Development and Validation of Teachers’ Assessment Belief of Mathematical Thinking Instrument

<p style="text-align: justify;">This study was conducted to corroborate in understanding the teachers’ beliefs about assessment practices. The prior studies related to teachers’ assessment beliefs in mathematics have been done to assess teachers’ beliefs in the general context of mathematics teaching. This study developed an instrument to assess teachers’ assessment beliefs of mathematical thinking. The research aimed to develop and validate a scale of assessment beliefs of mathematical thinking by using the confirmatory factor analysis. The first draft of the scale contained 25 items. The sample of the study consisted of 537 mathematics teachers from public schools in Oman. The instrument was a questionnaire with a 5-point Likert scale. The scale was validated by asking a number of experts in mathematics educational measurement and evaluation. Exploratory and confirmatory factor analysis was applied to test the model of assessment beliefs of mathematical thinking scale using AMOS 25.0. All constructs had acceptable reliability. The model had a good model fit for the assessment beliefs of mathematical thinking scale which obtainable from the fit indices tests. The findings revealed that all fit criteria indices were realized. The results also showed acceptable validity and construct reliability for the scale.</p>

Responsiveness to Students’ Mathematical Thinking in Middle-Grades Classrooms

Responsiveness to students’ mathematical thinking is a characteristic of classroom discourse that reflects the extent to which students’ mathematical ideas are present, attended to, and taken up as the basis for instruction. Using the Mathematically Responsive Interaction (MRI) Framework and data from 11 middle-grades classrooms, we illustrate varied enactments of responsiveness and describe fluctuations in and relationships among different components of responsiveness. We found positive associations between different components of responsiveness, but they were not entirely predictive of one another. Individual classrooms appeared more or less responsive depending on which component was foregrounded. Our findings offer a more comprehensive characterization of responsiveness that documents the intertwined nature of teacher moves and student contributions during all whole-class instruction.

Pengaruh Pembelajaran Rigorous Mathematical Thinking (Rmt) Terhadap Peningkatan Kemampuan Berpikir Kreatif Siswa Ditinjau Dari Tingkat Habit Of Mind (Hom)

Salah satu tujuan pendidikan matematika adalah menjadikan siswa berpikir kreatif. Hasil dari berpikir kreatif disebut kreatifitas. Namun pada kenyataanya kreatifitas ini kurang diperhatikan oleh guru dalam pembelajaran. Sehingga kemampuan berpikir kreatif perlu dikembangkan lagi. Pemberian stimulus adalah salah satu cara untuk mengembangkan kemampuan berpikir kreatif dengan memperhatikan tingkat habit of mind siswa melalui pendekatan Rigorous Mathematical Thinking. Penelitian ini penelitian eksperimen dengan Quasi Eksperimental Design dan menggunakan desain factorial 3 x 2. Populasi dalam penelitian ini adalah siswa kelas VII MTs. Daar El Qolam 2020/2021. Sampel yang digunakan 2 kelas, dimana 1 kelas sebagai kelas eksperimen dan 1 kelas sebagai kelas kontrol. Instrumen yang digunakan berupa tes kemampuan berpikir kreatif matematis, skala sikap habit of mind, observasi dan wawancara. Data yang digunakan untuk menguji perbedaan dua rerata adalah uji-t, anova dua jalur dan korelasi. Hasil penelitian ini menunjukkan bahwa 1) terdapat perbedaan pengaruh implementasi pembelajaran pendekatan rigorous mathematical thinking dan pendekatan konvensional terhadap peningkatan kemampuan berpikir kreatif matematis siswa, 2) tidak terdapat perbedaan pengaruh tingkat habit of mind terhadap peningkatan kemampuan berpikir kreatif matematis siswa, 3) tidak terdapat pengaruh interaksi pendekatan pembelajaran dan tingkat habit of mind terhadap peningkatan kemampuan berpikir kreatif matematis siswa, 4) tidak terdapat korelasi positif antara kemampuan berpikir kreatif matematis siswa dengan tingkat habit of mind.

Practice-oriented tasks as a means of teaching mathematics to cadets of fire-technical specialties

The article is devoted to the problem of mathematical training of future fire safety engineers. In the process of training, cadets should have developed mathematical thinking, focused on the problems of civil protection. The basis for the formation of such thinking is the implementation of practice-oriented teaching of mathematics. Practice-oriented mathematical problems are an effective teaching tool. In the process of training specialists in fire-technical specialties, such tasks ensure the assimilation of mathematical concepts in the context of their interpretation in the professional field of activity of rescue engineers; creation of the mathematical basis necessary for studying the disciplines of the professional training cycle; development of the skill of constructing mathematical models of processes and phenomena in the field of protection of the population and territories. In this work, the author's definition of a practice-oriented mathematical problem is given, reflecting the real conditions of the service activities of specialists of the Ministry of Emergency Situations. Requirements for the content of such tasks for cadets of fire-technical specialties are formulated. A classification of practice-oriented tasks is proposed, taking into account the specifics of the future service activities of fire and technosphere safety engineers. Mathematical skills and abilities are indicated, the formation of which presents each type of problem, the corresponding practice-oriented mathematical skills necessary in the practical activities of civil protection specialists. Examples of tasks of all considered types are given.

USE OF COMPUTER TOOLS TO DEVELOP MOTIVATION OF STUDENTS TO STUDY MATHEMATICS: CRITERIA OF EFFICIENCY

The article considers the problem of development of cognitive activity of students in mathematics lessons. The peculiarities of the use of the formative system of assessment in the process of teaching mathematics with the use of computer tools in the context of the tasks of personality-oriented learning. The main risk factors for increasing the mathematical anxiety of students are identified. The pedagogical factors of motivation development and increase of interest in learning, development of mathematical thinking and reduction of mathematical anxiety due to the development of methods to increase the clarity of learning and cognitive activity of students related to the use of computer tools are substantiated. The criteria are substantiated and the indicators of assessment of the development of cognitive activity of students of 7‒9 grades of gymnasiums in the process of teaching mathematics with the use of computer tools are distinguished: motives of students learning at school; interest in studying the study of mathematics (algebra and geometry); success in the study of mathematics (algebra and geometry); motivation to study mathematical disciplines; mathematical anxiety. A method of assessing the impact of the use of computer tools to study certain topics and sections of mathematics in grades 7‒9 in general secondary education, which will increase the motivation of students to study the subject and reduce the level of mathematical anxiety of students. The results are presented and the dynamics of the indicators of the experimental influence of the use of computer interactive tools on the motivation of students to study mathematics is analyzed. Keywords: personality-oriented learning; mathematical disciplines; mathematical anxiety; pedagogical conditions; mathematics teaching aids; motivation to study mathematics; interactive computer learning tools; success in the study of mathematics.