FORMATIVE ASSESSMENT IN DIAGNOSTICS OF PROFESSIONAL COMPETENCIES OF FUTURE TEACHERS OF MATHEMATICS

FORMATIVE ASSESSMENT IN DIAGNOSTICS OF PROFESSIONAL COMPETENCIES OF FUTURE TEACHERS OF MATHEMATICS

Elena Sukhovienko

Doctor of Pedagogical Sciences, Professor, South Ural State Humanitarian Pedagogical University,

Russia, Chelyabinsk

Searching for the diagnostics tools associated with formation of professional competencies in the to-be-teachers of mathematics [7], we turned to the method of formative assessment, which is not just a diagnostic technique, but also contributes to improvement of educational outcome, development of self-assessment skills in students, and can be used directly within the educational process. B. Bell and B. Cowie [1], by defining formative assessment as a process applied by teachers and students to acknowledge and respond to students’ learning in order to improve this learning, point to its often subtle character among the specifics of formative assessment, possibility to carry out formative assessment by a teacher and students alike, and disclosure of information to students.

Researchers distinguish between convergent and divergent approaches of providing feedback [8]. The convergent approach focuses on mastering traditional curriculum, while the divergent approach positions a pupil and, according to Vygotsky, pupil’s potential ‘zone of proximal development’ in the center of attention. That is, it becomes important to convey to pupils not only their level of mastering the subject, but also the level that they are able to master [4]. In formative assessment, the divergent approach enables adaptation of further learning process to the needs of students [6].

D.J. Nicol and D. Macfarlane‐Dick [2] formulated seven principles of organization of the feedback in formative assessment. Quality feedback helps clarify goals, criteria and expected standards; it boosts development of self-esteem (reflection) in education; it provides students with high quality information about their learning; it encourages a student-teacher dialogue and a dialogue with peers during the learning process; encourages positive motivational beliefs and self-esteem; it gives opportunities to narrow the gap between current and desired performance; it provides educators with information that can be used for the purposes of learning improvement.

The research undertaken by P. Orsmond, S. Merry and K. Reiling [3], focuses on application of patterns in order to conduct formative assessment. The use of samples makes it possible to provide meaningful formative feedback, and for each student to compare their self-esteem with the group assessment. For that reason, in order to conduct formative assessment, we decided to use open criteria as regards formation of professional competencies in students.

Describing formative assessment, D.R. Sadler [5] points out, that for enhancement of professional knowledge, it is required for students to develop their ability to control the quality of own performance during the real activity and build a set of tactics or techniques that can be used to modify their own activity. Thus, in order to diagnose professional competencies in the to-be-teachers of mathematics, we suggested that, with reference to the figure (Fig. 1), students compile geometric problems to brush-up or apply some theorems of the course of stereometry: signs of parallelism of a straight line and a plane, intersecting straight lines, perpendicularity of planes, a theorem of three perpendiculars and statements about line-plane intersection, with one of the planes passing through a straight line parallel to another plane. Alongside the diagnostics of design skills and use of teaching materials, this task was aimed at testing the knowledge of mathematics school course in students.

The students were supposed to pass the compiled problems on to their peers for solution and discussion.

Figure 1. Image to illustrate the theorems of the course of stereometry

Let us consider an example of a problem compiled by student X for the theorem of three perpendiculars: “Given is a regular quadrangular pyramid MABCD, with MO being its height. K is the middle of BC. Prove that segment MK is perpendicular to BC”.

When this problem was presented to a group of students, they were correct in making a point that, in order to solve this problem, it is possible to proceed without the theorem of three perpendiculars, because pupils know that the side edges are equal in a regular pyramid. This means that in triangle MBC with two equal sides, median MK is the height. The students devised a method to correct this problem so that it would serve to brush-up the theorem in question: “Given is a quadrangular pyramid MABCD, with MO being its height. It is known that OB=OC, and K is the middle of BC. Prove that segment MK is perpendicular to BC”.

Another problem, compiled by student X for application of the theorem of line-plane intersection, with one of the planes passing through a straight line parallel to another plane, was approved by the students, because when solving it, not only the theorem in question was required to be used, but also transitivity of parallelism of straight lines in a plane: “At the base of pyramid MABCD lies a four-square. ML is the line intersecting planes AMB and CMD. Points K and F are the midpoints of edges AD and BC. Prove that lines ML and KF are parallel”.

Discussion and solution of problems ended with self-assessment of the results of each student’s activity, and by giving them marks by the group and the teacher (Fig. 2). The following criteria were used to assess problems: 1) whether this theorem should really be applied when solving a problem; 2) how difficult or challenging this problem is for pupils; 3) how well the problem is defined. Satisfaction of each criterion was rated with one point.

Figure 2. Results of formative assessment of competence

Analyzing the results of formative assessment, it is possible to conclude that competencies are developed at a high level in students A, C and X, and at a low level in students D, F and G. This needs to be taken into consideration further, when carrying out remedial activities.

In overall, insufficient variety of tasks compiled by students should not go unnoticed. This means that educating students in problem compilation requires a separate study of techniques for problems compilation and modification.

This research paper was written with funding from Federal State Budgetary Educational Institution of Higher Education Mordovia State Pedagogical University named after M.E. Evseviev under the contract for performance of research and development work No. 16-618 dd. 27.07.2021 on Monitoring of development of professional competencies in to-be-teachers of mathematics in the context of implementation of the occupational profile of a teacher.

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