메뉴 건너뛰기




Volumn 28, Issue 1, 2010, Pages 113-145

The precalculus concept assessment: A tool for assessing students' reasoning abilities and understandings

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77951271521     PISSN: 07370008     EISSN: None     Source Type: Journal    
DOI: 10.1080/07370001003676587     Document Type: Article
Times cited : (95)

References (52)
  • 6
    • 63349112419 scopus 로고    scopus 로고
    • Obstacles for college algebra students in understanding functions: What do high performing students really know?
    • Carlson, M. (1997). Obstacles for college algebra students in understanding functions: What do high performing students really know? American Mathematical Association of Two-Year Colleges Review, 48-59.
    • (1997) American Mathematical Association of Two-Year Colleges Review , pp. 48-59
    • Carlson, M.1
  • 8
    • 17444383058 scopus 로고    scopus 로고
    • The cyclic nature of problem solving: An emergent multidimensional problem solving framework
    • Carlson, M., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem solving framework. Educational Studies in Mathematics, 58, 45-75.
    • (2005) Educational Studies In Mathematics , vol.58 , pp. 45-75
    • Carlson, M.1    Bloom, I.2
  • 9
  • 10
    • 85140174155 scopus 로고    scopus 로고
    • Modeling dynamic events: A study in applying covariational reasoning among high performing university students
    • In R. Lesh & H. Doerr (Eds.), Hillsdale, NJ: Lawrence Erlbaum
    • Carlson, M., Larsen, S., & Lesh, R. (2003). Modeling dynamic events: A study in applying covariational reasoning among high performing university students. In R. Lesh & H. Doerr (Eds.), Beyond constructivism in mathematics teaching and learning: A models & modeling perspective (pp. 465-478). Hillsdale, NJ: Lawrence Erlbaum.
    • (2003) Beyond Constructivism In Mathematics Teaching and Learning: A Models & Modeling Perspective , pp. 465-478
    • Carlson, M.1    Larsen, S.2    Lesh, R.3
  • 13
    • 34447522468 scopus 로고    scopus 로고
    • Developing and connecting calculus students' notions of rate-of-change and accumulation: The fundamental theorem of calculus
    • Honolulu, HI
    • Carlson, M., Smith, N., & Persson, J. (2003). Developing and connecting calculus students' notions of rate-of-change and accumulation: The fundamental theorem of calculus. Proceedings of the 2003 Joint Meeting of PME and PME-NA, 2, 165-172. Honolulu, HI.
    • (2003) Proceedings of The 2003 Joint Meeting of PME and PME-NA , vol.2 , pp. 165-172
    • Carlson, M.1    Smith, N.2    Persson, J.3
  • 14
    • 84970694132 scopus 로고
    • Problems in the measurement of latent variables in structural equations causal models
    • Cohen, P., Cohen, J., Teresi, J., Marchi, M., & Velez, C. N. (1990). Problems in the measurement of latent variables in structural equations causal models. Applied Psychological Measurement, 14(2), 183-196.
    • (1990) Applied Psychological Measurement , vol.14 , Issue.2 , pp. 183-196
    • Cohen, P.1    Cohen, J.2    Teresi, J.3    Marchi, M.4    Velez, C.N.5
  • 17
    • 0002370194 scopus 로고
    • The nature of the process conception of function
    • In G. Harel & E. Dubinsky (Eds.), Washington, DC: Mathematical Association of America
    • Dubinsky, E., & Harel, G. (1992). The nature of the process conception of function. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy. MAA Notes, 25, 85-106. Washington, DC: Mathematical Association of America.
    • (1992) The Concept of Function: Aspects of Epistemology and Pedagogy. MAA Notes , vol.25 , pp. 85-106
    • Dubinsky, E.1    Harel, G.2
  • 19
    • 77951078486 scopus 로고    scopus 로고
    • Proceedings of the 27th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Roanoke: Virginia Tech
    • Engelke, N., Oehrtman, M., & Carlson, M. (2005). Composition of functions: Precalculus students' understandings. Proceedings of the 27th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Roanoke: Virginia Tech.
    • (2005) Composition of Functions: Precalculus Students' Understandings
    • Engelke, N.1    Oehrtman, M.2    Carlson, M.3
  • 20
    • 33947199278 scopus 로고
    • The initial knowledge state of college physics students
    • Halloun, I., & Hestenes, D. (1985a). The initial knowledge state of college physics students. American Journal of Physics, 53,1043-1055.
    • (1985) American Journal of Physics , vol.53 , pp. 1043-1055
    • Halloun, I.1    Hestenes, D.2
  • 25
    • 0011991957 scopus 로고
    • Patterns in students' formalization of quantitative patterns
    • In G. Harel & E. Dubinsky (Eds.), Washington, DC: Mathematical Association of America
    • Kaput, J. (1992). Patterns in students' formalization of quantitative patterns. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy, MAA Notes, 25, 290-318. Washington, DC: Mathematical Association of America.
    • (1992) The Concept of Function: Aspects of Epistemology and Pedagogy, MAA Notes , vol.25 , pp. 290-318
    • Kaput, J.1
  • 26
    • 84970156708 scopus 로고
    • Functions, graphs, and graphing: Tasks, learning, and teaching
    • Leinhardt, G., Zaslavsky, O., & Stein, M. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1-64.
    • (1990) Review of Educational Research , vol.60 , Issue.1 , pp. 1-64
    • Leinhardt, G.1    Zaslavsky, O.2    Stein, M.3
  • 27
    • 42349108647 scopus 로고    scopus 로고
    • A suggested change in terminology and emphasis regarding validity and education
    • Lissitz, R., & Samuelsen, K. (2007). A suggested change in terminology and emphasis regarding validity and education. Educational Researcher, 36(8), 437-448.
    • (2007) Educational Researcher , vol.36 , Issue.8 , pp. 437-448
    • Lissitz, R.1    Samuelsen, K.2
  • 29
    • 0000507908 scopus 로고
    • Students' understanding of a function given by a physical model
    • In G. Harel & E. Dubinsky (Eds.), Washington, DC: Mathematical Association of America
    • Monk, S. (1992). Students' understanding of a function given by a physical model. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy, MAA Notes, 25 (pp. 175-193). Washington, DC: Mathematical Association of America.
    • (1992) The Concept of Function: Aspects of Epistemology and Pedagogy, MAA Notes , vol.25 , pp. 175-193
    • Monk, S.1
  • 30
    • 0038379371 scopus 로고
    • National Center for Education Statistics, Office of Educational Research & Improvement, U.S. Department of Education. Retrieved from
    • National Center for Education Statistics. (1995). Third international mathematics and science study. Office of Educational Research & Improvement, U.S. Department of Education. Retrieved from http://nces.ed.gov/timss/timss95/index.asp
    • (1995) Third International Mathematics and Science Study
  • 33
    • 84928359408 scopus 로고    scopus 로고
    • Layers of abstraction: Theory and design for the instruction of limit concepts
    • In M. Carlson & C. Rasmussen (Eds.), Washington, DC: Mathematical Association of America
    • Oehrtman, M. (2008a). Layers of abstraction: Theory and design for the instruction of limit concepts. In M. Carlson & C. Rasmussen (Eds.), Making the connection: Research and practice in undergraduate mathematics, MAA Notes Volume, 73, 65-80. Washington, DC: Mathematical Association of America.
    • (2008) Making the Connection: Research and Practice In Undergraduate Mathematics, MAA Notes Volume , vol.73 , pp. 65-80
    • Oehrtman, M.1
  • 34
    • 69249198270 scopus 로고    scopus 로고
    • Collapsing Dimensions, Physical Limitation, and other Student Metaphors for Limit Concepts
    • Oehrtman, M. (2008b). Collapsing Dimensions, Physical Limitation, and other Student Metaphors for Limit Concepts. Journal for Research in Mathematics Education, 40(4), 396-426.
    • (2008) Journal For Research In Mathematics Education , vol.40 , Issue.4 , pp. 396-426
    • Oehrtman, M.1
  • 35
    • 84928373279 scopus 로고    scopus 로고
    • Foundational reasoning abilities that promote coherence in students' function understanding
    • In M. Carlson & C. Rasmussen (Eds.), Washington, DC: Mathematical Association of America
    • Oehrtman, M., Carlson, M., & Thompson, P. W. (2008). Foundational reasoning abilities that promote coherence in students' function understanding. In M. Carlson & C. Rasmussen (Eds.), Making the connection: Research and practice in undergraduate mathematics, MAA Notes Volume, 73, 27-41. Washington, DC: Mathematical Association of America.
    • (2008) Making the Connection: Research and Practice In Undergraduate Mathematics, MAA Notes Volume , vol.73 , pp. 27-41
    • Oehrtman, M.1    Carlson, M.2    Thompson, P.W.3
  • 36
    • 0002893760 scopus 로고    scopus 로고
    • New directions in differential equations: A framework for interpreting students' understandings and difficulties
    • Rasmussen, C. (2000). New directions in differential equations: A framework for interpreting students' understandings and difficulties. Journal of Mathematical Behavior, 20, 55-87.
    • (2000) Journal of Mathematical Behavior , vol.20 , pp. 55-87
    • Rasmussen, C.1
  • 37
    • 0347960821 scopus 로고    scopus 로고
    • A coherent curriculum: The case of mathematics
    • Schmidt, W., Houang, R., & Cogan, L. (2002). A coherent curriculum: The case of mathematics. American Educator, 26(2),10-26.
    • (2002) American Educator , vol.26 , Issue.2 , pp. 10-26
    • Schmidt, W.1    Houang, R.2    Cogan, L.3
  • 38
    • 0000174590 scopus 로고
    • The problem iceberg in science, mathematics and engineering education: Student explanations for high attrition rates
    • February
    • Seymour, E. (1992a, February). The problem iceberg in science, mathematics and engineering education: Student explanations for high attrition rates. Journal of College Science Teaching, 230-232.
    • (1992) Journal of College Science Teaching , pp. 230-232
    • Seymour, E.1
  • 39
    • 0009390844 scopus 로고
    • Undergraduate problems with teaching and advising in SME majors: Explaining gender differences in attrition rates
    • March/April
    • Seymour, E. (1992b, March/April). Undergraduate problems with teaching and advising in SME majors: Explaining gender differences in attrition rates. Journal of College Science Teaching, 284-292.
    • (1992) Journal of College Science Teaching , pp. 284-292
    • Seymour, E.1
  • 40
    • 0036109280 scopus 로고    scopus 로고
    • Tracking the process of change in US undergraduate education in science, mathematics, engineering, and technology
    • Seymour, E. (2001). Tracking the process of change in US undergraduate education in science, mathematics, engineering, and technology. Science Education, 1, 79-105.
    • (2001) Science Education , vol.1 , pp. 79-105
    • Seymour, E.1
  • 43
    • 0012881236 scopus 로고
    • Calculational and conceptual orientations in teaching mathematics
    • In A. Coxford (Ed.), Reston, VA: National Council of Teachers of Mathematics
    • Thompson, A. G., Philipp, R. A., Thompson, P. W., & Boyd, B. A. (1994). Calculational and conceptual orientations in teaching mathematics. In A. Coxford (Ed.), 1994 Yearbook of the National Council of Teachers of Mathematics (pp. 79-92). Reston, VA: National Council of Teachers of Mathematics.
    • (1994) 1994 Yearbook of The National Council of Teachers of Mathematics , pp. 79-92
    • Thompson, A.G.1    Philipp, R.A.2    Thompson, P.W.3    Boyd, B.A.4
  • 44
    • 0002269268 scopus 로고
    • The development of the concept of speed and its relationship to concepts of rate
    • In G. Harel & J. Confrey (Eds.), Albany, NY: SUNY Press
    • Thompson, P. W. (1994a). The development of the concept of speed and its relationship to concepts of rate. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 179-234). Albany, NY: SUNY Press.
    • (1994) The Development of Multiplicative Reasoning In the Learning of Mathematics , pp. 179-234
    • Thompson, P.W.1
  • 45
    • 0000019871 scopus 로고
    • Images of rate and operational understanding of the fundamental theorem of calculus
    • Thompson, P. W. (1994b). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26, 229-274.
    • (1994) Educational Studies In Mathematics , vol.26 , pp. 229-274
    • Thompson, P.W.1
  • 46
    • 0003130954 scopus 로고
    • Students, functions, and the undergraduate mathematics curriculum
    • In E. Dubinsky, A. H. Schoenfeld & J. J. Kaput (Eds.), Providence, RI: American Mathematical Society. Retrieved from
    • Thompson, P. W. (1994c). Students, functions, and the undergraduate mathematics curriculum. In E. Dubinsky, A. H. Schoenfeld & J. J. Kaput (Eds.), Research in collegiate mathematics education, 1 (Vol. 4, pp. 21-44). Providence, RI: American Mathematical Society. Retrieved from http://pat-thompson.net/PDFversions/1994StuFunctions.pdf
    • (1994) Research In Collegiate Mathematics Education, 1 , vol.4 , pp. 21-44
    • Thompson, P.W.1
  • 47
    • 37349095729 scopus 로고    scopus 로고
    • The design of tasks in support of teachers' development of coherent mathematical meanings
    • Thompson, P. W., Carlson, M. P., & Silverman, J. (2007). The design of tasks in support of teachers' development of coherent mathematical meanings. Journal of Mathematics Teacher Education, 10, 415-432.
    • (2007) Journal of Mathematics Teacher Education , vol.10 , pp. 415-432
    • Thompson, P.W.1    Carlson, M.P.2    Silverman, J.3
  • 52
    • 0000039692 scopus 로고    scopus 로고
    • A theoretical framework for analyzing student understanding of the concept of derivative
    • In E. Dubinsky, A. H. Schoenfeld, & J. Kaput (Eds.), Providence, RI: American Mathematical Society
    • Zandieh, M. (2000). A theoretical framework for analyzing student understanding of the concept of derivative. In E. Dubinsky, A. H. Schoenfeld, & J. Kaput (Eds.), Research in Collegiate Mathematics Education IV. (pp. 103-127). Providence, RI: American Mathematical Society.
    • (2000) Research In Collegiate Mathematics Education IV , pp. 103-127
    • Zandieh, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.