Students’ Intuition in Solving Mathematics Problems: The Case of High Mathematics Ability and Gender Differences

Students are required to find their appropriate strategies to solve mathematics problems so that intuition is needed. Male and female students have different intuition on mathematical problem-solving. Thus, gender is influencing how to obtain mathematical knowledge. This descriptive qualitative study aimed to analize the intuition differences of male and female students who have high-level mathematical abilities at secondary school in solving mathematics problems. Data was collected through tests of mathematical problem-solving and interviews then analysed through data reduction, data presentation, and conclusion. This study found that: (1) There are differences in the characteristics of male and female intuition in mathematical problems solving, (2) The intuition of male and female in mathematical problems solving based on Polya's steps is different in re-checking the answers, (3) There are differences in intuition when students solve linear equation system problems. There are differences in intuition between male and female students with high matematical abilities in each material. Students with problem-solving abilities have affirmative intuition to understand problems, anticipatory intuition for problem-solving plans and solutions, and conclusive intuition to re-examine problems.

Exploring Children's Science and Mathematics Ability with Leaf Diary: A Case Study

Purpose – This study aims to explore Leaf diary activity to develop the Science and Mathematics ability of children aged 6 years.Design/methods/approach – The method used is a case study. The unit of analysis is based on predetermined criteria, using the purposive sampling technique. Research informants are mentors and children involved in leaf diary activity in Solok, Indonesia. The data collection process used participant observation, documentation, and in-depth interviews. Data analysis used structural analysis techniques.Findings – The results showed that leaf diary activity could develop: (1) children's ability to classify leaves based on their shape; (2) the ability to compare leaf size based on length, as well as large or small size.Research implications/limitations – All research informants were from Solok District, Indonesia, which may limit the generalizability of the findings.Practical implications – This case study contributes to the implementation of Leaf diary as an alternative activity that teachers or parents can do to develop children's science and mathematics ability.Originality/value – Leaf diary activity can help children explore the natural environment so that basic science and math abilities and concepts in this activity are carried out well. Paper type Case study

The relationship between numerosity perception and mathematics ability in adults: the moderating role of dots number

Background It has been proposed that numerosity perception is the cognitive underpinning of mathematics ability. However, the existence of the association between numerosity perception and mathematics ability is still under debate, especially in adults. The present study examined the relationship between numerosity perception and mathematics ability and the moderating role of dots number (i.e., the numerosity of items in dot set) in adults. Methods Sixty-four adult participants from Anshun University completed behavioral measures that tested numerosity perception of small numbers and large numbers, mathematics ability, inhibition ability, visual-spatial memory, and set-switching ability. Results We found that numerosity perception of small numbers correlated significantly with mathematics ability after controlling the influence of inhibition ability, visual-spatial memory, and set-switching ability, but numerosity perception of large numbers was not related to mathematics ability in adults. Conclusions These findings suggest that the dots number moderates the relationship between numerosity perception and mathematics ability in adults and may contribute to explaining the contradictory findings in the previous literature about the link between numerosity perception and mathematics ability.

Using Multi-Group Invariance Analysis in Exploring Cross-Cultural Differences in Mathematics Anxiety: A Comparison of Australia and Russia

Mathematics anxiety is well known and studied concept. Most of the studies have been focused on the effects of mathematical anxiety on students’ academic achievement, especially from the viewpoint of analysing large national and international data sets. We aim to bring a different perspective to the existing research on mathematics anxiety and resilience by considering the measurement equivalence across cultures, so they can be compared fairly. We used Multi Group Invariance analysis with this purpose. Our findings suggested that full metric and partial scalar model invariance were confirmed which advise that the mathematics anxiety scale can be compared across two countries. We also ran multiple regression using Fisher’s Z to understand the reciprocal relationship among the variables across two samples. Preliminary results revealed that the perceived mathematics anxiety and perceived mathematics ability predict the measured mathematics anxiety equally well for both Australia and Russia.

Pembinaan Instrumen Pencapaian Awal Matematik untuk Kanak-kanak Prasekolah

Kajian ini adalah membina instrumen untuk mengukur pencapaian awal matematik untuk kanak-kanak prasekolah. Dalam membina instrumen ini, penyelidik telah memilih kaedah konsistensi dalaman menggunakan Model Rasch. Dua set instrumen pencapaian awal Matematik kanak-kanak prasekolah diadaptasikan daripada Test of Early Mathematics Ability (TEMA) (Ginsburg dan Baroody, 2003) berdasarkan Kurikulum Standard Prasekolah Kebangsaan. Instrumen-instrumen ini merupakan ujian pra dan ujian pasca yang boleh digunakan untuk mengenal pasti kesan intervensi Matematik. Data kajian diperoleh melalui kaedah temu bual dan pemerhatian tulisan kanak-kanak yang seterusnya diterjemahkan kepada data kuantitatif. Kesemua item dalam kajian ini mempunyai kesahan konstruk iaitu berada dalam lingkungan 0.77 dan 1.30 semasa kajian rintis dijalankan.

PROFIL PEMAHAMAN MATEMATIS SISWA DALAM MENYELESAIKAN MASALAH BERDASARKAN KEMAMPUAN MATEMATIKA DI SMK MUHAMMADIYAH 1 BARON

Mathematics has a special characteristic that is an abstract object of study. Because of this specificity, learning mathematics requires mathematical understanding. Mathematical understanding in solving mathematical problems is different between each student. This difference is because each student has different mathematical abilities. The purpose of this study was to describe (1) the profile of mathematical understanding of students with high mathematics ability in solving problems (2) the profile of mathematical understanding of students with moderate mathematics ability in solving problems (3) the profile of mathematical understanding of students with low mathematics ability in solving problems. This research is a qualitative descriptive study with 3 students as the subject of class XI SMK Muhammadiyah 1 Baron. The selection of research subjects was based on students' mathematical abilities, namely high, medium and low mathematical abilities. Data collection techniques in this study using problem solving test techniques and interviews. The validity of the data used in this study used time triangulation. Based on the results of data analysis, the results showed that (1) The profile of mathematical understanding with high mathematical ability in solving quadratic function problems is the subject of reading the problem until it understands, writing correctly what is known and asked, conducting problem exploration appropriately, choosing the right problem solving strategy, looking for answers by doing algebraic calculations correctly and checking the answers back from the solutions obtained. (2) The profile of mathematical understanding with moderate mathematical ability in solving quadratic function problems is that the subject reads the problem until he understands, correctly states what is known and asked, skips problem exploration, looks for answers by doing algebraic calculations even though inaccurate answers are obtained and does not check answer back. (3) The profile of mathematical understanding with low mathematical ability in solving quadratic function problems is that the subject reads the problem until he understands, correctly states what is known and asked, skips problem exploration, looks for answers by doing algebraic calculations but gets inaccurate answers and does not check answer back. ABSTRAKMatematika memiliki karakteristik khusus yaitu objek kajian yang abstrak. Karena kekhususannya ini maka dalam mempelajari matematika diperlukan pemahaman matematis. Pemahaman matematis dalam menyelesaikan masalah matematika berbeda antar setiap siswa. Perbedaan ini dikarenakan setiap siswa memiliki kemampuan matematika yang berbeda. Tujuan penelitian ini adalah untuk mendeskripsikan (1) profil pemahaman matematis siswa berkemampuan matematika tinggi dalam menyelesaikan masalah (2) profil pemahaman matematis siswa berkemampuan matematika sedang dalam menyelesaikan masalah (3) profil pemahaman matematis siswa berkemampuan matematika rendah dalam menyelesaikan masalah. Penelitian ini merupakan penelitian deskriptif kualitatif dengan subjek penelitian kelas XI SMK Muhammadiyah 1 Baron berjumlah 3 siswa. Pemilihan subjek penelitian berdasarkan pada kemampuan matematika siswa yaitu kemampuan matematika tinggi, sedang dan rendah. Teknik pengumpulan data dalam penelitian ini menggunkan teknik tes pemecahan masalah dan wawancara. Keabsahan data yang digunakan dalam penelitian ini menggunakan triangulasi waktu. Berdasarkan hasil analisis data diperoleh hasil bahwa (1) Profil pemahaman matematis berkemampuan matematika tinggi dalam menyelesaikan masalah fungsi kuadrat adalah subjek membaca masalah sampai paham, menuliskan dengan benar apa yang diketahui dan ditanyakan, melakukan eksplorasi masalah dengan tepat, memilih strategi penyelesaian masalah dengan tepat, menacari jawaban dengan melalukan perhitungan aljabar dengan tepat serta melakukan pemeriksaan jawaban kembali dari solusi yang diperoleh. (2) Profil pemahaman matematis berkemampuan matematika sedang dalam menyelesaikan masalah fungsi kuadrat adalah subjek membaca masalah sampai paham, menyebutkan dengan benar apa yang diketahui dan ditanyakan, melewatkan eksplorasi masalah, menacari jawaban dengan melalukan perhitungan aljabar walaupun diperoleh jawaban yang kurang tepat serta tidak melakukan pemeriksaan jawaban kembali. (3) Profil pemahaman matematis berkemampuan matematika rendah dalam menyelesaikan masalah fungsi kuadrat adalah subjek membaca masalah sampai paham, menyebutkan dengan benar apa yang diketahui dan ditanyakan, melewatkan eksplorasi masalah, menacari jawaban dengan melalukan perhitungan aljabar namun diperoleh jawaban yang kurang tepat serta tidak melakukan pengecekan jawaban kembali.

Kemampuan Pemecahan Masalah Matematika Pada Soal Open Ended Materi Lingkaran Berdasarkan Kemampuan Awal Matematika Siswa

The research was aims to describe the problem solving in mathematics ability on open ended with circle material based on the early mathematical ability of the students at 9th grade junior high school 8 mataram. The type of the research is a descriptive study with quantitative approach. The research subject are 28 students which selected with purposive sampling. The subject is grouped according to early abilities of high, moderate, and low mathematics using the midterms. The data-collection method used is an open-ended problem-solving test on a loop of 2 terms of description and interview methods. The results were analyzed based on an indicator of problem solving capability according to Polya. Based on the data analysis, student problem solving capabilities with advanced mathematical abilities fall into good category, averaged 79.69. The student problem-solving capability with the early math skills is in good category, with an average score of 77.50. Student problem solving with early abilities of low math falls in the less category, with an average value of 48.30. The students with advanced math skills and are filling indicators of understanding the problem, planning a settlement and carrying out a completion plan, but have not yet met the checking indicator.

Pengaruh Kemampuan Penalaran dan Representasi Matematis terhadap Hasil Belajar Matematika Kelas VIII di SMP

This Research aims to know about the reasoning ability and mathematic representation ability to the results of mathematic lesson in students grade VIII SMP Negeri 1 Batulayar year academic 2019/2020. This research used quantitative approach with ex post facto research type. The population of this research is the eighth grade students of SMP Negeri 1 Batulayar. In determining the sample, probability sampling technique with the type of cluster sampling was used. The sample in this research is the students of class VIII B SMP Negeri 1 Batulayar amounted to 22 students. Data analysis used was multiple linear regression analysis. From the result of the data analysis we found the significant influence between reasoning ability and representative mathematic’s ability to the mathematics learning result of mathematic lesson in students grade viii smp negeri 1 batulayar year academic 2019/2020 with Fcount = 78,812 > F(2,19) = 3,52. The data we wroute as the same regration that Ŷ=-2,452+0,466X1+0,575X2. The equation show us that reasoning ability and the representative mathematic’s ability increase 1 unit and the learning result will increase to 0,466 from reasoning mathematics ability plus 0,575 representative mathematic’s ability.

KEMAMPUAN BERPIKIR KREATIF SISWA DALAM MENYELESAIKAN SOAL OPEN ENDED DITINJAU DARI KEMAMPUAN MATEMATIKA

The research describes the students' creative thinking ability in solving open-ended questions based on mathematics ability. Indicators of the ability to think creatively used in this study are fluency, flexibility, and novelty. This research is qualitative descriptive research. The subjects in this study were eighth-grade students of Baitul Fattah Junior High School, Sambikerep, Surabaya, 2019/2020 school year. The instruments used were the mathematics ability test, creative thinking ability test, and interview. The sum of the subjects who do the mathematics ability test is 30 students, the researcher chooses six students for the creative thinking test. Of the six students, three students were select to be an interview. There are five levels of TKBK (Creative Thinking Ability Level), namely fourth level (very creative), third level (creative), second level (quite creatives), first-level (less creative), and level 0 (not creatives). Based on the results of the analysis and discussion, it can be concluded that subjects with high ability have TKBK at the third level, namely creative with the acquisition of a score of four. Subjects with moderate ability have TKBK at the fourth level, namely highly creative with the acquisition of a score of thirty-six. While subjects with low ability have TKBK at the first level, namely are less creative with the acquisition of a score of thirteen.