Day 1: Gongshang Primary School

July 10, 2013

Today we visited our second school, Gongshang Primary School. They are graciously hosting us for 2 days.

We began our visit by learning about the school. Through a presentation and question time we gained so much insight on what this school is all about. Gongshang is a co-ed neighborhood school that operates on 2 sessions. Similar to our previous school, the P3-6 session runs from 7:30am-1:30pm and P1-2 runs from 12:15-6pm. They serve around 1,500 pupils and will be working on expanding their campus to serve all pupils in one session. Gongshang truly believes in educating the whole child to build strong academics and character for all students. Their school values include: Perseverance, Thrift, Integrity, and Respect.

They also have a comprehensive program, PALS, to incorporate subjects like Dance, Gymnastics, and Cartoon Drawing (depending on the time of the year, activities will vary). As part of our schedule for the day, we had the pleasure to visit these classes. It truly is an awesome opportunity for the students. We watched as kids learned a choreographed dance, gymnastics moves, and practiced drawing cartoon faces. It would be amazing to have a program like this at all American schools.

For the last part of the day, we had the privilege of having a session with the schools LSM (Learning Support for Maths) teacher. Her work is primarily with the students who enter Primary 1 (P1) who do not have the foundational skills necessary for P1. All students are tested at the beginning of the year and those who are at a certain level are designated to the LSM class. These students only have Maths with the LSM teacher who provides differentiated instruction for these students. A similar structure is in place for English literacy.

As she described her work, we learned that she has to put a greater emphasis on the concrete, using many manipulatives during her class. From her prior experience teaching P1-2, she always has a few strategies she can use to teach each subject. This type of intervention had proved to be very effective.

She also shared with us her typical lesson plan structure, this structure was provided for LSM teachers at a training with the MOE (Ministry of Education). We were very excited to see that it was similar to our lesson structure. Here are my notes from her explanation:

*Lesson Introduction: ~10 min

       What did we learn yesterday? 

       Revoice the concept 

       Review task

       New learning

       Read objective 

       Explain

       Example 

*Lesson Development: ~20-30 min

       I Do: teacher demonstrates using visuals

       We Do: give students an activity and T checks for understanding (adjusts as needed)

*Lesson Consolidation: ~15 min

       You Do: students do it on their own, T checks for mastery, generally involves a worksheet 

      

*Lesson Closure: ~5 min

       Recap what they have learned 

       Probe for interest (did they like doing it?)

       Revoice for students 

       Update charts and word cards

Things we are curious about:

-we learned about a test used in Singapore to determine a students Math Age. Is there anything like this in the US?
-the last few schools we have seen use leveled math classes starting in P3. Would this be beneficial to our students?
-teacher specialization is very common and teachers know their subjects inside and out. Could we promote this among elementary school teachers in the US?

It was great to spend the day learning about all that Gongshang has to offer before entering the classrooms to see some Math lessons. Now we have the proper lens to understand better!

We are looking forward to tomorrow when we will be able to see the teachers in action!

Arriving at the school 

School campus

Cartoon Drawing Class

Collaboration room with awesome group tables

Day 2: Gongshang Primary

July 11, 2013

It was so much easier to get to the school today since we had done the same route yesterday. 

Again, we were warmly welcomed by the staff as we arrived. Everyone has been so incredible! 

First on our list of observation was a series of lessons where students are working on special projects for ePals (pen pal program). Through this website Gongshang has been paired up with a few schools around the world to connect the kids as ePals. Their special project is regarding traditional games- they will learn about their own culture's traditional games, make the materials, and lastly share them by shipping the materials and instructions to their partner school. Once they receive their package they will not only have learned about their own country's games but also of another. We are so trying this next year!!

Some great ideas we saw regarding this project were:

-Have students interview their parents for them to learn their own family's traditional games. 

-Have students present their findings from the interview

-Play the games (most fun of course!)

-After playing: explain the rules in writing and evaluate which you like most

-Survey the class on their favorite game and create a bar graph (explained in detail below).

-Involve Math as you make the materials i.e measurement, counting, geometry 

During these activities, students were extremely engaged and learning about their heritage! 

One of the Math lessons we were able to watch in full involved the survey and bar graph of the class' favorite games. This was in a P3 classroom. Here are some notes of what we saw:

*T gives students a few dot stickers to vote on their favorite games on the chart the teacher had on the board (see picture below)

*Next T gives markers to kids to go count how many stickers are in each column, Sts write number above

*T analyzes the chart a bit with the kids just to see how they differ. She asked questions like: can you tell for sure that its more? Is our chart organized enough for you to see it visually? (Stickers were not aligned and did not match up from column to column).  

*T defines a bar graph (reminds kids of a previous lesson) 

*T says: "We can also ask questions about a bar graph". Asks a few students for examples- "which 2 have the same number?"

*Now T reminds the students that they have done the data collection together now they must organize it in a bar graph. T says she will provide the paper but students will have to decide in their groups how they will make their graph and especially what scale they will choose. 

*T models how a 1 by 1 scale would not be advisable because their is not enough space. She adds "you must discuss as a group". 

*Next Sts broke up into groups and were off to work. Many discusses intently about which scale they would use. Then most groups designated tasks to each team member to get it all done. 

We were amazed at how well they worked together and the rich mathematical discussions they were having around graphing!!

*As groups finished T assigned then to think of questions they could ask their friend about the graph and write them on the back. 

This lesson reminded us of the importance of group work and discussions. We saw a great deal of engagement as students were voting and making their graph. This is definitely a lesson we can do with our students!!!

Another Math lesson we observed was in a P1 classroom where the teacher used the smartboard to teach addition within 40. She used the number line, base 10 drawings, number bonds and the algorithm to show addition within 40. This variety of representations gave students many opportunities to learn the concept. It also a great way to warm the students up before getting to the content. See pictures below.

There was so much more we saw that day but its hard to include it all. Thank you to all the teachers that welcomed us into their classrooms. 

We ended the day with some discussion time with a few of the teachers and here are some of the topics we touched on:

Q: How do you teach problem solving strategies? 

A: SEAL acronym for procedure of problem solving (search, explore, apply, look back***very important). Also, using the Heuristics Approach (new topic to us) that involves a set of problem solving strategies you can use according to each kind of problem (ex model drawing, guess and check, working backwards...)

Each strategy is taught, student are encouraged to practice it that day and add it to their list of strategies. Later students have the ability to choose the strategy that makes the most sense to them and with that type of problem. 

Q: How do you teach student to work in groups? 

A: start working in groups from an early age, review rules every time, and assign roles (leader, timekeeper, speaker, secretary). 

Q: What percentage of instruction involves group work?

A: About 40%, because of our number of students we must also do frontal teaching. 

We were so thankful of all the time that the Gongshang teachers and administrators sat with us and answered all of our questions, because we had many!! :)

We also thank them for their hospitality, generosity and time!

Can't believe how much we have already seen and learned, and we are only half way! Next week we will be visiting 2 more schools...until then! :)

Realia- traditional games they have been talking about

Class graph

Counting up each column 

Figuring out the scale

Final graph

One student referring to her textbook (Discovering Maths)

Sums lesson on the smart board (using base ten representations)

Sums (using number bonds)

Life size Sudoku- in the math room that students can use to play math games

Magnets on both sides

Picture with our wonderful hosts

Shay with all the goodies we got

Information you need to know about Singaporean education

To fully understand the teaching in Singapore, we needed a little background about the educational system there.  Beyond the fact that Singapore is ranked #1 (or #2) on international math assessments/studies (such as TIMSS), this is what our research uncovered:

1)      Singapore takes the education of its citizens very seriously.  Having no natural resources, Singapore considers its citizens to be its most valuable resource, and it shows.  Teachers there are paid well, and their country’s education budget is second only to defense.  

2)      Elementary school is called Primary school.  It starts in Primary 1 (P1 for short) and is for students about the age of our 1^st graders.  Kindergarten is not compulsory (mandatory), but most children attend.  It is not government funded or taught in Primary school buildings. It's is completely private. 

3)      Primary school ends at P6 (our 6^th grade).  At the end of the year, students sit for (take) the National exam (the PSLE, their first national exam), the scores on which help decide what secondary school they will attend.

4)      Students are referred to as ‘pupils’ :)

5)      All teachers in Singapore get certified by attending training through the MOE (Ministry of Education).  Once they are teachers, they can elect to take many offered trainings through the MOE and as provided by their own school staff.

6)      The MOE put out a syllabus that all schools use (similar to grade-level standards in the states).  Schools may choose from several texts that cover the material, all distributed by the same publisher.

7)      Students do not repeat grades in Singapore.  However, if a student does poorly on the P6 National Exam (PSLE), they may retake P6 twice (for a total of three times total in P6).  Students in P1-P5 are automatically promoted.

8)      School is on a January-December calendar.  They go to school for a similar number of days as we do.

9)      The average classroom has 40 students.

10)   More than one teacher uses each classroom.  Each teacher has a work station with his or her materials in a large room set up with cubicles.  Teachers work there, and then bring all materials needed to wherever their students are (most often a cohort, grade level group, will stay in the same classroom as different teachers come in to teach).

11)   At many schools, due to lack of facility space, students in P1 & P2 go to school from 1:00-6:00PM while P3-6 start at around 7 and end around 12:30 or 1 (depending on the school). They call these "sessions", the session breakdowns were chosen by the MOE. It has been decided that by 2015 all students will attend during the morning session, buildings are being renovated/expanded to allow for this change. 

12)   Starting at P3, many teachers specialize in 1-2 subjects instead of teaching all subjects.

13)   All students take Mother Tongue, a class where they learn Chinese, Tamil, or Malay, depending on their cultural background.  All other the subjects are taught in English (whew, we thought so!).

Lucky 13!  We’re sure we’ll learn much more, and we’ll update you as we do :)

Our first school: Raffles Girls Primary School

July 9, 2013

Day 1, and we’re at our first school: Raffles Girls’ Primary School!  After a subway, a bus, and a lot of walking, we’re still ½ hour early.  They welcome us in and give us a bonus tour before our planned program.

Raffles [named after Sir Stamford Raffles (1781–1826), a British statesman, Lieutenant Governor of Java and founder of Singapore in 1819] was established in 1844.  They have 2,000 students and over 100 teachers.  Their morning session is for P3-P6, and P1 & P2 come in the afternoon (their school is being expanded starting next year).  They are 1 of 9 schools in Singapore to have a Gifted program—based on an exam in P3, students are selected for this group of pupils whose curriculum is more challenging to push them farther.  All other students are in heterogeneous classes, though Maths and Mother Tongue are separated by ability or, well, mother tongue :)

The first class of the day is a P4 (Primary 4= 4th grade) gifted group during mathematics.  Unlike the other classes of 30+-40 students, gifted classes generally contain 20-25 students.

After a warm introduction from the class, the students go straight to work!  They start a warm up that will help them summarize their previous lesson and reinforce prior knowledge needed for todays lesson. In groups of 4, they draw figures on big paper that follow a rule and rotate every 5 minutes:

Draw a figure that…

1)      has only 1 pair of ⊥ lines.

2)      has only 1 pair of perpendicular lines and 1 pair of parallel lines.

3)      has 2 sets of perpendicular lines.

4)      has only 1 pair of ⊥ lines and 2 pairs of ∥ lines.

5)      has 2 pairs of perpendicular lines and 2 pairs of ∥ lines.,

Students were not allowed to repeat a figure.

Some of the papers had the word written, while others used the symbol…what a great way to reinforce the connection right out of the gate!

Students all referenced their notes during this activity.  They were all organized differently.  Later, we asked how students learn to take notes.  The teacher said that students are guided, but expected to write down what is important for them.  This high expectation for students was repeated throughout the day.

After 15 minutes, students came to sit on the floor.  They discussed various figures and noted similarities.  The teacher asked questions like:

1)      Do these figures share similar properties?

2)      Could you create a __ sided figure with these properties?

3)      (When a student questioned the validity of a response):  How many of you do not accept that response?  Why?

This type of questioning was exciting to hear, as were the responses from the students; they were using higher level language and explaining their thinking!

Ten minutes later, they were diving into the lesson of the day.  Students were asked to explore the possible number of points of intersection from differing number of lines:

No. of lines	2	3	4	5	6	n
Possible no. of intersection	0,1	0, 1, 2, 3
Max no. of points	1

They began by drawing examples on the board.  Questions and comments that stood out to me from the teacher included:

1)      “Based on ____, are there any properties that____?”

2)      “Based on ____, is there any relationship between ____ and ____?”

3)      “It is important to explore this and look for relationships between…”

4)      Writing a word bank on the board, “Write key words first”

While students were working as a whole class, the teacher pushed their thinking by noting “I said lines, not line segments” and “She says this has two points of intersection, I say there are three.  Why do I think that?”  Students were obviously comfortable with making mistakes, and looking to their classmates to help them solve problems.  It was also clear by the way she interacted that the teacher appreciated trying new things (changing the lines to line segments), even if it was not a part of the lesson.   The students were aware that she would continue to push them, and were furiously scribbling in their notebooks to try to figure out if three lines can be drawn to have 4 points of intersection.

Then the group work began (at 10:35), and students were tasked with filling out the table above and drawing their evidence on a poster.  After a quick discussion in each group for how they were going to organize their posters (I had noticed leaving organization open-ended in other aspects of the lesson, as well), they begin to Draw and Explore.  The teacher rotates, answering questions and guiding students.  While some students were putting information on the chart, others were trying out different ideas in little notebooks.  (When I asked, the students said that they can try things out in their notebooks before presenting it.)

After 20 minutes of work, groups were in varying levels of completion.  The teacher passed out a worksheet she had created with her organization of this question as the students cleaned up.  She announced that the students should complete the worksheet in order to be prepared for the discussion tomorrow.  I really liked that idea, giving homework a purpose.

We were so excited after seeing a lesson that pushed the students so far and gave them so much responsibility for their learning.  While we were told that lessons like this are not done every day, the teacher said she tried to do them more often than not to keep students interested and engaged, and to keep them pushing themselves and problem solving.

Other things that stood out to us during the visit to Raffles:

1)      Each school gives a twice yearly assessment (much like our benchmarks).  Students are judged for growth based on these assessments, as opposed to a national exam yearly, and vary from school to school.

2)      Many people reiterated the importance of completing the spiraling curriculum every year.  The next teacher needs to know that students have the background information needed for the next level of the spiral.

3)      While the teachers had never heard of sprints (which we use at our school), they mentioned using ‘mental sums’ (which sounds like our ‘mad minutes’) occasionally to aid students in learning their sums and times tables.  They mentioned that these were the first thing to go when classrooms get busy, since the conceptual understanding must be held to a higher level of importance than math facts.

4) We noticed, and teachers emphasized to us, the philosophy of teaching from concrete->pictorial->abstract, something that has been very important to us as we implemented Singapore math at our school. In the P1 classroom that we observed, we saw the teacher reinforcing addition and place value with unified cubes and place value mats. We we're very excited to see some elements we have also used in our classrooms!!

5) The strategy of group/partner work was implemented in all of the lessons we saw that day. Students are very used to solving problems together and discussing their ideas. 

6) Lastly, hands on activities we widely used from addition with unifix cubes, to measuring volume with water and different sized water bottles, to figuring out how many ways you can draw a geometric figure with certain properties. The teachers stressed the need for hands on activities to keep the girls engaged and grounded in the conceptual math concepts. 

And something that really stood out to us, when we inquired about formatting of lesson plans, was:

1)      The idea of turning in weekly lesson plans was new to these teacher and administration, and they asked us questions about it.

2)      All teachers do nightly reflections about their lessons:

a.       What did I try?

b.      What went well?

c.       What would I change?

3)      Beginning teachers are observed by supervisors (experienced teachers).

Wow!  Day 1 in Singapore was fantastic!!  It was so great to see Singaporean math in action, and compare and contrast them to what we do in our school.  If today is any indication, this trip is going to be amazing!

Thanks to the teachers, staff, and students of Raffles Girls’ Primary School!  You were so welcoming and willing to take the time to answer our (many, many, many) questions.  What a great start to our Singapore experience!

 

Arriving at the school

Two group representations of the intersecting points question:

Group estimating and measuring the capacity if a water bottle (water bottle not in the pictures, sorry) 

Pair of students solving the sum 14+25 (each represented an addend and then they put it together) 

And so it begins...

About the authors:

We are two teachers from Los Angeles. We love teaching and are always looking for ways to improve our practice. Within this blog, we will be sharing our discoveries about math during our trip to Singapore. 

Our story: 

A few years ago, we started working at a school that had adopted the Singapore Math program. This program had been adapted to the United States from studying Singaporean pedagogy and the state standards. 

As we used the program, the teachers' guides and text books, we had many questions. We wondered what this math looked like in practice in Singapore. Since Singapore has been ranked in the top 3 countries for achievement in  mathematics, we wanted to know all that made their program so successful. 

We found out about an organization that could help us make this a reality. Fund For Teachers is an organization that provides grants for teachers for professional development projects during the summer. These projects are fully created by the teachers and as long as it's for professional and student growth- the sky is the limit (on ideas, not $, though they are very generous!!!). 

From their website: Fund for Teachers enriches the personal and professional growth of teachers by recognizing and supporting them as they identify and pursue opportunities around the globe that will have the greatest impact on their practice, the academic lives of their students and on their school communities.

See http://www.fundforteachers.org/ for more info on Fund For Teachers.  

After hearing all the great things about the program from our colleagues who had received grants before, we knew this would be a great opportunity. We began to plan our proposal to visit Singaporean schools, which are actually in session during our summer vacation! For the application process we had to build an itinerary and budget for our proposal.  

Our proposal (introduction):

Math is a universal language.  For the English Language Learners in our community, math can be a gateway to success.  While learning the many languages of every subject in school, students are able to actively participate in the tangible language of math.  Math gives students a voice; they can often express themselves mathematically before they can in speaking or writing.

Working with a population of 95% English Language Learners, we notice the positive affects math can have on a student’s desire to learn in all arenas.  Success in math can lead to increased perseverance in all subjects.   By giving students a strong math foundation, we are providing them tools to compete in the increasingly global economy.

“While there are no simple answers, I know from experience that when you focus on basics like reading and math, when you embrace innovative new approaches to learning, and when you create a professional climate that attracts great teachers--you can make a difference for children.” --Arne Duncan

Singapore is the international leader in math instruction. According to the TIMMS (Trends in International Mathematics and Science Study) assessment,  Singapore has been consistently ranked among the top 3 in mathematics proficiency since 1995.  Because of Singapore’s success, many schools in the United States have adopted the curriculum. The Singapore curriculum focuses on conceptual knowledge rather than computational knowledge. It offers innovative ways to develop concrete explanations, fluency and mental math. They have a strong progression for explaining mathematical concepts that goes from with concrete explanations (working with manipulatives) to pictorial representations (pictures and drawings) and finally with abstract representations (numbers and symbols). For these reasons our school has adopted the Singapore Math model for teaching mathematics school wide. We have been using the Singapore Math curriculum at our school for three years now, and we want to refine our practice and utilize the resources in the way they were created. 

Unfortunately, our conversations with colleagues who were taught math in the ‘traditional’ way of the United States have prevented us from seeing the potential of ‘non-traditional’ math systems.  It is our goal to research and see first-hand Singaporean philosophy and pedagogy, so we can better implement and faithfully practice the tenets of our adopted math curriculum. 

How is mathematics instruction structured in a country which is so successful in its math education?  What hands-on opportunities are provided to the students in Singapore that give them such a strong foundation?  How do teachers design year-, unit-, and weekly plans to reach learning targets?  How is the school day structured to provide students the time to explore concepts and apply concepts in real-world situations? What types of mathematical conversations are teachers in Singapore having to push their thinking, and their students’ thinking, to the depth required to truly understand math?  Because our Singapore curriculum was created by American educators, modeled after the Singaporean model, we want to learn from the source to ensure we’re not losing important elements that have added to Singapore’s success in mathematics instruction.  How would a faithful implementation of the program improve our students’ learning and prepare them for the increased expectation of the Common Core Standards around reasoning and problem-solving?

Our passion to provide high-quality education and future opportunities for our school population has driven us to seek out the chance to solidify our school’s math instruction.  If we can strengthen our math curriculum, our students will have the mathematical understanding they need for college, and be prepared to join the global society.  With all of the obstacles our students face daily, as an immigrant and high-poverty community, mathematics is a way to overcome challenges.  Through math instruction, we want to disprove the deficit model and exceed the standards society has set for them because of where they live.  

We’ve seen the power Singapore Math has already had at our school.  Through this fellowship, we will have the opportunity to take mathematics instruction to the next level.  Through our planned structure of research, observation, and reflection, we will be empowered with the knowledge to improve our planning and execution of math instruction, and provide student-centered curriculum school-wide.

Our goal is to spend 2 weeks visiting Singaporean schools where we will learn about the school and observe teachers teaching mathematics. During this time we want to see if we are correctly implementing Singaporean practices for teaching math. We also want to learn strategies for improving our practice.

We are so thankful to Fund For Teachers for approving our proposal and giving us the opportunity of a lifetime! We are so ready for our adventure....