2013 Conference Proceedings - University of Nevada, Las Vegas

More documents

Recommendations

Info

SUPPORT FOR STUDENTS LEARNING MATHEMATICS VIASTUDENT-CENTERED CURRICULAHannah SlovinUniversity of Hawai‘i at Mānoahslovin@hawaii.eduKavita RaoUniversity of Hawai‘i at Mānoakavitar@hawaii.eduFay ZenigamiUniversity of Hawai‘i at Mānoazenigami@hawaii.eduRhonda BlackUniversity of Hawai‘i at Mānoarblack@hawaii.eduWe conducted research on supports needed for at-risk students learning mathematics throughcurricula developed for a constructivist environment. Classroom observation data from a firstgrade class and a sixth grade class identified areas where the respective curriculum andpedagogy promoting student-centered learning posed specific challenges for struggling learnersand suggested the potential supports that could help students access critical content andprocesses. Mathematics education faculty and special education faculty from the University ofHawai‘i, College of Education collaborated on this study.What does research say about “best practice” for students to learn mathematics withunderstanding? What does it say about “best practice” for a struggling student or one withspecial needs placed in a general education mathematics class? While we have moved to includestudents with varying needs into the same general education classes, the research traditionsguiding us in that endeavor do not necessarily recommend the same strategies for the generalstudent population and those newly integrated students to be successful. We sought to identifyelements of two reform-based curricula that afforded at-risk and struggling studentsopportunities to be successful learners in mathematics class and to use the results to makerecommendations to the classroom teachers for further supports.Literature ReviewThe equity principle in the NCTM Principles and Standards for School Mathematics (PSSM)(NCTM, 2000) calls for all students to have opportunities to access challenging curriculum“regardless of personal characteristics, backgrounds, or physical challenges” (p. 12). In addition,legislative measures, such as the Individuals with Disabilities Education Improvement Act(IDEA, 2004) require that all students be exposed to the same curriculum and assessed by thesame means. The task has fallen to classroom teachers—both general education and specialeducation teachers—to provide a substantive mathematics education for all students but withlittle guidance on how best to accomplish the charge. One reason for the paltry support forProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 197
teachers is the discrepancy between the numbers of research studies on students’ mathematicsdisabilities versus students’ reading disabilities. From 1996 to 2005, the ratio of studies focusingon reading versus those focused on mathematics was 14:1 (622 reading disability studies to 43mathematics disability studies) (Gersten, Clarke, & Mazzocco, 2007). With so little directionfrom research, teachers must do the best they can to meet the needs of all students.One model suggested to support students with special needs in general mathematics classes iscollaborative teaching (Boyd & Bargerhuff, 2009; Sileo & van Garderen, 2010; van Garderen,Scheurmann, Jackson & Hampton, 2009). This model relies on the mathematics teacher and thespecial education teacher each contributing their unique knowledge and expertise to ensurestudents’ success. The mathematics teacher’s knowledge of the curriculum and content and thespecial education teacher’s knowledge of effective intervention strategies work together tomaximize students’ learning.But as van Garderen and her colleagues (2009) point out, this collaboration is “easier saidthan done” (p. 57). With little guidance, tension can arise between the mathematics teacher andthe special education teacher whose approaches to practice can stem from different and oftencontradictory philosophies and theoretical foundations. “Best practice” from the mathematicseducation perspective envisions students engaged in explorations of new ideas posed by nontraditionalproblems that have multiple solution paths and often multiple solutions. Classroominteractions are built on social constructivist theories in which students negotiate meanings andestablish understandings through activity and discussion with peers. By contrast, for the specialeducation teacher, “best practice” means using students’ individualized strengths and weaknessesto set learning goals that emphasize specific, measurable objectives geared mostly to developingprocedural accuracy and fluency. Special education teachers use an instructivist approach toteaching, including giving clear, unambiguous directions, modeling how to carry out a procedureand allowing sufficient time for guided practice (Boyd & Bargerhuff, 2009).Education researchers interested in equity matters for students with diverse culturalbackgrounds (e.g. Delpit, 1988; Parks, 2010) have also suggested that reform methods may notadvantage all children, particularly with respect to the dynamics of classroom interactions. Someof their concerns can be applied to at-risk and struggling learners. However, Delpit (1988) doesnot subscribe to the debate over which approach is better, process-focused reform programs orskill-focused traditional programs, saying the dichotomy is “false” (p. 296). She does, however,Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 198
Page 1 and 2:
….where the Mathematicscomes swee
Page 3 and 4:
THANK YOU TO OUR REVIEWERSKeith Ado
Page 5 and 6:
Table of ContentsPreservice Teacher
Page 7 and 8:
Support for Students Learning Mathe
Page 9 and 10:
own problem solving, which is criti
Page 11 and 12:
to get started and persistence. Tea
Page 13 and 14:
Posamentier, A. S., Smith, B. S., &
Page 15 and 16:
conceptual understanding, applicati
Page 17 and 18:
Table 1Identified Mathematical Prac
Page 19 and 20:
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 and 72:
triangulation necessitated examinat
Page 73 and 74:
their ability to teach the mathemat
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
Page 93 and 94:
isolated and often occur in tandem
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
Page 121 and 122:
I had never been brave enough to tr
Page 123 and 124:
THE PATH OF REFORM IN SECONDARY MAT
Page 125 and 126:
Our collaboration model was formed
Page 127 and 128:
internal evaluator) were analyzed.
Page 129 and 130:
DiscussionOn part I of the survey t
Page 131 and 132:
whole department of secondary mathe
Page 133 and 134:
discussion. Many texts include wild
Page 135 and 136:
Data collection consisted of tests,
Page 137 and 138:
I've not used children's literature
Page 139 and 140:
could extend this inquiry to high s
Page 141 and 142:
course titled Calculus with Busines
Page 143 and 144:
no mathematical sense and should no
Page 145 and 146:
Adopts the “111” (a term coined
Page 147 and 148:
Specifically, clicking the “Click
Page 149 and 150:
algebraic expression is carried out
Page 151 and 152:
Retrieved from http://secc.sedl.org
Page 153 and 154: furthermore, each model may result
Page 155 and 156: After instruction in the course, th
Page 157 and 158: Table 4The group’s categories and
Page 159 and 160: you choose three place values, æ 4
Page 161 and 162: APPENDIXTable 5Description of Combi
Page 163 and 164: of the presented number. Later, the
Page 165 and 166: Figure 1: Mean trajectories and MD
Page 167 and 168: Figure 2: Mean trajectories and MD
Page 169 and 170: Performance, 33, 1410-1419.Cohen Ka
Page 171 and 172: Moyer, 2007). At his or her own pac
Page 173 and 174: logged by the system and then retri
Page 175 and 176: curriculum. The nature of the onlin
Page 177 and 178: Cox, G., Carr, T., & Hall, M. (2004
Page 179 and 180: curriculum locally, within individu
Page 181 and 182: Popularity tallied whether or not a
Page 183 and 184: Amazingly, despite there being a fe
Page 185 and 186: ReferencesBlack, M. (1962). Models
Page 187 and 188: connections are connections or rela
Page 189 and 190: Table 1Instructional TasksSquareTab
Page 191 and 192: t-charts made it easier for student
Page 193 and 194: Figure 2. A Display of Student Stra
Page 195 and 196: ReferencesAnderson, J. R., Greeno,
Page 197 and 198: their parents in phenotype (observa
Page 199 and 200: student learning calls for differen
Page 201 and 202: Figure 2. (A) P3. (B). Extension of
Page 203: the usual phenotypic assessments an
Page 207 and 208: expected to learn and the inquiry a
Page 209 and 210: his partner about his observations,
Page 211 and 212: hard for some children? The nature
Page 213 and 214: Lakoff and Nunez: specifically, tha
Page 215 and 216: Figure 5: Average hand trajectories
Page 217 and 218: Figure 6: Distributions of maximum
Page 219 and 220: ReferencesAnderson, J. R. (2005). H
Page 221 and 222: Social system perspectives view the
Page 223 and 224: urged students to think of some way
Page 225 and 226: Figure 1: The Discourse Patterns Du
Page 227 and 228: Figure 3 blow illustrates the devel
show all

2013 Conference Proceedings - University of Nevada, Las Vegas

Create successful ePaper yourself

Delete template?

Save as template?