An Analysis of Students' Mathematical Reasoning and Mental Computation Proficiencies

The purpose of this study was to examine fifth graders’ mathematical reasoning and spatial ability, to identify a correlation with their learning styles, and to determine the predictive power of their learning styles on their mathematical learning profiles. This causal study was conducted with 97 fifth graders (60 females, 61.9% and 37 males, 38.1%). The data were collected using three instruments: the Test on Learning Styles, the Mathematical Reasoning Test, and the Spatial Ability Test. Considering the combined view of the data on a plane, correlation and regression analyses were performed to identify correlations and prediction. The results showed that the students’ spatial ability was better than their mathematical reasoning ability. Their scores for visual, auditory, kinesthetic, reading, and combined learning accounted for 17% of the total variance in mathematical reasoning, whereas their scores accounted for 20% of the total variance in spatial ability. Of the learning styles, only visual l...

This research was examining students’ mathematical reasoning by the open-ended approach. This research has a purpose to train students’ mathematical reasoning abilities to think logically and know how much is the effect of open-ended approach to students’ mathematical reasoning abilities. The subjects of this research are the students of 5th grade in elementary school Gugus I, Buleleng sub-district, Bali. The instrument using mathematical reasoning test which made by the researcher with reference to indicators of mathematical reasoning abilities of P4TK Yogyakarta. This research is a quasi-experiment research with randomized control group pre-test post-test design. The outcomes of the research tell us that in the experimental group, where the students in the experimental group were treated by open-ended approach during the learning process and the students in control group were treated by conventional approach during the learning process. Students’ mathematical reasoning in the experimental group was better than students’ mathematical reasoning in control group after post-test was given. Both groups had similar performance in the pre-test. Both groups were following common work schedule. Open-ended approach gave positive influences on students’ logical thinking abilities.

Bu araştırmanın amacı matematik öğretmen adaylarının matematiksel muhakeme etme kavramına yönelik öz yeterlik inançlarını konu edinen bir değerlendirme yapmaktır. Bu amaç doğrultusunda öğretmen adaylarının matematiksel muhakeme etme öz yeterlik düzeyleri ve bir problemde yer alan matematiksel muhakeme etme göstergelerini belirleyebilme durumları arasında bir değerlendirme yapılmıştır. Araştırmada nicel araştırma yöntemlerinden biri olan tarama deseni kullanılmıştır. Araştırmanın çalışma grubunu 51 matematik öğretmen adayı oluşturmaktadır. Araştırmada kullanılan veri toplama araçları “Matematiksel Muhakeme Öz-Yeterlik Ölçeği”, “Matematiksel Muhakeme Etme Problemleri” ve “Matematiksel Muhakeme Etme Göstergeleri Tablosu” dur. Araştırmanın sonucunda, öğretmen adaylarının matematiksel muhakemeye yönelik öz yeterliklerinin ölçek ortalamasının üstünde olduğu ve öz yeterliklerinin yaratıcı düşünme alt boyutunda en düşük, ilişkilendirme alt boyutunda ise en yüksek olduğu belirlenmiştir. Öğretmen adayları matematik problemlerinde yer alan matematiksel muhakeme etme göstergelerini belirleyebilme açısından yeterince başarılı olamamışlardır. Bunlara ek olarak öğretmen adaylarının matematiksel muhakeme etme öz yeterlik düzeylerinin matematiksel muhakeme etme problemlerinde yer alan matematiksel muhakeme etme göstergelerini belirleyebilme durumları üzerinde istatistiksel olarak anlamlı bir etkisinin olduğu görülmüştür. Sonuç olarak öğretmen adaylarının matematiksel muhakeme etmelerinin desteklenmesi ve matematiksel muhakeme etmeye yönelik içsel inançlarının güçlendirilmesi onların ilgili alanda donanımlı birer öğretmen olmalarına katkı sağlayacaktır.

The aim of this study is to determine the seventh-graders’ levels of mathematical reasoning and to reveal their performance. The present study was carried out with 167 seventh-grade students studying at randomly selected three elementary schools that served low and middle socioeconomic areas in a city of Turkey. “Mathematical Reasoning Test (MRT)” was developed and used as data collection tool. In analyzing the data, participants’ scores of the test was computed and which mathematical reasoning level they were in was determined. Sample responses of the some students regarding any question (Q7) in the test were presented directly and discussed. As a result of the analysis, it was found that about half of the students (45.5%) had medium and 27.5% of them had low level of mathematical reasoning. When the results are evaluated, it is probable to say that that most of the students’ mathematical reasoning is at medium or low level in general. On the other hand, it is remarkable that rather than the familiar classical problems, students need to be enabled to deal with the problems that they can do reasoning and thus their mathematical reasoning could be improved.

Pseudo construction thinking occurs when students assume that true/false belief is actually not totally true/false. The study aimed to describe the characteristics and causes of students’ pseudo thinking in solving mathematical reasoning about number operation based on mindset. This research was descriptive qualitative research. The subjects of this study were 30 Junior High School students in Kebumen. Data collection techniques used mathematical reasoning test, questionnaire mindset, and interview. The mathematical reasoning test was constructed with making a conjecture as indicators. Questionnaire of mindset adapted from Mindset Work. Interviews were used to support the validity of data related to subjects indicated to have pseudo. Based on the result of the research: (1) there are 20 students with growth mindset and 10 students with fixed mindset; (2) fixed mindset students do false pseudo, 3) growth mindset students do both types of pseudo and 4) the cause of these pseudo are conceptual and procedural error.

Students' ability to solve mathematical adaptive reasoning problems is still relatively low. As a result, students have difficulty in solving mathematical adaptive reasoning problems. The cause of the low mathematical adaptive reasoning ability of students is the lack of learning tools that facilitate mathematical adaptive reasoning ability. Therefore, a Collaborative Problem Solving-based tool was developed that can stimulate an active learning process, motivate students and improve mathematical adaptive reasoning skills. This research is a development research using the Plomp development model. The products developed are lesson plans and worksheets based on Collaborative Problem Solving for class VIII junior high school statistics material. The purpose of this research is to produce Collaborative Problem Solving-based tools that are valid, practical, and effective on the mathematical adaptive reasoning skills of grade VIII junior high school students. The results showed that the learning tools in the form of lesson plans and LKS based on Collaborative Problem Solving for students in grade VIII junior high school were valid, practical, and effective. The results of the validation of the learning tools developed are very valid, adjusting 5 indicators of mathematical adaptive reasoning skills seen from the aspects of making conjectures, providing reasons for the answers given, drawing conclusions from a statement, checking the validity of an argument, and finding patterns from a mathematical problem. The results of the practicality of learning devices are very practical in terms of ease of use, suitability of time allocation, attractiveness and usefulness. Furthermore, it is said to be effective because it has an impact on students' mathematical adaptive reasoning ability of 82.70% with a very good category.

It is crucial to have suitable learning models in the Freedom curriculum, allowing students sufficient time to delve into concepts and improve skills, particularly in mathematical reasoning and disposition. CORE learning (Connecting, Organizing, Reflecting, and Extending) is a different approach to enhancing upper school students' mathematical reasoning and disposition abilities. This quantitative study employs descriptive and two-way multivariate analysis to examine the impact of learning models and gender on students' mathematical reasoning and disposition abilities. The study focuses on grade IX students at a public senior high school in Surakarta, Indonesia. The control group is class Phase E-8, which follows a direct learning approach and is known as the Non-CORE class. In the meantime, the Phase E-10 class is an experimental class implementing the CORE learning model. The study findings show variances in mathematical thinking and attitude among high school students in CORE versus non-CORE classes. Additionally, there is no reliance on enforcing CORE learning on male and female students, suggesting that CORE learning can be suggested for enhancing mathematical reasoning skills and disposition ability of all students irrespective of gender. CORE learning has been proven to be an effective strategy for improving students' mathematical reasoning and disposition through education oriented towards a constructivist approach centered on students, where students actively construct their knowledge through a series of processes that connect, organize, reflect, and extend concepts. This study contributes to the discourse on constructivist pedagogy by providing strong evidence that the CORE learning model improves mathematical reasoning and attitudes among upper secondary students. Those taught with CORE outperform peers in traditional settings in both cognitive and attitudinal measures. The lack of gender-based differences indicates CORE supports equitable learning. Aligned with Indonesia’s Freedom Curriculum, the model promotes active, student-centered learning and shows promise as a scalable, inclusive approach to improving math proficiency and engagement.

This research is based on the importance of logical-mathematical thinking skills in solving logical-mathematical problems. The research purpose is to describe high school students' logical thinking abilities on geometric transformation material in terms of mathematical self-concepts. The research used a qualitative approach, with the research subject as many as six students of 12th grades science class from one of Bandung Regency high schools selected by sampling technique. Students' logical thinking ability is known from the test scores in solving compiled problems. The score refers to logical-mathematical thinking ability indicators, and the problem-solving technique refers to the Polya stages. Data analysis techniques used are data reduction, data presentation, descriptive statistical calculations, and conclusions/verification. The results showed that the overall students’ logical-mathematical thinking ability in the geometry transformation material is in the medium category. In the self-concept category, subjects with high self-concept can fulfil logical thinking questions based on Polya stages. As for subjects with moderate self-concept, the students can only fulfil several indicators of logical-mathematical thinking skills with problem-solving techniques. The result is still not perfect refer to the Polya stage. As for the subject with low self-concept, almost all Polya stages are not fulfiled. The students in the low self-concept category answered the questions incompletely. They had difficulty understanding the problem and planning a solution so that their answers did not match the questions.

Mathematical reasoning skills are essential in understanding mathematical concepts and solving problems. This study aims to examine the influence of learning discipline, mathematical anxiety, and self-efficacy on students' mathematical reasoning ability through critical thinking skills. The study utilized an ex-post facto research design with a sample of 100 eighth-grade students from UPTD SMPN 2 Barru. Data were collected through questionnaires on learning discipline, mathematical anxiety, and self-efficacy, as well as critical thinking and mathematical reasoning tests. The findings indicate that learning discipline, mathematical anxiety, and self-efficacy significantly influence mathematical reasoning ability both directly and indirectly through critical thinking skills. Moreover, students with high discipline tend to have better reasoning skills, while those with high mathematical anxiety demonstrate lower reasoning ability. The study suggests that improving students' learning discipline and self-efficacy while reducing mathematical anxiety can enhance their mathematical reasoning ability.

This study aimed to investigate the effect of a training program based on the trends in international mathematics and science study (TIMSS) on developing the habits of mind and mathematical reasoning skills among pre-service math teachers in Oman. The study sample consisted of 24 female pre-service math teachers divided into two equal groups: experimental and control. The study data was collected by sued the mathematical reasoning test and questionnaire that measured the level of habits of mind after appropriate validity and reliability. The study results showed statistically significant differences between the two study groups in favor of the experimental group in the mathematical reasoning test and the habits of mind scale. The study recommended that the need for pre-service math teachers to use programs based on international studies such as TIMSS, PISA, PIRLS, and TAILS; this was done to prove their effectiveness in developing the levels of habits of mind and mathematical reasoning skills by subjecting them to training programs, courses, and workshops with the aim of training teachers to implement the training programs effectively.

The aims of this study are: 1) to describe the ability to understand concepts through students' mathematical reasoning on the Cube and Block material; and 2) to determine the relationship between the mathematical reasoning abilities of MTs. students NW Senyiur with the ability to understand the concept of Cube and Block material. This research is a qualitative descriptive study conducted on 25 MTs. students NW Senyiur on the material of cubes and blocks. Data on students' mathematical reasoning abilities were collected through Mathematical Reasoning Tests (non-routine questions), while students' conceptual understanding abilities were collected through Concept Understanding Tests (routine questions). The two tests given each consist of 2 questions. In addition, interviews were conducted to collect more complete information from the sample that had been studied. Research data were analyzed by Pearson Product-Moment Correlation Test. The results of this study indicate that: 1) the average grade IX MTs. students NW Senyiur has good reasoning ability and conceptual understanding; and 2) there is no relationship between mathematical reasoning ability and concept understanding ability of grade IX MTs. students NW Senyiur on the material of cubes and blocks. The magnitude of the significant value that exceeds the provisions and the standard significance value is > 0.05, then there is no significant correlation (H0 is accepted). Thus, it can be concluded that, in this study, there is no relationship between mathematical reasoning abilities and students' conceptual understanding abilities.

This study aims to examine the effectiveness of the application of the Group Investigation cooperative learning model in optimizing student motivation and learning outcomes on ratio material, as well as analyzing its contribution to mathematical reasoning skills. This study used a quantitative approach with a pre-test and post-test design involving 20 junior high school students in grade VII. Data were obtained through mathematical reasoning ability test, motivation questionnaire, and analysis of students' learning outcomes. The results showed an increase in the mean score from pre-test to post-test by -6.50 (p = 0.001) which reflects more uniform student learning outcomes. Regression analysis showed a very strong relationship between the independent variable (mathematical reasoning) and the dependent variable (motivation and learning outcomes) with an R value of 0.929 and R2 of 86.4%, indicating that motivation and learning outcomes explained most of the variation in reasoning ability. Specifically, the contribution of mathematical reasoning (X) to student learning outcomes (Y2) was 38.94% while the contribution of motivation (Y1) to mathematical reasoning reached 45.83%. In addition, regression analysis shows that motivation has a significant influence on mathematical reasoning ability, while learning outcomes have a positive but statistically insignificant influence. This finding indicates that the Group Investigation cooperative learning model is not only effective in improving student learning outcomes, but also has an important role in strengthening mathematical reasoning skills through increased motivation. Therefore, cooperative learning strategies that emphasize increased motivation need to be applied in mathematics learning to optimize students' analytical thinking skills.

Mathematical reasoning is the ability to think about mathematical problems, namely by thinking logically about mathematical problems to get conclusions about problem solutions. There are several factors that can affect students' mathematical reasoning, including mathematical abilities. Dissimilarity of students' mathematical abilities allows for dissimilarity in their mathematical reasoning abilities. So, this research intends to describe students' mathematical reasoning abilities in solving social arithmetic problems based on dissimilarity in mathematical abilities. The purpose of this research was to describe qualitative data about the mathematical reasoning abilities of students with high, medium, or low abilities in solving social arithmetic problems. The instrument used was the Mathematical Ability Test to determine the three research subjects, followed by a Problem Solving Test to get qualitative data about students' mathematical reasoning abilities, then interviews to get deeper data that was not obtained through written tests. Thus, the research data were analyzed using mathematical reasoning indicators. From the result of data analysis, it was found that all students understood the problem well. Students with high and medium mathematical abilities are determining and implementing problem solving strategies properly, namely writing down the step for solving them correctly and making accurate conclusions by giving logical argumens at aech step of the solution. However, students with low mathematical abillities have difficulty in determining and implementing problem solving strategies because they do not understand the concept, thus writing the steps to solve the problems incorrectly and not giving accurate conclusions about the correctness of the solution.
 Keywords: mathematical reasoning, problem solving, mathematical abilities

Schools play a critical role in enabling students to discover, develop, and express their creative potential. However, instructional practices that explicitly promote students’ creative thinking skills in mathematics learning remain limited. Therefore, this study aims to examine and describe the creative thinking processes of junior high school students in solving mathematical reasoning problems. This study employed a qualitative case study design involving 35 eighth-grade students. A mathematical reasoning test was administered to identify students’ levels of creative thinking. Based on the results, four students representing different categories of creative thinking (imitative, routine, creative, and very creative) were purposively selected as research subjects. Data were collected through students’ written work, in-depth interviews, and document analysis. The findings indicate that each category demonstrates distinctive characteristics in terms of problem-solving strategies, flexibility of ideas, and originality in constructing solutions. Students in the higher creative categories tended to generate multiple strategies and more original solution processes. These findings emphasize the importance of designing mathematics learning activities that encourage exploration of diverse strategies, idea generation, and reflective thinking.

This study aims to determine the relationship between the skill of weaving various types of rattan woven motifs with the ability of mathematical logical thinking of students in schools around the Galmantro Rattan Tourism Village of Cirebon Regency. The method used is a quantitative research method with a One-Shot Case Study research design. Data collection techniques used in the form of observation, tests, and questionnaires. The results of this study are (1) during the training, the respondents felt interested in knowing how to weave and the types of woven motifs for rattan crafts because in reality the respondents had never tried directly to weave rattan woven motifs; (2) based on the correlation coefficient test between weaving skills and the mathematical logical thinking test the t and t_table test values are 7.711 more than 2.045, so that the two variables have a significant relationship with the relationship level of 0.599 in the medium category. Keywords: weaving skills, woven motifs, mathematical logical thinking