عنوان مقاله [English]
Teachers need a variety of knowledge and competencies to teach mathematics well, and examining teachers' status of these skills and competencies can be a good area of research. One of the competencies needed by teachers is the competence of designing mathematical tasks. mathematics task plays a key role in students' mathematics learning, and " what students learn is largely defined by the tasks they are given." There are various definitions of mathematics task in research literature. Watson and Sullivan (2008) define mathematics task as information that serves as the prompt for student work, presented to them as questions, situations, and instructions that are both the starting point and context for their learning. Various classifications for mathematics tasks have been presented so far. One of them is the classification of tasks according to the type of their function in the teaching process. In this type of classification, tasks are classified to 1- warm up task; 2- learning task; 3- review task; 4- Practice task; 5. Assessment tasks. Assessment tasks are tasks that the teacher uses to evaluate students' performance, and because of the role and importance of assessment in the mathematics teaching and learning process, can play an important role in the teaching and learning process. With Considering the importance of the ability to design task, one of the appropriate situations that can study teachers' ability in this case by that, is the mathematical problem posing situation. Silver (1994) defines the mathematical problem posing as producing of a new problem from a situation or experience, new formulating of problems. Stoyanova and Ellerton (1996) classified problem-posing situations according to their structure into three categories: 1) free; 2) semi-structured; and 3) structured. A review of the research literature revealed that one of the areas deceived by researchers is examining the relationship between teachers' task design ability and teacher' problem posing ability, and evaluating teachers' task design ability using problem posing situations. Accordingly, the present study aimed to investigate the elementary school teachers' ability of designing assessment tasks based on problem posing situations regarding two addition and subtraction operations. The reason for this study of the two acts of addition and subtraction is the role and importance of these two actions in the mathematical learning of individuals. addition and subtraction is the foundation of school mathematics and has an impact on mathematical content across different grades. The following statement portrays the essential function of addition and subtraction (Ma 2010): 1) It is foundational because it provides a foundation for students’ further mathematics learning. 2) It is elementary because it is at the beginning of mathematics learning. 3) It is primary because it contains the rudiments of more advanced mathematical concepts (p. 106). A descriptive survey method was used to conduct this study. The statistical population of the study consisted of elementary teachers of the country from whom 151 of whom participated in one of State Mathematics Supply Courses New Mathematics Textbooks for Elementary School were selected by convenience sampling. To collect the data, a researcher-made test was used in which the teachers' ability of assessment task design for two addition and subtraction operations was evaluated through the free problem posing situation. The issues raised by the teachers were analyzed on two basis: 1) addition and subtraction and 2) task design. For the analysis of problems based on addition and subtraction action axis, closed-ended symbolic problems were analyzed using Van de Walle et al. (2015) model and closed-ended verbal problems were analyzed using Riley et al. (1983) model. To analyze issues based on task design, symbolic issues regarding their open-ended and closed-ended responses and verbal issues based on 1- open-ended and closed-ended questions, 2- Shao (2018) model and 3- Shimizu et al. (2010) model Were analyzed. The results of the posed problems based on the addition and subtraction action axis showed that the problems that the teachers posed symbolically were more limited to the two forms of "unknown result (addition)" and "unknown result (subtraction)" and the problems presented in others formats were low (less than 10% each). The analysis of the verbal problems revealed that the questions were mostly in two modes of change and composition and the percentage of the issues in the form of comparison was very low (7%). It was also found that the verbal issue was not in the form of "Compare 6". In analyzing problems base on the task design axis also revealed that very few of the posed problems (4% symbolic and almost 0% verbal) were open-ended and most of the questions were closed-ended. The results of the verbal problem analysis revealed that although most of the verbal questions had real-life contexts (89%), there was no task designed to engage students in solving practical problems. The results also revealed that among the designed tasks, there was no task that was completely "authentic", "rich" and "complex", and although most of the designed tasks involved students at the “application” level, they were tasks that link them. With real life and application, it was limited to mentioning an object or an event from the real world and not really contextual. On this basis, it can be concluded that most of the tasks designed were low-level tasks.
Given the impact of math textbook content on teachers' task design ability, it is suggested to improve the math textbook design capability so that the content of math textbooks can be modified to Have the necessary diversity generally in all topics and specifically in both addition and subtraction operations. Another suggestion is to enhance teachers' task design ability, provide appropriate instructional content on mathematics tasks, and conduct empowerment courses and workshops based in these content.
This study was conducted using convenient sampling method, so the results of this study cannot be generalized to the whole elementary school teachers. Accordingly, it is recommended that a similar study be conducted with appropriate sampling methods that can be generalized to the whole population. Another limitation of this study was that teachers were asked to design tasks for evaluation. This can lead to limiting them in the design of diverse tasks given teachers' perception of evaluation as final assessment. Accordingly, different studies are suggested to investigate the ability of teachers to design task based on different tasks in the teaching process.