The time-distribution of individual learning needs is a complex process. A longitudinal research on the distribution of learning needs for low achieving on standardized tests community college students  has been conducted and the visualizations of this distribution are presented. The most important element of this study is to provide learning services as needed during the entire time in which learning needs are traced.

    The theory of Lev Vygotsky about the absolute and relative student's ability to learn new concepts and skills is used as a guide. As Cole (1962) described Vygotsky's concept: "The Zone of Proximal Development is the distance between the actual developmental level as determined by independent problem solving and the level of potential as determined through problem solving under adult guidance or in collaboration with more capable peers." (Cole, 1962.)  

Fig. 1 The time scope is within one semester. The Zone of Proximal Development (ZPD) for one particular task and student (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).

The Highest Level of Intellectual Challenge For more details click math151 - college algebra Maximum time 2.2 hour   Intermediate level of Intellectual Challenge For more details click math091 - beginning algebra Maximum time 2.4 hour   The Lowest Level of Intellectual Challenge For more details click math081 - arithmetic review Maximum time 3.4 hours   Fig. 3 The total time of all students' visits for each day and time 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.

    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. All students, enrolled in three mathematics courses were free to visit or not the learning center. It was important to help each student as much as the student needed, but only in the zone of proximal development and not to do the work for students under their individual zones of proximal development.  The number of students are more than one hundred in each block, 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.

     During the equal number of days for each block of data, 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.

         Conclusion: The theory of Vigotsky 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's Theory, URL: http://facultyweb.cortland.edu/andersmd/VYG/ZPD.HTML

               Accessed    Nov. 8, 2003

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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• LEARNING DEMAND AND ZONES OF PROXIMAL DEVELOPMENT

• LEARNING ORIENTATIONS

• FROM THEORY INTO PRACTICE

 

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Last Updated - 11/19/2005

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