Mathematical Problem-solving Tasks Research Articles

EEG-Based Focus of Attention Tracking and Regulation During Dual-Task Training for Neural Rehabilitation of Stroke Patients.

Dual-task training under variable-priority instructions (DT-VP), during which subjects are required to vary their focus of attention (FOA) between two concurrent tasks, has shown a more significant improvement in neural rehabilitation than that under fixed-priority instructions. Failed FOA switching not only diminishes the recovery benefits, but also causes anxieties, which is detrimental to rehabilitation. Developing a strategy for tracking and regulating patients' FOA to achieve a better performance in task priority-following during DT-VP is thus imperative. In this study, fifteen stroke patients participated in DT-VP that comprised two tasks: a mathematical problem-solving task and a cycling task, during which their electroencephalograms were recorded simultaneously. The significantly differentiated power spectra of four brain regions extracted from single-task training were fed into a support vector machine to build a FOA tracking algorithm for patients' attention assessment during the DT-VP. Moreover, dual-task difficulty adaptation method was designed to regulate patients' FOA when their FOA and the high-priority task were not coincident. The comparison experimental results showed that the proposed method significantly improved patients' FOA distributed on the high-priority task (analysis of variance, 0.05). Meanwhile, the absolute power spectral densities of the motor cortex and the frontal region could also be improved during DT-VP under high motor and cognitive task priority instructions, respectively. These phenomena demonstrated the feasibility of the proposed method in helping stroke patients better implement FOA switching and maintenance.

A Qualitative Microanalysis of the Immediate Behavioural Effects of Mindfulness Practices on Students’ Self-Regulation and Attention

The study examined the immediate effects of mindfulness practices on students’ attention and self-regulation during mathematical problem-solving tasks. Participants were 15 4th-grade Finnish students and their teacher. Data were collected during six study sessions of mathematical problem-solving, with and without mindfulness practices. The sessions were video-recorded, and children responded to the Freiburg mindfulness inventory and the cognitive and affective mindfulness scale-revised. A qualitative video micro-analysis focused on coding the observable behaviours related to attention and self-regulation. Self-report instruments were scored and tabulated for comparison. The findings indicate microbehavioural changes indicating positive effects of mindfulness practices on students’ self-regulation, with higher signs of engagement and lower signs of disengagement after mindfulness practices. This study enlightens the use of mindfulness practices in school routines and discusses the impacts of these practices while evidencing that future research on the topic is needed.

Identifikasi Penalaran Kreatif-Imitatif Siswa dengan Gaya Kognitif Reflektif

This research is aimed to describe the creative and imitative reasoning of students with reflective cognitive styles on math problem solving. The study uses a qualitative approach with a data collection instrument used of Matching Familiar Figure Tests, math ability test, mathematical problem-solving tasks, and interview guidelines. The research result studies indicate that a student with reflective cognitive style that have imitative reasoning in problem solving is less able to provide comprehensive information, still using a problem-solving strategy previously known, nor does he make a return check on the results received. It is different with reflective subjects that have proven creative reasoning capable of delivering well-known information, that can provide novel and thought-provoking solutions. Moreover, he also looking back the resulting solutions to the problem.

Assessing students’ self-efficacy when solve mathematical problem based on gender

Self-efficacy, problem solving, and gender differences are aspects that many researchers concern to today. Therefore, the purpose of this study was to describe the profile of students’ self-efficacy in solving problems based on gender. We used a qualitative approach with exploratory research to answer the research objectives. We used the Mathematical Ability Test (TKM) instrument, Mathematical Problem-Solving Tasks (TPMM), and interview guidelines to consider the selected subjects. Next, two students were selected (14 years old, of different gender, and had good math skills) to participate in the study. Data from transcripts and student work were used to perform data analysis. The results revealed that there were fundamental differences between the two subjects based on three dimensions of self-efficacy (magnitude, strength, and generality). This is discussed further in this article. Finally, we suggest to explore the influence of regional culture on students’ self-efficacy in the classroom.

SELF-EFFICACY ANALYSIS OF STUDENTS' MATHEMATICAL PROBLEM-SOLVING ABILITY IN ABSOLUTE VALUE EQUATIONS MATERIALS

Participants can profit from the ability to solve issues by first understanding them, then choosing the best technique, and then applying it to problems in both mathematical and non-mathematical situations. Many variables contribute to students' inability to answer mathematical questions, one of which is a lack of confidence in their abilities. The purpose of this study is to describe how well-equipped pupils are to deal with arithmetic challenges associated with absolute value equations. Study participants were selected from each level after each level's self-efficacy was assessed using questionnaires. The tools used in data collection procedures, which are training tactics, include short interviews, self-efficacy questionnaires, and assessments of one's ability for solving mathematical problems. The data processing and analysis process have three stages: data reduction, data presentation, and conclusion-making. The research subjects were three students from each of the three self-efficacy levels—very high, high, and medium—and their propensities for resolving mathematical puzzles were then evaluated. Students with a very high level of self-efficacy perform mathematical problem-solving tasks more effectively than students with high and medium levels of self-efficacy.

Exploration of high school students' reasoning in solving trigonometric function problems

Reasoning has been extensively studied by many experts. However, Research on student reasoning in trigonometric problem solving, particularly those related to logical thinking skills is still sorely needed. This study aimed to explore students' reasoning in solving trigonometric function problems regarding logical thinking skills. The research was conducted using a qualitative approach. The research subjects involved high school students in Palopo, Indonesia. Based on the logical ability test results, three subjects were selected, namely students with high, medium, and low logical abilities. Research instruments in mathematical problem-solving tasks and interview guidelines are valid and reliable. Data collection was carried out through task-based interviews and think-aloud. The results of the study: (1) the reasoning subjects with high and moderate logical abilities in solving trigonometric function problems are the same in every type of question, always starting with inductive reasoning and then doing deductive reasoning (2) the reasoning of subjects with high and medium logical abilities is different in solving trigonometric function problems in the initial identification. Subjects with low logical ability showed no mental activity in solving trigonometric function problems. The research finding is that the subject has a high logical ability and is solving trigonometric function problems first by inductive reasoning and then deductive reasoning. In general, it is concluded that students with high and moderate logical abilities use inductive and deductive thinking patterns interchangeably in solving trigonometric function problems.

The Effects of Acute Exercise and Virtual Reality Tasks on Children’s Memory Function and Exercise Preference

Background: It is well established that regular participation in exercise and virtual reality (VR) environments are important tools for improving or maintaining human health and cognitive function. Objectives: This study examined the effects of acute exercise and VR environments on children’s memory function and exercise preference (i.e. cycling with or without the use of VR technology). Methods: Α 2×3 factorial design was adopted with two measures (pre, post) and three study groups. Forty-five healthy children aged 9 to 13 years (Mage = 10.91±1.24 years) voluntarily participated in the study. Participants were randomly assigned into three groups receiving different treatment: (1) an exercise+VR group that cycled for 15 min in a VR environment (forest path) combined with basic mathematical problem-solving tasks, (2) an exercise group that cycled for 15 min, and (3) a no-exercise group that sat in a specific place in a lab for 15 min (the control group). Before and after the acute exercise, all the groups completed the Sternberg Memory Task. Upon completion of the intervention, the two exercise groups completed measures of enjoyment, intention and attitudes towards cycling. The exercise+VR group also completed a scale capturing the VR’s usability. Results: The results show that the exercise group scored higher on Sternberg’s Memory Task (p .05) after the acute exercise treatment (post) than before it (pre). Similarly, the exercise+VR participants scored higher on the post-intervention memory task than did the exercise and control groups (p .05). Moreover, the exercise+VR group reported higher scores on enjoyment, intention and attitude towards cycling than the exercise group, but this difference was not statistically significant (p .05). Finally, the exercise+VR participants recorded high scores on the usability of the VR system during the acute exercise programme. Conclusions: These findings are in line with those of previous studies, underlining the important roles of exercise and VR environments on youths’ cognitive function.

How Does Working Memory Capacity Affect Students’ Mathematical Problem Solving?

<p style="text-align:justify">Problem-solving process requires information processing, and the information processing is related to working memory capacity (WMC). This study aims to determine the effect of WMC on students' mathematical abilities and to describe the ability of the students with high and low WMC in solving mathematical problems. This research used mixed method with Sequential Explanatory Design. The quantitative data were collected through the provision of OSPAN tasks and math tests to 58 students aged 15-17 years, while the qualitative data were collected through interviews based on mathematical problem-solving tasks. The results showed that WMC had a significant effect on students' mathematical abilities (R=0.536; p=0.000). Researchers found differences in students' mathematical problem-solving abilities with high and low WMC. Students with high WMC can remember and manage information well which supports the determination of more advanced problem-solving strategies and have better attention control so that they find varied appropriate solutions. Students with low WMC experienced decreased attention control as the complexity of the tasks increased, missed important information in problem solving strategies, and did not recheck their work, leading to wrong solution/answer. The mathematical performance of students with high WMC outperformed the mathematical performance of students with low WMC.</p>

DESKRIPSI KREATIVITAS MATEMATIKA DALAM PEMBELAJARAN BERBASIS MASALAH DENGAN PENDEKATAN OPEN ENDED

This research is qualitative descriptive research, which aims to describe: (1) student creativity in product aspects, (2) student creativity in process aspects, (3) student creativity in affective aspects. The data collection techniques in this study are, the provision of mathematical problem-solving tasks (TPM), and task-based interviews in a blended (online and offline). Furthermore, the data will be analyzed qualitatively which includes: (1) the triangulation of data aimed at obtaining valid data. Triangulation used is triangulation method, which is comparing data through interviews with the results of student work, (2) doing reduction, abstraction, exposing data, (3) interpreting data, (4) concluding. The results showed that one subject from a high level based on GPA was able to show all indicators of creative thinking ability well, namely fluency, flexibility, novelty and elaboration in solving problems and can be classified into level 3 (Creative). One other subject from a high level based on GPA was able to show 2 indicators of creative thinking ability, namely fluency and elaboration in solving problems so that they can be classified into level 2 (Quite creative). While two subjects from the moderate level and two subjects from a low level based on GPA are only able to show one indicator of creative thinking ability, namely the elaboration indicator so that it can be classified into level 2 (Quite Creative).

Neural Correlates of Single-Task Versus Cognitive-Motor Dual-Task Training

Single-task and cognitive-motor dual-task training (CMDT) has been extensively studied for the post-stroke function rehabilitation. However, little is known about the difference between the brain activities when these two types of tasks are being implemented. Therefore, neural correlates of single-cognitive/motor-task training (SCT/SMT) versus CMDT are investigated in this study. Specifically, a pure mathematical problem-solving task and a pure cycling task were designed for the SCT and SMT paradigms, respectively. For the CMDT, subjects should perform these two tasks simultaneously. Electroencephalography signals acquired during performing these two types of training are used to analyze the brain dynamic properties by event-related potential and event-related (de-)synchronization analyses. It can be seen from the results that compared with the SCT, theta event-related synchronization can be increased significantly by the CMDT (frontal theta: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -value <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$= 5.44e-05 &lt; 0.0001$ </tex-math></inline-formula> and temporal theta: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -value <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$= 9.18e-06 &lt; 0.0001$ </tex-math></inline-formula> ) and, meanwhile, the mu and central beta event-related desynchronization induced by the CMDT is significantly lower than that induced by the SMT (mu: p-value <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$= 2.28e-06 &lt; 0.0001$ </tex-math></inline-formula> and central beta: p-value <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$= 4.37e-06 &lt; 0.0001$ </tex-math></inline-formula> ). Therefore, it is proved in this study that the SMT can induce higher motor neural engagement than the CMDT and, meanwhile, compared with the SCT, higher cognitive neural activity can be induced by the CMDT, which can be explained by that the multitask coordination induces more neural activities. In addition, it is found that more attention has been paid on the relatively difficult task during the dual-task training. Therefore, the difficulty level of each task in the CMDT paradigm can be designed subject specific to implement the personalized training.

Understanding the Problem Solving Strategy Based on Cognitive Style as a Tool to Investigate Reflective Thinking Process of Prospective Teacher

The development of reflective thinking has been a highlight and important in the education of prospective mathematics teachers. It provides them with the opportunities to take a conscious and logical decision on the complex problems they faced. The quality of the problem solving and reflective thinking will differ between one student and another due to their characteristics. This study presents a description of reflective thinking skills of prospective teachers in solving mathematical problems based on the difference in cognitive style. The instruments used in this study consist of (1) GEFT cognitive-style test, (2) a mathematical problem solving task which is a non-routine and open-ended (3) the interview guidelines based on the reflective thinking component. By choosing analysis of qualitative approaches, the data of interviews that are in the form of interview's transcript based on mathematical problem solving results are gathered from two students of prospective mathematics teachers as research participants. One prospective teacher use cognitive field independent style (PTFI) and field dependent style (PTFD). Research findings show that PTFD tends to use the experience to be implemented in mathematical problem solving but PTFD cannot utilize the new information contained, so that PTFD has a reflective-dynamic characteristic. While PTFI tends to use the experience to utilize the new information contained in the problem in order to construct the problem solving strategy so that PTFI has reflective-generative characteristic. It is indicated that there are differences in the characteristics of reflective thinking process among prospective teachers based on difference of cognitive style.

Shifting of perfective metacognitive activities in solve math problems

This study aims to describe the shift in the perfective metacognitive activities of students in solving mathematical problems. The subjects in this study were students who experienced a shift in the perfective metacognitive activities of students in solving mathematical problems. This research is a qualitative research with a descriptive exploratory approach. The instrument used was a mathematical problem solving task type MEA (Model Eliciting Activities), interview guidelines, and questionnaires. Data collection procedures in this study consisted of five stages. In the first stage, the researcher asks each student to solve the problem given while thinking alouds. The second stage, students are asked to solve the same problem as a group while discussing with two other students, then researchers observe and listen to the results of think alouds as well as the results of conversations during group discussions from a computer screen. The third step is giving the questionnaire. The fourth stage is task-based interviews to explore information that needs to be confirmed from the results of think alouds and questionnaires. Next to the fifth stage, researchers analyzed data from student work outcomes, think alouds, questionnaires, recorded conversations of students during discussions, and interviews. Based on the results of the study, there were students who experienced a shift in perfective metacognitive activity in solving mathematical problems.

Mathematical problem solving tasks in the form of high order thinking skill

This article describes mathematical problem solving task which is categorized in form of high order thinking skills. The study used descriptive qualitative as research methodology and involved junior high school students in Palembang city as research subject. Data collections consist of students’ worksheet, observation, and interview. The result showed that mathematical problem solving tasks categorized into form of high order thinking skill were mathematical tasks that contain commands to do analysis, evaluation, or creativity. A question that requires students to recognize elements needed and their relationship is kind of analysis type. Furthermore, a question containing command to accept or to reject a statement based on their analysis is included into evaluation type. Moreover, if it provokes students to make new structures that have never existed before or to generalize an idea then this is creation type. The classification of mathematical problem solving tasks including HOT problems is based on the top of Bloom’s cognitive taxonomy.

Exploration of students’ representation in solving pythagorean theorem problems based on cognitive style

This study aims to explore the students’ representations in solving Pythagorean theorem problems. Participants of this study consisted of a female student with reflectiv estyle and a female student with impulsive cognitive style. They had an equivalent mathematical ability. This study used the qualitative method. The researcher decides on the methods of data collection based on mathematical problem-solving tasks and task-based interviews. To obtain valid data, the researcher performs the time triangulation. The findings of the study showed that: (1) the mathematical representations of reflective student were (a)recognizingand presenting known and unknown information visually by sketching the car’s path, (b) revealing then formulating problem-solving strategy using visual representation, (c) revealing mathematical model manipulation involve Pythagorean theorem, and (d) looking back the solution by using verbal representation;(2) the mathematical representations of impulsive student were (a)recognizing then presenting known and unknown information verbally, (b) revealing then formulating a problem-solving strategy using visual representation, (c) revealing mathematical model manipulation by saying that the distance between point A and B can be determined using the Pythagorean theorem, and (d) looking back the solutions by using verbal representations.

Kemampuan Pemecahan Masalah Matematis Ditinjau Berdasarkan Kecerdasan Emosional Siswa Kelas VII SMP

The research aims to get an overview about the ability of students in solving mathematical problem based on their emotional intelligence. This is qualitative research with a case study design. The subjects of this research were seventh-grade students who has high emotional intelligence, consisting of a student from catholik junior high school in Kefamenanu and one students from state secondary school in Kota Kupang, They were obtained using purposive. The data were collected using a questionnaire of emotional intelligence, a mathematical problem-solving task, and a interview sheet. The analysis of what is obtained from both subjects, being the high crossing of catholik junior high school students Kefamenanu, it is obtained from cross-leg’s ability: students can understand the matter, make quick plans, to implement completion plans and examine back. The state junior high school in Kupang have the ability of low-vang problems acquired from abilities of emerging problems: students cannot understand matter, students are less able to create completion plans and students cannot examine the return settlement sequences

Does chess instruction improve mathematical problem-solving ability? Two experimental studies with an active control group

It has been proposed that playing chess enables children to improve their ability in mathematics. These claims have been recently evaluated in a meta-analysis (Sala & Gobet, 2016, Educational Research Review, 18, 46–57), which indicated a significant effect in favor of the groups playing chess. However, the meta-analysis also showed that most of the reviewed studies used a poor experimental design (in particular, they lacked an active control group). We ran two experiments that used a three-group design including both an active and a passive control group, with a focus on mathematical ability. In the first experiment (N = 233), a group of third and fourth graders was taught chess for 25 hours and tested on mathematical problem-solving tasks. Participants also filled in a questionnaire assessing their meta-cognitive ability for mathematics problems. The group playing chess was compared to an active control group (playing checkers) and a passive control group. The three groups showed no statistically significant difference in mathematical problem-solving or metacognitive abilities in the posttest. The second experiment (N = 52) broadly used the same design, but the Oriental game of Go replaced checkers in the active control group. While the chess-treated group and the passive control group slightly outperformed the active control group with mathematical problem solving, the differences were not statistically significant. No differences were found with respect to metacognitive ability. These results suggest that the effects (if any) of chess instruction, when rigorously tested, are modest and that such interventions should not replace the traditional curriculum in mathematics.

Constructive metacognitive activity shift in mathematical problem solving

This study aims to describe the constructive metacognitive activity shift OF eleventh graders in solving a mathematical problem. Subjects in this study were 10 students IN grade 11 of SMAN 1 Malang. They were divided into 4 groups. Three types of metacognitive activity undertaken by students when completing mathematical problem are awareness, regulation, and evaluation. This was a descriptive qualitative research with exploratory approach. Data collection instruments used were mathematical problem solving task of Model Eliciting Activities (MEA) and interview. In the first stage, students completed MEA mathematical problems individually while doing think aloud. In the second stage, students worked in small groups consisting of three students to solve the same problem and then the researchers recorded the results of the discussion by using a handycam. In the third stage, the researchers conducted task-based interviews to determine the metacognitive activity performed by students when solving problems either completed them individually or in group. Based on the analysis results of students’ work, think aloud, students’ conversations record group during discussion and interviews, the data show that three students spread into 4 groups of constructive metacognitive activity shift. Key words: Metacognitive activity, socially metacognition, constructive metacognitive activity shift, problem solving.

Elementary students’ metacognitive processes and post-performance calibration on mathematical problem-solving tasks

Calibration, or the correspondence between perceived performance and actual performance, is linked to students’ metacognitive and self-regulatory skills. Making students more aware of the quality of their performance is important in elementary school settings, and more so when math problems are involved. However, many students seem to be poorly calibrated, with a tendency towards over-confidence. The present study analyzes the relationship between post-performance calibration accuracy and the metacognitive process shown by 524 fifth- and sixth-grade students while solving two math problems. After calculating a calibration index and establishing the stability of students’ judgments and actual performance, differences in the metacognitive process exhibited by students with different calibration accuracy (Accurate vs. Inaccurate groups) were analyzed. The emergence of different calibration patterns and differences in the metacognitive process as a function of mathematics achievement and grade level were also examined. Results indicated that: (a) students in the overall sample were little calibrated and over-confident, showing high stability in their judgments and actual performance across problems; (b) inaccurate students reported using information representation sub-processes (drawing/summarizing) less frequently, but writing and reviewing (and also correcting mistakes) more frequently than their accurate peers; and (c) differences in calibration patterns and the metacognitive process were found when achievement level was considered, whereas grade level did not generate any important effect. These findings suggest the usefulness of process-based measures to examine the metacognitive processes involved in making post-performance judgments, considering achievement and its possible mediating role in this relationship.

EEG-Based Attention Tracking During Distracted Driving.

Distracted driving might lead to many catastrophic consequences. Developing a countermeasure to track drivers' focus of attention (FOA) and engagement of operators in dual (multi)-tasking conditions is thus imperative. Ten healthy volunteers participated in a dual-task experiment that comprised two tasks: a lane-keeping driving task and a mathematical problem-solving task (e.g., 24+15=37?) during which their electroencephalogram (EEG) and behaviors were concurrently recorded. Independent component analysis (ICA) was employed as a spatial filter to separate the contributions of independent sources from the recorded EEG data. The power spectra of six components (i.e., frontal, central, parietal, occipital, left motor, and right motor) extracted from single-task conditions were fed into support vector machine (SVM) based on the radial basis function (RBF) kernel to build an FOA assessment system. The system achieved 84.6±5.8% and 86.2±5.4% classification accuracies in detecting the participants' FOAs on the math versus driving tasks, respectively. This FOA assessment system was then applied to evaluate participants' FOAs during dual-task conditions. The detected FOAs revealed that participants' cognitive attention and strategies dynamically changed between tasks to optimize the overall performance, as attention was limited and competed. The empirical results of this study demonstrate the feasibility of a practical system to continuously estimating cognitive attention through EEG spectra.

Knowledge and knowing in mathematics and pedagogy: a case study of mathematics student teachers’ epistemological beliefs

This study focuses on mathematics student teachers’ epistemological beliefs in mathematics and education. The study aimed at gaining insight into the challenges that students experience in the consolidation of knowledge in the two disciplines. The case study with three mathematics pre-service teachers utilised mathematical and pedagogical problem-solving tasks, interviews and stimulated recall. The findings suggest that epistemologies are domain-specific, and that students may struggle with the consolidation of mathematical and pedagogical knowledge. We identified six aspects that can challenge consolidation: the students believed that pedagogical knowledge is highly relative; their knowledge of methods of inquiry in education was weak; they viewed theoretical pedagogical knowledge as unrelated to practice; they held formalistic beliefs about mathematics; they were performance-orientated in solving the mathematical problems; and they relied on authority, rather than proof, as a justification for mathematical knowledge.