Applying experiential learning cycle to enhance pre-service teachers’ teaching skills through the course of practice teaching mathematics

 TẠP CHÍ KHOA HỌC 
TRƯỜNG ĐẠI HỌC SƯ PHẠM TP HỒ CHÍ MINH 
Tập 17, Số 5 (2020): 775-784 
HO CHI MINH CITY UNIVERSITY OF EDUCATION 
JOURNAL OF SCIENCE 
Vol. 17, No. 5 (2020): 775-784 
ISSN: 
1859-3100 Website:  
775 
Research Article* 
APPLYING EXPERIENTIAL LEARNING CYCLE TO ENHANCE 
PRE-SERVICE TEACHERS’ TEACHING SKILLS THROUGH 
THE COURSE OF PRACTICE TEACHING MATHEMATICS 
Bui Thi Thanh Mai 
Ho Chi Minh City University of Education, Vietnam 
Corresponding author: Bui Thi Thanh Mai – Email: maibtt@hcmue.edu.vn 
Received: October 23, 2019; Revised: November 15, 2019; Accepted: May 26, 2020 
ABSTRACT 
Developing student teachers’ teaching competence is a key task of the teacher training 
programs at Ho Chi Minh City University of Education (HCMUE), one of the largest teacher 
education institutions in Vietnam. However, there remains a huge gap between theoretical 
knowledge and teaching practice in these programs. This article introduces solutions implemented 
at the Department of Mathematics, HCMUE since 2015 to bridge the gap. In particular, we focus 
on the development of a learning sequence in the Teaching Mathematics Practice course based on 
David Kolb’s experiential learning cycle. This learning sequence was applied at two classes of 20 
senior students at the Department during the first semester of the school year 2019-2020 in order 
to help them improve teaching skills before taking part in the Teaching Practicum. Although we 
received positive feedback from students, futher research needs to be conducted to measure the 
effectiveness of the new learning sequence. 
Keywords: experiential learning cycle; teaching skills; teacher training 
1. A problem arose: the knowing-doing gap 
According to the four-year Mathematics Teacher Training Curriculum at Ho Chi 
Minh City University of Education, student teachers are equipped with Content Knowledge 
(mathematics) (CK), Pedagogical Knowledge (PK) and Pedagogical Content Knowledge 
(PCK) throughout seven semesters. In addition, it is mandatary for them to take part in two 
practicum before being fully licensed as a teacher: Teaching Practicum 1 and Teaching 
Practicum 2. The former lasts 5 weeks in the fifth semester of the training program, and the 
later lasts 10 weeks in the eighth semester. During the Teaching Practicum 1, pre-service 
teachers mainly observe in-service teachers’ classes, while the Teaching Practicum 2 
Cite this article as: Bui Thi Thanh Mai (2020). Applying experiential learning cycle to enhance pre-service 
teachers’ teaching skills through the course of practice teaching Mathematics. Ho Chi Minh City University of 
Education Journal of Science, 17(5), 775-784. 
HCMUE Journal of Science Vol. 17, No. 5 (2020): 775-784 
776 
provides them with opportunities to apply theories into teaching practice under the 
mentorship of experienced teachers. 
 And problems emerged in this transitional step: while their university courses 
commonly involve lectures, textbooks reading, and homework assignments. This means 
that they learn the “knowing what.” When student teachers going to high schools, they are 
expected to design lesson plans, conduct classroom lessons, and perform other duties of a 
schoolteacher, which means “knowing how”. As a result, many pre-service teachers 
struggled to fill this knowing-doing gap. They are unable to put the knowledge 
accumulated at university into practice and usually performance poor during the practicum. 
Figure 1. The “knowing-doing” gap in Mathematics Teacher Training Curriculum 
2. Strategies to bridge the gap 
Being fully aware of this “knowing-doing” gap in the curriculum, as the teacher 
educators at the Department of Mathematics, Ho Chi Minh City University of Education, 
since 2015, we have suggested and implemented two solutions in order to tackle the 
problem: 
- The first solution was to innovate the curriculum as well as methods of teaching and 
assessment. In the new curriculum, there are more credits for PCK: 15 credits compared to 
10 credits in the old curriculum, adding two courses including Assessment in Mathematics 
Education (2 credits) and Mathematics Curriculum Development (2 credits). We have also 
sized down the number of students in each class from about 60 students in the past to only 
15-25 students. This change has allowed us to use modern approaches to lesson delivery. 
Instead of lecturing, project-based learning and more hands-on activities have been 
employed so that student teachers have more occasions to apply the knowledge. In almost 
all courses involving PCK, they have to work in group of 2-4 students, designing a lesson 
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plan on a chosen topic and practicing teaching (about 15-20 minutes). In terms of 
assessment methods, the current trends such as authentic assessment, performance-based 
assessment, and portfolio assessment have been used instead of written tests. 
- The second solution was to add a course, a complete new course titled “Practice 
Teaching Mathematics” to the curriculum. Pre-service teachers have to complete this 
course in the seventh semester as a prerequisite before they are allowed to take part in the 
Teaching Practicum 2. In this course, student teachers will conduct a lesson in a simulation 
of real classes under the guidance of a university lecturer in order to improve their teaching 
skills. This aims at preparing students for the Teaching Practicum 2. 
These two solutions are considered as scaffolds to bridge the knowing-doing gap. 
Figure 2. Strategies to bridge the knowing-doing gap 
In this study, we put focus on the second solution and how we applied David Kolb’s 
Experiential Learning Cycle to enhance pre-service teachers’ teaching skills through the 
course of Practice Teaching Mathematics. 
3. David Kolb’s Experiential Learning Cycle 
“I hear and I forget. I see and I remember. I do and I understand” – the Confucius 
quote reflects the spirit of “learning by doing” theory which was developed by an 
American philosopher John Dewey. Experiential learning is an approach of “learning by 
doing”, in which students learn through experience, taking part in hands-on activities. 
However, mere experience is insufficient because an important characteristic of 
experiential learning is the reflection on experience (Felicia, 2011). The most common 
model of experiential learning was developed by David Kolb (1984), based on the work of 
John Dewey, Kurt Lewin, and Jean Piaget, compassing four stages shown in Diagram 1. 
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Diagram 1. David Kolb's Experiential Learning Cycle (ELC) (Kolb, 1984) 
The cycle begins with the learners actively participating in an experience (Stage 1), 
they then consciously reflect on that experience (Stage 2). It is from the observation and 
reflection that learners are able to generalize a model of what is experienced (Stage 3), and 
finally apply that model to a new experiment (Stage 4). According to Kolb, each stage is 
mutually supportive of and feeds into the next, and it is possible to enter the cycle at any 
stage and follow it through its logical sequence. However, effective learning only occurs 
when a learner can pass all four stages of the ELC (McLeod, 2017). 
4. Applying the ELC in the Practice Teaching Mathematics course 
4.1. Introduction to the course 
The course of Practice Teaching Mathematics is a 10-week-course for senior students 
at the Department of Mathematics, HCMUE, who have already taken the courses including 
Introduction to Mathematics Teaching Methodology, Methodology of Algebra and 
Analysis Teaching, and Methodology of Geometry Teaching. There are about 15 to 20 
students in each class. 
This course provides pre-service teachers with an occasion to apply the knowledge 
attained from previous courses to teaching practice. Thanks to the process of preparing 
lesson plans and putting them into practice, the trainees are expected to foster their 
professional development. 
4.2. The learning sequences in the course of Practice Teaching Mathematics 
Based on David Kolb’s Experiential Learning Cycle, we have designed the learning 
sequences in the Practice Teaching Mathematics course with the aim of enhancing pre-
service teachers’ teaching skills. In order to ensure the instructional effectiveness, we tried 
to make sure that the learning sequences comply with two following fundamental 
principles: 
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- The learning sequences facilitate the reflection on experience rather than the mere 
experience; 
- The learning sequences lead student teachers through the full cycle of Kolb’s model. 
We summarize the step-by-step process of applying the ELC to the course of Practice 
Teaching Mathematics in Diagram 2. 
Diagram 2. Learning sequences in the Practice Teaching Mathematics course 
 Step 1 
On the first lesson of the course, the lecturer briefly reviews some knowledge on 
methods of teaching mathematics, especially how to design a lesson plan and different 
approaches to lesson delivery. Student teachers are then guided to use free writing 
technique to identify their teaching beliefs and set learning goals through answering the 
questions: 
- What is the purpose of learning in general and learning mathematics in particular? 
How should students learn mathematics? 
- What is the image of the teacher that you I would like to build? 
- What level is your professional competence at present? And what do you need to 
improve in order to become a teacher like that? 
The learning sequences of the course, the assessment criteria of a lesson plan and an 
instruction are also introduced. Finally, the lecturer instructs student teachers to use Sway 
to keep their “class diary” after each lesson, and the very first task is to specify their 
learning objectives in the diary. 
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Translation 
My commitment: 
- Read more mathematics documents 
(textbooks, online materials, common 
core national standard) to get deeper 
insight into the subject and be more 
confident in teaching. 
- Practice writing on board three times a 
week (45 minutes each time, on 
Wednesday evening, Friday evening, and 
Saturday morning. 
- Practice lowering my high-pitched 
voice so that it will be warmer and 
deeper. 
- Practice controlling my speaking speed 
as I sometimes speak too fast with words 
being repeated quite often 
Figure 3. Learning objectives in a student’s diary 
 Step 2 – 3 – 4 
Each pair of student teachers are given a mathematics lesson in high school 
curriculum to prepare for. They need to collaborate to design a lesson plan and upload it to 
Google Classroom (Step 2) so that other student teachers can view and give feedback 
through a Google form (Step 3). The lesson plan is then modified by that pair of students 
(Step 4) before teaching. The assessment criteria of a lesson plan that lecturer gives pre-
service teachers on the first lesson are used in these steps. 
Translation 
- The first activity engages 
students; however, it is 
essential to specify the 
materials (how many boxes 
need to be prepared, and who 
prepares them, teacher or 
students?) 
- Time estimation is not 
reasonable (7 minutes for 
students to discuss, find 
solutions, presentation, and 
for teacher to give feedback?) 
- How does teacher comment 
on students’ work as the 
solution can be only figure 
out at the end of the lesson? 
Figure 4. A part of a student’s feedback on the lesson plan “Cauchy-Schwarz inequality” 
HCMUE Journal of Science Bui Thi Thanh Mai 
781 
 Step 5 
After modifying the lesson plan, the pair of student teachers practice teaching 
themselves, they then play the role of teachers while other student teachers attend the class 
as high school students as well as observing and taking notes on their peers’ teaching. The 
lecturer also observes and takes notes. 
 Step 6 
The pre-service teacher trainees self-evaluate their lesson delivery, then others give 
lesson feedback based on their observation, notes and the criteria in the instructional 
assessment rubric. It is important for them to keep in mind that the objective of lesson 
feedback is not to judge or assess their peers’ classroom performance, but to support them 
and help them to improve teaching skills. Hence, the student teachers are encouraged to 
provide constructive feedback: the positive points are dealt with before the negative points, 
and the negative points are followed by some planning about what might be done instead 
next time. At the end of this step, the lecturer adds supplementary comments if needed and 
summarizes the main points. He/she might sometimes raise a question involving the lesson 
for the student teachers to examine. For instance, after a lesson in which the pre-service 
teachers integrated technology, the students were asked to figure out what is an effective 
technology integrated lesson and how to build it. 
 Step 7 
After each lesson, the pre-service teachers are required to fill in the class diary to 
record their experiences, feelings, then analyze these experiences and draw conclusions 
from them. It is obligatory for student teachers to have a strict routine of keeping up 
regular entries as much of the details and feeling of recollection data fades within 24 hours. 
Translation: 
Observing the teaching practice 
of two groups this morning helps 
me to gain some experiences: 
- It is important to choose the 
appropriate approach to deliver 
the lesson. 
- Question technique also plays 
crucial role in teaching. 
- Teacher should let students 
present their group work in order 
to know their level of 
understanding, it is also a good 
occasion to develop students’ 
presentation skill 
Figure 5. A part of a student’s class diary 
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 Step 8 
The pair of pre-service teachers modify the lesson plan after receiving feedback from 
the lecturer and other students. Then the cycle repeats with other pairs of student teachers. 
At the end of the course, pre-service teacher trainees look back on their class diary, 
especially the learning objectives they set at the beginning of the course and self-evaluate 
their improvement in teaching skills. 
4.3. Analyzing the learning sequences according to ELC 
The designed learning sequences of the Practice Teaching Mathematics course 
involves two types of experiences: designing a lesson plan and practice teaching of a 
lesson. Both of them go through four stages of Kolb’s experiential learning cycle 
(Diagram 3). 
Diagram 3. Analyzing the learning sequences in the course of 
Practice Teaching Mathematics according to ELC 
Student teachers enter the cycle at Step 1 (arrow position in Diagram 3), which is the 
planning for experience. Free writing technique and setting objectives in class diary are 
used as the methods for preparing them prior to teaching so that they make the most of 
those experiences. This also provides a valuable aid to the students’ reflection and self-
assessment after the experience. 
At step 2, pre-service teachers pass concrete experience (Stage 1 of ELC) of 
preparing a lesson plan. They then need to give lesson feedback at step 3, which is the 
refection stage (Stage 2 of ELC). The act of modifying the lesson plan after receiving 
feedback (step 4) is the active experimentation (Stage 4 of ELC). While there is no specific 
step corresponding to the “abstract conceptualization” (Stage 3 of ELC), student teachers 
absolutely learn from the feedback so that they could perfect their lesson plan. 
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783 
At step 5 and 6, a pair of pre-service teacher trainees practice teaching (Stage 1 of 
ELC) while others observe and take notes to give feedback on the lesson (Stage 2 of ELC). 
Both experiences of delivering and observing a lesson are valuable to improve teaching 
skills. Student teachers can realize how their peers use the teaching methods, how they 
interact with students, how they deal with problems arising from their lesson on a daily 
basis and, to certain extent, can discover effective teaching strategies that the observer has 
never used in class before (Phat, 2019). The reflection is then be generalized to their own 
knowledge shown in their class diaries Step 7 (see Figure 5). This is the abstract 
conceptualization stage (Stage 3 of ELC). Finally, they apply new knowledge gained to 
modify the lesson plan the second time (Step 8), which is the active experimentation stage 
(Stage 4 of ELC). 
5. Conclusion 
This article presents the learning sequences in the course of Practice Teaching 
Mathematics which are based on Kolb’ ELC model. We have analyzed the learning 
sequences according to four stages of the ELC. This model has been applied in the Practice 
Teaching Mathematics course in the first semester of the schoolyear 2019-2020 and has 
received positive feedback from student teachers. However, more qualitative and 
quantitative researches need to be conducted in order to validate the effectiveness of this 
model in terms of fostering pre-service teachers teaching competence. This could be the 
focus of our future research in which we are planning to use video-recording technique and 
a rubric to evaluate the instructional quality of preservice teachers before and after 
the course. 
 Conflict of Interest: Author have no conflict of interest to declare. 
REFERENCES 
Department of Mathematics, Ho Chi Minh City University of Education (2015). Mathematics 
Teacher Training Curriculum. 
Dixon, N. M., Adams, D. E., & Cullins, R. (1997). Learning Style. Assessment, Development, and 
Measurement. p. 41. 
Felicia, P. (2011). Handbook of research on improving learning and motivation through 
educational games: multidisciplinary approaches. Hershey: IGI Global, 
Kolb, D. (1984). Experiential learning as the science of learning and development. Englewood 
Cliffs, NJ: Prentice Hall. 
McLeod, S. A. (2017). Kolb’s learning styles. Simply Psychology. Retrieved on 23rd November 
2019 from https://www.simplypsychology.org/learning-kolb.html 
HCMUE Journal of Science Vol. 17, No. 5 (2020): 775-784 
784 
VẬN DỤNG MÔ HÌNH HỌC TRẢI NGHIỆM ĐỂ NÂNG CAO KĨ NĂNG SƯ PHẠM 
CHO SINH VIÊN THÔNG QUA HỌC PHẦN THỰC HÀNH DẠY HỌC TOÁN 
Bùi Thị Thanh Mai 
Trường Đại học Sư phạm Thành phố Hồ Chí Minh, Việt Nam 
Tác giả liên hệ: Bùi Thị Thanh Mai – Email: maibtt@hcmue.edu.vn 
Ngày nhận bài: 23-10-2019; ngày nhận bài sửa: 15-11-2019; ngày duyệt đăng: 26-5-2020 
TÓM TẮT 
Phát triển năng lực giảng dạy cho sinh viên là trọng tâm của các chương trình đào tạo giáo 
viên tại Trường Đại học Sư phạm Thành phố Hồ Chí Minh. Tuy nhiên, tồn tại một khoảng cách lớn 
giữa lí thuyết và thực hành trong các chương trình đào tạo. Phần đầu của bài báo trình bày những 
chiến lược được triển khai tại Khoa Toán – Tin học từ năm 2015 nhằm thu hẹp khoảng cách này. 
Sau đó, chúng tôi tập trung trình bày chuỗi hoạt động học trong học phần Thực hành dạy học Toán 
được xây dựng dựa trên mô hình học trải nghiệm của David Kolb. Chuỗi hoạt động học này đã 
được triển khai cho hai lớp học phần Thực hành dạy học Toán với sĩ số 20 sinh viên/ lớp trong học 
kì 1 năm học 2019-2020 nhằm giúp các sinh viên năm tư nâng cao kĩ năng sư phạm trước khi đi 
thực tập tại trường phổ thông. Chúng tôi nhận được các phản hồi tích cực từ phía sinh viên, tuy 
nhiên, để khẳng định và đo lường tính hiệu quả của chuỗi hoạt động học này cần tiến hành thêm 
các nghiên cứu tiếp theo. 
Từ khóa: mô hình học trải nghiệm; kĩ năng sư phạm; đào tạo giáo viên