GPS: Nothing Like a Puffin

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.

The aim of the study was to identify possible individual differences effects on school mathematics performance and feelings of difficulty (FOD). Cognitive ability (general and domain-specific), affect (anxiety and achievement need), age, and gender were considered the main sources of individual differences. The effect of the testing experience (i.e., the repeated exposure to the testing situation) was also taken into account. Two hundred forty three subjects, of both genders, from 13 to 15 years of age were tested with three task batteries: the cognitive ability, the affective battery and the school mathematics battery. Ratings of the difficulty of each of the mathematics items were also collected. A second testing of the affective battery, mathematical tasks and FOD was effected one year after the first. A series of path analyses and ANOVAs were performed on the data. It was found that ability directly influenced performance whereas both ability and affect influenced FOD. Feelings of difficulty were also influenced by performance. Age differentiated FOD only at the 2nd testing. Gender interacted with both person and task characteristics and had an effect on FOD but not on performance.

This study aimed to analyze how mathematical connection, a newly introduced competency in the 2022 revised mathematics curriculum, is reflected in elementary school mathematics textbook tasks. For this purpose, a total of 7410 tasks presented in nine approved mathematics textbooks for 3rd and 4th grades were analyzed to examine the proportion of mathematical internal and external connection tasks by grade level and content domain. The findings revealed the following. First, approximately 48.9% of all tasks were identified as mathematical connection tasks, with the proportion of mathematical external connection tasks being higher than that of mathematical internal connection tasks. Second, when analyzed by subcategories of mathematical connection, tasks involving connection with real-life contexts, a subcategory of mathematical external connection, showed the highest proportion, while tasks involving connection between domains, a subcategory of mathematical internal connection, showed the lowest proportion. Third, the proportion of mathematical connection tasks tended to decrease as grade level increased, and by domain, the highest proportion was found in the data and chance domain, while the lowest was found in the change and relationships domain. Based on these findings, this study suggests that textbook development should incorporate a balanced representation of mathematical internal and external connection tasks and provide students with opportunities to experience various types of mathematical connection through project units that integrate multiple domains. Additionally, the study emphasizes the need to enhance teachers' competency in developing mathematical connection tasks.

The argument of this theoretical paper is that the existence and availability of suitable digital curriculum resources, accelerated by the recent pandemic, have required a revision of the pedagogical landscape in terms of ways in which students can be empowered to (co-)design their own curriculum trajectories. For this purpose, I argue, students need to be supported in considering many connections, to arrive at coherent trajectories. Based on complexity thinking and curriculum design with digital resources, I propose the concept of connectivity as a crucial principle for creating coherent curriculum trajectories. If students are to become the co-designers of their own curriculum, they need a frame that raises their awareness about the many connections to be made and that supports their capability for actually realizing them. Drawing strongly on my own work and related work by others, I analyse and illustrate the connections made by students, teachers and curriculum designers in their design of mathematics tasks, lessons and learning trajectories with digital resources. Results show that connections can be made at several levels, namely, at a social level, at a material level, at programme level, and at a didactical level. Leaning on systems thinking, connections can be systematically considered, which is likely to help students to enhance the coherence of their designs. I contend that a student-designed ‘connected curriculum trajectory’ is likely to become the focus of future research activities in innovative learning environments: this endeavor would connect aspects of curriculum, mathematical content, learning strategies of students, and the use of new technologies.

Relevance. The research's relevance is due to the need to explore optimal ways to improve the education of pupils in mathematics for the formation of mathematical literacy, by independently solving text-based tasks in mathematics regardless of the orientation of their interests and the chosen specialty. Purpose. The purpose of the article is the characterization of methodical conditions conducive to teaching pupils to solve mathematical tasks on their own. Methodology. The methodology of the research consisted of the use of a set of theoretical methods (general scientific, specific-scientific), which allowed processing of the scientific literature, distributing the information array, studying and clarifying terms and concepts, and structuring the collected information. And empirical methods – interviews and sociological surveys with teachers and experts in the field under study. The participants in this study were 70 primary school mathematics teachers in 2-5 grades. Results. The article analyzes the process of the collaboration between teacher and students during solving textual problems in various ways, which allows students to form not only knowledge and skills on the relevant issue, and also to develop such elements of mathematical literacy as logical thinking and form a literate mathematical language. Conclusions. The study's applied value is that the main points, factual materials, and conclusions can be used in the school system by teachers, methodologists, and research educators to develop recommendations for improving the teaching of schoolchildren's autonomy in solving text-based problems in mathematics.

The article is devoted to the problems of teaching mathematics in a school with practiceoriented content. The aim of the study is to develop a methodology for teaching students to solve problems with practical content in the process of implementation of practice-oriented teaching mathematics. The development of students ‘ abilities to solve practice-oriented problems in the process of teaching mathematics should be considered as one of the ways of forming their mathematical competence. Practice-oriented tasks are understood as mathematical tasks, the content of which describes the situation of reality associated with the formation of practical skills of using mathematical knowledge and skills needed in everyday life. The solution of this type of problem is largely based on the construction of a model of the real situation described in a particular problem. This model of compilation requires a high level of mathematical training and is the result of training that is appropriately called culture-universal. The constant use of practice-oriented tasks in teaching mathematics at school will allow the learner to generalize and deepen knowledge, acquire skills and knowledge on the subject, be able to link the learning process with the real conditions of life, to show initiative and independence. The researchers describe didactic goal-setting and examples of practice-oriented tasks in mathematics developed by the authors. Monitoring of learners ‘ activities indicates that the frequent use of practice-oriented tasks increases the interest of learners in educational activities, forms a positive motivation in the classroom Key words: secondary school mathematics, practice-oriented tasks, motivation.

Children's number competencies over 6 time points, from the beginning of kindergarten to the middle of 1st grade, were examined in relation to their mathematics achievement over 5 later time points, from the end of 1st grade to the end of 3rd grade. The relation between early number competence and mathematics achievement was strong and significant throughout the study period. A sequential process growth curve model showed that kindergarten number competence predicted rate of growth in mathematics achievement between 1st and 3rd grades as well as achievement level through 3rd grade. Further, rate of growth in early number competence predicted mathematics performance level in 3rd grade. Although low-income children performed more poorly than their middle-income counterparts in mathematics achievement and progressed at a slower rate, their performance and growth were mediated through relatively weak kindergarten number competence. Similarly, the better performance and faster growth of children who entered kindergarten at an older age were explained by kindergarten number competence. The findings show the importance of early number competence for setting children's learning trajectories in elementary school mathematics.

Mathematics is an important discipline in education which provides a basis for problem solving, critical thinking and analytical skills. Textbooks are as important for mathematics as they are for other subjects. Problem posing is one of the important activities in mathematics education. The purpose of this study is to analyze the activities of problem presentation in the mathematics’ textbooks of primary schools from the first to the fifth grade provide by the Ministry of Education and Science. For this purpose, five elementary school mathematics’ texts were analyzed with the method of analysis, educational fields and types of problem presentation. The results show that in the textbooks of the subject of mathematics from the first to the fifth grade, excluding the mathematics book for the third grade, they are presented in total 20%, 29%, 34% and 37%, respectively, problem tasks have been presented. From the results, it is considered necessary to increase the number of problem activities in textbooks, their application in everyday life and to diversify the type of problem presentation.

By modeling learning students enjoy learning and doing mathematics in new ways. This study aimed firsly to produce senior high school mathematics modeling tasks, lesson plan, and student worksheet for valid mathematical learning; secondly, to produce senior high school mathematics modeling, lesson plan, and student worksheet for practical mathematics learning; lastly, to produce senior high school mathematics modeling tasks, lesson plan, and student worksheet for potentially effective mathematics learning. This study used method of development research that consisting of 3 steps, i.e., analysis, design, and evaluation. In the analysis stage, researcher did student analysis, curriculum, and mathematical modeling. Second stage are to design and product. Finally, researchers applied a design of formative evaluation consists of self-evaluation, one-to-one, experts review, small group, and field test. Based on experts review, one-to-one, small groups, and field test were obtained valid, practical, and potentially effective, i.e. mathematical modeling tasks, lesson plan, student worksheet to teach mathematical modeling in senior high school and Mathematical modeling tasks and student worksheets to learn mathematical modeling in senior high school.

A growing body of research indicates the importance of creating strong partnerships in mathematics between home and school (Civil & Andrade, 2003; Civil, 2007; Civil et al., 2019; Colegrove & Krause, 2017; Kelly, 2020; Stoehr & Civil, 2019). Connections that are made between home and school can greatly benefit student learning. This is especially true for mathematics (Anhalt & Rodríguez-Pérez, 2013; Civil, 2007; Civil et al., 2019; Colegrove & Krause, 2017; Kelly, 2020; Stoehr & Civil, 2019). Therefore, providing opportunities that promote authentic and meaningful engagement around mathematics in ways that position parents as active and knowledgeable participants in the education of their children is essential, especially for families from underserved communities (Civil, 2007; Colegrove & Krause, 2017; Kelly, 2020; Stoehr & Civil, 2019). Civil and Andrade’s (2003) work reveals the importance of creating a two-way dialogue between home and school that views parents as intellectual resources. To create an authentic two-way dialogue, teachers and schools need to commit to a genuine partnership with parents that is interested and respectful of parents’ views and ways that mathematics is used in their homes and communities. Building rapport and trust with families are situated at the core of the parents as an intellectual resources framework. Given that more than 50% of students in public schools are from homes and communities that are culturally, linguistically, and racially diverse, (Kena et al., 2015) it is critical that teachers explore ways to tailor their mathematics instruction to reflect parents’ rich mathematical knowledge and experiences. Additionally, Civil and Andrade (2003) also recognize that it is important for parents to learn about how mathematics is being taught at their children’s school so that parents can connect school mathematics to the mathematics that takes place in their homes on a daily basis. Such symbiosis between home and school has the potential to optimize student learning and build a healthy sense of identity for them as well. This chapter examines the interviews of 72 parents at one of the two study sites who upon completing the workshops shared their own mathematics experiences of learning mathematics and their reflections of participating in the workshops. The research was part of a professional development grant titled Math and Language, Literacy Integration in Dual Language Settings (MALLI). While the grant provided professional development to preservice and in-service teachers that focused on three components of instruction in mathematics classrooms (discourse, vocabulary, and literacy), mathematics workshops were offered to parents/caregivers of the students whose teachers who took part in this study. Specifically, five cohorts of parents who had children in MALLI teachers’ classrooms received targeted mathematics learning opportunities. The parents attended four mathematics workshops with the goal of (a) strengthening their own mathematics skills; (b) showcasing their ways of solving mathematics tasks; (c) building their confidence and competence around mathematics; (d) shedding light on the relationship between home mathematical and language practices and the expected learning goals of the classroom; (e) acknowledging and embracing their everyday mathematical interactions with their children; and (f) engaging in mathematics tasks with their children’s teachers.

To take its due place in the world of education, Turkey has been through serious reform initiatives in the curriculums of various school subjects since 2003. The new Turkish elementary school curriculum was prepared considering the research studies conducted in Turkey and in other countries, as well as the educational systems of developed countries and previous experiences with mathematics education in Turkey. This study attempts to provide a perspective on the nature of the instructional tasks in the new elementary school mathematics curriculum. In particular, our focus is to explore the level of cognitive demands (LCD) in the algebra tasks provided in the national elementary mathematics curriculum guidebook. This curriculum document is a major resource for administrators, stakeholders, textbook publishers and ultimately for teachers. For every learning objective, it provides sample tasks to be used in mathematics instructions. In this study, our purpose is to explore the LCD of each of these tasks by utilizing a framework developed by Smith and Stein (Math Teach Middle School 3:344–350, 1998). The framework classifies mathematical tasks according to the level of demands: lower-level and higher-level demands. While the lower-level demands are related to memorization and procedures without connections, the higher-level demands are related to procedures with connections and doing mathematics. The findings revealed that 60% of algebra tasks for each grade level required higher LCD and a great majority of the remaining tasks were at the level of procedures without connections. The findings of the study particularly inform curriculum developers about issues regarding the quality of the tasks given in the curriculum guide and provide possible suggestions to improve the implementation of the curriculum change process.

Even though basketry is an age old occupation in Ghana and the world over, it appears mathematics tasks and activities involving the designs and structures have remained unnoticed and inadequately tapped for early school instructions. This qualitative survey therefore, purposively sampled four teachers, two basket artisans and six pupils in the Bolgatanga Municipality of Upper East Region of Ghana to harness, discuss and apply the tasks and activities indigenous basket resources could be employed to enhance conceptual knowledge and understanding in prenumber and early work. The findings showed that apart from providing employment and income for local artisans, teachers and pupils were equipped with prenumber activities that lead to the acquisition of early number work in pre-algebra, pre-geometry and pre-statistics tasks and activities in mathematics. We therefore, recommended instructional policies and programmes that promote and improve upon conceptual learning of prenumber and early school mathematics with indigenous resources.

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.

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.

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.