Week 1 in schools and grad school class

15 - 19 January 2018

Monday, 15 Jan
Shirley (works at AST) met me at the Yio Chu Kang MRT station this morning to come with me to my first school attachment. It sure is a trek to get out to the secondary school I will be at from now until 23 Feb.  It takes about an hour and fifteen minutes one-way which is a long way in Singapore.  I'm not looking forward to this commute, but am downloading lots of podcasts to prepare for 2 and a half hours on the train round-trip.  Derek (works at AST) also meets us at the school to help with the explaining the Fulbright program and helping me navigate my role with at this school.  We meet with the vice principal and head of the math department both who are friendly and welcoming.  I'm at the school for a little over an hour.  We spend time talking about what I'd like to accomplish while at this school (observing math classes across multiple ability levels, interviewing teachers, interviewing students, learning about how the concrete-pictorial-abstract method is presented at the secondary level, learning from the head of department which opportunities teachers have for professional development, leading professional development workshops for their teachers, and how problem-solving is (or is not) explicitly taught to kids).  I get the feeling that observing in classrooms may not be as easy and flexible as I originally thought and the same goes for interviewing teachers and students--but only time will tell.  Additionally, I got a tour of the school.  It is a large school complex with 4 floors, classrooms on one side, an open air courtyard/gym in the middle, and labs. offices, and the canteen (cafeteria) on the other side.  It's interesting to me that it is hot almost year round here, but none of the classrooms or cafeteria are air conditioned.  There are huge fans in each room, but I guess students and teachers just adjust to the heat.  I'm not allowed to post on this blog identifying details of the school (like the name, teachers names, or students names), but I will do my best to still capture the essence of my learning and teaching while there.  Bren and I walked to dinner at an Indian food hawker stand tonight.  Here's a cool picture I took of a cat on the roof:

Tuesday, 16 Jan
I had the morning free today, and Bren and I went running today at Ang Mo Kio Town Garden West (the park near us).  I hadn't run since cross country season ended in November, and Bren hadn't run in months either.  We only made it two miles in the heat and humidity, but it's a good start and allowed us to explore the park more.  Also, we ran up these stairs (my quads hurt):

At 12:30 I met Freddy, Katie and Carrie at AST and we headed to NIE for matriculation.  NIE (the National Institute of Education) is the university through which I'll be auditing an education grad school course.  Matriculation at the school consisted of taking all my original education documents (undergrad transcripts, master's degree transcripts, and both original diplomas to the registars office.  Freddy says if we were Singaporean we'd also have to present all education testing  records from Primary school outward--a pretty extensive process.  Everything went through without a hitch though so I was able to be entered in to the system enough to attend the first class tonight.  We also went by the book store.  You can tell it's a teacher education school because check out this selection of pens (#teacherheaven):

I am fortunate that the course I am taking actually takes place at AST instead of on campus as NIE.  AST is much more centrally located which will be nice since my commute to my first attachment school is so far.  I wasn't aware that that class started this evening so I was dressed fairly casually.  Although Freddy said what I was wearing was "fine", I figured I didn't want to show up as the only non-Singaporean, undressed on the first day of class.  It may be surprising to others because I am generally laid back and don't care what other people think about my appearance, I have a slight fear of showing up to a thing for the first time inappropriately dressed.  I didn't have time to head home, and unfortunately thrift stores don't seem to be a thing here.  On my way back to AST though I found an H&M with lots on sale and bought a dress for 15 SGD.  I got some quick dinner at a place called Porn's Sexy Thai Food (hah...what?!) and headed to class.

The course I am taking is "MME 823 Psychology of Learning Mathematics at the Primary Level" which meets every Tuesday night from 6:00-9:00pm.  Although I work in high school math in the US, when I originally applied to come to Singapore I was hoping to be attached to primary schools.  I wanted to learn more about how foundation math concepts were taught here because the a lack of the basics (number sense, place value, fractions, decimals, percentages, and integer operations) are what hold kids back the most when they enter Algebra in high school.  Since I teach high school math, they would only let me be attached to secondary schools here.  So I figured I'd make the most of my grad school class and learn more about primary mathematics in Singapore through this course.  The syllabus for the class lists the following as course objectives:  At the end of the course, students are expected to be able to do the following:

• Explore and critically reflect on the processes of learning mathematics, particularly the cognitive and psychological challenges faced by primary school students.
• Articulate the awareness of the multiple research methods and methodologies used in research for the psychology of learning mathematics by primary school students.
• Review and critically evaluate the literature and findings of research associated with the psychology of learning mathematics by primary school students.
• Draw implications for practices and theory from research in psychology of learning mathematics by primary school students.
• Develop an in-depth theoretical perspective of psychology of learning mathematics by primary school students from local and international perspectives.  

Today's first class topic was "Introduction to Course and Special Education Needs in Mathematics Low Attainers in Mathematics."  It was interesting to learn that Singapore is relatively new in providing special education services compared to the US, and actually uses many of the same structures we have in place in the US to support students in special education here.  The professor actually asked me many questions throughout the class discussion about our special education services and practices in the US.  Our discussions and readings focused on three constructs:

1. Special Educational Needs
2. Mathematics Learning Disabilities vs Mathematics Learning Difficulties
3. Dyscalculia and Dyslexia

There were only 15 people in class and we were each assigned a portion of a reading to read and present on during the last hour of class.  I was assigned math learning disabilities as they relate to counting.  Children's understanding of the principles associated with counting appear to emerge from a combination of inherent constraints and counting experience.  Researchers, Gelman and Gallistel list 5 implicit principles:

1. One-to-one correspondence which means one and only one work tag is assigned to each counted object.
2. Stable Order which means the order of the word tags must be invariant across counted sets.
3. Cardinality which means the value of the final word tage represents the quantity of items in the counted set.
4. Abstraction which means objects of any kind can be collected together and counted.
5.  Order Irrelevance which means items withing a given set can be tagged in any sequence.  

As children learn to count they also make inductions about basic characteristics of counting by observing standing counting behaviors and associated outcomes.  This sometimes results in unessential features of counting believed by children to be essential.  The first is standard directions which is the incorrect belief that counting must start at one of the endpoints of a set of objects.  The second is adjacency which means the incorrect belief that items must be counted consecutively and that jumping around during the act of counting results in an incorrect count.  An experiment was done where the child's task was to determine if the puppet performed the procedural aspect of counting "Ok" or "not OK and wrong."  Children with MLD/RD (Mathematics Learning Disability/Reading Disability) would correctly identify counts as erros when the last item was double counted, suggesting they understood the one-to-one correspondence principles.  However, double counts were often labeled as correct when the first item was double counted, suggesting that many children with MLD/RD had difficulties holding information in working memory.  Additionally, many children with MLD/RD did not understand the order irrelevance principle and believed that adjacency was an essential feature of counting.  Before class today, I hadn't given much thought to how little kids learn to count so it was really quite interesting to consider. Additionally, it is important for Pre-K and Kindergarten teachers to have an understanding of these principles so they are able to dispel misconceptions like adjacency.  As a high school math teacher, it is sometimes these basic misconceptions or a belief that a pattern always has to hold true that confuses and holds kids back from achieving higher level math mastery.

References: Geary, D.C. (2004) Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15.   

Wednesday
I spent the day at my first attachment school learning more about their math curriculum, school programs, and more generally about the Singaporean school system.  I mostly spent time with the head of the math department as well as the school staff developer (who plans professional development opportunities for teachers).  One thing I found interesting is that students purchase all their own textbooks.  I actually learned this last week, but I got copies of all the secondary math textbooks from the math department chair to peruse.  Unlike in the USA where there are hundreds of different textbooks, here there are only a select few (less that 5) available for each course and they have to be approved and sealed/stamped by the Ministry of Education.  They are also paperback and quite affordable (around 25 SGD) so students are able to write in them and keep them.  I'm interested to see how frequently or infrequently textbooks are used in classrooms.  I personally don't use a textbook in math courses I have taught because I find they are rather stifling to learning a topic in a specific manner.  Before parents understand my teaching style though (and see the type of notes/work packets I provide for students), they often ask for a textbook resource to have as a reference at home.  It would be nice if we had these inexpensive options available.  But I guess there is always the internet and specifically videos as well. The head of the math department expressed that teachers would feel nervous and anxious to have a visitor in their classroom and said he would need to arrange planned times for me to observe in classrooms.  This is also interesting to me because at the school I teach at in Atlanta we often have visitors in and out of our classrooms.  Although I didn't get to observe in any classrooms today, the senior teacher offered to let me join her lesson tomorrow at 8:00am.  Students will be learning to solve quadratic functions by completing the square.  Also, I'm feeling official with this badge:

Thursday
I arrived at school this morning at 8:00am which means I left our apartment at 6:30am.  This commute is long, but I started listen to the Serial podcast so it's making time go by faster.  The train system is quite easy to navigate here, but it is definitely busy at rush hour in the morning and evening. I met briefly with the senior teacher whose class I would be joining.  She ran me through the lesson objective (completing the square) and the general flow of the class.  There were 18 students in the class I observed which is quite small compared to some class sizes here of around 40 students.  These students were in Sec 2 (approximately 14 years old) and part of the Normal Academic stream.  Based on primary school (PSLE) test results, students are "streamed" into different academic pathways in secondary school: Normal Technical stream, Normal Academic stream, and Express Stream.  This is the opposite approach in some schools in the US which try to have integrated and non-tracked courses (besides AP classes).  It was so fun to observe in this classroom and see that teenagers will act like teenagers no matter where in the world you are.  Although in the hallways they will show respect by bowing at teachers in passing, they don't hesitate to talk to each other, giggle, and generally get distracted from the lesson in class.  The teacher I observed used white boards for the majority of class.  Rather than writing down problems in a notebook or on a worksheet, they solved almost all of the problems on a dry erase board and would hold them up for the teacher to check.  The classroom management was much more relaxed than I would have expected initially.  Students did not raise their hands and would call out and talk over each other, but the teacher did not seem to mind.  I'm curious to see if this is common across classrooms or just a classroom culture specific to this teacher.  Another example of teenagers just being teenagers occurred towards the end of class.  The teacher introduced me and told the students I was visiting from the USA at which point they all applaud and yelled "YAY!" I briefly introduced myself and then the teacher told them they could ask me any questions.  One girl asked me if I was from LA or if I'd ever been to LA and if it was the same as in the movies.  Another student, a boy, asked me if I was single.  Hah, these are the same type of questions I bet my students in Atlanta would ask a young, visiting teacher.  It was refreshing to be around students, and made me realized how much I missed my own kids back in Atlanta.  But also made me thankful to get to be around these teenagers more often now that I am attached to a school here.  Looking forward to working with kids (and teachers) more in the coming weeks.  Bren met me at the Woodlands MRT station for a late lunch.  We got this snack at a Pakistani food stall.  I can't remember the name, but they were delicious stuffed, fried balls:

I love walking around and seeing all the decorations for Chinese New Years and especially the Year of the Dog items.  I think I assumed that "Year of Dog" would be a mighty, powerful looking dog, but instead I keep seeing all these adorably cute dogs:

In the Woodlands Mall (there is basically a mall at every MRT station), there was also a western, specially, American food restaurant with this advertisement:

"Freedom to ignore your waistline!" and "Freedom to burp aloud!"  We couldn't stop laughing :)