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 Shiang-Tung Liu Professor [Publication Lists]


A. Position & degree

Professor & Director, Graduate school of math & science education, National Chiayi University, Taiwan, R.O. C.

1.National Kaohsiung Normal University(Bachelor of Science, Major in Mathematics)
2.The University of Memphis (Master of Science, Major in Mathematics Education).
3.The University of Memphis (Doctor of Education, Major in Mathematics Education).


B.My book & Book Chapter

1.Liu, S. T. (2007). The use of questioning in helping students solve rational and proportional
       problems in math instruction (2nd edition). Taipei City:Shtabook Publishing.
2.Liu, S. T. (2001). Practicing mathematics writing activities to develop problem posing ability in
       elementary school teachers. Taipei County:Wenjing Publishing.
3.Huang, K. H., & Liu, S. T. (2005). The Study of Practicing Lesson Plan of Matching Up
   Activities. (Book chapter). Taipei: Psychology Publishing.


C.Services & Academic Accomplishments

1.The director of Graduate school of math & science center, National Chiayi University (2010.08-).
2.The director of Teacher education center, National Chiayi University (2006.08-2008.07).
3.The chairman of department of math education, National Chiayi University (1998.08-2002.07).
4.The chairman of the graduate institute of math education, National Chiayi University (2000.08-
    2002.07).
5.The director of teacher education center, National Chiayi University (2007.08- ).
6.A committee member of mathematical curriculum and instruction, Ministry education of Taiwan
   (2000.08-2010.7).
7.Mr. Wang, my advisee got excellent thesis prize from the association of curriculum and
   instruction  (2008).
8.Ms. Yang, my advisee got fund for mathematics textbook analysis from National Compilation
   Organization(2008).
9.Ms. Weng, my advisee got excellent thesis prize from the association of curriculum and
   instruction (2004).
10.Mr. Hwang, my advisee got the thesis prize from Education foundation fund of Professor Jia,
     Fu-ming (2004).
11.Ms. Weng, my advisee got the thesis prize from National Science Council (2003).
12.Mr. Hwang & Ms. Wu. My advisees got recognition of contribution in Great Teaching 2003 and
     an award of excellence from National Taiwan Normal University and Chinese Creativity
     Development Association  (2003).
13.Ms. Chen, my advisee got the thesis prize from National Science Council (2002).
14.1995、96、98 & 99 got research rewards from National Science Council.


D.Publication list (Journal)

1.Liu, S. T., Huang, K. H., & Su, Y. C. (2010). The visualization presentation for problem solving 
    strategies – Taking examples from the contrasted activities of part to whole relationships. 
    Science Education Monthly, 329, 2-7.
2.Huang, T.W., Liu, S. T., & Lin, C. Y. (2009). Pre-service teachers’ mathematical knowledge of  
    fractions [Electronic version].  Research in Higher Education Journal, 5, 1-8. (NSC- 96-2511-S-
     415-002).
3.Liu, S. T., & Ho, F. C. (2008). Conjecture Activities for Comprehending Statistics Terms through 
     Speculations on the Functions of Imaginary Spectrometers.  The Australian Mathematics 
     Teacher, 64(3), 17-24.
4.Liu, C. Y., & Liu, S. T. (2008). Analyses of Problem Solving Performance of Factor and Multiple 
     Problems of Gifted Seventh Grade Students. Journal of Gifted Education, 2008, 8(1), 47-66. 
     (Correspond author:Liu, Shiang-tung).
5.Li, P. H., & Liu, S. T. (2008). The analysis of a gifted child’s spontaneous strategies of problem 
      solving for the cross proportional problems. Submitted to Gifted Education Quarterly. 
      (Correspond author:Liu, Shiang-tung).
6.Tsai, Z. Y., & Liu, S. T. (2007). How are gifted students thinking about “Speed”. Journal of
      Gifted Education, 2007, 7(1), 29-47. (Correspond author:Liu, Shiang-tung).
7.Liu, S. T. (2007). The way how should we teach and the content what should be taught for the 
      school mathematics: Reflection from the visiting public secondary schools of the Melbourne 
      city, Australia? Science Education Monthly, 300, 26-31.
8.Wang, Z. M., & Liu, S. T. (2007). An analysis of a gifted child’s spontaneous strategies used in 
      solving fractional division problems. Gifted Education Quarterly, 104, 8-19. (Correspond 
      author:Liu, Shiang-tung).
9.Chen, G. C., & Liu, S. T. (2007). The study of a seventh grader’s concept development of ratio 
      and proportion.  Taiwanese Mathematics Teacher, 10, 12-38.(Correspond author:Liu, Shiang-
      tung).
10.Lin, H.L, & Liu, S. T. (2006). The applications of Farey sum on solving rate problems. Science 
       Education Monthly, 287, 20-29.(Correspond author:Liu, Shiang-tung).
11.Hung, C. H., & Liu, S. T. (2006). The development and practice of situated cognition teaching
       activities in the factors unit—using poker games as an example. Chinese Journal of Science
       Education, 14, 1-27. (Correspond author:Liu, Shiang-tung).
12.Yen, T. B. , & Liu, S. T. (2005). A six grader’s performance on solving ratio problems case
        study   norming performance at fraction numbers. Research and Development in Science
        Education Quarterly, 41, 44-73(Correspond author:Liu, Shiang-tung).
13.Liu, S. T., & Se, H. H. (2005). Which is the sweeter solution between two honey cups?
        Edumath,  21, 75-80. 
14.Se, H. H.,& Liu, S. T. (2005). A fourth grader’s performance on solving operator problems.
        Research and Development in Science Education Quarterly, 40, 13-34. (Correspond
        author:Liu, Shiang-tung).
15.Yeh, G. D., Liu, S. T. (2005). A seven grader’s performance on solving speed problems,
        Science Education Monthly, 279, 2-20. (Correspond author:Liu, Shiang-tung).
16.Liu, S. T., & Huang, K. H. (2005). The types and examples of mathematics writing. Taiwanese
        Mathematics Teacher, 1(1), 1-7.
17.Huang, K. H., & Liu, S. T. (2005). Using poker games in mathematics as a creative means of
        teaching factor problems:An action research approach. Bulletin of Educational Research,
        51(1), 95-129.
18.Chang, Y. P., & Liu, S. T. (2005). A fifth grader’s performance on solving ratio problems. 
        Research and Development in Science Education Quarterly, 39, 39-59.
19.Hung, C. H., & Liu, S. T. (2004). A fifth grader’s performance on solving the unit partition of 
        fraction problems. Research and Development in Science Education Quarterly, 35, 53-75.
20.Liu, S. T. (2003). Is constructivism instruction of mathematics from the way of simplicity to of
        complication? Teacher Companion, 44(1), 8-11.
21.Weng, Y. C., & Liu, S. T. (2003). A study of solving simple proportion problems by a third
        grader.  Research and Development in Science Education Quarterly, 31, 32-53.
22.Wey, T. M., & Liu, S. T. (2003). The construction of proportion problems of schoolchildren. 
        Research and Development in Science Education Quarterly, 32, 87-108.
23.Huang, K. H., Liu, S. T. (2003). The fifth graders’ difficulties of learning factors unit. Research
        and Development in Science Education Quarterly, 30, 52-70.
24.Huang, K. H., Liu, S. T. (2003). Practicing an innovative mathematics teaching activity- Using
        poker games to teaching factors unit as examples. Research and Development in Science
        Education Quarterly, 33, 70-90.
25.Ho, F. C., & Liu, S. T. (2003). The innovative teaching for statistics measures-Conjecturing the
        role of spectrum instrument. Research and Development in Science Education Quarterly, 33,
        54-69.
26.Li, M. L., & Liu, S. T. (2003). The new window of algebra teaching. Science Education 
        Monthly, 265, 2-15.
27.Liu, S. T., Weng, Y. C.,& Wu, M. Z.(2003). The effects of calculator teaching activities to
        decimal   comparisons-A case study from a sixth grader. Teacher Companion, 10, 251-280.
28.Huang, W. C.,& Liu, S. T.(2003). Overcoming a sixth grader’s misconception of decimal 
        numbers by using the base ten blocks. Research and Development in Science Education
        Quarterly, 30, 71-93.
29.Liu, S. T.& Huang, K. H.(2003). The study of practicing teaching module of divisors’ number. 
        Chinese Journal of Science Education, 11(3), 235-256.
30.Chen, S. J., & Liu, S. T. (2002). The accessible teaching strategies of mathematics discussion
         in an elementary classroom. Chinese Journal of Science Education, 10(1), 87-107.
31.Lo, J. J., Hung, C.C., & Liu, S.T. (2002). An analysis of teacher education reform in Taiwan
         since 1994 and its potential impact on the elementary school level.  International Journal of
         Education Research, 37, 145-159.
32.Shen, M. H., & Liu, S. T. (2002). Analyzing literatures of students’ solving proportion problems
         - Suggestions for curriculum and instruction of elementary mathematics. Research and
         Development in Science Education Quarterly, 27, 81-96.
33.Chen, H. M., & Liu, S. T. (2002). A case study of a fifth grader’s probability conceptions. 
        Journal of Research on Elementary and Secondary Education, 8, 133 -158.
34.Chen, H. M., & Liu, S. T.(2002). To explore instruction and curriculum from document analysis 
        of  children’s probability misconceptions. Research and Development in Science Education
        Quarterly, 26, 40-51.
35.Huang, K. H., & Liu, S. T. (2002). Happy mathematics classes from practicing innovating
        teaching on divisor teaching unit. Research and Development in Science Education Quarterly,
        26, 52-64.
36.Liu, S. T., Wu, M. Z., & Weng, Y. I. (2002).The effects of using calculator teaching activities on
         learning decimal numbers. Research and Development in Science Education Quarterly, 26,
        22-39.
37.Liu, S. T., Chou, L. S. (2001). Developing elementary school teachers’ problem posing
        abilities: Examples of teaching multiplication and division of fractional numbers.  Chinese
        Journal of Science Education, 9(1),15-34.
38.Chen, Y. T.,& Liu, S. T.(2001).The implications of multiple intelligence for math instruction.
        Research and Development in Science Education Quarterly, 25, 81-100.
39.Chen, S. J., & Liu, S. T.(2001). The difficulties of mathematics discussion from an elementary
        school teacher. Educational Research & Information, 9(2), 125-146.
40.Liu, S. T., Wu, R. X.,& Huang, C. I. (2000). Mathematics problem posing of an elementary
        teacher: Analysis from students’ mathematics writing on number & quantity. Educational
        Research & Information, 8(4), 141-166.
41.Wu, M. R.,& Liu, S. T. (2000).The study of calculators integrated into math instruction of
        Elementary school. Research and Development in Science Education Quarterly, 19, 61-72.
42.Lin, C. R., & Liu, S. T. (2000).The instruction of volume concept from the viewpoint of unit
        quantity. Research and Development in Science Education Quarterly, 21, 44-55.
43.Liu, S. T, & Chou, L. S. (1999).The development of teaching practice curriculum at proportion
        problems. Chung-Shi Bulletin of Mathematics and Science, 3(1), 1-25.
44.Chou, L.S., & Liu, S. T. (1998).The effects of math writing activities on problem solving abilities
         of Elementary Students. Education Research and Information, 6(3), 46-62.
45.Liu, S. T., & Ho, S. H. (1997).The evaluation of available CAI courseware used by children with
         mild mental retardation. Bulletin of Chiayi Teacher College, 11, 309-342.
46.Liu, S. T.,& Chou ,L. S.(1997). Mathematics writing activities – A communication tool of
        instruction for the elementary mathematics. Journal of Research on Elementary Education, 3,
         239-262.
47.Chou, L.H., & Liu, S. T. (1997). The relations between problem-solving strategies and math
        abilities of elementary school students – An exploration in solving “Blocks Problem”. Journal
        of  Research on Elementary Education, 3, 25-44.
48.Liu, S.T. (1994). The exploration of integrating calculators into elementary mathematics
        education. Bulletin of Chiayi Teacher College, 8, 313-336.
49.Liu, S. T. (1994). The role of writing activities on mathematics instruction. Teacher Companion,
        35(5),32-36.
50.Liu, S. T. (1990). The methods of using microcomputer to increase the effective decimal
        numbers: Overcoming the situations of overflow value. Science Education Monthly, 133,
        2-11.
51.Liu, S. T. (1989).The relationships between the characteristics of recurring decimal and prime
        numbers. Science Education Monthly, 125, 48-53.
52.Liu, S. T. (1989). The explanatory to Fabonacci sequence. Teacher Companion, 30(5), 6-10.
53.Liu, S. T. (1985). Relationships between student Piagetian cognitive development and the
        learning mathematics in junior teachers college. Bulletin of Chiayi Junior Teacher College,
       15,253-274.


E. Conference papers
1.Tseng, C. C., & Liu, S.T. (2010). The comparison study on mathematics problem-solving
        performance between traditional assessment and writing assessment:Exploration of
        pattern problems. 2th Conference on Technology and Mathematics Education. Department
        of mathematics Education, National Taichung University.
2.Liu, S.T., Chen, J. C. & Yao R. F. (2010). Mathematizing Binary Numbers for Gifted Seventh
        Graders through Conjecture Activities. 2th Conference on Technology and Mathematics
        Education. Department of mathematics Education, National Taichung University.
3.Liu, S.T., & Su, Y. J. (2010). A case study: Role of meta-cognition in solving non-routine
        mathematics problems.  8th Hawaii International Conference on Education.  Honolulu, Hawaii.
        Jan. 7-10, 2010.
4.Liu, S.T., & Chen, J. C. (2009). How did Tom use visual representations to solve non-routine
        problems?   National Association of Gifted Children 56th Annual Convention & Exhibition, 
        Nov. 4-9, 2009. St. Louis, Missouri.
5.Liu, S. T. (2006). Scaffolding for a gifted child’s mathematics problem solving.  Paper presented
        at Mathematical meeting and annual meeting of the mathematical society. Department of
        mathematics, National Taiwan Normal University.
6.Liu, S. T., & Steinle, V. (2006). Analyses of spontaneous problem solving strategies: Case
        studies of gifted Taiwanese children. Paper presented at 53rd Annual Convention National
        Association for Gifted Childen, Novermber 1-5, 2006. Charlotte, North Carolina.
7.Liu, S. T., & Ho, F. C. (2006). Conjecture activities to learn statistics terms. Paper presented at
        the conference of the Perspective of mathematics curriculum development and teaching at
        National Chiayi University, Minghsiung campus.
8.Liu, S. T. (2005). Formulating the target problems to develop a third grader problem solving
        ability: analyzing strategies of the source problem as resources. Paper presented at The
        ICMI Eastern Asia Regional Conference of Mathematics Education 3 at East China Normal 
        University, Shanghai City, China.
9.Liu, S. T., & Ho, F. C. (2005). Conjecture activities for comprehending statistics terms through
        speculations on the functions of fictitious dpectrometers. Paper presented at the PME 29 at
        University of Melbourne, Australia.
10.Liu, S. T., & Kao, S. (2005). Developing Tony’s rational number concept through math writing.
         The International Conference of Reading and Writing on Science and Mathematics
         Education  at National Changhua University of Education。
11.Lo, j. j., Hung, C .C., & Liu, S. T. (2001). An analysis of the recent reform in elementary
         teacher education in Taiwan and its potential impacts on the mathematics teaching at the
         elementary school levels. Paper presented at the Research Profession of the 2001 Annual
         Meeting of the  National Council of Teachers of Mathematics. April 2-4, 2001, Orlando, FL.
         (2001).


F. Research directions & projects

Research direction
1. Mathematics concept development
2. Mathematics writing activity
3. Mathematics problem solving
4. Gifted mathematics education

My research grants
1.Liu, S. T. (2010). Develop Higher Order Mathematics Problem Solving Scale from Analyzing
      Problem Solving Performance of Elementary Students (2/3)(NSC-98- 2511-S-003-MY3).
2.Liu, S. T. (2009). Develop Higher Order Mathematics Problem Solving Scale from Analyzing
      Problem Solving Performance of Elementary Students (1/3)(NSC-98- 2511-S-003-MY3).
3.Liu, S. T. (2008). The study of analysis of problem solving and designing mathematics activities
      for gifted children(2/3).(NSC-95- 2521-S-004-MY3)
4.Liu, S. T. (2007). The study of analysis of problem solving and designing mathematics activities
      for gifted children(1/3).(NSC-95- 2521-S-004-MY3)
5.Liu, S. T.(2006). The study of constructs、operation ability、and norming ability of rational
      numbers for the senior elementary students (3/3). (NSC-94-2521-S-425-001).
6.Liu, S. T.(2005).The program of science education production:The theory and practice of
      mathematics questioning(NSC-93-2511-S-415-005).
7.Liu, S. T. (2005). The study of constructs、operation ability、and norming ability of rational
      numbers for the senior elementary students.(2/3)(NSC-93-2521-S-425-001).
8.Liu, S. T.(2004). The program of science education production:Problem posing design and
      problem solving analysis of elementary mathematics (NSC-92-2521-S-415-004).
9.Liu, S. T. (2004). The study of constructs、operation ability、and norming ability of rational
      numbers for the senior elementary students(1/3).(NSC-92-2521-S-425-001).
10.Liu, S. T. (2003). The development and practice of instructional module for integrated nine 
        years  math curriculum. (NSC-91-2521-S-415-002).
11.Liu, S. T. (2001). The development of proportional concepts from the viewpoint of unit quantity.
        ( NSC-89-2511-S-415-002).


G. My graduated advisees and their theses.

1.Tseng, C. C. (2010). The comparison study on mathematics problem-solving performance
       between traditional assessment and writing assessment:Exploration of pattern problems.
       Unpublished thesis of the Graduate institute of math education, National Chiayi University.
2.Tseng, H. H. (2010). The Study of Implementing Open-ended Approach-Exemplar from factor 
       and multiple. Unpublished thesis of the Graduate institute of math education, National Chiayi
       University.
3.Chiang, C. W. (2010). The Study of a Gifted Student’s Performance on Speed Problem Solving.
       Unpublished thesis of the Graduate institute of math education, National Chiayi University.
4.Ching, K. P. (2009). The Study of Open Approach for The Seventh Grade student cases in
       Junior  High School Mathematics Class. Unpublished thesis of the Graduate institute of math
       education, National Chiayi University.
5.Yang, M. C. (2009). A Study on the Multiplication Topic of Elementary Mathematics Textbooks
       for  Second and Third Grade Students between Taiwan and U.S.A. Unpublished thesis of the
       Graduate institute of math education, National Chiayi University.
6.Yeh, C. C. (2009). The case studies of performance for the two seventh grade gifted students
       on solving number pattern problems. Unpublished thesis of the Graduate institute of math
       education, National Chiayi University.
7.Liu, C. Y. (2009). The Study of problem Solving Related to Factor and Multiple Problems for the
       Seventh Grader Difted Cases. Unpublished thesis of the Graduate institute of math education,
       National Chiayi University.
8.Jhang, S. R. (2009). The Study of Analyzing Gifted Students on Solving Speed Problems.
       Unpublished thesis of the Graduate institute of math education, National Chiayi University.
9.Chen, S. G. (2008). The study of questioning techniques used in the Elementary classroom.
       Unpublished dissertation of the graduate institute of education, National Tainan University.
10.Lin, H.L, & Liu, S. T. (2008). The study of achievement of mathematics learning by questioning
       approach — solving on the fraction norming problems by a 7th graders’, for example.
       Unpublished dissertation of the graduate institute of education, National Tainan University.
11.Kang, S. J. (2008). The study of decision making from an school teacher’s questioning
       instruction. Unpublished thesis of the Graduate institute of math education, National Chiayi
       University.
12.Tsai, Z. Y. (2008). Investigate the performance of sixth-grade gift students on speed problems.
        Unpublished thesis of the Graduate institute of math education, National Chiayi University.
13.Lee, P. H. (2008). Scaffolding students’ learning the continued proportion problems : base on
       spontaneous strategies of gifted students. Unpublished thesis of the Graduate institute of
       math education, National Chiayi University.
14.Wang, C. M. (2008). The study of scaffolding students’ learning of fractions division from gifted
        children spontaneous strategies- exemplar from extended partititve division. Unpublished
       thesis of the Graduate institute of math education, National Chiayi University.
15.Chen, J. W. (2007).Exploring the sixth graders’ ability in fraction norming problem. Unpublished
       thesis of the Graduate institute of math education, National Chiayi University.
16.Chen, C. C. (2007). A case study of a junuor high school student’s development in solving
       mathematical problems of ratio and proportion. Unpublished thesis of the Graduate institute
       of math education, National Chiayi University.
17.Huang, S. M. (2007). The effect of questioning on quotient problems solving of fifth students.
       Unpublished thesis of the Graduate institute of math education, National Chiayi University.
18.Tseng, C. F. (2007). Effects of revising writing and feed backing activities to the sixth grades
       elementary school students on rational numbers as measure task. Unpublished thesis of the
       Graduate institute of math education, National Chiayi University.
19.Wu, S. H. (2007). A study of integrating caculators into remedial instruction on comprehension
       of division algorithm for decimals. Unpublished thesis of the Graduate institute of math
       education, National Chiayi University.
20.Yen, C. P. (2006). Exploring the sixth graders’ problem solving patterns and their levels of
       understanding of norming task-division of fraction, for example. Unpublished thesis of the
       Graduate institute of math education, National Chiayi University.
21.Chiu, W. C. (2005).A seventh grader’s performance in solving equivalent fraction task.
       Unpublished thesis of the Graduate institute of math education, National Chiayi University.
22.Hung, C. H.(2005).A sixth grader’s performance in solving rational numbers as measure task.
       Unpublished thesis of the Graduate institute of math education, National Chiayi University.
23.Chang, Y. P.(2005).The solution categories of two elementary students in solving rational as
      ratio task. Unpublished thesis of the Graduate institute of math education, National Chiayi
      University.
24.Shin, H. H.(2005).Exploring a fourth grader’s performance of solving rational-as-operator tasks-
       Form the perspective of a junior high school teacher. Unpublished thesis of the Graduate
       institute of math education, National Chiayi University.
25.Yen, G. D.(2005).A seventh grader’s study of solving speed problems. Unpublished thesis of
       the  Graduate institute of math education, National Chiayi University.
26.Ho, M. H.(2005).A research on ninth graders’ solving the inclusive relation of quadrilaterals.
       Unpublished thesis of the Graduate institute of math education, National Chiayi University.
27.Hwang, J. C.(2005).A study of solving inverse function problems from first  grader of senior
       high school students. Unpublished thesis of the Graduate institute of math education, National
       Chiayi University.
28.Li, M. L.(2004).A study of solving arithmetic sequence problems from a second grader of a
       middle school student. Unpublished thesis of the Graduate institute of math education,
       National  Chiayi University.
29.Ho, F. C.(2004).Using tangram to study on abilities of developing fraction norming in the sixth-
       grade elementary students. Unpublished thesis of the Graduate institute of math education,
       National Chiayi University.
30.Huang, K. H.(2003).A study of the implementation of divisor numbers instructional module in
       two  upper grade elementary classrooms. Unpublished thesis of the graduate institute of
       elementary education, National Chia-Yi University.
31.Weng, Y. C.(2002).A study of solving proportion problems from a third grader of an elementary
        school student. Unpublished thesis of the graduate institute of elementary education, National
       Chia-Yi University.
32.Chen, H. M.(2002).A case study of three elementary school students’ solving probability
        problems. Unpublished thesis of the graduate institute of elementary education, National
       Chia-Yi University.
33.Shen, M. H.(2002).The study of practicing teaching module of proportion problem-「Stretchers
        and shrinkers」unit as an example. Unpublished thesis of the Graduate institute of math
        education, National Chiayi University.
34.Lin, R. R.(2001).The volume concept of elementary students: From the viewpoint of unit
        quantity.  Unpublished thesis of the graduate institute of elementary education, National Chia-
        Yi University. 
35.Huang, W. J.(2001).A case study of referents’ activity to improve the decimal concept of six-
        grade students in the elementary school. Unpublished thesis of the graduate institute of
        elementary education, National Chia-Yi University.
36.Wu, M. R.(2000).The case study of using calculators activity to enhance students number
        concept. Unpublished thesis of the graduate institute of elementary education, National Chia-
        Yi University.
37.Chen, S. J.(1999).The study of a mathematics class discussion in an elementary school by
        collaborative action research. Unpublished thesis of the graduate institute of elementary
        education, National Chia-Yi University.
38.Yang, G. L.(1999).The study of solving proportion problems from fifth and sixth graders.
        Unpublished thesis of the graduate institute of elementary education, National Chia-Yi
        University.
39.Juang, S. C.(1998).Elementary school teachers’ beliefs of mathematics. Unpublished thesis of
        the graduate institute of elementary education, National Chia-Yi University.
40.Wei, T. M.(1997).The study of implementing writing activities on math classrooms. Unpublished
         thesis of the graduate institute of elementary education, National Chia-Yi University. 


H. Courses
1. The study of math concept development.
2. The data analysis of qualitative research.
3. The constructivism and math learning.
4. The teaching materials and methods of secondary mathematics.
5. The teaching practice of secondary mathematics.



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