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This study aimed at finding out how to achieve the criteria of communication and representation in mathematics for the higher basic school stages in Jordan in light of 2000 (NCTM) standards. The study attempted to answer the following two questions: Q1: How can the criterion of mathematical communication be achieved for the higher basic stage students in Jordan in light of 2000 (NCTM) standards? This question may be divided into the following four sub-questions: 1- How do higher basic stage students express their mathematical ideas in writing? 2- How do higher basic stage students express their mathematical ideas verbally? 3- How do higher basic stage students evaluate the mathematical ideas of peers and others? 4- How do higher basic stage students read the mathematical content? Q2: How can the criterion of the mathematical representation be achieved for the higher basic students in Jordan in light of 2000 (NCTM) standards? This question may be divided into the following three sub-questions: 1. How can higher basic stage students organize the mathematical ideas? 2. How can the students of higher basic stage translate the mathematical ideas? 3. How can higher basic stage students model the real situation? To answer the questions of the study, the researcher intentionally chose two schools from different rural areas. Two sections from each school were chosen, one from the 8th grade, and the other was from the ninth grade, 5 students were chosen from each participant section as participant students: one of them was high achiever, the other was a good one, two were middle level, and the 5th one was below the middle . Students levels were chosen according to the maximum variation sampling strategy.
In collecting data, the following tools were used: 1- Observation sheet: to observe the skills of mathematical communication and representation for the participant students in their classes during the learning process in light of a program approved by teachers. 2- Analyzing two student documents: participants’ summaries for the 1st and 2nd semesters, and their semester final examination papers as regards writing, organizing, translation, and modeling mathematical ideas. The researcher’s role was as participant observer, his role included: living the situation, registering observations directly on the observation sheet, analyzing data gradually, interpreting data from the participants points of view. The researcher attended 54 periods divided equally between two schools and the two classes, 27 periods each grade. To increase the internal validity, the researcher used the cross validation through triangulating resources and locations, extending field work, registering class notes directly, analyzing data, consulting with supervisors, teachers and participant students, using participants’ language to present results. The data was analyzed according to the qualitative method by categorizing it into two main dimensions: content dimension which included: concepts, generalizations, skills, problem solving ;and skill dimension . The skill dimension included two skills ; communication and representation . Communication skill included four basic skills : verbal expression, non-verbal expression, written expression, reading and evaluating. The representation skills were categorized into three basic skills: organizing, translation, and modeling. The categorized data was analyzed according to standards based on 2000 - NCTM standards in the fields of communication and representation. The results of the study in the communication field showed the following patterns. - None accuracy in verbal expression of algebraical and geometrical concepts, and generalizations. - Students used their body language such as: raising hand and nodding heads to show their agreement and understanding. - Algebraic quantities, roots, inequalities, angles, and shapes could not be read accurately by students. - Using algebraic and geometric signs & symbols could not be expressed precisely by students . - The mathematical problems could not be solved in a coherent way. As regards the representation field the results showed the following patterns: - Organizing algebraic and geometric problems in shapes and relations were not accurate. - Representing equations , inequalities and functions in tables and charts were not be precise. - Students could not translate the algebraic quantities precisely. - Students could not translate the geometrical generalizations to symbols and shapes precisely. - Students did not use modeling in life situations.
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