Assignment topic: Critique of an approved textbook for the Singapore Mathematics Curriculum
In Singapore schools, textbook is one of the key resources to students and teachers – it is not only the “book of knowledge”, but many a times, the “book to success”. There is because most, if not all of us – parents, students, and even teachers, hold the strong belief that it has everything that is expected to be covered in the examination syllabus. We will not go wrong if we follow it strictly. Sometimes, parents even ask the school why cover beyond the ‘syllabus’ when they found materials and scope beyond what is “stipulated” in the textbook.
It is therefore important for us, as educators, to ask the question, “Has the approved textbook served our needs?” To be even more specific: Our Curriculum Needs
Some of us may argue that “Textbook is just a supporting resource” in the classroom. Teacher is the key to the learning experience that students have. I agree. Nevertheless, my point of argument is, it is a resource that teachers, especially beginning teachers, rely heavily on. It is also a primary resource that students would make reference to in the absence of teachers for their learning, and definitely, it is also the main reference source that parents turn to when guiding their children in learning. Therefore, textbooks today no longer just serve as the ‘content’ source, it should also support the delivery of the curriculum.
Syllabus is part of the curriculum. It spells out mainly the scope of the content (and of course, depending on the nature of the subject discipline, it may cover a set of discipline-related skills). However, the curriculum encompasses more – which includes values, dispositions and attitudes, just to name a few.
I think, more specifically, as a Maths teacher, I would ask the question, “Has the design of the textbook been relevant and adequate to support the desired outcomes in the Singapore Mathematics Curriculum, in today’s context?”
Definitely, as spelled out in the Maths Curriculum, there are more than the subject content. That is where I find the value of critiquing the textbook to surface its merits and areas it lack of, and I hope to make recommendations to enhance the existing resource.
The Background
It is important for us to understand this background. And I think this explains the need to critique the “approved textbooks”. All schools in Singapore adopt “MOE approved textbooks” in the classroom.
Up to early 2000s, the Curriculum Planning and Development Division (CPDD) that oversees the Singapore school curriculum design all the textbooks. Hence, at that time, textbooks do not just deliver the content (syllabus), but (I believe that) also had the expectations of curriculum weaved into the design of the lesson materials. Materials could be designed in a manner that supports the pedagogical approach or strategies advocated by CPDD.
Since early 2000s, the Ministry took steps to open the publication market and as a result, textbooks are now written by writers engaged by the publishers. Many of these writers are from the Education sector – academics from the National Institute of Education (Singapore’s only teacher training college), some were ex-teachers from the service. While CPDD would brief the publishers on the syllabus and curriculum, how the materials are put across or presented is largely dependent on the publisher (or more specifically, the writer and the editor). Of course, publishers must submit their proposed materials from CPDD for approval, and that is where the “MOE approved” textbooks come into the picture.
In fact, there are no less than 3 titles of approved Maths textbooks available in the market. While the syllabus is taken into consideration, has the way the materials designed and delivered in the textbook meet the thinking behind the curriculum?
Every year, the schools would be presented with a list of “approved textbooks” which they have to “pre-order” for the students. Notice the last sentence in paragraph 1 says, “Schools should use a basic texts only those books which have been listed here.” This shows how important these approved textbooks are, amongst the many teaching resources and materials that are available.
Syllabus Design
As I proposed in the title, to critique the textbook, there are 2 parts to it – the syllabus and the curriculum.
First, let us examine the primary (which is also the key) component of the textbooks – the Syllabus.
Does the way textbooks design to deliver the content aligned to the way the syllabus is designed?
In the Mathematics syllabus document, it is clearly spelled out that Mathematics is seen as a hierarchical subject. The building of knowledge and skills follows Piaget’s Stages of Cognitive Development - from the primary to secondary Maths syllabus, it progresses from concrete to formal operational. Models were adopted in Problem solving in Primary Mathematics whereas Algebra is introduced in Secondary Mathematics to deal with more abstract problem solving (and it replaces the Modelling Approach).
On top of that, the introduction of new knowledge takes into consideration of past learning, which, obviously aligns itself very well with Vygotsky’s “Zone of Proximal Development” – to make connections of knowledge.
Here's an attempt to illustrate how the theories are weaved into the design of the syllabus, through the strand, “Statistics and Probability” in Secondary Maths: One would notice that in Secondary 1, students learnt to interpret data from various kinds of graphical representation. In fact, this is built on the Primary mathematics when students were learn to read information from the different kinds of graphical representation. It progresses from simply drawing superficial information to interpreting data in graphs, which is a higher order of thinking.
In Secondary 2, students move on to interpret more ‘abstract’ kind of graphical representation, which is not so commonly used in everyday application. However, they could ‘borrow’ the skills to interpret data (acquired in Sec 1) to interpret new graphs. More complex level of interpretation such as the different kinds of averages are now introduced to students. In upper secondary, students would have consolidated enough foundation knowledge and start to interpret ‘real’ statistical charts.
One would also notice that the syllabus adopted a spiral approach. This gives students time to develop their understanding from the more concrete stage towards the abstract level over time. At the same time, students would get the chance to revisit their prior learning hence not forgetting the entire topic at the end of 4 years.
Having understood the syllabus design, let us turn to the way the textbooks design the learning (content). It is not difficult to find that textbooks adopt the syllabus design in the way they deliver the content. If we refer to the content page of the series of textbooks - it is not difficult to find alignment. Hence, in terms of the syllabus content, we could conclude that textbook publishers did a good job.
What to examine?
Recall that, right from the beginning, my preposition is to examine, “Has the design of the textbook been relevant and adequate to support the desired outcomes in the Singapore Mathematics Curriculum, in today’s context?”
Having examined the relevance, now to what extent the design of the Maths textbook has adequately address to the outcomes of the Mathematics Curriculum?
Now let us look at the Singapore Mathematics Curriculum – which comprises of 3 parts, the Mathematics Framework, Integration of Information Communication Technology (ICT) and the Infusion of National Education in the Curriculum.
On top of that, I’m also looking at how well these are integrated – I’m seeking for seamless integration – so that these components do not exist as discrete components or being ‘force-fit’ in the design.
The Curriculum document sets the direction for teaching, learning and assessment of mathematics in Singapore. The aim of the Maths curriculum is to develop the ability in every student to as high as possible through a differentiated and targeted approach.
Look at the Maths framework: Problem solving is central to mathematics learning – acquisition of and application of mathematics concepts and skills in a wide range of situations, including non-routine, open-ended and real world problems.
There are 5 domains in the Maths curriculum – Concepts, Skills, Process, Attitudes and Metacognition.
In a typical Maths textbook,
Mathematical concepts: it usually presents the “facts” (and different scenarios) directly, upfront. Hence the learners would be expected to read and ‘understand’. Similarly, with the ‘facts’ and various scenarios presented, the teacher would likely to elaborate further the given examples, and give more examples. It somehow frames’the “way” the teacher or the student thinks.
Mathematical skills: The direct inference from the textbook is, there is still a firm belief of “Drill and Practice” leading to “Practice makes Perfect”
It goes from “Basic Practice” to “Further Practice", “Maths@Work” and “Brainworks” … These are practices at varying degree of difficulty
Knowledge skills are, more often than not, presented in the form of ‘solved problems’ with steps clearly listed, …
Is this the way our learners learn? Currently, yes… they play the role as passive learners – because the ultimate aim, after reading all these examples, is to apply similar ‘strategies’ or operational steps to solve similar problems!
The question is, while it is a textbook, does it has to adopt such a didactic approach? This is definitely not the approach that the curriculum advocates (as we see proceed to understand the other aspects of the Maths curriculum).
While there is attempt to illustrate the application of Mathematics in real life, hence to ‘promote’ its usefulness, the attempt however often seems ‘force-fit’ as it might appear under a small section “Extend Your Learning Curve” and it’s seen as an ‘extension’. Similarly the thinking of mathematics, beyond what is presented also appears as an optional item – that becomes a ‘can-do’, ‘can don’t do’ item.
From the flow of the materials, it is obvious that the textbook basically adopts the Objectives Model (in its delivery): Stating the Objectives, Selecting Learning Experiences, Organising Learning Experiences and Evaluation.
From this preliminary examination, using the Maths framework as a reference, it is obvious that the textbook design has not cater to the non-content and non-content-related skills areas, i.e. the ‘softer’ part of the curriculum – the dispositions, the attitude and even the metacognition aspects!
Another area which is obviously absent is the seamless integration, without seeing each component as a discrete entity.
What I propose?
As such, I am proposing to the design of the textbook, to make it relevant to the curriculum, to weave in elements of “constructivism” approach, whereby materials are designed such that it provides learners with the space to construct their own knowledge, their own understanding.
While we usually see “Constructivism” as a process play out in the classroom, and facilitated through the teacher. I believe that, the way the materials designed could be along this line; and this should trigger the user (be it the teacher, student or even the parent) to look at the materials in a different light. It could be such that the materials no longer provide information/ answers directly, but it comes with triggers (questions) to set the user thinking or the users to think together.
Next, in terms of technology, we notice that there was no mentioned in the ‘chapter’ on “Data Handling” (used for illustration earlier). So, technology has yet quite be positioned as a common tool in the way the content is delivered although, in the curriculum document, ICT is expected to be used to facilitate the following…
So, why these opportunities are not created within the design of the materials? While the textbook is a printed medium, it does not necessary confine its activities to non-ICT based. In fact, the textbook that I make reference to, comes with a digital version. However, the digital version is simply “A” digital version without links to resources or other ICT-enabled activities. So, the publisher has not fully leveraged on the medium and potential opportunities that exist.
It is obvious that technology could be leveraged on to support self-directed learning and collaborative learning. These are the expectations of the Maths curriculum, which also echoes the outcomes of the 3rd ICT Masterplan in Singapore. At a bigger picture, self-directedness and collaborative skills are 21st century skills that every child should have.
National Education plays a critical role in the Singapore Education system, in particular to address to the unique make-up in this multiracial society.
Having touched on the various aspects and expectations of the curriculum, I would like to propose changes to the way the textbooks are designed so that the various aspects of the curriculum is more well-integrated, and presented as a whole to the learners, as well as teachers.
It is time to move away from the belief that “a textbook is just a print medium and therefore let’s live with its limitation.” There is no limit to the way the materials could be designed and being a basic text, it has great influence to the learners and the teachers.
Here is an example of how several aspects of the curriculum expectations are weaved into the design of a learning activity – where students, with the aid of technology, develop their own understanding and able to see the application of what they learn is applied in real world.
Introduction of the topic “Data Handling”
- Leveraging on their prior knowledge, students searched for the use of graphs in real life (and they were told, preferably in the Singapore context).
- Each student found a chart and post it in a sticky on a digital wall called “Wallwisher”.
- They could also insert the website where they found the resource.
- With the visuals on a common wall, the teacher could reorganise the charts by grouping them (e.g. putting all the bar charts together, all the line graphs together). This is followed by getting students to identify similar features across the similar charts. E.g. Students could point out the horizontal axis of all line graphs are somehow related to time. Hence, they notice that line graphs are used to feature trends (i.e. the primary function of line graphs).
- Having understood the purpose of these graphs, students return to the wallwisher to click at links that they or their peers had put in so that they could read about the real world context that these graphs are being used to represent data.
- The teachers could also identify relevant charts to discuss NE related issues – for instance, a discussion on the use and conservation of resources like water could start when referring to charts that illustrate the use of water over months.
Topic: Approximation and Estimation
- In a news article that reports the community celebrating the Chinese New Year with the “lou-hei”, 2 types of figures were reported “646” and “4000”. Students read the context and made an attempt to explain why the journalist chose to report the figures in the way shown.
- Note: An exact figure 646 is reported because we have to account for the number when submitting it as a world record.
Next steps…
I will look, in more detail, the textbook on how the various broad topics are designed – to identify areas that it has not addressed to the curriculum adequately. I would make an attempt to propose suggestions how the topic could weave in the desired components in an integrated manner.
To do this, I would also attempt to draw up a checklist that would guide me in examining the materials and making recommendations.
Thank you.
