Thursday, July 12th, 2007: Visit to Geylang Methodist Secondary School

Due to a scheduling change, we were able to pay a morning visit to the brand new Geylang Methodist Secondary School (GMSS). Founded in 1924, GMSS is a middle-ranked Methodist government school with 1,300 students in 35 classes distributed between express and normal tech levels. With a highest possible score of 280 points on the Primary School Leaving Exams (PSLEs – administered in math, science, English and mother tongue), the express students at GMSS scored between 189-240 points. The normal tech students scored below 111 points, with a range of 71-111 points. They have a 70% pass rate on the “O” levels for Normal Technical schools (the bottom strand); the national average for students at this level is 55%.

The current facility had been occupied for just two weeks at the time of our visit. Schools undergo minor or major renovations approximately every five to seven years. When buildings are to be replaced, as occurred with GMSS, the entire school population relocates to another facility while a new building is constructed (over a period of two years).

Introductions
Our hostess, Mdm Foo Kum Fong, whose office is at GMSS, is a master teacher of mathematics for one of the clusters. There are 160 schools serviced by 19 master teachers who travel to the different schools in their cluster. Of the two mathematics master teachers one is Mdm Fong and the other specializes in primary school.

First Observation
After short introductions in the boardroom we went to observe, for 15 minutes, a sec 1 (grade 7) mathematics Express 4 lesson (the lowest of the higher level academic track, covering the entire curriculum, 7th-10th, in four years) on ratios and improper fraction ratios. The class textbook was Discovering Mathematics by Chow Wai Keung. The students were, overall, rowdier than those we observed at the primary schools, but were still fairly well on task. The class began when the teacher asked us (the visitors) to introduce ourselves to the students. He then used the numbers of visitors, three male visitors and ten female visitors, to create a ratio: the number of male visitors to female visitors is 3:10. The teacher asked “Have you worked with ratios before?” and the students answered “yes.” Then he asked “Do you remember what it is?” and the students answered “no.” The class reviewed ratios using the worksheet below, and some students shared their answers on the board as they went through the worksheet. One procedure the teacher gave for simplifying 2/5 : ¾ is
2/5 : ¾ = 2/5 x 4/4 : ¾ x 5/5 = 8/20 : 15/20 = 8:15 since the denominators are the same. Several of us had not seen ratios with three quantities (A:B:C) and problems using them in the United States. For example, one of the problems on the worksheet was: P:Q = 6:7 and Q:R = 3:5. Find P:Q:R.



















Second Observation
From the sec 1 class, a group of us moved to observe a normal tech 3 class (students that are on track to learn a technical trade) working on factoring quadratic equations. We were warned that these students would be rowdy, but we did not find them rowdier than the rest of the students in the time we were there. In this 35-minute lesson, the teacher, Mr. Joseph Lim Tuan Zheng, showed an alternative method for factoring a quadratic expression, "the cross method," using direct instruction, step by step. The teacher gave us a lesson plan detailing the knowledge of the students prior to the lesson and the lesson focus.
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(From the teacher's lesson plan)
Knowledge Prior to the Lesson:
-Students have just learnt Expansion and Factorization of Quadratic Expression by Grouping Method.
-They have learnt the 4 operations of positive and negative integers.

Lesson Focus:
1. My Target Audiences are students who are weak in Mathematics but they are willing to learn. 2. Algebra is a topic students find hard to understand. They get confused along the way.
3. I will break the Cross Method into parts so they understand how to do it.
4. The challenge is for the whole class of 42 students to follow the steps and not get lost along the way.
These Normal Technical students get restless easily and have very short attention span. Questioning their understanding of the topic after 5 minutes and asking them to do on the board will keep them on task and awake.
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The teacher taught the "cross method" using a visual model. He connected each term in the quadratic expression to its corresponding place in the model using circles, squares and triangles (see problem 1 in the worksheet below). The second example (problem 2) and the rest of the problems paralleled the first, with the exception that the shapes all became squares to be filled in. The students were to repeat the steps of the procedure by following the locations of the squares. There were numerous steps involved, and the teacher asked questions while working through the steps. For example, for problem 1, when the teacher determined that the quadratic expression could be factored into (v+1)(v+1), the teacher asked how this should be written and the students answered (v+1)^2. He also asked if the order of (a+12)(a-2) could be switched, and explained that -8-1=-9 by drawing one minus sign and eight minus signs, counting them and getting 9 minus signs (or 9-), which we "call -9."

For problem 7, the teacher, with input from the class, went through a couple of incorrect or incomplete ways of factoring 9t^2+24t+15 before arriving at the correct and complete factorization. First (9t+5)(t+3), followed by (3t+3)(3t+5). When the teacher said that the latter was incorrect, the students noticed that a 3 could be factored out, resulting in 3(t+1)(3t+5). The teacher used this opportunity to show the students that the 3 could be factored out of the original expression, "making the expression smaller and easier to factor." After they went through the process of factoring 3(3t^2+8t+5) into 3(3t+5)(t+1), the teacher asked for a vote: "Which process is easier (factoring a common term first, or using the "cross method" first and then finding and factoring common terms)?" Then he told the students to "Stick to ONE RULE: take out the common factors first."

When the quadratic equation involved a coefficient greater than one for the x^2 term (starting on problem 6), body language indicated that some students had lost their way. When the third term required more choices, body language again seemed to show student confusion. Students shared their solutions on the board and those who needed help could look at the answer. Students were asked to work in pairs on the worksheet. Some did, while some of them worked individually and others simply copied each other’s results. Many students waited for the teacher to come around and answer their questions.

Third Observation
Two people in our group observed a sec 3 express level 3 math class working on similar triangles. They reported there were four boys with behavioral issues in the classroom, which led us to wonder how discipline is handled in Singapore schools.

Music Lesson
On our way back to the boardroom we passed by a music class; each student had an everyday object that could be used for percussion (pots, pans, buckets, washboards, etc.). Seated in a circle, they took turns making a sequence of sounds for the others to imitate. This music lesson was part of the theme for the week, which was respect. In this class, respect was shown by listening and following the lead of each student.

More Information
Back in the board room we continued our conversation with Mdm Foo Kum Fong and the school principal Lim Yan Hock. We learned that sec 3 students take 10 subjects, including history (two periods/week), geography, English (six periods/week), literature, mother tongue, music, PE, art, chemistry, biology, physics, and mathematics (six periods/week). Classes begin at 7:25 am and end at 1:50pm. Secs 1 and 2 take general science, which includes chemistry, biology and physics. Sec 4 (grade 10) students encountering difficulty are required to stay after school for help from 2:30 to 4:00pm four days a week. Ninety-six percent of the students continue with school beyond sec 4. We also found out that there is a very small turnover of teachers. Last year three out of 75 teachers left.
Origami made out of paper plates by Mme. Foo.


Post created with input from Tobe, Cassie, Tricia and Patsy