SMT beliefs
2. The practices of teachers
2.2. Comparison of the observed practices in the two groups Considering the indicators listed in the COC, teachers from both groups
2.2.1. Practices common to most participants of both groups
Table 22 reflects the HPS and LPS teachers’ practices that lean towards IMT. The last two columns indicate the percent of HPS and LPS teachers who demonstrated the indicator considered. To recall, each indicator in the COC is rated as either 0 (not observed), or 1 (lean towards SMT), or 2 (midway between SMT and IMT) or 3 (lean towards IMT). The term “by most of the participants” implies the greatest percentage of participants from those given ratings 1, 2 or 3 in the items considered.
Table 22
Practices that Lean Towards IMT by the Teachers in Both Groups.
Activities Both Groups % of
HPS
% of LPS 7) Type of examples
used
The teacher used the objects from real life life/magazine/tv (or within the environment of the students) as examples.
90 95
8) Nature of the teacher talk
Teacher talk was in the form of question rather than directive.
80 60
12) Classroom atmosphere
The teacher keeps the discussion open and friendly.
75 95
21) The nature of the learning environment
The students were allowed to work anywhere, or the students were allowed to discuss among themselves or an activity was prepared for the students to work in groups.
85 85
23) Treatment of teacher on the students’ output after activity
The students explained their outputs. 60 85
24) Treatment of teacher on the students’ output after activity
The students output were displayed on the board or wall so that other students may examine the work of their classmates.
65 85
Table 22 (continuation)
Activities Both Groups % of
HPS
% of LPS 30) Allotment of
class time
The students spent more time engaged in their
own work than listening to teacher talk. 70 55 31) The teacher’s
purpose for having problem solving
The teacher used the problem as a means for developing concepts.
75 50
Data in classroom activities # 7 and #31 reflected in Table 22 indicate that majority of the teachers in both groups try to practice Mathematics not only as a set of facts and procedures, but also as a set of inter related concepts which have real life applications, and that Mathematics is a tool for problem solving. Moreover, data in activities # 8, 12, 21 and 30 prove that most of them create a classroom environment where discussions among students were given more emphasis than teacher-controlled ones; while data in activities # 23 and 24 show that most of the teachers give the students enough opportunity to explain and justify their works, and to examine the works of others.
Table 23 reflects the HPS and LPS teachers’ practices that lean towards SMT
Table 23
Practices that Lean Towards SMT by the Teachers in Both Groups.
Activities Both Groups % of
HPS
% of LPS 4) Start of
presentation
The teacher gave the students detailed step by step directions on what they are to do before an
activity begins.
50 75
6) Approached used by the teacher for the students to learn the concept
Deductive approach.
The principle was already given and the students
were just verifying the result. 40 65
Table 23 (continuation)
Activities Both Groups % of
HPS
% of LPS 9) Treatment if the
student’s answer is incomplete during discussion
If the student’s answer was incomplete/inaccurate, the teacher considers it wrong and just calls on
another student. 50 70
10) Treatment if the student’s answer is wrong during discussion
If the student’s answer was wrong, the teacher ignored it and called on another student, or the teacher immediately correct the false statement made by the students.
55 75
discussion made by the students.
15) Student’s activity during board work
While some students were working on the board, the other students were simply seated quietly and watched their classmates do the board work.
45 45
16) Treatment if the student’s work is correct during board work
If the works (answers) were correct, these were simply checked without justification.
50 45
17) Treatment if the student’s work is wrong during board work
If the work was wrong, the teacher simply
declared it as wrong and called on another student to work on it (or showed himself the correct answer.)
50 60
22) Treatment of teachers when students presented/used alternative solutions
The teacher did not entertain alternative solution. 65 65
25) (open forum:
Does the teacher encourage students to ask questions?)
The teacher did not encourage the students to ask questions (either address to him or to other students).
55 80
26) Source of questions for discussion
The teacher was the only one asking questions. 75 100 28) Type of activity
for evaluation
The teacher wanted the students to follow procedural instructions to obtain the correct answer.
50 75
Responses in classroom activities # 4, 6, 9, 10, 22, 25 and 26 reflected in Table 23 indicate that most of the teachers assume their role as transmitter of mathematical
knowledge more than a facilitator of students’ inquiry and learning. Furthermore, data in activity # 15 show that most of the teachers would like their students to watch attentively while their classmates solve the problems on the board. Moreover, this observation is affirmed through the data in activities # 16, 17 and 28 where the teachers give more
emphasis on the ability of the students to follow procedural instructions than their ability to explain and justify their solutions.
Considering all the respondents, the results in Table 22 and 23 show that the practices of teachers do not fall on a single tradition. Some of their practices lean towards IMT while some lean towards SMT. To be more specific, most of the teachers use problem solving as a means of developing concepts, thus, they create a learning
environment where the students are given the opportunity to explore and to discuss things among themselves. However, although the teachers assume their role as facilitator of students’ inquiry during group work, they do not give up their role as the authority in the classroom when the students go back to the big group discussion. Moreover, while the teachers give their students the opportunity to explain their solutions to the problems, the problems created by the teachers aim at mastery of specified mathematical procedures.
Hence, the students explaining their solutions are more evident than the students justifying their actions.