Preschool education is fundamental to shape children’s aptitudes and skills in early life. Ecuador is following a global education trend for starting-up mathematical thinking at earlier development ages, but this is only reflected in vehement curricular changes that are not supported properly. As a result, the safeguarding of a good children’s education appears to be lessened. This work aimed to evaluate the mathematics thinking practices in preschools of Pasaje city, Ecuador. The investigation employed a descriptive approach, hence data were collected from 65 teachers and 810 parents from public and private preschools by means of interviews and questionnaire in an attempt define some causes (teacher’s education, children’s socio-economical and family circumstances) that impair the initiation of the numerical, spatial and metric and geometric aptitudes in children. The results showed that not only preschool practices but also the home environment linked to socio-economic status appear to have positive or unfavorable influences on their children’s education.

Problem-solving is considered one of the thinking skills that must be possessed in 21^st-century education because problem-solving skills are required to solve all problems that arise. The problem-solving stages that can be used are Polya's four steps, namely, understanding the problem, devising a plan, carrying out the plan, and looking back. Problem-solving skills are essential for solving word problems. Word problems based on arithmetic operations are divided into three types: one-step, two-step, and multistep. This qualitative research aimed to see problem-solving skills viewed from the type of word questions and elementary school students’ third, fourth, and fifth grades. A purposive sampling technique with 22 third-grade students, 28 fourth-grade students, and 21 fifth-grade students was used. The data were collected using documentation, testing, and interview methods. The findings of the study showed that fourth-grade students’ problem-solving skills are better than those of third-grade students, and the problem-solving skills of fifth-grade students are better than those of fourth-grade students. The percentage of Polya's steps always decreases because not all students master problem-solving. Based on the types of questions, the percentage of the one-step word problem is better than that of the two-step while the percentage of the two-step word problems is higher than that of the multistep.

Numerical thinking is needed to recognize, interpret, determine patterns, and solve problems that contain the context of life. Self-efficacy is one aspect that supports the numerical thinking process. This study aims to obtain a numerical thinking profile of Mathematics pre-service teachers based on self-efficacy. This study used descriptive qualitative method. The data obtained were based on the results of questionnaires, tests, and interviews. The results of the self-efficacy questionnaire were analyzed and categorized (high, moderate, and low). Two informants took each category. The results showed the following: informants in the high self-efficacy category tend to be able to interpret information, communicate information, and solve problems with systematic steps. Informants in the moderate self-efficacy category tend to be able to interpret and communicate information, but tend to be hesitant in choosing the sequence of problem-solving steps. Meanwhile, informants in the low self-efficacy category tend not to be able to fully interpret the information. As a result, the process of communicating information and solving problems goes wrong. Another aspect found in this study is the need for experience optimization, a good understanding of mathematical content, and reasoning in the numerical thinking process.

The aim of this work is to characterise the understanding that students in compulsory secondary education (14-16 years old) have of number sequences in graphical representations. The learning of numerical sequences is one of the first mathematical concepts to be developed in an infinite context. This study adopts the focus of semiotic representations as its theoretical framework. The participants consisted of 105 students and a qualitative methodology was used. The data collection instruments were a questionnaire and a semi-structured interview. The results allowed for three student profiles regarding number sequences in graphical representations to be identified. These profiles may facilitate a possible progression in the learning of number sequences for students in compulsory secondary education to be considered. Therefore, the results presented in this study can provide information about the learning hypotheses of mathematical tasks related to numerical sequences and can help in the design of such tasks.

This study is qualitative with descriptive and aims to determine the process of generalizing the pattern image of high performance students based on the action, process, object, and schema (APOS) theory. The participants in this study were high performance eighth-grade Indonesian junior high school. Assignments and examinations to gauge mathematical aptitude and interviews were used to collect data for the study. The stages of qualitative analysis include data reduction, data presentation, and generating conclusions. This study showed that when given a sequence using a pattern drawing, the subjects used a number sequence pattern to calculate the value of the next term. Students in the action stage interiorize and coordinate by collecting prints from each sequence of numbers in the process stage. After that, they do a reversal so that at the object stage, students do encapsulation, then decapsulate by evaluating the patterns observed and validating the number series patterns they find. Students explain the generalization quality of number sequence patterns at the schema stage by connecting activities, processes, and objects from one concept to actions, processes, and things from other ideas. In addition, students carry out thematization at the schematic stage by connecting existing pattern drawing concepts with general sequences. From these results, it is recommended to improve the problem-solving skill in mathematical pattern problems based on problem-solving by high performance students', such as worksheets for students.

Digital puzzle worksheet (DPW) is innovative teaching material designed using open-source software such as Canva and Liveworksheets. Subsequently, puzzle games in the form of questions can improve problem-solving skills by engaging in metacognitive processes. This research used a case study method to describe the impact of applying the DPW to identify the metacognition levels of students through the assignment of contextual maths problems. The source of informants was third-grade elementary school students in West Java, Indonesia. Test instruments, observation sheets, and interviews were used, while data analysis adopted an iterative model. Furthermore, the method and time triangulation increased confidence in the resulting conclusions. The results showed that male students were at the metacognitive level of ‘strategic use’ and ‘aware use’ for females, based on the characteristics of the observed metacognitive level. The most prominent feature was identifying and determining problem-solving strategies with metacognitive awareness. The reaction of students to the DPW improved problem-solving abilities, expanded conceptual understanding, and enhanced digital technology competence. Therefore, this experience was applied when solving contextual mathematical problem assignments.

This research aims to describe secondary school students' functional thinking in generating patterns in learning algebra, particularly in solving mathematical word problems. In addressing this aim, a phenomenological approach was conducted to investigate the meaning of functional relationships provided by students. The data were collected from 39 ninth graders (13-14 years old) through a written test about generating patterns in linear functions. The following steps were conducting interviews with ten representative students to get detailed information about their answers to the written test. All students' responses were then analyzed using the thematic analysis software ATLAS.ti. The findings illustrate that students employed two types of approaches in solving the problem: recursive patterns and correspondence. Students favored the recursive patterns approach in identifying the pattern. They provided arithmetic computation by counting term-to-term but could not represent generalities with algebraic symbols. Meanwhile, students evidenced for correspondence managed to observe the relation between two variables and create the symbolic representation to express the generality. The study concludes that these differences exist due to their focus on identifying patterns: the recursive pattern students tend to see the changes in one variable, whereas the correspondence ones relate to the corresponding pair of variables.

This study aimed to compare and examine the effectiveness of interactive STEM learning and paper-and-pencil STEM learning in terms of mathematical literacy skills of elementary school students. This research is of a quasi-experimental type with a non-equivalent pretest-posttest control group design. Sampling was carried out on the elementary school populations in Bengkulu and South Sumatra Provinces in two stages. In the first stage, schools in rural and urban areas were selected, and in the second, classes in each school were randomly selected. The selected sample consisted of fifth-grade students of the Public Elementary School of Terawas, Musi Rawas, with an experimental class A (n = 20) and an experimental class B (n = 19), as well as fifth-grade students of the Public Elementary School of Bengkulu City, with an experimental class A (n = 25) and an experimental class B (n = 22). Data collection was conducted using mathematical literacy skills tests in reference to the PISA and Minimum Competency Assessment (level 1–3). Data analysis was performed using descriptive and inferential statistics; it employed an independent t-test for the comparative testing and an N-gain test for testing the effectiveness of STEM learning. The results showed that there were differences in math literacy skills between interactive STEM and paper-and-pencil STEM for students in urban schools, but not significantly different for students in rural schools. General STEM learning was effective in increasing the literacy of elementary school students, and interactive STEM in particular demonstrated the highest level of effectiveness in the urban school.

Mathematical confidence and critical thinking are essential in preparing preservice teachers. Thus, this study explored the perceived confidence and critical thinking levels in mathematics of elementary and secondary preservice teachers. A descriptive-correlational-comparative research design was employed, with a sample of 107 randomly selected preservice teachers enrolled in the Bachelor in Elementary and Secondary Education programs of a state university in West Philippines. The study used arithmetic mean, standard deviation, Spearman’s rank-order correlation, and independent samples t-test to analyze and draw conclusions from the data. The findings revealed that the preservice teachers have high confidence and critical thinking skills. Their program significantly correlates with their perceived critical thinking and confidence level. Besides, the preservice teachers’ confidence levels and perceived critical thinking skills significantly correlate. Further analysis found significant confidence and critical thinking differences favoring the secondary over the elementary preservice teachers. These findings provide insights that would benefit mathematics educators in providing priority programs to enhance the preparation of future math teachers.