فصلنامه نوآوری های آموزشی
پیاپی 53 (بهار 1394)

Over the recent decade cognitive diagnostic measurement approach in spite of the prevalent (common) educational measurement approaches such as classic theory and item-response theory has attained a special status, because this approach integrates cognition theories with learning so as to provide a profile of students’ cognitive competencies. With regard to such approach, a diagnostic test concerning students’ math literacy cognitive competencies consisting of 20 questions based on cognitive model of PISA (2012) was devised. The test included Communication & Using symbolic, formal and technical language and operations; Mathematising & Representation; Reasoning & Argument and Devising strategies for solving problems. The statistical population of the present research consisted of 10th grade students in the field of mathematics, science and literature, during the academic year of 1392-1393. Through Probability Proportional to Size approach, a sample of 688 students was selected and the test was administered. Students’ responses were analyzed by using DINA model and R software. Diagnostic capacity of test at the item level and producing students’ competency profiles were reported. The research findings indicated that through a diagnostic test based on cognitive competencies and by using DINA model, students’ competency profile could be identified.

This study utilizes a meta-analysis for combining the numerical results of studies on the relation between learning strategies and math problem solving performance. The population of this meta-analysis was the available published researches relating to learning strategies and math problem solving performance in Iran from 1369 up to 1389. Based on the defined inclusion and exclusion criteria as well as sensitivity analysis, 59 effect sizes on 25 primary researches were investigated. After checking the inclusion and exclusion criteria, the findings of selected primary studies were analyzed using the CMA2 and SPSS18.The results showed that the learning strategies have had significant effect on problem solving math performance and according to Cohen's criteria the combined effect size of learning strategies and math problem solving performance was moderate to high (ES =0/44). Based on the heterogeneity analysis, gender and research methods were used as moderators’ variables. The results of t-test showed that the combined effect size of the learning strategies and mathematics problem-solving performance differences between male and female learners were not insignificant, but the combined effect sizes significantly were different between experimental and correlation research. In summary, it can be concluded that teaching the learning strategies and encouraging learners to use them can have a significant impact on their math problem solving performance.

Using the data of TIMSS 2011 and the statistical methods, namely hierarchical linear modeling, in this study we suggested a mathematic achievement model for Iranian students in terms of the selected variables. The data was collected from 4837 students nested in 227 schools. Variables were entered into the model at two levels, i.e., student (gender, parents’ education level, number of books available at home, student’s perception of school, mathematic values, selfconcept of ability in mathematics) and teacher/school (teacher’s experience, teacher’s education level, teacher’s perception of school, teacher’s cooperation with others) to demonstrate the most important mathematical achievement predictors. The analysis of the data using the hierarchical linear model showed that among the levels of the student variable, the self-concept of ability in mathematics, numbers of books available at home, and student’s perception of school; and among the levels of the teacher/school variable, teacher’s experience and his perception of school predicted students’ mathematics achievement. Finally, the Mathematical Progress Model indicated the most important variable as “self-concept of ability in mathematics” and it showed that 1 unit increase in self-concept of ability in mathematics leads in 46.05 unit increase in the mathematics achievement level. This model also decreased the18.2 percent of “within-school” variances and 16.3 percent of “between-school” variances, in comparison with the first model.

Understanding the concept of variable is a foundation for comprehension of many concepts of algebra. Abstract nature and multiple applications of variables are perceived as difficult by students. The goal of current research - which was a descriptive survey - was to identify misconceptions about the concept of variable in preliminary algebra. In this study, 185 female 10 years old students in two educational districts of Tehran were selected based on convenience sampling method. Measurement tools for this study were a written exam and a semi-structured interview. The reliability of the test was calculated using Cronbach’s Alpha (α = 0.811).The results showed that many students have a limited understanding of the concept of variable. Students’ performance in understanding the variable as a general number was weaker than the other application of variable as a specific unknown and its application in functional relationship. Moreover, they had various misconceptions such as considering variable as a label or abbreviation of the name of objects, considering a variable as a specific number, determining the amount of variable according to its sign, processing the non-homonymous units as homonymous ones, and supposing variable as positive number. They also believed that different variables cannot hold the same value.

From 2011, the structure of educational system in Iran has undergone another drastic change in terms of grade levels. The previous one was in the form of 5 years primary school, 3 years guidance school (grades 6 to 8), 3 years high school and 1 year pre-university. In the new system that has been mandated in 1390 (2011) and gradually implemented since 1390- 91 (2011- 2012) school year, there are 6 years primary school, 3 years junior high school and 3 years senior high school (6-3-3). In this new system, there is a plan to re-write the national mathematics textbooks according to the new curricular aims and based on the assessment results of the current mathematics textbooks. The purpose of this paper is to illustrate the mathematics teachers’ perspectives at the guidance school to help curriculum developers and textbook authors to cultivate more clear and realistic views about the current situation at this grade level (i.e., grades 6 to 8) according to the mathematics curriculum. The variables of the study are: the level of teaches’ understanding of objectives, content and the other components of mathematics curriculum; and teachers’ perspectives about mathematics curriculum and textbooks, teaching and learning methods, and instructional materials. The data were collected using a teacher's questionnaire, interview and focus group. To analyze the quantitative data, we used descriptive statistics, as well as inferential statistics, including nonparametric ratio test, parametric t-test and single sample z-test. The data that were collected through focus groups and interviews were analyzed, categorized and summarized to complete and support the quantitative part of the data. Findings showed that there is a lack of consistency between the mathematics curricula of the grades 6 to 8 (guidance school). From the teachers’ perspective, the main reason for the lack of consistency is the difference between the mathematics curriculum objectives and the reality of educational environment including teacher's proficiency, cultural and educational beliefs, students’ needs, and the content of textbooks, assessment methods, classroom environment and the time of instruction.

The purpose of this study was to investigate the effect of chess training on 5thgrade students’ problem solving abilities. The review of literature started with the research on novice and expert problem solvers. We then found a number of studies regarding the mathematics’ problem solving and chess training. The findings paved the way to conduct the present study. The study was experimental and we used one-group pretest-posttest design. A cluster random sampling method was used to choose 25 fifth graders from the population of all 5th grade students in the center of one of the south-eastern provinces of Iran. Cronbach Alpha coefficient was used to insure the reliability of the tests. In addition، 52 sessions of chess training was offered by one of the authors as “treatment”. The research showed that chess training had a positive and meaningful effect on the 5th grade students’ mathematical problem solving abilities. This finding could help the mathematics curriculum developers and textbook writers to use chess as an effective tool to promote students’ problem solving abilities either as extra-curricular activity or integrated with the formal school mathematics curriculum.