2013 Conference Proceedings - University of Nevada, Las Vegas

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linked mathematical empowerment with pedagogical empowerment; they described theirnewfound confidence to teach others the mathematics content they felt comfortable. Forexample, one student stated “I know I will be able to teach certain math well because Iunderstand it,” and another said “Since taking this course, I have already begun to help myfriends and younger siblings with their mathematical endeavors. I think that with more practice Iwill be an effective teacher with more than just my stronger subjects.”Although, separated initially, these perspective changes into the categories of “Perspectiveson Mathematics” and “Perspectives about Self,” the intertwining of their beliefs aboutmathematics, teaching and learning mathematics, and their ability in mathematics form such adynamic relationship that separating statements into these categories felt like a reduction of sorts.Therefore, below are participant statements about changes in their viewpoints after participationin this non-traditional mathematics content course.In the beginning of [this] class I thought she would be a teacher from the textbooklike every other kind of math class I have took in the past. But with [this] class it wasdifferent. She not only took a little from the standard textbook but from her ownways. She makes us think outside the box… This class has opened my eyes to a newmath world, a math world that I will gladly share with my students and colleaguesover the years that will come.During the course of this past semester I have learned so much. I was apprehensivetaking what I felt was a lower level math class again. Because I am not good at mathand have never had good math instructors I felt that it would be like every othergeneric math class I have ever taken; the kind of class where the teacher stands in thefront of the classroom and lectures and teaches only from the book and the examplescome straight from the book and no further. However this class challenges its studentsto think outside the box and to get the answer by thinking in a non-traditional sense.DiscussionThe structure, format and experiences designed as part of this non-traditional mathematicscourse served to empower participants both mathematically and pedagogically. The wordempowerment encompasses feelings about capability as well as self-confidence (Ernest, 2002).This course eliminated traditional lecture (focused on procedural reasoning) as a primary sourceof instruction and instead focused on problem-based instruction, student-led solutions, andcollaboration time (Gasser, 2011). This study found that the format of class practice affectedstudents in that they reported feeling more confident in their mathematical prowess as well asProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 65
their ability to teach the mathematical topics covered in the course which supports Anderson andPiazza’s findings (1996). For instance, participants statedI think, in general, most of the experiences in this course have enhanced myconfidence and enthusiasm for mathematics. Being encouraged to work with outof-the-boxalgorithms has expanded my perceived horizons and opened up a newfield of interest for me.I used to view all mathematics very negatively because I was never good at it.However, in here by using visual manipulatives and other methods I was able tobetter understand mathematics, therefore I can feel more confident aboutit….because this class gave me a better understanding of mathematics I am able toenjoy it more, instead of being stressed out by it.While the results of this study are not intended to be generalized, it may be used to informpre-service teacher preparation programs as well as point to future directions to pursue inresearch on this topic. After investigating the results of this study, one area for future studieswould be to examine how and why pre-service teachers assimilate new ideas to fit existingbeliefs rather than accommodate their existing beliefs to internalize new ideas. Moreover, sincethis study focused on perturbing a variety of mathematical beliefs and found that those perturbedmost were seemingly impacted the most, future studies might focus on perturbing specificmathematical beliefs throughout a course to observe the effect on belief structure.ReferencesAnderson, D., & Piazza, J. (1996). Changing beliefs: Teaching and learning mathematics inconstructivist preservice classrooms. Action in Teacher Education, 18(2), 51-62.Ball, D. B. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1), 40-48.Ball, D. B. (1990). Breaking with experience in learning to teach mathematics: The role of apreservice methods course. For the Learning of Mathematics, 10(2), 10-16.Ball, D. B. (1996). Teacher learning and the mathematics reforms: What we think we know andwhat we need to learn. Phi Delta Kappan, 77(7), 500-508.Burnaford, G., Fischer, J., & Hobson, D. (2001). Teachers doing research: The power of actionthrough inquiry. Mahwah, NJ: Lawrence Erlbaum Associates Inc.Calderhead, J., & Robson, M. (1991). Images of teaching: Student teachers’ early conceptions ofclassroom practice. Teaching & Teacher Education, 7, 1-8.Cooney, T. J. (1999). Conceptualizing teacher’s ways of knowing. Educational Studies inMathematics, 38, 163-187.Ernest, P. (2002). Empowerment in mathematics education. Philosophy of MathematicsEducation Journal, 15. Retrieved July 15, 2012 fromhttp://people.exeter.ac.uk/PErnest/pome15/empowerment.htmFennema, E., & Sherman, J. (1977). Sex-related differences in mathematics achievement, spatialvisualization, and affective factors. American Educational Research Journal, 14, 51-71.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 66
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….where the Mathematicscomes swee
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THANK YOU TO OUR REVIEWERSKeith Ado
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Table of ContentsPreservice Teacher
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Support for Students Learning Mathe
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own problem solving, which is criti
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to get started and persistence. Tea
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Posamentier, A. S., Smith, B. S., &
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conceptual understanding, applicati
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Table 1Identified Mathematical Prac
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justify their statements, included
Page 21 and 22: Finally, engagement in MP.6 was ass
Page 23 and 24: PRESERVICE TEACHERS’ EMOTIONAL EN
Page 25 and 26: “experiences that are charged wit
Page 27 and 28: Number of journals containingEmotio
Page 29 and 30: ConclusionsStruggle and frustration
Page 31 and 32: Mathematics Teacher Candidates’ U
Page 33 and 34: function and applied the vertical l
Page 35 and 36: semester, about half of the course
Page 37 and 38: They further state that “the impo
Page 39 and 40: C. Laborde (Eds.) International Han
Page 41 and 42: (SCK), or knowledge of mathematics
Page 43 and 44: level of difficulty for each partic
Page 45 and 46: MKT Measures ScoresMathematics in G
Page 47 and 48: deep rooted belief in a single way
Page 49 and 50: THE INTERVIEW PROJECTAngel Rowe Abn
Page 51 and 52: involving addition and subtraction:
Page 53 and 54: 6+7 4+9=6+(6+1) Substitution =4+(10
Page 55 and 56: We strongly believe that this inter
Page 57 and 58: AN INNOVATIVE APPROACH FOR SUPPORTI
Page 59 and 60: Practice throughout the investigati
Page 61 and 62: are expected to pursue. Teacher not
Page 63 and 64: students to organize their reports
Page 65 and 66: Slovin, H., Venenciano, L., Ishihar
Page 67 and 68: The research presented in this pape
Page 69 and 70: students’ confidence. Because bel
Page 71: triangulation necessitated examinat
Page 75 and 76: SPATIAL REASONING IN UNDERGRADUATE
Page 77 and 78: journal prompt would be given as a
Page 79 and 80: given to the 33 students on the MPI
Page 81 and 82: to advance our way of life, then sp
Page 83 and 84: STUDENT CONCEPTIONS OF “BEST” S
Page 85 and 86: students are likely to interact wit
Page 87 and 88: opinion of the student body. This q
Page 89 and 90: At the highest level of reasoning a
Page 91 and 92: APPENDIXTo use two decks of cards t
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Page 95 and 96: with the CCSSM. Teachers read and d
Page 97 and 98: teachers’ role-play of SFMP #4. A
Page 99 and 100: Durkin, D. (1978-1979). What classr
Page 101 and 102: as well as the alignment between th
Page 103 and 104: Table 2Number of teachers per grade
Page 105 and 106: Table 4Classification Categories fo
Page 107 and 108: field so that research on the initi
Page 109 and 110: dynamic approach to learning conten
Page 111 and 112: Kindergarten Lesson FormatHow May W
Page 113 and 114: team’s goals? As much as possible
Page 115 and 116: 6. While preparing the lesson, teac
Page 117 and 118: active learning and collective part
Page 119 and 120: classroom. “I would like to know
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THE PATH OF REFORM IN SECONDARY MAT
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Our collaboration model was formed
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internal evaluator) were analyzed.
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DiscussionOn part I of the survey t
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whole department of secondary mathe
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discussion. Many texts include wild
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Data collection consisted of tests,
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I've not used children's literature
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could extend this inquiry to high s
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course titled Calculus with Busines
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no mathematical sense and should no
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Adopts the “111” (a term coined
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Specifically, clicking the “Click
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algebraic expression is carried out
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Retrieved from http://secc.sedl.org
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furthermore, each model may result
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After instruction in the course, th
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Table 4The group’s categories and
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you choose three place values, æ 4
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APPENDIXTable 5Description of Combi
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of the presented number. Later, the
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Figure 1: Mean trajectories and MD
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Figure 2: Mean trajectories and MD
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Performance, 33, 1410-1419.Cohen Ka
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Moyer, 2007). At his or her own pac
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logged by the system and then retri
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curriculum. The nature of the onlin
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Cox, G., Carr, T., & Hall, M. (2004
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curriculum locally, within individu
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Popularity tallied whether or not a
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Amazingly, despite there being a fe
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ReferencesBlack, M. (1962). Models
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connections are connections or rela
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Table 1Instructional TasksSquareTab
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t-charts made it easier for student
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Figure 2. A Display of Student Stra
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ReferencesAnderson, J. R., Greeno,
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their parents in phenotype (observa
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student learning calls for differen
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Figure 2. (A) P3. (B). Extension of
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the usual phenotypic assessments an
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teachers is the discrepancy between
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expected to learn and the inquiry a
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his partner about his observations,
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hard for some children? The nature
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Lakoff and Nunez: specifically, tha
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Figure 5: Average hand trajectories
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Figure 6: Distributions of maximum
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ReferencesAnderson, J. R. (2005). H
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Social system perspectives view the
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urged students to think of some way
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Figure 1: The Discourse Patterns Du
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Figure 3 blow illustrates the devel
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