Martyn Krügel’s INFORMATION REPORT Part 3 3.0

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Contents – Part 3

Introduction Page | 4

Part 1

CHAPTER 1 The Teacher’s Guide Project

CHAPTER 2 New and Improved TEACHER’S GUIDE 2.0

CHAPTER 3 Implementing Content and Language Integrated Learning (CLIL)

CHAPTER 4 Preparatory Work for Conducting the CLIL Experiment

CHAPTER 5 The Pretest and Posttest Collaboration with Dr. Angel

Part 2 CHAPTER 6 Year 4 Mathematics and TEACHER’S GUIDE 3.0

CHAPTER 7 Curriculum Implementation

Part 3 CHAPTER 8 The Curios Case of Ms. Mejal Page | 5

CHAPTER 9 A Continuous Improvement Page | 28

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Foreword I accidentally stumbled into the field of education when the opportunity to work as a teacher at a bilingual school in Bangkok presented itself to me in 2012. After first working as a teacher for three years, I was then appointed the head of academic affairs of the primary department of that school. In this new role it was my responsibility to put into practice academic and learning theories –as suggested and assigned by the school– with the goal of raising the academic standard and in particular the English proficiency of the students in primary who as bilingual learners, studied the subjects of mathematics, science and social studies in English.

The work I subsequently produced, steered me in the direction of thinking in terms of systems and programs, especially as it pertains to implementing curricula and also because I was being guided and informed by research I conducted. What started off as a few suggestions, I then turned into my own research and development project to create a proper bilingual program –in the very unique context of a Thai bilingual school– based upon my own initiatives but more importantly, in an attempt to address some specific needs that I had identified.

I completed the first edition of this report in November 2017 as an internal report. I wanted to present my previous employer with a comprehensive overview of the work I had done, but in addition, I also wanted a documented record for myself to be put to use in the future. After careful deliberation and also to protect the integrity of the work, I decided that it would be best to continue this work in a more independent capacity. This new second edition is an edited version of the original report –containing only the relevant information– to share some of the insights I have gained on how one could potentially go about in developing a program for bilingual primary school children who are required to learn subjects like mathematics and science in English as the second language. In addition, I also now want this report to serve as an introduction to and sample of my work because a standard résumé would be an insufficient mechanism to convey the experience I have gained. This is in line with my personal philosophy that people who can do, are people who can show.

I called the first edition an INFORMATION REPORT but this was only because I wanted to place a specific emphasis on the concept of INFORMATION in the environment I was working. Perhaps this work would be better described as a case study or research project, but now this label has stuck. Communicating in a multi-cultural environment can at times be quite challenging. In an attempt to address this, I started incorporating lots of tables, diagrams, and pictures in my presentations to convey information visually, but perhaps and on a more interesting note, is that it’s the knowledge of mathematics itself –and here I’m merely referring to primary school mathematics– that has drastically improved my own ability to visualize. Primary school mathematics is rich with wonderful tidbits of mathematical concepts that once digested can be immediately applied in practice. Maybe I’m just an old fool, but after I took a closer look at many different primary mathematics curricula and in particular the Singaporean primary mathematics syllabus, and engaged with the informational content these materials are referring to, I started thinking better. Anyhow, this INFORMATION REPORT is neither a new treatise on mathematics nor a new treatise on education, but an honest account by a concerned outsider who asked a very simple question: What are the children learning?

Martyn Krügel

Bangkok, Thailand April 2018

A few notes on style: I apologize in advance for my long sentences, I blame this on the landscape orientation of my pages. And for me to go and put commas in all the right places, will take me several ages. The bolded and capitalized words were intended to focus attention. The coloring of the tables was done purely for my own amusement. All the “I did this and I did thats”, was the tone of a frustrated

person. And all the “Based on initiatives that work”, well… That was just stating the facts.

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Introduction

8. Since the entire project can be summarized as an attempt to improve the academic standard of bilingual primary school children, it is vitally important to

take the WORK SAMPLES produced by the children and initiated by the teachers into consideration. This section contains numerous work samples, the original pre-and posttests of the Year 4 CLIL experiment, additional administrative tasks

that were completed and also some random bits of research taken into consideration for the development of the project.

7. The purpose here was to display the INFORMATION CONTENT as well as the INFORMATION QUANTITY taken

from the new and updated INFORMATION and LANGUAGE SUPPORT (the merging of the teacher’s guide and language support) from the latest version of the journals in operation

during the first semester of the 2017/18 academic year.

1. The journey started with the TEACHER’S GUIDE PROJECT conducted during the second semester of the 2014/15 academic year. This work served as a foundation for all the work

that followed.

2. The teacher’s guide project then continued into the first semester of the 2015/16 academic year starting with a new

and improved TEACHER’S GUIDE 2. 0 for Year 4 mathematics. A lot of curriculum related research occurred during this stage which was applied throughout the project.

3. During the first semester of the 2015/16 academic year the need for systemic solutions arose since the work started generating huge

quantities of information that necessitated thinking in terms of SYSTEMS.

4. Then the direction slightly shifted with the assignment to IMPLEMENT CLIL which was possible as a result of the previous

research done for the teacher’s guide project and thinking in terms of systems. This resulted in the big CLIL experiment that took place

during the second semester of the 2015/16 academic year.

5. During the 2016/17 academic year and from the insights gained from the teacher’s guide project, thinking in terms of systems and also the big CLIL experiment – I was then able to

produce EIGHT JOURNALS that were in operation during the 2016/17 academic year. During this stage the Singaporean Syllabus for Primary Mathematics came into play which

further produced valuable insights for the development of this project.

6. The COMPLETE CLIL ARTICLE submitted at the end of the first

semester of the 2016/17 academic year shed some light on the project.

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CHAPTER 8: The Curios Case of Ms. Mejal Throughout this report I have made several references to the complete CLIL article that I wrote of which a shortened version appeared in the Closer magazine which was published in the 2016/17 academic year. That article contained valuable information shedding light on the entire project. Consider the following two extracts from that article:

The function of the journal is to lay bare what the content information for a particular lesson is, and the content information is being mediated through the LANGUAGE SUPPORT since language is a TOOL for mediating INFORMATION. So, the LANGUAGE SUPPORT functions as “language support” for the bilingual children, but it also functions as INFORMATION SUPPORT. This means, that if a student worked through (processed the information) said LANGUAGE SUPPORT/INFORMATION SUPPORT (and any other additional information presented by the teacher during a lesson) and if that process has been recorded (this would be the work the students produce/process in the journal and around which the journal has been designed i.e. its function) then there will be strong EVIDENCE that a student was engaged in a LEARNING/KNOWLEDGE ACQUISITION PROCESS or at the very least, a record that a specific lesson was presented to the student by the teacher and educational institution. Earlier I mentioned that one of my guiding principles throughout the development of this project was addressing the needs of a particular learning environment and providing INFORMATION SUPPORT to teachers and making the information explicit in the journals is an attempt to address one of these needs which is the lack of content and linguistic knowledge of teachers and that include(d) me because when I first started teaching, I also did not know the content and linguistic knowledge of the subjects I was teaching and that I could only address by first working through the information to be taught, before I started teaching.

Or perhaps, the burden has fallen on me to provide evidence of knowledge. Now to provide evidence of knowledge one first has to take into consideration how knowledge is (or can be) obtained and to illustrate this by example, let’s quantify this knowledge as: The knowledge of Year 5 mathematics in English. However, to present the evidence of knowledge of Year 5 mathematics in English, for example, and evidence of knowledge acquired in the context of this particular bilingual mathematics program, I am obligated to take into consideration the work samples of students for the reasons set out in the following diagram:

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In chapter sixteen of this report I will elaborate on the topic of evaluation and also how evidence of knowledge can be

obtained.

The keyword here is “acquired”.

If a person has acquired the facts, information and skills of Year 5 mathematics in English, then that person would have the knowledge of Year 5 mathematics in English and being engaged in this acquisition process would also constitute an instance of an experience.

This makes it clear that there is a prerequisite that facts, information and skills has to be acquired first, before one can reach a state of knowledge.

The implication therefore is that the processing of facts and information and the practicing of skills, a necessary prerequisite is (a procedural step to be completed first) for the acquisition of knowledge to occur.

If the facts and the information and the practicing of skills are omitted, then a state of knowledge cannot be reached.

A student’s work sample shows how facts and information was and has been processed. A work sample is therefore irrefutable evidence that a student was engaged (as revealed through the work sample) in a knowledge acquisition process.

To deny the validity of a work sample as evidence (or to not even take it into consideration) would imply that the acquisition of facts and information and the practicing of skills can be omitted but this step cannot be omitted since facts, information, and skills acquired, is the very definition of knowledge.

So, in order for me or anyone to provide evidence of knowledge of Year 5 mathematics in English for example, I first have to establish whether the facts, information and skills were acquired. If I cannot give an account of this step in the knowledge acquisition process, then I wouldn’t be able to provide evidence of knowledge.

And if for example a small group of let’s say ten Year 5 bilingual students clearly show knowledge (perhaps through an English mathematics test in which all 10 students scored 100%) but without a record of the process during which facts and information was processed and skills practiced, then all that would reveal is a mystery of how these students were all able to score a 100%. However, and in real life, a closer investigation of such a scenario would quickly reveal the actual reasons of how the 100% was obtained and it is most unlikely that the knowledge of Year 5 mathematics in English was an instantaneous manifestation.

There are also numerous other factors to be taken into consideration when someone demands evidence of knowledge. For example, a school is not the only place where knowledge can be acquired and in a bilingual school some transferrable knowledge is also obtained in another language.

It is essential that the first step in obtaining evidence of knowledge, is establishing how the facts and information and the practicing of skills were acquired which can be done, by looking at the work samples in the journals because the journals present the information/language support together with a space in which the information can be processed. Of course, there are other ways of processing information but as I have stated before, a workbook like a JOURNAL, is an efficient medium to track and monitor exactly what the students have learned especially when dealing with large groups of students. If there was a computer in every class for every student, then there may not even be a journal, but as mentioned on several occasions before, I am addressing the needs of a particular learning environment.

The very simple philosophy of this program lies in the identification of the information by interpreting curricula, then finding that information through research, then presenting that information in the journal, and then the students guided by the teacher should work through this information.

In consideration of the above reasons, I think it is therefore important to take a closer look at the work samples that Ms. Mejal produced in this chapter, and also because it is very interesting.

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At the end of the 2016/17 academic year, Ms. Mejal submitted a batch of that academic year’s first semester’s Year 5 mathematics journals (random in terms of whatever she could get her hands on) together with a batch of the second semester’s journals (again, random for the reason mentioned before). I have also mentioned before (before the writing of this report) that this work constitutes EVIDENCE and it constitutes evidence because facts, information and skills have to be acquired first, before one has a knowledge of whatever facts, information and skills were acquired and the journal provides a record of what information and also how the information was processed. For the successful development of an academic program and especially a primary school academic program, the work that students produce, are of the utmost importance:

Here is a depiction of 1098 pages taken only from some of the first semester’s batch of journals that Ms. Kanyapat diligently scanned and her final contribution to this project. Analyzing the students’ work has always been an objective of mine, but since the amount of work that I was doing is so vast, I only had time this year to take a closer look at these work samples. The images depicted below are very small but the reason for presenting it here, is to illustrate that there is a substantial record of EVIDENCE that students were engaged in the acquisition of facts and information and the practicing of skills which is a prerequisite for obtaining knowledge. The 1098 work samples depicted below was also produced by a first time Year 5 mathematics teacher (albeit a tremendously talented one) but she did follow this program and I can only provide evidence of this program:

This is the batch of the first semester’s journals. This batch contains well over

1098 pages.

This is the batch of the second semester’s

journals. There are over a 100 journals here and if

there’s at least 30 pages of work samples in a journal, then there’s approximately

3,000 pages of work samples here.

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25 of the 48 work samples previously exhibited in this report.

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Ms. Mejal who followed this program also made use of the TEACHER’S LESSON PLANNER and here is a tiny glimpse of Ms. Mejal’s work:

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Again, it is interesting to consider the following:

If we were to compare the “Daily Lesson Plan” depicted above with one of Ms. Mejal’s lessons depicted on the right and that she completed in the TEACHER’S

LESSON PLANNER and in accordance with this program, we can make the following observations:

In Ms. Mejal’s lesson, there is a complete account of a teacher who has prepared

sufficiently for a lesson. A person engaged in this manner of lesson planning is LEARNING by default and absorbing the subject matter by being engaged in the

learning process themselves. This is a far better guarantee that the person standing in the class actually taught the students something than the description given in the

“Daily Lesson Plan” which is an administrative task.

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Not only does the journal allow some freedom for the children to work through the necessary information in their own individual ways, but it also provides an opportunity for the teachers to let loose their own creativity. Ms. Mejal immediately grasped this concept and exhibited her own creativity through the work that she initiated and all credit belongs to her. In fact, the work that she initiated and that the students produced was SO creative that it took me a while to come to a full appreciation of what it is she is capable of and what it is she has accomplished. But now that I’ve dedicated some of my time during the first semester of the 2017/18 academic year to take a closer look and analyze the work that the students produced, I have an even deeper respect and appreciation for her talents and her work. And keep in mind, that all of this work comes from a first time Year 5 mathematics teacher. And again, the complete CLIL article that I wrote did shed some light on this:

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However, after a lesson observation of one Ms. Mejal’s lessons by administrators it was remarked, “But where is the concept?” However, since the JOURNALS allow us to peer straight into a classroom, this question can now be answered:

Earlier, I pointed out that: A student’s work sample shows how facts and information was and has been processed. A work sample is therefore evidence of a student’s engagement (as revealed through the work sample) in a knowledge acquisition process. The work that the student produced here clearly shows how the facts and information pertaining to this topic has been processed.

It also appears that this student had a pretty good time creating this work. Through the journal the student can basically produce his or her own child-friendly mathematics textbook. This work sample is also exhibiting good use of the mathematical language associated with this topic. This is also a record that a student expended energy which is a requirement for information processing.

And now this child is ready to go and APPLY this knowledge (the mathematical knowledge and also the English rendition of this mathematical knowledge) in the solving of mathematical problems in the exercises of a traditional mathematics textbook to further reinforce what he or she has learned.

There’s a standard “counter-argument” that this entire process can be omitted and that in lesson after lesson, and in year after year, a child would only have to be subjected to the exercises in a traditional mathematics workbook for knowledge acquisition but, I disagree with this opinion and it is also not in accord with STRAND 6 of the B.E.C.C. for primary school mathematics education.

I believe a child should be taught something first (in line with the basic definition of knowledge) and this work sample is evidence that this occurred.

And based on this topic in the Singaporean Syllabus, I formulated the following question that Ms. Kanyapat

researched (information in the teacher’s guide) and that Ms. Mejal then

presented to the class.

The Singaporean Syllabus topic here is relatively simple to understand. Implied here is that children should have

the KNOWLEDGE of rounding numbers off to the nearest 10, 100 or 1 000.

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Not every work sample is a clear cut case that the necessary information was adequately processed by every student. However, and as mentioned before in this report, these work samples are even more valuable. Consider the following:

A brief digression: The publisher’s interpretation of this syllabus topic here is wrong. The syllabus topic clearly states, “without using calculators” and I’m in

agreement with the syllabus topic. Yet, in the publisher’s materials the use of calculators are

introduced at this stage.

The LESSON TOPIC QUESTION for this page 9 of the first semester’s mathematics journal of the 2016/17 academic year is: How do we divide numbers by 2 digits, 3 digits and 4 digits?

I like Mr. Boom Man here but from this work sample I have no assurance that this child would be in a position to answer the lesson topic question. This needs further investigation and in line with my philosophy that if a problem can be identified then a problem can be addressed but first that problem needs to be fully investigated and only then can measures be taken or a strategy be developed to assist this child if indeed there is a problem. And if this child is capable of solving division problems then that is fine but I think (to be confirmed by a thorough investigation) that a child in Year 5 should be able to produce work of a higher standard than this. None of this should be construed as a PROBLEM, the only thing made clear here is the OPPORTUNITY to HELP someone.

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And creativity is not a matter of drawing pictures. Consider the following work sample taken from the latest and improved edition of the Year 5 mathematics journal of the first semester for the lesson corresponding to Mr. Boom Man’s lesson on the previous page:

Through his own creativity, this child injected a bit of humor into a mathematics lesson. Nothing wrong with that…

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It seems the children are enjoying working in the journals:

This kid knows what a keyword is…

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The journals allow for a bit of freedom and since writing and speaking are forms of expression, this freedom goes a long way. This child likes to create little dialogues:

The example here also

contains a small typo error that

should be rectified.

A small error occurred here, the 3 should have been a 1. The denominators should have been (1 x 1) and that would have produced the correct answer of 2/1 = 2. But I don’t think this is reason for concern. The student merely transposed the wrong digit. I think that this student has an understanding of the topic.

This child likes to write little

dialogues in these cartoon speech

bubbles and they all have to do with mathematics and

are written in English. To recall

information in this manner is an

extremely effective learning approach.

This child is not copying the examples. She’s using her

own values.

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As mentioned before, but worth repeating, “it should also be taken into consideration that this particular methodology rose out of addressing the needs of a particular and unique learning environment” and let me now elaborate more on that. An adequately trained and qualified Year 5 mathematics teacher may have a good knowledge of the subject matter and be in a position to successfully deliver and impart their mathematical knowledge to the children, but in this particular learning environment there is no guarantee that every position will be filled with sufficiently qualified or skilled personnel every year. It is therefore essential that the subject’s CONTENT INFORMATION be made explicit as it is being made through the LANGUAGE SUPPORT that also functions as INFORMATION SUPPORT presented in the journal to ensure that the correct INFORMATION is delivered to the children. And this is not to say that a person who is not a technically qualified teacher (like myself) cannot teach and cannot teach as well or even better than a qualified teacher. The teachers that I personally hold in the highest regard are in fact not technically qualified in terms of possessing a paper credential yet they are some of the best teachers I have encountered. And as a university student myself, I have plenty reservations about the quality of tertiary education that produces “qualified” individuals but that’s a discussion for another day. The only thing I am taking into consideration, is reality itself.

And to successfully manage a class of 30+ students who are between 10 and 12 years old to the degree that the majority of them is sufficiently stimulated (the mental stimulation of children is of the utmost importance in learning) and guiding them through the subject of mathematics is a difficult undertaking. How would one ascertain or effectively monitor that each individual child was engaged in a knowledge acquisition process otherwise known as learning? The answer is by taking into consideration their individual work.

The following photographs convey a general sense of well behaved students as a direct result of being stimulated through a creative process:

These photos were

meant for the first

edition.

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A journal also allows for a concrete form of information processing by INDIVIDUAL children. If a child is only presented with let’s say a text (any subject) to be read (reading abilities also has to be taken into consideration) as the only way of processing information, with a few questions being asked to determine if the information presented in the text was adequately processed or not (the only form of monitoring that can be employed here to assess if the information was adequately processed) is not as concrete a form of information processing as the information processing that can be initiated in the journals as already exhibited through the numerous work samples produced by the children who had the opportunity to work in the journals. The same would apply to lecturing if the lecture (any subject) is the only way of delivering information to be processed by the children (by listening) is also not as concrete a form of information processing since the introduction of new subject matter (the new information of the new topic) often necessitates the use of new language that the bilingual children may not have encountered before (they don’t know the new language being used in the new topic) and as a result, it may be difficult for children to process the auditory information of the new words in the new topic presented during the lecture.

All of these factors (and many more) have been taken into consideration for the development of this program and the reason why I stated that this particular methodology rose out of addressing the needs of a particular and unique learning environment. A learning environment with only qualified and highly skilled personnel, with a maximum of 25 students per class, with a computer for each student in each class, with a substantial amount of resources that can be allocated to activities such as project based learning or a complete project based approach for implementing a curriculum or putting a syllabus like the Singaporean Syllabus into operation are not the factors of this particular learning environment. The journal that I designed, came about as a result of taking into consideration a unique and particular learning environment and addressing what I have identified as the needs of this environment. And all of this still ties up with my two initial assignments of creating teacher’s guides (for the delivery of information) and implementing CLIL (developing the language proficiency of bilingual children in specific subjects).

On a side note, the successful implementation of a project based learning approach is also dependent upon information processing. The only difference being the manner in how the information is being processed (through projects) but if an educational institution wants to successfully implement a project based learning approach, such an institution would still have to account for the information of the subjects since the information of the topics will dictate what the projects can or should be. If knowledge is the ultimate goal, then the information cannot be ignored. If a knowledge of Year 5 mathematics, for example, is the goal, then knowing what the information of year 5 mathematics is, is quite important. A syllabus and a curriculum do not contain the actual information, it only indicates (pointing out) what the information should be. Fortunately, language is a tool capable of conveying information and then by putting that information in the journals, both the INFORMATION and the LANGUAGE can simultaneously be presented. But in addition to that, all of the previous factors have to be taken into account together with sound educational practices, together with a good dose of educational psychology and the ever important factor of creativity. And good traditional theoretically based instruction (emphasis on good) shouldn’t be summarily dismissed to be replaced by a project based learning approach, especially if the notion of information is not understood.

These photos were

meant for the first

edition.

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To continue, the work samples to be presented on the following four pages were all taken from the second semester’s Year 5 mathematics journals of the 2016/17 academic year. It was during one of these lessons that Ms. Mejal was observed after which it was concluded that: The concepts are not clear and that the journal is an “activity” and that the students can merely read the publisher’s materials to gain an understanding of the subject matter. Fortunately, since a journal is a record of a student’s work, and a record of the information processed, and a window into the classroom, these lessons can now be analyzed properly:

All of the information presented here adequately answers the LESSON TOPIC QUESTION that was based on a syllabus topic from the Singaporean Syllabus. To

convert meters to centimeters one can multiply by 100 to find the smaller unit. The teacher also took the “vice versa” as stipulated by the syllabus into consideration in

addition to examples as exhibited in the upper right quadrant of the work space. This topic could possibly be presented in a thousand different ways (of which reading the

exercise book would probably be the least effective as suggested) but from this work sample and numerous others, we can safely conclude that a BILINGUAL mathematics

lesson was adequately delivered.

The first thing to take into consideration is the syllabus topic. Observe the syllabus topic and observe the LESSON TOPIC QUESTION that was subsequently formulated.

Observe the use of language that is

also required to be processed by

students.

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And in the following lesson, it appears that the children were then given an opportunity to build upon the previous lesson and look, in this lesson the teacher changed the task that the children had to complete. This changing of task is important because this is an effective way to keep the students ENGAGED and STIMULATED. For this task the children had to do some cutting which we were told, after Ms. Mejal’s observation, took too long and to which I replied: The motor skills that the children need to develop in their earlier years need a bit of working according to common educational practices:

Observe the facts and information all in line with the syllabus topic.

This particular lesson is not mathematically very demanding BUT THIS IS ALSO A BILINGUAL

MATHEMATICS CLASSROOM and that implies that we have to work in great detail for the nuances of

the language to get through to the children. This is an excellent

lesson and it is very obvious that the children enjoy these lessons

not only because Ms. Mejal imbued the lesson with some

craftwork, but because there is a little bit of freedom allowed for the processing of information.

This idea (THIS CONCEPT) was introduced in the previous lesson. Here the children repeated it. Building upon ideas in this manner is an extremely effective teaching tactic (also consider syllabus design). Not only is the teacher building upon ideas, but she uses the ideas repeatedly. Again,

very effective. After the observation I was told that the observers couldn’t see the CONCEPTS and reducing the journal as being merely an “activity”.

This was an inappropriate conclusion given that “reading a book with exercises” was suggested as being a better alternative (but what should also be taken into consideration is that in this series of materials there is

no standard textbook in the traditional sense of what a textbook is).

Here we have a conversion of km to m and vice versa

in line with the syllabus topic and lesson question.

Here we have a conversion of kg to g and vice versa in line with the syllabus topic

and lesson question.

Here we have a conversion of L to ml and vice versa in line with the syllabus topic

and lesson question.

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With the solid foundation provided in the first two lessons of this unit of measurement it looks like Ms. Mejal could now again (to keep that stimulation factor going) assign a new task for the students to complete. From this work sample (and from numerous others of this lesson that she submitted) we can clearly see that the children were now presented with a proper SOLVING PROBLEM task of first, designing a “unique house” with measurements (the practicing of visualization and geometrical skills are also in effect here in accordance with GOOD mathematics educational practices) that had to be converted. Now that the children had a PROBLEM SOLVING TASK (after the successful introduction of facts and information during the first two lessons) the work that the children produced for this lesson are all uniquely different and individual. The phenomenon of “copying” is a problem that is prevalent with the excessive use of textbooks that are filled with gap-fill exercises for one correct possible answer. A teacher displaying information on a board in an attempt to teach the students something like a conceptual map with students required to reproduce such information is sometimes necessary. “Bad copying” is the copy ing done in textbooks. The degree of originality and creativity flowing out of the journals and as shown by the numerous work samples is CLEAR EVIDENCE that the journal inspires original work:

Yet another lesson in accord with the

Singaporean Syllabus….

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For the fourth and final journal lesson in this unit of measurement in Year 5 mathematics, it appears that Ms. Mejal wanted to revise and reinforce the LANGUAGE pertaining to this unit. This is excellent preparation for the students because the language here or the mathematical concepts here contain information that is required to be understood in order for the students to complete the exercises in the publisher’s materials and in line with my very basic philosophy that first a child has to be taught something, before the child can go and do that thing:

Here the student wrote, “I love

mathematics.” This is quite a

significant statement in educational terms

and especially mathematics

education. Thank you Ms. Mejal.

This final lesson of the unit appears to be a revision based lesson with an emphasis on the language applicable to the entire unit. This will place the student in a good position to do the exercises in the publisher’s materials.

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The four lessons that Ms. Mejal conducted here for this unit of measurement in Year 5 mathematics entailed the delivery of information, facts and the practicing of skills as exhibited very clearly in the randomly selected work samples. The work samples indicate a satisfactory level of information and fact processing (a necessary step to acquire the actual knowledge). The entire process is not that complicated:

Step 1: Consult the Singaporean Syllabus because the materials are based on the Singaporean Syllabus. Step 2: Formulate QUESTIONS based on the SYLLABUS TOPICS and also take the materials into consideration. Step 3: Research and find the THEORETICAL BACKGROUND INFORMATION that would adequately answer the lesson topic questions. Step 4: The theoretical background information is also the source of the subject’s LANGUAGE to be used for the compilation of the LANGUAGE SUPPORT and it also functions as INFORMATION SUPPORT. (Use language the children can digest). Step 5: Present the LANGUAGE/INFORMATION SUPPORT in a JOURNAL. Step 6: ALLOW both teachers and children to work through and process the information. This step requires TIME and ENERGY. Step 7: ONLY NOW the children are ready to complete the exercises in a traditional mathematics workbook filled with exercises.

The book below has a function and that function is to reinforce and consolidate

learning (as stated by the publishers themselves). Yes, it is very important

that the students do these exercises and this part should not be omitted. But its

function should be clearly understood. It is a tool to check the children’s

understanding and for them to apply the knowledge they have gained AFTER THEY

LEARNED something.

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It’s worth noting that the crux of the process outlined on the previous page was succinctly expressed in the Year 4 mathematics Teacher’s Guide contents page that was in use in the school during the 2016/17 academic year which was openly available for anyone to evaluate. Observe this SHARING OF INFORMATION:

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CHAPTER 9: A Continuous Improvement

It is worth noting that through every stage in the development of this project I made a concerted effort to constantly and continuously improve on the work. This is evident first and foremost in the work samples that the students produced throughout this project, but also evident in the reduction of the amount of information presented to the teachers, but most of all it is evident in the improvement of the language support provided to the bilingual children. To follow will be a brief overview giving an account of these continuous improvements starting with the children’s work samples:

Depicted below are work samples produced during the first CLIL experiment conducted in Year 4 mathematics during the second semester of the 2015/16 academic year. Even though the images depicted below are quite small, we can get a general sense of how the students were occupied during these lessons and compare this work with the subsequent work produced. However, one should also keep in mind that the individual teacher initiating a lesson has a huge influence over what the children put out, but the objective still stands to see if there has been a general improvement in the work:

Even the use of color had to be introduced. This group of teachers worked under the notion that the use of colored pencils were not allowed. We can also see

the use of a “mind map”. I think that there is an

overuse of “mind maps” such as these because often mind maps are used purely

to memorize the surface information but good mathematics lessons

require a deconstruction of the mathematical concepts

and ideas.

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And now observe the following work samples produced only the following semester in Year 4 mathematics during the first semester of the 2016/17 academic year:

The journal’s simplified design seems to provide a better work area, allowing the teachers and children more freedom to work in. I think it is also convenient to have the LANGUAGE/INFORMATION SUPPORT at

hand for each lesson. When primary school children are given too many additional printouts and handouts like additional and separate glossary books they don’t use it during the lessons. With this particular design the additional language and information support is always ready at hand. I also think that there is an improvement in the work. The final image here also shows a lesson not done since the teacher was

unable to work through the entire journal during that semester. Ms. Mejal is busy developing strategies on how to get the work done in the limited amount of time available.

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The following work samples come from Year 5 mathematics. The three samples in the first row dates back to the first semester of the 2016/17 academic year and the two at the bottom from the second semester:

The work that Ms. Mejal initiated in the journals is so creative it requires a closer look to gain a full understanding and appreciation but I think the analysis done in an earlier chapter already made this clear. But a continuous improvement is also evident in Ms. Mejal’s work as will be revealed on the following pages.

The two work samples below stems from the second semester.

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And then, during the first semester of the 2017/18 academic year, and in the new and improved Year 5 mathematics journal, Ms. Mejal initiated the following work:

In the latest Year 5 mathematics journal it appears that Ms. Mejal is encouraging the children to work more independently in the journals. This approach has produced more original work and ties up directly to the METACOGNITION component in the Singaporean Syllabus which has to do with self-regulation of learning.

Page | 32

And here are four more work samples from Year 5 mathematics:

Observe the geometry, use of language, mathematics and creativity.

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One problem that became evident in the development of this project was the quantity of information that I continuously and with each new edition tried to reduce to make it more manageable for the teachers to work with. Observe the notes in the following diagram:

The first big CLIL experiment conducted in Year 4 mathematics produced a teacher’s guide with

five units’ theoretical background information totaling 100 pages. The five workbooks which also

included the additional language exercises totaled approximately 171 pages. This produced a sum total of 271 pages to be worked

through during a second semester with only three mathematics

periods per week.

And in the latest new and improved Year 4 and Year 5 mathematics journals, in which I attempted to MERGE the LANGUAGE SUPPORT and INFORMATION SUPPORT that were in operation during the first semester of the latest 2017/18 academic year the page counts are:

70 Pages 74 Pages

Page | 34

However, the most significant improvement can be found in the LANGUAGE SUPPORT that also now functions as the INFORMATION SUPPORT as illustrated in the following diagram:

This excerpt was taken from the glossary of the Year 4 fractions book used during the CLIL experiment:

This excerpt was taken from the new and improved Year 4 mathematics journal in operation during the first semester of the latest 2017/18 academic year:

End of Part 3. Copyright © Martyn Krügel, 2018

All rights reserved

The quality of the information to be presented to the students is very important. The first definition and example sentence for the term “fraction” used during

the CLIL experiment is purely technical and does not convey a simple and complete conceptual understanding in comparison to the IDEAS used in the latest version of the journal for the same term. I strongly believe that the

quality of the INPUT has a tremendous impact on the quality of the OUTPUT, so to ensure that the students produce good quality OUTPUT, it is vital that the

quality of the INPUT, is of the highest standard.