A survey of the practice of a largescale implementation of inquirybased mathematics teaching: from Taiwan’s perspective
ErhTsung Chin
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1
FouLai Lin
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F.L. Lin Department of Mathematics, National Taiwan Normal University
, Taipei,
Taiwan
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E.T. Chin (&) Graduate Institute of Science Education, National Changhua University of Education
, Changhua,
Taiwan
researchers within the last 20 years. The National Science Council also implemented a nationwide ''High Scope Project'' (NSC 2006) 7 years ago for promoting senior and vocational high school students' science and mathematics inquiry competences. Further, many individuals, institutions and governmental organizations have supported professional developments for teachers in various aspects of IBL for more than a decade [e.g., teacher professional development for IBL teaching has been one of the themes of the calls for projects from NSC for 10 years; see http:// www.nsc.gov.tw/sci/lp.asp?CtNode=1618&CtUnit=1221& BaseDSD=7 (in Chinese)]. In this issue of ZDM, nine papers are included focusing on inquirybased mathematics education (IBME) and its implementation. It is our pleasure to share some opinions based on the experiences of educational reform in Taiwan.

This is a brief commentary from the perspective of Taiwan.
We first introduce the background of Taiwans involvement
in the global educational reform related to inquirybased
learning in mathematics and science. In the main part, we
share some important ideas based on our experiences of
conducting nationwide teacher professional development
projects in Taiwan, followed by some discussion and
suggestions. The commentary concludes with some remarks.
Inquirybased learning (IBL) has been a popular issue in
the trend of science and mathematics education reform for
decades all over the world. More than 20 years ago, the
National Council of Teachers of Mathematics (NCTM)
indicated that inquiry is one of the most important contexts
for students learning of mathematical concepts and
knowledge, to include exploring, conjecturing, reasoning
logically and evaluating whether something makes sense or
not (NCTM 1991). As an active member of the global
village, Taiwan, of course, is part of this global trend of
educational reform. Even though our student performances
in international assessments, such as TIMSS and PISA, are
always among the leading group of the world (Mullis et al.
2008, 2012; Organization for Economic and Cooperation
Development (OECD), 2005), students low learning
motivation and lack of inquiry habits of mind have been
noted by both researchers and the government (Lin and Liu
2011). As a result, many research projects about science
and mathematics inquiry have been conducted by
1 Some ideas based on our experiences in Taiwan
1.1 Impediments to implementing daytoday IBME
Although most teachers possess a positive disposition
towards IBL/IBME, their teaching practices are not
consistent with it, being rather more expository oriented. This
phenomenon is also the case in Europe, but occurs in
Taiwan more conspicuously. The reasons behind this
phenomenon are not fully understood. However, some
impediments to carrying out daytoday IBME might be
generalized as follows (Chin 2008, 2011):
3. the allocated teaching hours are not enough;
4. the great influence of teaching to the test;
5. being alone and lack of administrative support from
school or government.
As can be seen from the other papers of this issue, these
impediments are also of importance in Europe.
1.2 The transforming of mathematics teacher
professional development in Taiwan
More than 10 years ago, the Ministry of Education (MoE)
in Taiwan started to advance the cultivation of seed
teachers enthusiastically with the expectation that these
seeds could blossom (influencing their peers) and bear
fruit (materializing in the success of educational reform) in
the near future. However, many years of endeavor did not
result in satisfactory rewards. Most of the seed teachers did
get good professional development themselves, but their
influences seldom spread out to their peers. The main
reason for this is that the soil around these seeds is too
infertile for the seeds to blossom and bear fruit. Therefore,
MoE began to adjust the strategy from recruiting individual
teachers as seeds of reform to schoolbased professional
development. The considerations behind this transform
were basically to deal with the soil and trying to solve
the aforementioned fifth impediment directly. A year ago,
the nationwide Light Spot for Mathematics Teaching
project (LSMT) (Lin 2013a) was carried out which
required that the principal and all mathematics teachers of
each participant primary or junior high school must sign a
letter of consent to participate in twelve 3h workshops led
by a teacher educator (who is also a mathematics educator
from a university) within an academic year (6 workshops in
a semester). The aim of LSMT is to facilitate teachers
professional development by means of longterm
continuing support. There are several topics, including IBL, ICT
integrated teaching, mathematics proficiency, conjecturing
and argumentation, models and modeling, and reading
comprehension, for the 45 participant schools (26 primary
and 19 junior high schools) to choose from. Taking the IBL
group as an example, the design of the 12 workshops
consists of experiencing IBL activities as a learner,
literature reviews for constructing the theoretical backing for
IBL, exemplary teachers demonstration of IBL teaching,
and designing and implementing their own IBL activities
through action research. During the first year of running
LSMT, professional development did start to flourish in
most of the participant schools. However, we still noticed a
lack of experience for most of the teacher educators in
leading a teacher professional development community.
Hence, another workshop called the Lighting Up project
(Lin 2013b) has been organized to help the teacher
educators become more competent at leading schoolbased
teacher professional development communities.
Light Spot for Mathematics Teaching is a largescale
project initiated by the government. Whereas in PRIMAS
(see Maa and Doorman 2013) there are about 100
voluntary participant teachers in each consortium country,
LSMT is schoolbased like IMST (Krainer and Zehetmeier
2013) and all the mathematics teachers of the 45
participant schools have to attend the project (about 600
mathematics teachers in total participated in LSMT in the first
year). The focus of LSMT is provision of longterm
support for teachers who form a schoolbased professional
development community. However, the idea of running the
adjunct Lighting Up project of LSMT seems consistent
with the multipliers education in the design of PRIMAS.
1.3 Designing detailed lesson plans is a good approach
to learning IBL teaching
In our experience of running teachers professional
development projects, a remarkable finding is that training
teachers to design a detailed lesson plan of a new teaching
strategy stepbystep is very helpful for them in
successfully implementing the new teaching strategy into their
classroom teaching (Lin and Chin 2013). As for IBL,
within the many strategies (e.g., 5E inquiry learning cycle
of engagement, exploration, explanation, elaboration and
evaluation, Bybee 1997); the predictobserveexplain POE
learning model of White and Gunstone 1992; Siegel et al.s
1998 inquiry teaching model), sophisticated teachers and
students tasks are always required. Hence a detailed lesson
plan is needed for a teacher to master the relevant teaching
skills when conducting an IBL activity.
Directly providing a readydesigned IBL lesson plan
could motivate a teacher to attempt to implement IBL
teaching; however, this might be only helpful for the
beginning and would not be a longterm solution. There are
several obstacles hindering teachers from designing their
own teaching activities, including: insufficient
understanding of the students (Yoshida 2008), lack of explicit
principles for designing IBL activities (Lin 2013a), and
being unfamiliar with what kinds of materials could be
adopted in the design of IBL tasks (Lin et al. 2012). A
complete lesson plan should include a detailed teaching
schedule and student worksheet. It is almost impossible for
a teacher to finish a detailed lesson plan of a new teaching
strategy in one step: in most cases, teachers start by
designing a student worksheet, then extend it gradually to a
more detailed lesson plan or even a teaching module.
During this process, teachers need to continually carry out
thought and teaching experiments and make improvements
as they would in conducting action research. In this way,
1.4 Expert or learner? Change of attitudes makes
the difference
In Taiwan, perhaps because of the influence of
Confucianism (Confucius is venerated as the Most Sage and
Greatest Teacher), most of the teachers possess high
selfesteem and consider themselves as having authority of
knowledge over the students. This phenomenon is
particularly true with mathematics teachers. Thus, being afraid
that students might discover there are problems the
teacher cannot solve causes very heavy pressure for the
teacher. When promoting a new teaching strategy to
mathematics teachers, a common response from the
teachers is that their teaching is good enough and they do
not need to make any change. During the running of
LSMT, we clearly noticed this phenomenon, especially
when the teacher educator came to lead the workshop as
an expert who is to instruct the participant teachers how
to teach. Teachers were concerned that their teaching
practices were being criticized (Lin 2013a). Therefore, in
the Lighting Up project, the teacher educators were
encouraged to change their attitudes from an expert to a
learner when leading an LSMT community. When we
humbled ourselves first as being a learner (learning from
the process of leading the professional development
community), not playing the part of an expert or professor
(looking down on these teachers from a higher
hierarchical position), the teachers were less resistant and more
willing to learn the new teaching strategy. This change of
attitude helped to break down the invisible hierarchy
between the teacher educator and these inservice
teachers, and increase the mutual identification with the
community, as well as the teachers participation becoming
more and more central to the functioning of the
community, in the sense of the theory of Legitimate Peripheral
Participation (LPP) (Lave and Wenger 1991)). In the same
way, the teachers were also encouraged to swallow their
pride before their students by confessing that they are not
omniscient, and to use every chance to show their skills of
IBL as an exemplar. The confession that they also need to
learn helps to free teachers from pretending to be
omniscient.
2 Discussions and suggestions At the beginning of this commentary, we pointed out some reasons why IBL is not a common feature in the daytoday mathematics teaching in Taiwan:
1. teachers did not experience IBL in mathematics when
they were at school;
2. teachers do not have complete understanding of IBL/
IBME;
3. the allocated teaching hours are not enough;
4. the great influence of teaching to the test;
5. being alone and lack of administrative support from
school or government.
As our explanations show, LSMT addresses the
impediments 1, 2 and 5: teachers get the chance to
experience IBL and learn about IBL and its theoretical
background; and obviously, by its very nature, teachers receive
support from the government. However, the great influence
of teaching to the test and, in connection with it, the
number of allocated teaching hours, still remain as
impediments.
Teaching to the test is a common phenomenon in
classroom teaching all over the world. Especially the form
of high stake examination dominates teachers classroom
teaching. Of course, if the patterns of assessment could be
modified from stressing procedural fluency and knowledge
recall to less restrictive modes that are supportive of
students inquiry, it would be definitely beneficial for
implementing IBL practices in classrooms.
However, good mathematics learning means that
students are able to develop the integrity of mathematical
proficiency. According to Kilpatrick, Swafford and
Findells version, there are five strands of mathematical
proficiency: conceptual understanding, procedural fluency,
adaptive reasoning, strategic competence, and productive
disposition (NRC 2001). If we consider that IBL is a better
way of learning mathematics, we should have faith that the
students can develop all the five strands of mathematical
proficiency evenly. Therefore, when we can only passively
accept the patterns of assessment (especially the high stake
test), we should still be confident that IBL can help the
students cope with these. This aspect also needs to be
considered when designing professional development
activities.
Being short of allocated teaching hours is not only a
problem for mathematics, but also happens in most school
subjects. Therefore, arguing for more teaching hours for
teaching mathematics would not be feasible and we have to
accept the reality. Although IBL activities do require more
time compared with traditional expository teaching, it is a
myth that IBL should be implemented in all classroom
teaching. A counter to the argument of insufficient teaching
hours might be suggested as follows. One of the powerful
features of IBL is helping students construct their own
understanding of mathematical concepts. When students
better understand these, less time for practicing algorithms
should be needed. Another myth is that all the contents in
the textbook have to be taught in the classroom.
However, teachers cannot warrant that what has been taught by
them is actually learned by their students, nor that what
their students have learned is all taught by them. Therefore,
when students motivation for learning is aroused by IBL
activities, teachers can use homework as students
extended learning, and need not go through every detail of the
contents in the textbook.
As aforementioned, designing detailed lesson plans can
be a good approach to learning IBL teaching. In fact,
whether a teacher is able to design a complete lesson plan
for IBL could be a criterion to ascertain whether the
teacher is ready to implement IBL in her/his teaching practice.
When reading this issue, we identified a gap between
teachers perceptions and the actualities of their teaching
practices in Europe. This gap is worthy of further
investigation. Therefore, if some data can be collected directly
from these teachers daytoday classroom teaching, there
will be concrete evidence for making more powerful
conclusions.
To sum up, as in Europe, IBL is not widespread in
daytoday teaching in Taiwan. The impediments for the
implementation of IBL relevant in Taiwan also seem to be
applicable in Europe. Whilst, in Europe, the European
Commission and some countries (see Krainer and
Zehetmeier 2013) have launched projects and initiatives to
make IBL more widespread in daytoday teaching, in
Taiwan the government has launched LSMT to change the
situation. In Europe the implementation strategies differ
from project to project (Maa and Artigue 2013); in
Taiwan we have had good experiences by providing
schoolbased professional development focusing on lesson plans
and changing attitudes.
3 Final remarks
Helping students foster their inquiry habits of mind and
inquiry skills is one of the main purposes for promoting
IBL in mathematics education. To achieve this needs
time and a constantly supportive learning environment.
Although it might be easier for the teachers to make a start
by designing some extra offclass IBL activities, putting
IBL into daytoday classroom teaching practice should be
the key. We look forward to seeing the popularization of
IBL in Europe in the future, rather than only the participant
teachers getting changed, as our former experience tells us
that the seed teachers seldom blossom and bear fruit.
Certainly the valuable experience of conducting largescale
projects such as those launched by the European
Commission is worthy of consultation and reference by other
countries.