I. Prologue
In Part 1 of this article, I described the historical background,
development and characteristics of the New Mathematics movement
in the United Kingdom (UK). Now I shall continue to describe the
New Mathematics movement in Hong Kong (HK) and compare the two curriculum
initiatives in the two places.
A few mathematics educators in HK have written extensively on various
issues relating to the New Mathematics movement in HK, e.g. Wong
(2000 & 2001), Leung (1974, 1977 & 1980), etc. I will try
to recapitulate in Section II below the main features behind the
historical background, development and characteristics of this curriculum
movement.
II. The New Mathematics Movement
in HK
1. The background behind the New Mathematics
movement
Till early 1970s, most of the secondary school mathematics textbooks
used in HK were imported from the UK. As a result, there was similar
dissatisfaction as in the UK (see Section IV.1 of Part 1) with the
secondary school mathematics curriculum among HK mathematics educators
and teachers. In particular, there was dissatisfaction with the
tedious calculations involved in the use of imperial units such
as miles, furlongs, yards, feet and inches; gallons, quarts and
pints. However, such dissatisfaction was less extensive as tertiary
education (there was only one university) and industry were relatively
underdeveloped in HK in the 1950s and 1960s.
Elements of New Mathematics were first introduced into university
mathematics courses in 1959. In the Foreword of the book Elementary
Set Theory – Part 1 by Leung & Kwok (1964), Prof. Y. C. Wong,
the Head of the Mathematics Department of The University of Hong
Kong (HKU) in that period, explicated that set theory was introduced
into the 1st Year Mathematics Course in 1959, followed by inclusion
of modern algebra in 1960. Set theory and symbolic logic were then
introduced into the 1964 Advanced Level Pure Mathematics Examination
Syllabus. Concerning the introduction of New Mathematics into the
secondary school curriculum, Prof. Y. C. Wong attended the seminar
on New Mathematics at Southampton University in 1961 and brought
back to HK ideas of this new movement. Subsequently HKU conducted
a series of seminars in the summer of 1962 on New Mathematics and
these seminars were attended by a considerable number of secondary
school mathematics teachers. Some teaching materials based on SMP
were distributed during the seminars. Around the same period, R.
F. Simpson, a senior lecturer in the Faculty of Education, HKU,
independently introduced the ideas of New Mathematics in public
talks given to mathematics teachers of the Hong Kong Teachers’ Association.
Simpson’s speech (1962) was published in the official publications
of the Association, in which the opportunity offered to students
by New Mathematics in selfdiscovery and creative thinking was emphasized.
This new pedagogy, in contrast to the expository approach of teaching
and emphasis on rote learning by students prevailing in the traditional
mathematics curriculum, appealed to the more enthusiastic teachers.
In fact, this new pedagogy is compatible with the contemporary theories
of learning. Furthermore, there were articles (e.g. Kwok, 1962)
in the Mathematics Bulletin, a periodical edited by the Mathematics
Section, Advisory Inspectorate of the former HK Education Department
(ED), discussing the New Mathematics movement happening outside
HK. These series of events set the scene for the launching of the
New Mathematics movement in HK. It is significant to note that mathematicians
and mathematics educators in HKU were particularly keen on promoting
and supporting the New Mathematics movement in this preliminary
stage. As remarked by Leung (1980), the modernization of university
mathematics education in HK was one of the driving forces behind
the reform in secondary school mathematics.
2. The development of the New Mathematics movement
and its characteristics
Many professionals in the HK mathematics community were very excited
by the series of events described above. However, since the school
mathematics curriculum was centrally controlled under the jurisdiction
of the Mathematics Section of ED, teachers themselves could not
initiate New Mathematics teaching in secondary schools, in contrast
to what had happened in the UK. In the 1962/63 school year, the
HK Secondary School Mathematics Project Committee was established
by the Mathematics Section to explore ways to experiment with New
Mathematics in secondary schools. Based substantially on the content
of SMP in the UK, the Committee devised a draft of a set of guidelines
on the content of New Mathematics and tried it out in the 1964/65
school year in Queen Elizabeth’s School, a government secondary
school. From a retrospective point of view, the implementation of
the New Mathematics movement in HK tended to follow, at least in
the initial stage, Fullan’s notion (1991) of “Think big, start small”
in curriculum development. The experimentation was soon extended
from one to ten secondary schools, though mostly prestigious ones
of the grammar school type. The number of secondary schools experimenting
with New Mathematics in the 1967/68 school year increased to over
24 (Poon, 1978), while the percentages of secondary schools adopting
the New Mathematics curriculum in the 1969/70 and the 1972/73 school
years rose to about 49 and 61 respectively. These figures show that
the New Mathematics movement was rapidly spreading among the HK
secondary schools and, to a certain extent, fulfilling the aspiration
of Y. C. Wong made in 1968 that “concerning the New Mathematics
movement, HK would not be satisfied to be just a spectator” (Wong,
2001, p. 31). It is interesting to note that in spite of its key
role in the development of the New Mathematics movement, ED had
been adopting quite a low profile in publicizing the new development.
Among all the Annual Summary and Triennial Survey issued by ED within
the period from 1960 to 1975, only the 1964/65 Annual Summary compiled
by Gregg (1965, p. 10) contained the following brief indication:
“In connexion with a project in Modern Mathematics, which was begun
in a government AngloChinese secondary school, a temporary outline
syllabus for Forms 1 to 5 and a detailed teaching syllabus for Form
l in Modern Mathematics were prepared.”
It might be speculated that ED was cautious when first launching
the New Mathematics project as an experiment and soon became impatient
and aggressive in pushing the movement forward as a mainstream policy
by hinting that the traditional mathematics syllabus would be phased
out very soon in public examinations
(Wong, 2001). This could indirectly lead to the rapid increase in
the number of schools adopting New Mathematics. The original “start
small” concept was soon forgotten and rapidly gave way to a tendency
for fullscale implementation. The government’s strong intervention
in the New Mathematics movement could also be discerned in the following
incident. There were only two series of locally developed textbooks
on New Mathematics and the most widely used one was Modern Mathematics
of the Mathematics Study Monoid published in 1965. The Mathematics
Study Monoid (a textbook writing group) consisted mainly of civil
servants working in government secondary schools and teacher training
colleges. This fact might have been interpreted by the public to
mean that the government was very much behind the promotion of the
New Mathematics movement, since civil servants would not be allowed
to write commercially published textbooks without the permission
of the government.
However, New Mathematics had not totally replaced traditional mathematics
(see statistical data given in a later section) as in the UK. Some
teachers/schools were skeptical about the benefits of New Mathematics,
particularly on the deemphasis of deductive plane geometry and
more complex manipulative skills in algebra. Papers on traditional
mathematics were offered side by side with New Mathematics in public
examinations for secondary school leavers throughout the New Mathematics
era.
According to Leung (1974), the following patterns of thought among
the proponents of New Mathematics formed the theoretical framework
underpinning its development in HK schools:
• The structure of mathematics and the rigour of this structure
were considered as the foundation of New Mathematics. Since the
structure of mathematics was developed by logical deduction expressed
through the language of set theory, therefore set language and symbolic
logic were very much emphasized.
• Mathematics was regarded as a theoretical system with common
properties or characteristics. Taking this view, one representative
example found in the HK New Mathematics curriculum was the treatment
of the number system. Starting from the set of natural numbers,
the set of whole numbers was constructed, then the set of rational
numbers, the set of irrational numbers, the set of real numbers
and finally the set of complex numbers. The commutative, associative
and distributive properties together with the existence of the identity
and inverse elements relating to the operations of these kinds of
numbers were formally discussed.
• The concise and precise use of mathematical symbolism and language
was essential in mathematics learning. Therefore, simple algebraic
equation like 2x – 4 = 0 was regarded as an open statement with
a certain truth set. Solving the equation was considered as finding
the elements of the relevant truth set and the solution x = 2 had
to be presented as “{2} is the solution set of the open statement”.
In contrast to the UK scenario where the development of New Mathematics
was essentially based on pragmatic classroom experiences, the development
in HK claimed to be very much based on a principled view of the
nature of the subject. With respect to this view, the New Mathematics
movement in HK could be regarded as more pedagogically meaningful
than that in the UK, i.e. the curriculum was based on what is important
or worth learning in mathematics rather than what students are capable
of learning in mathematics. However, the development in HK still
lacked a sound underpinning curriculum development framework.
The aims of the New Mathematics movement in HK were to emphasize
the structure and concepts of mathematics expressed through precise
mathematical language, to reduce complexity in calculations, eliminate
the more difficult parts of plane geometry and replace geometric
proofs by algebraic deduction. The first public examination of the
New Mathematics syllabus took place in the year 1969. The above
stated aims were reflected to a certain extent in the aim of the
examination as announced by the HK Certificate of Education (English)
Board (1968):
“The aim of the examination is to test ability to understand and
to apply mathematical concepts rather than to test ability to perform
lengthy manipulations. Candidates will be expected to do some deductive
thinking and to do some simple proofs. Credit will be given to a
clear and systematic presentation of an argument. Symbolic expressions
are often helpful in making statements concise and precise, and
candidates will be expected to be familiar with the use of approved
symbols which are listed in the syllabus.”
It is interesting to note that throughout the New Mathematics era
in HK, much more emphasis was placed on the subject content rather
than the teaching approaches, except the remark of R. F. Simpson
made in his public talks during the preliminary stage of development.
Though the proclaimed rationale and aims of the New Mathematics
movement in HK were rather different from those in the UK, the content
of the New Mathematics curriculum in HK was surprisingly similar.
In fact, as mentioned earlier, the guidelines on the content of
New Mathematics set down by the HK Secondary School Mathematics
Project Committee was essentially based on SMP. In contrast to the
opponents of the New Mathematics curriculum in the UK, who criticized
the insufficient training on deductive reasoning because of the
removal of formal Euclidean geometry from the syllabus, it is interesting
to note that the proponents of New Mathematics in HK argued that
the training of logical reasoning could be better taught through
algebraic deduction, including set and symbolic logic, than through
proofs in traditional plane geometry (Tsiang, 1961). This argument
is quite contrary to the observation of Davis & Hersh’s (1981,
p.7) that “... as late as the 1950s one heard statements from secondary
school teachers, reeling under the impact of the ‘new math’, to
the effect that they had always thought geometry had ‘proof’ while
arithmetic and algebra did not”. Basically much of the traditional
plane geometry and more tedious mechanical manipulations like finding
cube roots of given numbers were deleted to give way for new topics
like concepts of modern algebra, statistics, probability, coordinate
and transformational geometry, etc. Similar to the situation in
the UK, many inservice teacher training programmes were organized
by the government to familiarize teachers with the principles and
practices of the New Mathematics movement.
In the late 1960s and early 1970s, there had been a rather rapid
expansion of secondary schools in HK, which led to an increased
number of students with diversified learning capabilities receiving
compulsory secondary school education. It is interesting to note
that the social justice issue concerning curriculum entitlement
against differentiation of students and their curricula did not
arise in HK as was the case in the UK. The same curriculum was offered
to all schools adopting New Mathematics and setting was also uncommon
in HK schools during that period.
When New Mathematics was first introduced into HK, many members
of the mathematical community were enthusiastic and hopeful that
it would resolve some of the unsatisfactory elements in the teaching
and learning of the traditional mathematics curriculum. However,
in the early 1970s, heated debates on the advantages and disadvantages
of New Mathematics began to surface. Some schools started abandoning
New Mathematics and reverted back to the traditional mathematics
curriculum. As summarized by Leung (1977), the problems of the implementation
of New Mathematics in HK were formality replacing substantiality;
presentation format replacing mathematical content; emphasizing
trivial concepts/properties but not important skills; putting immaterial
concepts and theories before practice and applications of mathematics;
and as a result,「只見樹木，不見森林」. Leung’s criticism resonated with Goodstein’s
view of New Mathematics as “extreme and eccentric” as mentioned
earlier. Kline’s classroom episode where the teacher emphasized
the supposedly important yet intuitively trivial commutative property
of addition of numbers could also have happened in HK classrooms.
As a compromise between the two camps of New Mathematics and traditional
mathematics, and following the good Chinese tradition of ‘not going
to the extreme’ and adopting a ‘middle road’, a third curriculum
called Amalgamated Mathematics was developed by integrating the
‘good’ elements of the two extremes. This amalgamated curriculum
was first introduced to secondary schools in the school year 1975/76,
where there were three mathematics curricula  new, traditional
and amalgamated  for schools to choose from. Similar to what had
happened in the UK, this amalgamated curriculum then became the
only one to be offered in schools in the school year 1981/82.
III. Comparison and Contrast of
the New Mathematics Movement in Hong Kong and the UK
The following table sets out the key features of the New Mathematics
movement in HK and in the UK as a comparison.

UK 
HK 
Origins 
The ideas of New Mathematics originated from members of the
local mathematical community, though with some influence from
what happened in the US and Europe. 
The ideas of New Mathematics were mainly ‘imported’ from the
UK. 
Reasons of development 
The new developments of subject content for university mathematics,
the increased mathematical use in industry, the new developments
in teaching theories and desirability of learning mathematics
as a unified subject were the main reasons behind the dissatisfaction
with the traditional mathematics curriculum among members of
the mathematical community. 
There was similar dissatisfaction but to a lesser extent,
probably due to the state of development in tertiary education
and in industry. 
Ownership 
New Mathematics was developed solely as SBCD, initiated mainly
by school teachers without government intervention and support. 
New Mathematics was initiated and developed by the government,
with support from tertiary mathematicians and mathematics educators. 
Mode of development 
New Mathematics was introduced and remained as a teaching
experiment and there were various projects developing in the
same period for schools to choose from. 
New Mathematics was first introduced as a teaching experiment,
and soon the government tried to push the initiative as a mainstream
policy to be implemented in all schools. There were also no
alternative projects for schools to choose from. 
Design of development 
The development of New Mathematics was not based on any curriculum
development model, but developed on a pragmatic approach of
finding alternative content teachable to students of the schools
taking part in the project. 
Although also not based on any curriculum development model,
it was claimed that New Mathematics was developed to reflect
the nature of the subject. 
Objectives and choice of content 
Although there were no explicit curriculum objectives, content
of New Mathematics was developed and fieldtested in classrooms
with subsequent modifications and refinement. 
Although there were explicit curriculum objectives based on
the rationale that New Mathematics was to reflect the nature
of the subject, the teaching content was essentially modeled
on SMP. 
Emphasis 
New Mathematics emphasized both on new content (structure
and language of the subject) and new teaching approaches (discovery
of generalizations by students). 
New Mathematics seemed to emphasize only on new content (structure
and language of the subject). 
Inservice training 
SMP organized substantial inservice teacher training programmes
to better equip teachers. 
There were also substantial inservice teacher training programmes,
but organized by the government. 
Advantages 
New Mathematics seemed to improve learning atmosphere and
enhance enthusiasm for discovering ideas. 
There seemed to be no particular report on the good effects
of New Mathematics. 
Main criticism 
New Mathematics was criticized as extreme and eccentric. 
New Mathematics was criticized as「只見樹木，不見森林」in mathematics
learning. 
Social justice issue 
The replacement of the ‘tripartite’ system with a ‘comprehensive’
one posed the problems of curriculum entitlement against the
differentiation of students and their curricula. 
Such social justice issue had not been noted in spite of the
obvious widening of the range of attainments and needs of secondary
school students. 
Relationship with tradition mathematics 
New Mathematics had not totally replaced the traditional mathematics
curriculum. The number of OLevel candidates taking New Mathematics
constituted only about 20% of the national entry at its peak
in 1977. 
Similarly, New Mathematics had not totally replaced the traditional
mathematics curriculum. The number of candidates taking New
Mathematics constituted about 67% of the territorywide entry
at its peak in 1979. 
Evaluation 
There was no official evaluation on the effectiveness of New
Mathematics. However, its content was continuously adjusted
to cater for the needs of students in both grammar and comprehensive
schools. 
Similarly there was no official evaluation and the content
remained quite stable though the range of students’ attainments
and needs widened as secondary school education was provided
to more and more primary school leavers. 
Final outcome 
New Mathematics and traditional mathematics gradually merged
into a unified course of study in mathematics. 
There had been a compromise between New Mathematics and traditional
mathematics by creating a third curriculum called Amalgamated
Mathematics as a transitional arrangement until the Amalgamated
Mathematics became the only mathematics curriculum to be offered
in all schools. 
IV. Concluding Remarks
Three interesting points emerge regarding the New Mathematics movement
in HK and the UK. Firstly, unlike the situation in the US where
the New Mathematics movement was essentially brought to an end when
the NACOME Report (1975) indirectly announced it as a failure, New
Mathematics had never been officially evaluated in the UK and HK
to the extent of passing a final judgement on its success or failure.
Most members of the mathematical community in both places regarded
New Mathematics as a worthwhile experiment to tackle the problematic
issues of traditional mathematics. In the end, New Mathematics and
traditional mathematics interacted with each other and had gradually
evolved and transformed into a more unified and wellstructured
course of study.
Secondly, the New Mathematics movement in the UK could be considered
as a wellintentioned initiative tried out by groups of enthusiasts
in mathematics education, mainly consisting of secondary school
teachers. Their intention was to tackle the unsatisfactory situation
prevailing in school mathematics in the 1950s by a series of teaching
experiments. In many respects, mathematics projects like SMP were
pioneers of SBCD. However, the proponents of the New Mathematics
movement in the UK had not adopted a systematic and comprehensive
approach to work out a solution in response to Birtwistle’s appeal
(1961). As Flemming (1980) observes, before curriculum changes could
be effected, teachers had to be convinced of its desirability. Innovations
tended to come about slowly by a piecemeal process through the influence
of textbook writers, education researchers and agencies like the
Mathematical Association. By contrast, the New Mathematics movement
in HK in the 1960s was basically the government’s decision to keep
up with the global trend of mathematics education, particularly
following the footstep of its sovereign state.
Lastly, the two facets of understanding underpinning the New Mathematics
movement  precision of language and discovery of generalizations
– still leave their deep trail in recent mathematics curriculum
initiatives in the UK as well as in HK. For instance, the importance
of precise and concise use of mathematical language is still strongly
recognized by the Cockcroft’s Report (1982, p. 1) that “We believe
that all these perceptions of the usefulness of mathematics arise
from the fact that mathematics provides a means of communication
which is powerful, concise and unambiguous” and the Smith’s Report
(2004, p. 11) that “Mathematics provides a powerful universal language
and intellectual toolkit for abstraction, generalization and synthesis”.
Furthermore, the National Numeracy Strategy in the UK also emphasizes
the importance of exact and accurate use of mathematical vocabulary
by publishing a booklet for teachers’/students’ use (DfEE, 1999).
Concerning the discovery of generalizations, Cockcroft recommends
that investigation work should be an integral part of classroom
practice for students of all ages and “is fundamental both to the
study of mathematics itself and also to an understanding of the
ways in which mathematics can be used to extend knowledge and to
solve problems in very many field” (Cockcroft, 1982, p.73). In HK,
the recent Curriculum Reform stresses the importance of developing
students’ communication skills and inquiry skills in mathematics
learning at all school levels (Curriculum Development Council, 2000).
Furthermore, considerable amount of subject content introduced into
New Mathematics in the 1960s, such as statistics, probability, transformational
geometry, etc., are still regarded as important and worth learning
in the current mathematics curriculum in HK and the UK.
Notes:
The
Hong Kong Education Department (ED) was restructured as the Education
& Manpower Bureau (EMB) in January 2003 as part of an overhaul
of the government administrative structure in Hong Kong. EMB was
further restructured to become the current Education Bureau (EDB).
Before
the year 1977, the public examination HK Certificate of Education
Examination was under the jurisdiction of the Examination Section
of ED. In 1977, the Hong Kong Examinations Authority (HKEA) was
established as an independent statutory body to run all public examinations
in HK. HKEA was further restructured to become the current Hong
Kong Examinations & Assessment Authority (HKEAA).
According
to Flemming (1980), the number of candidates taking OLevel New
Mathematics rose from 919 in 1964 to 62,691 in 1977 which constituted
about 20% of the national entry. However, it was remarked that the
influence of SMP had almost certainly been greater than these figures
has suggested. More than half of the schools in the UK were said
to be making some use of SMP materials.
According
to the Annual Reports of the HKEA, the number of candidates taking
New Mathematics in the HK Certificate of Education Examination rose
from 330 in 1969 to 48,590 in 1979 which constituted about 67% of
the territorywide entry.
References 
‧ 
Birtwistle, C. (1961) Editorial  Research in Education, Mathematics
Teaching, No. 17, pp. 34 
‧ 
Cockcroft, W. H. (1982) Mathematics Counts — Report of the
Committee of Inquiry into the Teaching of Mathematics in Schools,
London, UK: Her Majesty’s Stationery Office 
‧ 
Curriculum Development Council (2000) Mathematics Education
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‧ 
Davis, P. & Hersh, R. (1981) The Mathematical Experience,
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‧ 
DfEE (1999) The National Numeracy Strategy: Mathematical Vocabulary,
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Flemming, W. (1980) ‘The School Mathematics Project’ in Stenhouse,
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Fullan, M. (1991) The New Meaning of Educational Change, New
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