Differentiation Strategies for MS Math in an International School Class in China

I currently teach in an International School in China that can accept Chinese Nationals. The student body is 80% Chinese, 15% South Korean, and 5% children of teachers in the school. The teachers in Middle and High School come from Australia, China, Colombia, Kenya, India, Macedonia, Pakistan, The Philippines, and the United States.

Differentiation in this school is complicated by the fact that parents tend to be in one of two broad categories: ones who overcommit students to outside lessons despite our advice not to, and those who do not want to accept the possibility that their son/daughter has a disability. Few parents have realistic after school activities for their child or are willing to discuss how to help a learning disabled child. A significant number of students are first or second year transfers from Chinese public schools where the language of instruction for Mathematics was Mandarin.

These two parental types mean that many classes have kids above grade level and many who are below grade level independent of the English level.

For my discussion about differentiation I will focus on what I do for Dyslexic students, ELL students, and other students.  Dyslexia does not really manifest in a character- based language like Mandarin, so many parents just don't understand what it is. Consequently, many parents refuse to get their children diagnosed as dyslexic. Our school has no one qualified to make the diagnosis, but the evidence seen in students is enough for the school to recommend  teaching the suspected students as if they are dyslexic rather than letting them flounder.

I teach a process-led classroom, so there is no categorization of advanced or less advanced students; merely ones who are applying the process to different levels of problems. This approach implies all students will become capable of applying the process to complex problems and subtly instills a growth mindset among students.


The flow of a typical lesson is shown in the following flowchart. Formative assessment is done through constant circulation, observation, and feedback of students. The process takes a lot of time preparing work for students and they end up stratifying at different levels that make giving one exit ticket difficult.

I also teach students how to prepare the next lesson at the start of the year. Students are already familiar with the process and I have found it useful in getting them to be more independent learners. Students are taught to preview vocabulary, connect the topic to past material and hypothesize or research connections to future topics. They then read example questions and try the "Got Its" after each example and check their answers from the back of the book. They write down any questions they have and write notes if needed.  If the answers to the "Got Its" are correct, they then solve basic problems that are at the start of an exercise set and check their work. The previewing can occur at the end of a given problem set as outlined above or at other points in the lesson depending on the pace of the student.

I use textbooks a lot as the only reliable internet resources are ones hosted on Chinese servers and these tend to be in Mandarin and not accessible. The wealth of games, websites, and interactive resources available to teachers in the rest of the world simply do not work reliably or quickly enough for one to count on. Until the day when the Chinese game based learning platforms provide English functionality, I am more comfortable using textbooks as they cannot be interfered with as they are approved by the censors. 

Kuta Software makes programs that generate exercises aligned with Common Core and their Pre-Algebra, and Algebra 1 programs are a key tool to use when differentiating. In situations where a student is working quickly or needs practice, I can create a pdf version of a worksheet and upload to for the student in minutes. You choose the topic, number, and difficulty of the questions and you get a worksheet instantly. The questions are more geared to recall and analysis than creativity and practical skills, so one also needs to have the questions in the textbook ready to account for students who learn better when presented problems that cater to creativity and practicality.

All Students:

I teach all students the following problem solving process that comes from my experience working as an engineer. It is provided in English and Chinese as I have been unable to get it translated into Korean.

This process is useful in differentiating as I can choose problems of a complexity that matches the abilities of different students. In addition, few students in MS and HS are really proficient in all the parts of the process. There is ALWAYS a problem I can assign a student that will stretch their ability in some stage of the process. Advanced students tend to struggle with writing their solutions in clear coherent fashion, while less advanced students tend to be inconsistent in setting up the problem. Average students,can struggle to  consistently recognize if their answers don't make sense. When one has a good textbook that presents problems that connect to other subjects, require creativity, practicality, analysis, and recall, you can break assignments into blocks that students can choose from and then apply the process to. Specifically I select problems that require rote learning, creativity, analysis, and practical thinking to give things accessibility and increase student engagement (McCarthy, 3 Ways to Plan for Diverse Learners: What Teachers Do, 2015).

I constantly refer to this process when giving feedback for students via questioning whether they have really done the parts of the process adequately enough, whether they have considered all the given information/prerequisite knowledge, or whether it is presented clearly enough for peers to understand. 

Metastrategic and Metatask Knowledge Aid Differentiation

Metacognition is the awareness, monitoring, and regulation of lower-order thinking. It is an essential part of higher order thinking and takes many years to develop (Kuhn, 2000).

Since many students develop differently, the difficulties faced by students may not be with the subject/material taught, but with a gap between the metacognition the student has, and that needed for the task.

Deanna Kuhn uses the concepts of Metastrategic and Metatask knowledge. They are the strategies used to prepare for and perform a task (Kuhn, 2000). The two categories make it easier to extend the idea of problem solving process to the lives students lead as adults. Once students see Mathematics as a tool to practice preparing for and executing tasks of increasing complexity, they realize that it is an ongoing task and they become less hung up on differences in individual skill. They instinctively know they will all lead different lives, so it seems logical they should all have differences in ability.

Making students aware that their ability to prepare for and execute a task can affect their results helps them realize that they all have things to work on and develop. They will start to focus on acquiring sound processes of preparation and execution for the tasks in front of them. 

Students who are lower level may get asked if they understand what prerequisite knowledge is needed before trying the problem, or get asked to practice some foundational skill first. Advanced students may get asked if they understand the significance of all the information presented to them in the problem, or they may get asked if they know enough about the situation to try and create a mathematical model of it. Likewise, students may get asked if they have followed all directions, or if they have checked their work. 

One aspect of how I differentiate that draws criticism from some is my use of textbooks. A well designed textbook is vital for enabling students of different abilities and interests to engage with the process you teach. Especially in China, where the internet censorship means many web resources are inaccessible, intermittent, or take so long to load, that they are ineffective. Publishers put a lot of resources into researching problems from different disciplines and arranging them in degrees of difficulty. Not taking advantage of this resource and relying on whatever search engines yield, seems a bit odd to me. If you manage your workflow so you can arrange problems to cater to student interests and knowledge preference, you can grow the range of problems you let then practice their processes on. As students improve the Metastrategic and Metatask knowledge, they will gain in confidence and often research things on their own.

One area where my hands are tied in differentiation is in summative assessments. Our school is steadfast in its policy of giving the same assessments to all students within a grade. Only students with diagnosed disabilities can get allowances such as more time. 

Dyslexic Students

Students will be paired with peers who learn by explaining. Dyslexic students will be allowed to solve problems on the main whiteboards or on portable ones. Writing equations on computers is tedious and time-consuming at present, so students will have to write answers on paper. However they can use the visually impaired assist feature and have the laptop read text aloud provided the student has headphones. Generally, they will be allowed to submit work that is more diagrammatic, or explain things verbally in detail before trying to write solutions down. More time will be given for summative assessments consistent with the accommodations given in the external Cambridge IGCSE and International Baccalaureate exams they will take in HS. I will also spend more time working with them in small groups as the rest of the class often loses interest if I address the dyslexic students as part of the greater class.


ELL Students

ELL learners are generally recent transfers from Korean schools or from Chinese Public Schools. They have little to no English and are immersed in instruction that is delivered entirely in English for most subjects.

Students are given a link for Mathematical glossaries in Mandarin and Korean at the beginning of the year and are required to download the relevant files for their language. Students refer to this glossary and to their online research for the Vocabulary Scroll activity that they use to review the vocabulary for a chapter. An example of the scroll is shown below.

Prior to the lesson where they will make their vocabulary scrolls, I will preview the chapter and list the vocabulary words and situations in the exercises they will likely not know. Putting items on Layaway is one situation that they have no experience of in China, as a translation will not be useful as no stores in China offer the service. Students make the vocabulary scroll for the vocabulary words listed in the textbook as well as the list of words I created after previewing the chapter. The scrolls need to include the meaning in English and the native language, use of the word in an English sentence, and identifying where in the textbook the word appears. As they work through the list and the chapter, I will ask them to list the problems they can do without help, with peer help, and with my help. I also expect that they have to explain what the directions are asking and what the question means in English before I let them say an answer to the class.

In situations where I may not have the time to have students make vocabulary scrolls, or have students who are not keen on the scrolls, I use Frayer Diagrams shown below.

Frayer diagrams are an effective tool for helping students make meaningful connections with the vocabulary (Texas Education Agency Region 13).

Conclusion

The way I do differentiation is not ideal. It requires a lot of advanced planning which is difficult to consistently do as I also teach International Baccalaureate Mathematics for grades eleven and twelve. There are times when the preps for those classes impact the time I have for this class, but that is the nature of the beast. I hope the next country I teach in will have internet access that is less restrictive so I can use more resources to reduce the workload of differentiation as it is overwhelming at times.

Works Cited

Kuhn, D. (2000). Metacognitive Development. Current Directions in Psychological Science, 9(5), 178-181.

McCarthy, J. (2015, August 28). 3 Ways to Plan for Diverse Learners: What Teachers Do. Retrieved December 30, 2018, from edutopia: https://www.edutopia.org/blog/differentiated-instruction-ways-to-plan-john-mccarthy

Texas Education Agency Region 13. (n.d.). Frayer Model. Retrieved December 30, 2018, from theteachertoolkit: http://www.theteachertoolkit.com/index.php/tool/frayer-model