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
2.2.2. Differences in the practices of the two groups of teachers
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.
Table 24
Practices Lean Towards IMT by most of HPS Teachers but Lean Towards SMT by Most of LPS Teachers
Activities LPS (n=20) HPS (n=20)
1) Mental Problem Only one teacher (out of 20) conducted the mental problem activity. The teacher is the one who asked the question.
Students simply answered the problem. If wrong, another student was called. If correct, no explanation was given by the student. (5%)
All teachers conducted the mental problem activity.
Students were the ones who asked the problem. Out of the 20 teachers 19 asked their students to explain the solution for the problem. (95%)
2) Checking of Assignment
The teachers or the students simply wrote the correct answers on the board and the students checked the
assignment. (65%)
The students wrote on the board and explained the solutions to their assignments.
(50%) 3) Review of Previous
Lesson
Students were asked to recall definitions and formula. (35%)
Students were asked to give real life examples of the concepts.
Students were asked to relate the concepts and processes.
(75%)
Table 24 (continuation)
Activities LPS (n=20) HPS (n=20)
5) Teaching the concept
The teacher demonstrated or explained the concept. (55%)
The students were given tasks to explore and understand the concept. (40%)
11) How the teacher handle student’s questions in class
The teacher did not encourage students to challenge other’s view.
The teacher did not encourage students to ask questions either
The teacher encouraged the students to challenge other’s view.
The teacher encouraged the students to ask questions either
students to ask questions either address to him or to their classmates. (70%)
students to ask questions either address to him or to their classmates. (65%) 13) Application of the
concept
The activity is focused on algorithm. Students are engaged in computations.
(50%)
The activity is focused on problem solving. Students are engaged in exploration, investigation or discussion, debate or argumentation as they solve problems involving the concept. (75%)
14) Teacher’s approach during problem solving activity
The teacher encouraged the students to follow the traditional procedure in solving problem so that they could finish the task in the shortest time possible. (80%)
The teacher allows the
students to spend more time to reflect on, discuss themselves and explore in a variety of ways on how to solve the problems. (55%)
18) Type of activity prepared for Fixing Skills
The emphasis was the execution of mathematical operations, and computation with speed and accuracy.
(65%)
The emphasis was the explanation and justification of the generalizations on concepts. (80%)
20) What the teacher does to help the student perfect the math skill
The teacher gave many exercises so the students can perfect the important skills.
(70%)
The teacher provided tasks to students that gave them the opportunity to apply the concept in real life situation.
(55%)
Table 24 (continuation)
Activities LPS (n=20) HPS (n=20)
27) Emphasis in the Generalization part
The teacher asked the students to simply recite the definition and/or the formula.
The application of the concept was not given attention. (90%)
The teacher asked the students about the application of the concept on real life situation or how the concept is related to the other concepts. (95%) 29) Execution of the
over-all plan (lesson
The teacher followed the lesson plan as closely as
The teacher allowed the discussion to continue longer
over-all plan (lesson plan) for the day
lesson plan as closely as possible at all times.
The teacher presented the lesson in a highly structured manner. (80%)
discussion to continue longer as planned when students showed particular interest.
(60%) 32) Type of questions
posed by the teacher
At most two questions posed by the teacher in a particular lesson were extended, while the rest were restricted. (65%)
At least three questions posed by the teacher in a particular lesson were extended. (70%)
Results in Table 24 reveal that when grouped according to the performance level of schools, the HPS teachers practice most of the items pertaining to the learning
activities in the math classroom in the IMT while the LPS teachers practice those same items in the SMT. To be more specific, data in activities # 1, 2, 3, 5, 14 and 20 show that HPS students are provided with more opportunities to explain, argue, and solve problems than the LPS students. Consequently, data in activities # 13, 18, 27 and 32 indicate that the HPS teachers do not only give emphasis on developing the students’ ability to follow procedural instructions, but to the students’ ability to explain and justify their solutions as well. On the other hand, the LPS teachers give emphasis solely on developing the students’ ability to follow procedural instructions.
Although earlier analysis show that most of the teachers create a classroom environment where a greater portion of class time is allocated for discussion and
negotiations among students, classroom activity # 11 differentiates the HPS from the LPS teachers. While the LPS teachers do not encourage students to challenge their classmates’
solutions, the HPS teachers do the opposite. That is, the HPS teachers encourage their students to challenge their classmates’ solutions. (However, as analyzed earlier, most
teachers in both groups do not encourage their students to ask questions addressed to them or to their classmates.)
Thus, in the LPS classrooms, students only discuss the answers to the problems and since most of the learning activities prepared by the teachers require students to simply replicate the discussed mathematical procedures, then seldom do the students create a new solution different from what has been discussed in class. As such, the event does not give them the opportunity to debate and negotiate on the solutions they use, to solve the problems given to them.
Meanwhile, in the HPS classrooms, aside from the students posing their own problems, the teachers prepared learning activities that will make the students explore and generate their own solutions, which are reflected in activities # 3, 5, 13, 14, 18, 20, 27 and 32. Hence, the activities give the students opportunity to generate their own solutions. As a consequence, the situation calls for the students to debate and negotiate whether the solutions offered are acceptable or not.