2013 Conference Proceedings - University of Nevada, Las Vegas

More documents

Recommendations

Info

While thinking about this problem, the teachers engaged in problem solving that expandedtheir own mathematical knowledge. Even though the CCSSM kindergarten standards state thatstudents “fluently add and subtract within 5” (CCSSI, 2010, p.11), the teachers felt that it wouldbe more robust to explore 10. During their discussion, the question ‘How many ways can wemake 10?’ was raised and as a group they engaged in figuring this out. Although severalremembered studying ‘something like this’, no one readily knew the solution, but all wanted toknow. With some guidance, they explored the patterns found with addition by exploring ‘Howmany ways can 1 be made?’ (One way: 1), ‘How many ways can 2 be made?’ (Two ways: 1+1,2), ‘How many ways can 3 be made?’ (Four ways: 1+1+1, 1+2, 2+1, 3), etc., and were pleasedwith their problem solving abilities to arrive at a solution. They also realized that the largenumber of possible ways might make the problem more accessible for their students.Phase 3 - Developing and planning a research lessonPhase 3 was designed so teachers would prepare lessons, research how the lessons workedwith children, and reflect on the experience. Teachers engaged in the typical Lesson Studyprocess involving (1) defining an instructional problem, (2) researching the problem andbrainstorming possible lessons that could speak to the issues, (3) anticipating possible studentmisconceptions that might occur, and (4) then, planning the lesson. While step (2) is oftenviewed as the most crucial, all steps should occur before the lesson is taught. This was importantbecause the research and deep thinking the teachers did before the teaching gave them ownershipof a lesson they planned and prepared to teach. In planning the research lesson, teachers used theresearch evidence they collected to prepare the lesson. When preparing the lesson they used aformat with three columns (Figure 1). In the first column they listed the planned sequence ofevents that would occur as the lesson unfolded, including key questions to ask and the rationalefor asking them. In the second column, they listed reactions and responses they anticipatedstudents would make. These responses were based on evidence they found in research as well asfrom their prior teaching experiences. Column 3 had suggestions for how the teacher couldrespond to the anticipated responses. The third column was also used to record student responsesand to think about how to use these responses when conducting whole class discussion.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 103
Kindergarten Lesson FormatHow May Ways Can you Make 10?Steps of the lesson: Learningactivities and key questionswith rationale (timeallocation)Anticipated student reactionsor responsesTeacher responses to studentreactions. Things toremember.Figure 1. Format used for preparing lessonStudying the LessonTo maximize the opportunity to study and reflect on the lesson while at the same timecausing the least disruption for the teachers and students, the following process was used: oneteacher taught the lesson while all others observed; this teacher led a debriefing session thatoccurred immediately after the lesson was taught; if deemed necessary, minor suggestions foradjusting the lesson were made; a second teacher taught the same lesson; and that second teacherled the next debriefing session. While not a part of the study sequence involving observers anddebriefing, the other three kindergarten teachers later taught the same research lesson.The goal of the research lesson, How many ways can you make 10?, was to develop a child’ssense for “ten-ness” which the teachers knew would support later work with numbers between 10and 20. As they brainstormed how to provide a context for their students, they realized they hada significant amount of scrip remaining from the school’s family fair. They created a story forthe students about how a collection of 10 scrip could be exchanged for an “ice pop” treat leftover from the fair, and prepared curriculum materials to deliver their lesson.For the lesson, students were provided containers of scrip with multiple lengths of 1, 2, 3, or4 scrip per container and asked to make a collection of 10 using anycombination of scrip they wanted. When students were sure theyhad 10 scrip, they were to glue the scrip on a strip of constructionpaper. Students were given enough time to make one set of 10 andencouraged to make more collections if they could. This task wasaccessible to all students, and the variety of responses wasinteresting, but more interesting was the discussion in which theteachers engaged the children. Samples of student work are inFigure 2Figures 2 – 4.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 104
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: dynamic approach to learning conten
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 and 204:
the usual phenotypic assessments an
Page 205 and 206:
teachers is the discrepancy between
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?