The goal of this paper is to explore students' proportional reasoning under conditions of human mediation as compared to computer-based mediation. The target of our dynamic assessment – proportional reasoning – is directly linked to mathematical problem solving and as such bridges between cognitive and instructional areas. Fifty three seventh grade male students (age 13-14) participated in the study. They were pre-and post-tested using a modified version of Harel et al (1992) Blocks task. In this task the students are shown two pairs of blocks (A,B and C,D), all bricks in blocks A and C weigh the same and all the bricks in B and D also weigh the same. The students are informed about the weight relation between blocks A and B and are asked to infer about the weight relation between blocks C and D. Students’ answers were ranked from reasoning Level 0 ("wild guess') to Level 6 (fully proportional explanation).

The first group of students received human mediation based on classroom discussion, while the second group received a computer-mediated program. The comparison of pre- and post-tests demonstrated that mediation in both groups was effective in enhancing the level of proportional reasoning. The effect size of computer mediation was 1.4, the effect size of human mediation was 1.2.  Though the students' proportional reasoning level was much lower than predicted by the classical Piagetian theory,  a considerable reasoning potential was within the students’ Zone of Proximal Development as revealed during a short (2 hours) mediation session. Computer-mediation turned out to be more effective than human mediation. At the same time different learning patterns were identified in these two forms of mediated learning. Students with identical pre-test performance demonstrated different learning potential thus confirming the educational value of dynamic assessment as compared to the static assessment paradigm. 

The goal of this paper is to explore students' proportional reasoning under conditions of human mediation as compared to computer-based mediation. Our research aimed at answering a number of still-open questions pertaining to the fields of dynamic assessment, mediated learning and cognitive foundations of mathematical reasoning. The absolute majority of dynamic assessment research (see Lidz and Elliott, 2000; Sternberg and Grigorenko, 2002) focuses on general cognitive functions that are rather distant from curricular material. The target of our dynamic assessment – proportional reasoning – is directly linked to mathematical problem solving and as such bridges between cognitive and instructional areas. In the developmental tradition of Jean Piaget proportional reasoning has often been presented as a natural form of human cognition reflecting individual experience and maturation. We, however, looked at this phenomenon from Vygotskian perspective in which development and instruction are inseparable and students' cognitive development is explored within their Zone of Proximal Development (ZPD). Finally, while the predominant trends of the mediated learning experience research (Feuerstein et al, 1980; 2006) focus on students' cognitive change produced by the involvement of the human mediator, we have created experimental conditions that allow us to compare the impact of direct human mediation and mediation provided via an interactive computer program

            Sixty eight seventh grade male students (age 13-14) participated in the study. All students were from medium socio-economic status families residing in the center of the country.

            The task that was used to assess the development of proportional reasoning was a modified version of Harel et al (1992) Blocks task. In this task the students are shown two pairs of blocks (A,B and C,D), all bricks in blocks A and C weigh the same and all the bricks in B and D also weigh the same. The students are informed about the weight relation between blocks A and B and are asked to infer about the weight relation between blocks C and D. The students were given four multiple choice answers: block C is heavier than block D, block C weighs the same as block D, block C is lighter than block D, it is impossible to tell. After making their choice students were asked to provide reasons for their answers. Students’ answers were ranked from reasoning Level 0 ("wild guess') to Level 6 (fully proportional explanation).

The participants were divided into two groups. The first group consisted of 30 students who received human mediation based on classroom discussion, while the second group consisted of 23 students who received a computer-mediated program. The remaining 15 students dropped out, for various reasons, during various stages of the research.

The computer mediation program was conducted in a computer room with each student working on his personal computer. The computer program was built based on algorithms adjusted to students' performance. First, the student was asked to extract the relevant data from the questions. Then the program, by a sequence of analytical reasoning steps guided the student to infer the correct answer. Throughout the program the student was able to return to previous screens and read the instructions or his previous answers. This enabled the student to learn from previous errors or to use the previous stages of problem-solving. The work of students was recorded with a capturing video program.

The human mediation program was conducted in a regular classroom. The teacher-mediator presented the material and moderated the classroom discussion using Feuerstein's principles of mediated learning experience. Presentation of the tasks was identical to its presentation in the computer mediation program. The mediation included a sequential process much alike the computer mediation program. All students were encouraged to participate and were given the opportunity to express themselves and confront each other regarding the reasons and conclusions. The teacher also kept record of the students’ calculations made on the whiteboard. The classroom activities were video and audio recorded.

Before the start of the two mediation programs, all the students performed a proportional reasoning pre-test and at the end of the programs a post-test The students were given an hour and a half for the pre and post tests. Both mediation programs lasted for two hours and included two proportion Blocks tasks.

            The comparison of pre- and post-tests demonstrated that mediation in both groups was effective in enhancing the level of proportional reasoning. The effect size of computer mediation was 1.4, the effect size of human mediation was 1.2.  The absolute gain in the computer mediation group was also significantly greater (p < 0.05) than the gain in the human mediation group.

            Because the two types of mediation – human and computer-based – are inherently different a special scale was developed that served as a weight function for the influence of mediation on students’ performance under both conditions of mediation. It was found that the distribution of mediation required for two Blocks tasks was different in human mediation and computer mediation groups. It took 15% less mediation under computer-mediation conditions than human mediation conditions to reach the mastery of these tasks.

            The present study demonstrated that on average 13-14 year old students' proportional reasoning level was much lower than predicted by the classical Piagetian theory. At the same time a considerable reasoning potential was within the students’ ZPD as revealed during a short (2 hours) mediation session. Computer-mediation turned out to be more effective than human mediation. At the same time different learning patterns were identified in these two forms of mediated learning. Students with identical pre-test performance demonstrated different learning potential thus confirming the educational value of dynamic assessment as compared to the static assessment paradigm.