Our Journey Ends: Final Reflections

July 21, 2013

In many ways today marks the end of this amazing, once-in-a-lifetime opportunity. However, it also marks the beginning of endless growth for our professional lives. As we begin our journey back home, we are ready to share our reflections/observations with other educators. We are also eager to try these lessons in our own classrooms! Throughout the past 2 weeks we have had many conversations and we kept trying to figure out: What makes Singaporean pedagogy internationally successful? AND, How can we replicate some of these approaches in the US and in our classrooms?

Among all that we have learned (sorry we cannot include it all) we would like to summarize our learning with the following list. Here we highlight our key findings during our trip to 4 school and over 15 classrooms:

1.     Emphasis on conceptual understanding with the model of concrete->pictorial->abstract

By taking the time to guide students through this process with countless experiences for them to understanding the concept.

There is more emphasis placed on deep understanding rather than memorization

2.     High level of specialization and differentiation

Most teachers in Singaporean school choose 1-2 areas to specialize in so that they can gain a greater understanding in that subject. This has helped many teachers in digging deep into the teaching and learning of mathematics.

School structures for most grade levels include differentiated math classrooms. This helps teachers provide more focused instruction based on student needs.

3.     Variety of learning structures with an emphasis on group problem solving

Students are exposed daily to whole group, small group, paired, and individual instruction. This variety helps students learn in many different ways and not only from the teacher but also from his/her peers. These emphases on rigorous group-problem-solving helps students engage in academic conversations and help them learn to challenge others and also change their own thinking. Always in a respectful and productive manner! These are the kinds of skills are critical to success in the 21^st century!!

4.     Teachers have a sophisticated understanding of mathematics concepts and misconceptions

Teachers are provided with countless resources within their school and the Ministry of Education. MOE not only offers their own program for future teachers but also continues to provide professional development for all teachers.

Teachers are confident in their knowledge and highly prepared!

5.     Promoting a balance between critical thinking (problem solving) and mental math

Students have the opportunity to solve rigorous problems to promote higher-level thinking and understanding. However, teachers also place an emphasis on mental math that will help them be more confident and efficient problem solvers. This balance is essential!

6.     Most importantly, a national and cultural support and appreciation of teachers and education as a whole.

With the support of the Singaporean governments’ financially and politically, the education system has flourished in the last few decades. No wonder they are the leading country in most of the international tests lately. Teachers are highly regarded and very well paid.

There is a strong cultural support for education and parents take a very active role in their child’s education. This environment is the perfect formula for a successful educational system.

Although our journey ends we would like to continue this conversation with teachers all around the world. We welcome questions, comments, and suggestions as we work to apply Singaporean pedagogy here in the US.

Last and foremost, we would like to thank FUND FOR TEACHERS for making with journey happen!!! These experiences will forever make a difference in our lives and in our classrooms. THANK YOU!!

For teachers who are interested in applying, the application process for Fund For Teachers begins in October and is due in January (generally). If you want an adventure of a lifetime that will help you grow professional please apply at: http://www.fundforteachers.org/

For those who want to support teachers in making these amazing adventures happen you can donate at: http://www.fundforteachers.org/unicx.cfm

Our Last Visit: St. Nicholas Girls Primary

July 19, 2013 

St Nicholas is our final stop on our school tour of Singapore.  After a very confusing beginning (guess you can’t trust GoogleMaps in Singapore J), we arrived!  At St Nicholas Girls Primary, we were lucky to see the same topic taught in different ways to very different learners.

Our visit began with a very special and unique cultural celebration that was happening that morning on campus for Racial Harmony Day. As we went into the courtyard, we were greeted by students in traditional outfits and visited parent volunteers running different booths. We had the pleasure of playing traditional games from different parts of the world. Also, we were delighted with a whole plate full of different traditional snacks form Singapore.  What an amazing experience!

After enjoying a bit of the celebrations, we continued to our observations. The first class we saw was a class with students who need more support, which had fewer than 10 students.  The P5 lesson was an introductory lesson about finding the average.  After the first few slides titled “What you will learn today” and “Expected behaviour during activity time”, the students were guided to 4 cups of cubes with a different number of cubes in each cup, and instructed to distribute the cubes equally.  The students used different methods to tactilely find the answer, and then saw a demonstration on the PowerPoint (I really need to brush up on my PPT skills; it was amazing!). 

Students worked in small groups, then in pairs, and then individual, with the teacher rotating to assist as necessary.  In one example, a cup had 0 cubes, because the students struggled with the concept of zero.  When they discussed it as a whole class, the teacher introduced the term ‘average’.  She explained that the method she was demonstrating was “a long-winded method” and pushed the students to find an easier way to solve it.  The teacher had the students come up with a definition of ‘average’ and shared a NON-definition to prevent confusion.

Finally the students were exposed to the formula and asked to write about it, using a number sentence or words.  Students brainstormed when they would use average in real life and then the teacher gave examples.  They revisited the questions from the beginning of the lecture, and then the teacher had the students start their homework for a couple of minutes to check for understanding before she sent them on their way.

Then we saw the same concept taught to an advanced group.  There were over 35 students in the class.  Students were given the task of measuring each of their hand spans on a piece of string and then dividing the string equally between the members of the group.  They were given 30 minutes of independent time to complete the task and answer questions.  While they were working, the teacher walked around, asking questions to push their thinking.

One question really pushed the students to think about averages.  Question 3 asked “If there is an additional member added to the group, will each pupil’s section of the string be longer or shorter?”  The discussions stemming from this question were extraordinary.  Each student had an idea of the answer, and was trying to prove it to her classmates.  They tried scenarios with remaining string, and then on the calculator, before coming to the conclusion that there is no definite answer.  The students then explained in writing which factors would impact the length of the string.

After 30 minutes, the teacher flicked the lights and the students returned to their seats.  The class went over the worksheet and discussed the different methods that students used to complete their challenge.  They compared ‘actual length’ and ‘average length’.

It was great to see the different ways to teach the same concept with rigor and student exploration.  All of the students received the support they needed and were able to understand the concept with clarity. The amount of teacher talk vs student talk was very different. The teacher took on the role of the facilitator and provided experiences for the girls to really discuss this topic.  This is something that many teachers struggle with but it is amazing to see what happens when we let students do the work and how much deeper their understanding can be.

It was incredible to see this kind of differentiation within one day. You can tell that teachers truly know their students and are prepared to provide the instruction that they need.  Furthermore, as we debriefed with the teachers, we heard their detailed thinking about the misconceptions that their students could have within the topic of average. Instead of waiting for the misconceptions to emerge, they provided examples and exercises that would challenge the misconceptions from the beginning. Like using a set with 0 cubes in the first lesson or asking those probing questions within the hand span lesson. We know it takes years of practice to get to this high level of teaching, but we also must urge our administrators and fellow teachers for the professional development to push our own understanding of mathematics.

We want to thank the staff and teachers at St. Nicholas from the bottom of our hearts for such an enriching cultural and professional experience! It was incredibly insightful to sit with so many teachers at your school and discuss education on both sides on the Pacific. We look forward to future conversations on mathematics education!

Playing traditional games at the Racial Harmony Celebration 

First observation: hands on approach to finding the average 

Group work

Pair work

Teacher summary of what they found

Provides definition after the hands on experience 

Real Life Application- What was the average amount of money we spent at the canteen (cafeteria) today?

Second Lesson- Average Hand Span

Girls measuring and cutting the string

The wonderful St. Nicholas Staff

Henry Park Primary Visit

July 17, 2013

Today we went to Henry Park Primary.  This school of 2000 students has a focus on character development.  We learned so many great ideas from them to take back to our school!

1)     Explicitly weaving into instruction the development of Math attitudes, such as beliefs, interests, appreciation, confidence, and perseverance.

2)     Integrating Math into Learning Journeys (which is probably the best term for field trip I’ve ever heard!!), to reinforce skills and demonstrate the real-world applications of skills. Some examples included going to the supermarket and totaling a groceries trip or taking a math trail on campus counting different things around the school.

3)     At HP, the banded math classes based on ability are different sizes.  The class with students who struggle more is fewer students (as few as 10) to give them the support they need.

4)     MATH JOURNALS!!  We were so lucky to be in a P5 class when they were reviewing what makes a good math journal (because we didn’t know!).  According to the class, a good math journal includes:

a.     Math vocabulary

b.     Examples!

c.     Words, numbers, pictures

d.     Strategies

e.     Questions

f.      Focus (in that the entry is focused)

g.     Feelings/opinions

5)      Pupils in one class were given a Student Self-Assessment Checklist.  Here’s the gist of it:

a.     Complete answer

                                               i.     Explained thinking

b.     Math language

                                               i.     Using math words

c.     Charts/diagrams

                                               i.     Explain written ideas

d.     Connections

                                               i.     To real life situations

                                             ii.     To previous learning

6)     Polya’s 4 Steps to Problem Solving:  After several teachers mentioned Polya, I finally asked one of them to spell his name for me.  After we got home, I researched his 4 principles to problem solving:

a.     Understand the Problem: ask yourself the following questions:

                                               i.     Do you understand all the words in the problem?

                                             ii.     What are you trying to show?

                                            iii.     Can you restate the problem in your own words?

                                            iv.     Can you think of a visual to help you understand the problem?

                                              v.     Is there enough information?

b.     Devise a Plan: use a strategy!  Some examples are:

                                               i.     Guess and check

                                             ii.     Look for a pattern

                                            iii.     Work backwards

                                            iv.     Use a model

                                              v.     Solve a similar problem

                                            vi.     Eliminate possibilities

c.     Carry Out the Plan

d.     Look back

                                               i.     Do NOT forget to look back!

7)     In one class, the following prompt is connected to a figure as a Do-Now:
“Write the question that a student could use to draw this figure.”

The lessons we observed had many activities that we could do with our students at home to promote both critical thinking in problem solving and mental math. Here are some examples: 

    *"You have 7 sticks- How many triangles can you create?" Sts were given 7 toothpicks and went to work recording each configuration. Some made figures that included 19 triangles...awesome!

    *Brainpop quiz- something we also use in the US, its fun and engaging

    *Mental Sums Challenge- teacher flashes 10 questions for a designated about of seconds (depending on level but normally SUPER FAST). Students record their answers in notebooks and later go through the answers with the teacher. This structure starts in the second half of P1- it was impressive!!

    *Logical Reasoning Questions- the teacher displayed a series of information points students had to use logical reasoning to figure out who married whom and on which day. 

    *Lastly, a teacher gave students certain parameters to draw a geometric figure (ex. draw a figure with 5 obtuse angles). When one student shared his and did not do it correctly, the teacher took it as a learning opportunity and had the class help him fix it. 

(see pictures below from these lessons)

There were so many instant take-aways from Henry Park.   I am really excited to get back and try some of these ideas (especially Math Journals!).  Thank you so much!!

Math Journal Poster

7 Stick Challenge

Student recording 7 stick formations

Mental Math Sums Challenge (10 questions total)

Logical Reasoning Question 

Students drawing figures with parameters set by both teacher and peers

Helping a student change his figure to be able to meet the parameters (his whiteboard projected while others adjusted the lines on the class whiteboard)