timer improved children’s cognitive efficiency without compromising performance compared to the unconstrained time condition. Additionally, the study found that anxiety levels were lower in the situation with a time constraint with a visible timer compared to the two other assessment contexts. These results suggest that a situation with a pre-established time constraint where children can manage their time could alleviate their anxiety and better cater to their needs during the assessment. Overall, these results underline the benefits of a visible timer in providing an organizational framework for children and helping them process time, thus avoiding draining their attentional resources.