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
2.2.3. Other observed differences
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.
their mental problems. Then the class tried to answer the problem and explained the solutions to class.
Meanwhile, in activity # 5, the activities proved routinary in nature, although all the LPS teachers prepared activities for the students. Moreover, classrooms in the LPS and in the HPS have almost the same areas, but LPS activities are all done inside the classrooms whereas almost all HPS classes utilize the corridors during their group activities for better movement. With this set up, the HPS students enjoy more space than the LPS students do. Thus, the HPS students can discuss and freely demonstrate their solutions to the problems without disturbing the other classmates. Furthermore, the HPS teachers freely move around to monitor the progress of the students and thus, the HPS students have more opportunity to interact with their teacher, than LPS students do.
The excerpts on pages 86 further illustrate the activities conducted in the classes of both groups. The topic was deriving the area of a parallelogram from the area of a rectangle.
Researcher’s note
Observed in H4, H8 and H10 classes Observed in L2, L3, L4, L5, L6, L14, classes
The teacher asked the students to recall how the area of a rectangle can be solved.
Then, the teacher gave cut-outs of
parallelograms to the students. They asked the students to describe the parallelogram;
i.e., opposite sides are parallel and equal.
Moreover, the teacher asked them to identify the different parts of the
parallelogram; i.e., base, height, interior angles.
Then, the teacher asked them: Find a way by which you can solve the area of that parallelogram. Remember how the area
The teacher asked the students to recall how the area of a rectangle can be solved.
Then, the teacher gave cut-outs of
parallelograms to the students. The teacher asked them to identify the different parts of the parallelogram; i.e., base, height, interior angles.
Then, the teacher asked them: Draw a line to denote the height of the
parallelogram. Then cut it along that line.
of a rectangle can be solved.
Then the students discussed among themselves, explored and discovered that when they cut the figure vertically, they can transform the given parallelogram to a rectangle.
What shapes are formed? (Students answered triangle and trapezoids.) Place the triangle to the other side of the trapezoid forming a rectangle. (Student followed.) Then, the teacher explained how the area of a parallelogram is derived from the area of a rectangle.
There are also two practices, which were observed only in the HPS teachers, although these teachers were not the majority. These practices are:
3. (19) The teacher emphasizes the process rather than the output.
4. (26) The students are given the opportunity to pose their own problems for everyone to solve.
For Activity #19, although most of the teachers from both groups asked their students to explain their outputs, there were also some HPS teachers like H3, H4, H6, H9 and H10 who asked their students thoroughly on the process by which the answers were derived.
In this way, students are really given the opportunity to explain and justify what they did.
Below were instances observed in H10 classes.
H10 Class Activities Researcher’s notes (This class is Grade 5 section 4, the lowest
in the school.)
(The students have just finished with their group work activity and a member is assigned to explain the group’s solution. A group having a correct solution and with correct explanation will be awarded one point. If the explanation is wrong, no point is awarded. )
H10: Group 1, could you explain your work?
(Mark, the Group leader goes to the board to explain.)
H10 usually starts talking and asking questions in English. Noticeably, around two or three students raise their hands to participate in the discussion.
Then, she shifted to Filipino saying the same messages and asking the same questions.
More students raise their hands.
She allows her students to communicate their ideas in Filipino. And when they do, H10 translates the answer in English. Then she asks the student concern to repeat his/her answer, this time, in English.
S2 (from other group): Ma’am, kung talagang group work po iyan, pwede po bang si Alvin ang mag-explain?
S3 (from other group): Yes Ma’am.
Subukan natin kung talagang nainitindihan po ng buong group 1 yung work nila.
H10: Alvin, please represent your group and explain your solution.
When interviewed:
R: When did you start to have group activities in your class, this being the lowest section? (The researcher noticed that the groupings have not yet established yet and the members do not know where to join.)
H10: Just recently. Noong una, ayaw ko sana kasi lower section ito. Baka walang mangyari sa amin. Pero, nakita mo naman, kaya naman pala nila. Hindi pa ako masyadong pagod ngayon.
R: Do you really encourage your students to ask their classmates to explain their works (referring to Alvin’s case.)?
H10: It’s their idea, and they are enjoying it. I also agree with the idea because that will force everyone in the group to understand what they are doing.
(continuation on the next page (continuation)
R: Are you really allowed to use Filipino as a medium of instruction in Math?
H10: Problema ko iyan. Pag Tagalog, maraming gustong sumagot. Pag English na, wala ng makainitindi sa akin.
R: May problema ba kung Tagalog na lang ang gagamitin ninyong medium sa
pagtuturo?
H10: Malaking problema yan. During observation, we have to use English as our medium. Pag hindi ako naintindihan sa English, kahit paulit-ulit pa ako ng sinasabi at paulit-ulit ang tanong ko, ok lang basta
English ang gagamitin ko. Second, all our achievement tests are written in English.
So, I cannot use Tagalog for the whole period.
It was also noted that some teachers in the HPS like H1, H3, H5, H6, H8, H9 and H10 codeswitch to Filipino once in a while when emphasizing concepts. Moreover, they also allow their students to express their ideas and questions in Filipino while the teachers help the students in expressing their ideas and questions in English.
On the other hand, all LPS teachers observed use English as a medium of instruction all throughout the class period.
Meanwhile, in the case of Activity # 26 where students are given the opportunity to pose their problems, H3 met this problem during the problem posing activity in her Grade 6, section A, class. The class just finished discussing percent, and how percent is
expressed in terms of decimal numbers. All the examples on percent discussed in class involved integers only.
H3 Class Activities Researcher’s notes T: Ok, class, who can give a question for everyone to
solve?
(Students raised hands. She called one student.) S1: Singapore has a population of 300,000. If ½ % are students, then how many are students?
S2: It’s ½% of 300000 which is 150000.
S1: That’s correct.
S3: Classmates, I have a question. Isn’t it that 1% is greater than ½%?
(Silence)
The teacher had discussed with them percent involving integers only. But since the students had a knowledge on fractions, they were able to construct questions such as this. The problem of the teacher then, was that she did not know right away how to solve the problem given by S1. She found the reasons of S2 and S3 both logical.
S3: Because 1% of 300000 is 3000. So the answer to the problem must be less than 3000.
S2: (went to the board) Let me show you my solution.
(wrote on the board: 300000 x .50 = 150000) S3: Which is greater 1% or ½ %?
(Discussion)
T: Ok class, since you cannot arrive at a decision, can we just discuss this on Monday? We now continue our lesson.
(And the teacher continued the activities reflected in her lesson plan.)
The lesson took place on a Thursday. She promised to resolve the issue on
Monday. When asked what she would do, she said that she would study over the week-end, and have to ask co-teachers on how to solve that problem.
Another practice that is evident in some of the classes in HPS is the emphasis on visualizing a certain measurement. At this point, the researcher does not claim that these observed practices were not present at the low performing schools. It is just that at the time of observations, these were not their topics and so the researcher cannot make any conclusion as to whether these activities are being practiced by the LPS teachers or not.
One observation included here involved a class in LPS.
Activities in the Classroom Researcher’s notes T: Draw segments of length 4 cm, 7 cm, 10
cm.
(Students draw segments.)
T: Compare the lengths of your segments.
Which segment is the shortest? Which one is the longest?
This activity was seen in the classes of H2, H4, H5, and H6.
Before the students compute for the
T: Draw circles of radius 3 cm, diameter 5 cm.
circumference and area of circle, they were given an opportunity to visualize circles of different sizes. This activity was seen in the classes of H4, and H9.
T: Draw a trapezoid, and describe it.
(Student draw trapezoids. Upon being called, student showed his trapezoid and said:)
S: This is trapezoid because it is a quadrilateral that has only one pair of opposite sides parallel (pointing the parallel sides).
This activity was seen in the classes of H2 and H6.
T: Draw triangles. Group 1, draw scalene triangles; group 2, draw isosceles triangles and group 3, draw equilateral triangles.
(Students draw triangles. Teacher called students to describe their triangles.) S1: (showed a right isosceles triangle) This is an isosceles triangle because these two sides (pointing to the legs) are equal.
S2: That is a right triangle.
(continued on the next page)
This activity was seen in the class of H1.
When asked, what would she do to resolve the issue, she said that she would consult books on it. If not found on the book, she would ask co-teachers. If she is not
convinced with the answers of co-teachers, she would ask her math supervisor on this.
Activities in the Classroom Researcher’s notes ( continuation)
T: (to S1) Is that an isosceles triangle?
S1: Yes Ma’am. (He got a ruler and showed the measurements of the two congruent sides.)
S2: It looks like a right triangle.
T: (also looked confused. She drew to the board an acute isosceles triangle.) This is the isosceles triangle I know. But the two sides of his triangle (referring to S1) are
equal.
(They continued the lesson and left the issue unresolved for a while
T: Using the protractor, draw an angle measuring 30o, 50o, 60o, 90o , 120o, 150o. (Students draw.)
T: From your figures, which are acute angles? Right angle? Obtuse angles?
(Students answer.)
T: So how does an acute angle look like? A right angle look like? Obtuse angle look like?
This activity was seen in the classes of H2 and H4.
T: How big is 1 cm2 ? (No answer.) T: Using your drawing materials, draw squares with the side measuring 1 cm.
(Students draw.)
T: What is the area of your squares?
S: The area of my square is 1 cm2. T: So, how big is 1 cm2 ?
This activity was seen in the classes of H8 and H9.
Activities in the Classroom Researcher’s notes (As an assignment, the teacher asked the
students to bring cut out papers with an area of 1 cm2. They call it “square tiles” In the next session: )
T: Draw rectangles of different sizes. The lengths must be whole numbers and in cm.
(Students draw rectangles.) T: Using your square tiles cover the rectangle.
(Students cover the rectangular region.) T: How many square tiles are there?
This activity was seen in the classes of H8 and H9.
To count the square tiles faster, the students multiply the number of tiles in each row to the number of tiles in each column.
Through this activity, students were able to derive the area of a rectangle to be the product of the length and width. ,
How many tiles in each row?
How many tiles in each column?
What is the area of the rectangle?
T: How big is 1 m2 ? Use your Manila paper to visualize how big is 1 m2. T: Using your square tiles, determine the area of our floor.
This activity was seen in the classes of H8 and H9.
They also used the outside corridor for their activities.
During the problem posing activity:
S1: My garden is in a form of a square with sides 5 cm. What is its perimeter?”
S2: How big is your garden?
(S1 looked at her teacher wondering why S2 asked that question.)
T: Yes, how big is your garden? Could you imagine how big is your garden?
The concept of measurement. This one was observed in the class of H6.
A similar incident happened in a class of L6 in the LPS, which was reflected below.
Activities in the Classroom Researcher’s notes (As an assignment, the teacher asked the
students to measure the dimension of their dining table at home and compute for the areas.)
S1: Our table has length 7 cm and width 5 cm. Its area is 35 cm2.
L6: Very good!
S2: Ma’am, ang liit naman po ng table nila!
L6: Wala tayong magagawa kung ganun ang table nila.
This was seen in the class of L6.
When the teacher was interviewed, she said she didn’t realize right away that the answer of S1 is not really possible.
She said, she was more concerned on the feelings of S1, not to get hurt by the reaction of S2.
The teacher seemed to protect more the feeling of S1, aware that some of her students come from the depressed area. In that instance, she was more concerned that S1 will not be insecure with the reaction of S2 regarding the size of their dining table,
not realizing right away that the answer of S1 is not really possible.
Lastly, of the eight (8) HPS teachers whose practices lean towards SMT, four (4) used powerpoint presentations in their classes. With only one monitor for the whole class, the students were no longer given the opportunity to explore. Although there were some indications that the students were exchanging talks with each other and would really want to participate in the classroom discussion, still, the focus of the teacher was on the monitor, wondering if the powerpoint presentation will work or not. It looked like the teachers have not yet mastered the full utilization of the newly acquired technology as a tool for teaching. However, considering the potentials that the audiovisual aids can offer, these four teachers might soon be observed having their practices lean towards IMT.