Zone of Proximal Development and

Learning Demand and Zones of Proximal Development

Zone of Proximal Development and Students' Learning Demand

Humans' learning needs and learning demands are two different constructs concerning humans' learning. In a learning process, the time-distribution of individual learning needs requires a complex analysis, involving knowledge and understanding on how humans feel, reason, and in learning settings. For each learning task and for each group of students, the zone of proximal developments in terms of Vygotsky (1978) is a distribution of students needs of tutoring; therefore, the utilization of learning services is also a measure for the distribution of zones of proximal development.

In this study, the measure of students' usage of different learning services is considered a measure of students' learning demand. Students' learning demand depends on learning services (observable) and learning needs (a hidden variable). The utilization of learning services (learning demand) in a learning center is an observable, measurable and controllable variable. On the bases of students' learning demand, some inferences about learning needs in terms of distribution of zones of proximal development are a resourceful step in the complex task of learning need analysis.

The variable of students' learning demand -- LD -- is presented in this study as thee dimensional variable: (OX) the day of visit in the learning center, (OY) the initial time of visit in the particular day, and (OZ) the duration of student's visit. All students' visits are presented in the study with the three dimensional point of learning demand (XYZ). If a student has more than one visit at the same day, each visit is considered a new event.

Student can perform some task or some challenging portions of the task under adult guidance in reasonable time. In general, tutoring emphasizes the individualized instruction in the zone of proximal development, while teaching emphasizes the content and evaluation. In the social process of learning, those who can and know how to approach certain learning problem help the novice to learn. At the same time, students do not need help nonstop to learn. There are areas of personal study, in which students can perform well without help or guidance. Today, many schools are trying to provide individualized instruction outside of the classroom; colleges and universities provide tutoring programs. The expanding e-learning requires different management of learning services, constant monitoring of students' learning needs, and fast change in case that the need of individualized instruction is not needed anymore. At the same time, e-learning requires knowledge of acceptable sequences of materials, level of intellectual challenges, and the dynamic of group ability to learn from each-other.

For every task, each student has particular level of challenge to which he/she can work independently; after that level, the student needs help. The ZPD is the measure for how much more the student can learn with help.

Fig. 1 The Zone of Proximal Development (ZPD) for one particular task and student is illustrated. (ZPD is the level of intellectual challenges at which the students can perform with tutoring or cooperative learning.)

Fig. 2 For each individual, the ZPD changes with the time, according to Bodrova and Leong (1998). The time scope in this picture is at least three semesters, not necessary consecutive.

The goal of this study is to observe and describe the zone of proximal development "encapsulated" in students' learning demand. How the total need of learning assistance will change with the advancement of a group of students? The study is focused on students in three mathematics courses during one semester time-interval for each course. The change of students' learning needs in advanced classes compare to learning needs in remedial classes are considered a dynamical observation of the change of student zone of proximal development. The goal is to provide visual evidence of Bodrova and Leong's (1998) ideas for a group of students.

The Hypothesis is that the distribution of students' learning demand will change in the long run as students move from remedial to pre-college math classes. The results of our observations are represented on Fig. 2. The visualization of students' learning demand is done with methods of cartography. Statistical methods used in the study are the same as methods used in modern physics to penetrate the fine structure of solid state materials. The size and the density of the individual zones of proximal development, if they depend on students' learning demand, should decrease although the intellectual challenges are increasing (The Tutoring Paradox).

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Fig. 3 The total time-distribution of students' visits for each day of the semester and the time in this day chosen by the student to utilize some learning services is presented as 3D maps. Students' visits at a learning center for three math classes with increasing (from bottom up) intellectual challenges. The horizontal time-axis also represent the direction of increasing intellectual challenges within one and the same developmental class.

To describe students' learning needs of assistance in mathematics, for three selected mathematics courses, the number of visitors in the learning center is measured with 3 variables;day of visit (OX), time of visit during the day (OY), and length of visit measured in hours (OZ). It the data presented on Fig. 3, during the equal number of days in one and the same semester, the students' visits at a learning center are measured by the time-length of their visits in the learning center to get help for the three math courses selected for the study -- arithmetic, beginning algebra, and college algebra.

The data, collected within the first seven weeks of the spring semester 2003, is grouped in 3 blocks - one for each of the three mathematics courses - arithmetic review (bottom), beginning algebra (middle), and college algebra (top). All students, enrolled in three mathematics courses were free to visit or not the learning center at any time at which the learning center was opened. It was important to help each student as much as needed, preferably in the zone of proximal development (if possible), and not to do the work for students under their individual zones of proximal development. With other word, tutors were trained and encouraged to help if student is stuck by explaining the problems, and if the students does not know the material and can do some study, tutors were trained to guide the student to do the study. Almost all tutor training programs emphasize the need of guidance, leading the student, helping with the learning cycle. what is missing in all tutor training programs, is the need of help in the zone of proximal development.

In this study, the number of students enrolled in each course is more than one hundred., and the number of students enrolled in different sections of one course is plus or minus 10% from course to course and through the semester. The number of students can not be held constant; some students are dropping, some are in the learning center every day and some just once or twice. The dynamic of students' learning demand is depict and presented in the paper as a first attempt to use data to identify the "shadows" of the distribution of zones of proximal development. The organized data is compared with some studies of the zones of proximal developments by Bodrova and Leong (1998)

Conclusion: The theory of Vigotsky (1978) about the Zone of Proximal Development can be used as a guide for students' need of tutoring services. This study tested a hypothesis of decreasing need of tutoring with the increasing intellectual difficulties. The results are obtained in a long period of time from the beginning of semester to the time before the midterm. All records after the midterm are ignored due to dominant role of curricular objectives. The results are very encouraging for students who are first generation to college and adult learners, students at risk and all students that feel mathematical anxiety and frustration.

References

Vygotsky, L.S. (1978), Mind and society: The development of higher mental processes.

Cambridge, MA: Harvard University Press.

Bodrova, E., & Leong, D. (1998). Scaffolding Emergent Writing in the Zone of Proximal Development.

Literacy, Teaching and Learning, 3(2), 1.

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