Algebra I Teachers’ Beliefs and Knowledge of Algebra For Teaching

Research indicates that teachers’ mathematical beliefs and mathematical knowledge for teaching impacts practices in the classroom. Research also suggests that success in Algebra I is the gatekeeper to higher-level mathematics. With the increased number of certification pathways in some states, it is important to identify those Algebra I teachers’ beliefs and knowledge of algebra for teaching. A study of current Algebra I teachers revealed that regardless of certification pathway, mathematical beliefs are not significantly different. Additionally, significant differences did exist in regards to the certification pathway and Knowledge of Algebra for Teaching (KAT) levels.

Primary Teachers' Mathematical Beliefs and Practices in the Maldives

<p>Recent reforms in mathematics education have been influenced by such theoretical perspectives as constructivism, which have reconceptualised teaching and learning. Mismatches between teachers’ beliefs about teaching and learning, and ideas underpinning reform are often viewed as major obstacles to implementing educational reforms. This study examined the mathematical beliefs and practices, and factors affecting practices, of eight primary teachers selected from four schools in two different regions of the Maldives. The research used a multiple case study approach within a qualitative methodology. A questionnaire, semi-structured interviews, and observations were used to collect data about teachers’ beliefs and practice. Teachers’ lesson notes, worksheets, samples of student work, and test papers were used to understand teachers’ practice. Data were analysed within and across cases using a thematic approach. Teachers demonstrated a range of beliefs that included both constructivist and traditional elements to different degrees. In general, teachers’ observed practice was more traditional than their beliefs about teaching and learning mathematics. The teachers’ practice showed some consistency with their beliefs about the nature of mathematics, mathematics teaching and learning; however, the degree of consistency between beliefs and practice differed from teacher to teacher. Overall, the findings indicated there are several factors affecting teachers’ practice, including methods of assessment, teacher accountability for students’ results, limited time to cover the curriculum, lack of resources, and parental pressure to use textbooks. National assessment practices, affecting many factors found to limit practice, emerged as being particularly influential on the teachers’ instructional behaviour. The study suggests the need to change the nature of national assessment, and remove other barriers if teachers are to be best placed to implement their constructivist beliefs and the Maldives mathematics curriculum. The findings also have implications for professional development and teacher education programmes.</p>

Primary Teachers' Mathematical Beliefs and Practices in the Maldives

<p>Recent reforms in mathematics education have been influenced by such theoretical perspectives as constructivism, which have reconceptualised teaching and learning. Mismatches between teachers’ beliefs about teaching and learning, and ideas underpinning reform are often viewed as major obstacles to implementing educational reforms. This study examined the mathematical beliefs and practices, and factors affecting practices, of eight primary teachers selected from four schools in two different regions of the Maldives. The research used a multiple case study approach within a qualitative methodology. A questionnaire, semi-structured interviews, and observations were used to collect data about teachers’ beliefs and practice. Teachers’ lesson notes, worksheets, samples of student work, and test papers were used to understand teachers’ practice. Data were analysed within and across cases using a thematic approach. Teachers demonstrated a range of beliefs that included both constructivist and traditional elements to different degrees. In general, teachers’ observed practice was more traditional than their beliefs about teaching and learning mathematics. The teachers’ practice showed some consistency with their beliefs about the nature of mathematics, mathematics teaching and learning; however, the degree of consistency between beliefs and practice differed from teacher to teacher. Overall, the findings indicated there are several factors affecting teachers’ practice, including methods of assessment, teacher accountability for students’ results, limited time to cover the curriculum, lack of resources, and parental pressure to use textbooks. National assessment practices, affecting many factors found to limit practice, emerged as being particularly influential on the teachers’ instructional behaviour. The study suggests the need to change the nature of national assessment, and remove other barriers if teachers are to be best placed to implement their constructivist beliefs and the Maldives mathematics curriculum. The findings also have implications for professional development and teacher education programmes.</p>

HAMBATAN SISWA DALAM BELAJAR MATEMATIKA DIKAJI DARI KEPERCAYAAN MATEMATIS

The purpose of this study was to find out the learning obstacles in linear program assessed by mathematical beliefs at the Mujahidin Senior High School. The form of research used in this study is a case study. The data source used in this study was the students of class XI MIPA 1 in Pontianak Mujahidin High School, the data of which were the results of students' mathematical belief questionnaires and the answers of research subjects on the given test. Students learning obstacles in linear program material revealed in this study were assessed from mathematical beliefs including: students with mathematical beliefs in believing about mathematical characteristics have obstacles in the form of not being able to determine the mathematical model of linear program because he not understand teacher explanations, students with mathematical belief in believing about self abilitiy have an obstacles like not being able to mention the benefits of a linear program, students with mathematical beliefs in believing about teaching mathematics experience obstacles like not being able to make mathematical models correctly and the last is students with mathematical beliefs in believing about the usefulness of mathematics experiencing obstacles like not being able to make mathematical models because forget..

Kemampuan Pemecahan Masalah Mahasiswa pada Kalkulus Integral Dilihat dari Keyakinan dan Pengetahuan Awal Matematis

Integral calculus is a course where students tend to have difficulties in problem-solving. This study examines differences in mathematical beliefs in students' problem-solving skills based on mathematics prior knowledge. This study's subjects were 120 students of the Mathematics Education study program from UPH Faculty of Education. The independent variable is mathematical beliefs, the moderator variable is prior mathematics knowledge, and the dependent variable is students' problem-solving skills. This study is an ex post facto quantitative research with instruments in a Likert scale questionnaire for mathematical beliefs, problem-solving, and mathematics prior knowledge test scores. Hypotheses were tested statistically with a two-way Anova test using SPSS 16.0. The results of the study were: (1) students' problem-solving of logical consistency beliefs is higher than memorized and procedural beliefs, (2) there is an interaction between mathematical beliefs and mathematics prior knowledge on problem-solving, (3) students' problem-solving in high mathematics prior knowledge group of logical consistency beliefs is higher than memorized, and procedural beliefs, and (4) students' problem-solving in low mathematics prior knowledge group of logical consistency beliefs is lower than memorized and procedural beliefs.

KEYAKINAN MATEMATIS DAN KEMANDIRIAN BELAJAR MAHASISWA PADA PROGRAM STUDI PENDIDIKAN MATEMATIKA [MATHEMATICAL BELIEFS AND THE SELF-REGULATED LEARNING OF STUDENTS IN A MATHEMATICS EDUCATION STUDY PROGRAM]

<p>In general, integral calculus courses are difficult for students because the problems involved require strong problem-solving skills. For university students, integral calculus courses also require them to do self-regulated, or independent, learning. Another aspect that makes learning difficult for these students is their mathematical beliefs and prior knowledge. This study aims to see how different types of mathematical beliefs affect self-regulated learning in terms of students' prior knowledge. This research was conducted on students in a mathematics education study program at a private university in Tangerang with a sample of 120 students. This research is an ex post facto quantitative study using a two factorial design. The variables in this study consisted of independent variables in the form of mathematical beliefs, the moderator variable in the form of students’ prior knowledge, and the dependent variable in the form of self-regulated learning. The results obtained are: (1) self-regulated learning by students with logical consistency mathematical beliefs is higher than students with memorized and procedural beliefs, (2) there is an interaction between mathematical beliefs and prior knowledge towards self-regulated learning, (3) student in the high prior knowledge gorup logical consistency beliefs had higher self-regulated learning than students with memorized and procedural beliefs, and (4) self-regulated learning in the low mathematics prior knowledge group with logical consistency beliefs is lower than students with memorized and procedural beliefs.</p><p><strong>BAHASA INDONESIA ABSTRACT: </strong>Mata kuliah kalkulus integral pada umumnya masih menjadi kesulitan bagi mahasiswa karena permasalahan yang terkandung membutuhkan pemecahan masalah yang kuat. Kalkulus integral juga membutuhkan kemandirian belajar bagi mahasiswa yang mempelajarinya. Hal lain yang menjadi kesulitan mahasiswa adalah faktor keyakinan<em> </em>matematis dan pengetahuan awal matematis. Penelitian ini bertujuan untuk melihat perbedaan jenis keyakinan matematis terhadap kemandirian belajar mahasiswa ditinjau dari pengetahuan awal matematisnya. Penelitian ini dilakukan terhadap mahasiswa program studi pendidikan Matematika pada salah satu universitas swasta di Tangerang dengan sampel yang digunakan sebanyak 120 orang. Penelitian ini merupakan penelitian kuantitatif <em>ex post facto</em> dengan menggunakan desain dua faktorial. Variabel pada penelitian ini terdiri dari variabel bebas berupa keyakinan matematis, variabel moderator berupa pengetahuan awal matematis, dan variabel terikat berupa kemandirian belajar. Hasil penelitian yang didapatkan adalah: (1) mahasiswa dengan keyakinan<em> logical consistency</em> memiliki kemandirian belajar lebih tinggi daripada mahasiswa dengan keyakinan hafalan dan prosedural, (2) terdapat interaksi antara keyakinan<em> </em>matematis dan pengetahuan awal matematis (PAM) terhadap kemandirian belajar mahasiswa, (3) mahasiswa pada kelompok PAM tinggi dengan keyakinan<em> logical consistency</em> memiliki kemandirian belajar lebih tinggi daripada mahasiswa dengan keyakinan hafalan dan prosedural, dan (4) mahasiswa pada kelompok PAM rendah dengan keyakinan<em> logical consistency</em> memiliki kemandirian belajar lebih rendah daripada mahasiswa dengan keyakinan hafalan dan prosedural.</p>