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ZNN 320 APPENDIX A PILOT STUDY Section 1: Relationships among figures Part A: Relationships among triangles Int: These cards have been placed into two groups. Can you tell me the way in which the cards have been sorted? (initial question to focus the student within the context of triangles and quadrilaterals) 321 Appendices Int: I would like you to sort them into smaller groups. As you sort them I would like you to explain your reasons for sorting them the way you have chosen. Probes include: Why have you placed these triangles together? Why is this triangle on its own? Is there anything else that you can tell me about the groups? Prompts include: Are there any other ways that the triangles can be sorted? What reasons do you think someone might have for placing the equilateral in with the isosceles? What would you think about doing that? Part B: Relationships among quadrilaterals The format above was repeated with the 6 quadrilateral cards below. Section 2: Relationships among properties Part A: Relationships among triangle properties Int: I would like you to think about all that you know about the equilateral triangle. Tell me all the properties that belong to that figure (these were listed on cards by the interviewer). 322 Appendices Int: I want you to think very carefully now, as I would like you to come up with a description or definition that accurately refers to that shape with the least number of properties needed. Int: Come up with as many combinations as you can. Probes include: Why would your friend need that combination of cards? Why is it possible to remove these cards? Prompts include: What would happen if I removed this card? Would your friend still recognise the triangle? Why? Questions repeated for the right isosceles triangle. Part B: Relationships among quadrilateral properties Format above repeated for the square, rhombus, and parallelogram. 323 Appendices APPENDIX B STUDIES 1 AND 2 INTERVIEW PROFORMA Study 1: Triangles Phase 1: Relationships among triangle figures (i) Int:? I would like you to write a list of all the triangle names you can think of. Begin with acute-angled scalene. Draw each triangle. (ii) Int Design a tree diagram which links the different triangles. Draw a sketch to link each type. (discussion follows concerning the reasons for links and/or lack of links) (the following three points are addressed if required) (iii) Int: There are some triangles that we can add to this list. (provide triangles not recalled) Draw a sketch of each new triangle. (iv) Int: Design a second tree diagram incorporating all the triangles on the list. (discussion follows concerning the reasons for links and/or lack of links) (v) Int: Return now to your first map. I would like you to add the new triangles to your original tree. (discussion follows concerning the reasons for links and/or lack of links) Study 2: Quadrilaterals Phase 1: Relationships among quadrilateral figures (i) Int:? I would like you to write a list of all the quadrilateral names you can think of. Draw each quadrilateral. (ii) Int: Design a tree diagram which links the different quadrilaterals. Draw a sketch to link each type. (discussion follows concerning the reasons for links and/or lack of links) (the following three points are addressed if required) (iii) Int: There are some quadrilaterals that we can add to this list. (provide quadrilaterals not recalled) Draw a sketch of each new quadrilateral. (iv) Int: Design a second tree diagram incorporating all the quadrilaterals on the list. (discussion follows concerning the reasons for links and lack of links) (v) Int: Return now to your first map. I would like you to add the new quadrilaterals to your original tree. (discussion follows concerning the reasons for links and/or lack of links) 324? Appendices Study 1: Triangles Phase 2: Relationships among triangle properties (i) Int: We are going to look closely at a few triangles. I have placed some cards in front of you with triangle characteristics on them. I would like you to begin by choosing the cards which belong to the equilateral triangle (selection made). Look carefully to make sure that you have included all the cards, which belong to that triangle. (ii) Int: Suppose you wanted to leave some clues for a friend. Do you think that your friend would need to see all these properties to know that you are thinking about an equilateral triangle? What combination could you leave? (discussion follows concerning reasons for cards included in the combination and those that have been removed) Do you think it could be made simpler? (discussion follows concerning reason for the simplification and inability to make simpler) (iii) Int: Let's put all the cards back. I would like you to make a different set of clues for your friend. (point (ii) repeated until student has provided all known combinations). (iv) First three steps repeated for the right isosceles triangle. Triangle Characteristic Cards 13 SIDES' 13 ANGLES' 13 SIDES EQUAL 13 ANGLES EQUAL) IHAS RIGHT ANGT .F1 11 AXIS OF SYMMETRY' INO AXES OF SYM1VIEIRYI 13 AXES OF SYMMETRY' IHAS OBTUSE ANGLE' IHAS ACUTE ANGLES' I2ANGLES EQUAL 12 SIDES EQUAL 325 Appendices Study 1: Quadrilaterals Phase 2: Relationships among quadrilateral properties (i) Int: We are going to look closely at a few quadrilaterals. I have placed some cards in front of you with quadrilateral characteristics on them (see below). I would like you to begin by choosing the cards which belong to the square (selection made). Look carefully to make sure that you have included all the cards, which belong to the square. (ii) Int: Suppose you wanted to leave some clues for a friend. Do you think that your friend would need to see all these properties to know that you are thinking about a square? What combination could you leave? (discussion follows concerning reasons for cards included in the combination and those that have been removed) Do you think it could be made simpler? (discussion follows concerning reason for the simplificationand inability to make simpler) (iii) Int: Lets put all the cards back. I would like you to make a different set of clues for your friend. (point (ii) repeated until student has provided all known combinations). (iv) First three steps repeated for parallelogramand rhombus. Quadrilateral Characteristic Cards 14 SIDES I4ANGLESI !ALL SIDES ARE EQUAL 'THERE ARE 4 RIGHT ANGLES) !OPPOSITE SIDES ARE PARALLEL' 'OPPOSITE SIDES ARE EQUAL !DIAGONALS ARE EQUAL 'DIAGONALS BISECT 'DIAGONALS MEET AT RIGHT ANGLES' 'OPPOSITE ANGLES ARE EQUAL 12 PAIR OF EQUAL ADJACENT SIDES' Il PAIR OF OPPOSITE ANGLES EQUAL I4AXES OF SYMMETRY1 I2AXES OF SYMMETRY' Ii AXIS OF SYMMETRY' 11 PAIR OF PARALLEL SIDES' il PAIR OF OPPOSITE SIDES EQUAL 326 APPENDIX C INTERVIEW RESOURCES Student Profile Name: School: Year: Age: Appendices 327 Appendices Study 1 Part 1: List of triangle names and sketches Triangle tree diagram — 1 and 3 321 Appendices Int: I would likeyou to sort them into smaller groups. As you sort them I would likeyou to explain your reasons for sorting them the way you have chosen. Probes include: Why have you placed these triangles together? Why is this triangle on its own? Is there anything else that you can tell me about the groups? Prompts include: Are there any other ways that the triangles can be sorted? What reasons doyou think someone might have for placing the equilateral in with the isosceles? What would you think about doing that? Triangle tree diagram 2 328 Appendices Part B: Relationships among quadrilaterals The format above was repeated with the 6 quadrilateral cards below. Section 2: Relationships among properties Part A:? Relationships among triangle properties nt: I would likeyou to think about all that you know about the equilateral triangle. Tell me all the properties that belong to that figure (these were listed on cards by the interviewer). 329 Appendices Study 2 Part 1: List of quadrilateral names and sketches Quadrilateral tree diagram - 1 and 3 330 Appendices Quadrilateral tree diagram 2 331 Appendices Study 1 Part 2: 3 SIDES Tl 3 ANGLES T2 3 SIDES EQUAL T3 3 ANGLES EQUAL T4 HAS RIGHT ANGLE T5 1 AXIS OF SYMMETRY T6 NO AXES OF SYMMETRY T7 3 AXES OF SYMMETRY T8 HAS OBTUSE ANGLE T9 HAS ACUTE ANGLES T10 2 ANGLES EQUAL Tll 2 SIDES EQUAL T12 332 Appendices Students triangle property choice 1.Equilateral triangle First Choice 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 Minimum Information 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 Made Simpler 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 2.Right isosceles triangle First Choice 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 Minimum Information 1? 2? 3? 4? 5? 6? 7? 8? 9? 10 11? 12 Made Simpler 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 Appendices333 Study 1 Part 2: Quadrilateral property characteristic cards 4 SIDES Ql 4 ANGLES Q2 ALL SIDES ARE EQUAL 03 . THERE ARE 4 RIGHT ANGLES 04 OPPOSITE SIDES ARE PARALLEL Q5 OPPOSITE SIDES ARE EQUAL 06 DIAGONALS ARE EQUAL 07 .. DIAGONALS BISECT Q8 DIAGONALS MEET AT RIGHT ANGLES Q9 OPPOSITE ANGLES ARE EQUAL Q10 2 PAIR OF EQUAL ADJACENT SIDES 011 1 PAIR OF OPPOSITE ANGLES EQUAL Q12 4 AXES OF SYMMETRY Q13 Appendices334 2 AXES OF SYMMETRY Q14 1 AXIS OF SYMMETRY Q15 1 PAIR OF PARALLEL SIDES Q16 1 PAIR OF OPPOSITE SIDES EQUAL 017 335? Appendices Students Quadrilateral Property Choice 1.Square First Choice 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Minimum Information 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Made Simpler 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 2. Parallelogram First Choice 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Minimum Information 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Made Simpler 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 ? 336? Appendices 3. Rhombus First Choice 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Minimum Information 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Made Simpler 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 Other Combination 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12 13? 14? 15? 16? 17 337 ? Appendices APPENDIX D INTRARATER AND INTERRATER RELIABILITY To enable a measurement of the congruity of the system utilised to code students' responses to tasks concerning relationships among figures, and relationships among quadrilaterals, it was necessary to calculate both intrarater and interrater reliability. In an attempt to measure intrarater reliability the consistency the researcher's coding between responses is assessed. Interrater reliability requires a co-marker to utilise the described marking scheme and compare this coding against the principal researcher's coding. This assessment is discussed below. Firstly, intrarater reliability was established through the random selection of one quarter of the students' responses to each of the seven tasks across Years 8-12. The percentage of responses, which were categorised into the same SOLO levels in both the initial codings and subsequent codings, was 96%. Secondly, another researcher who has considerable experience working within the SOLO model over many years then coded the randomly selected sample of one quarter of the responses. For each of the seven tasks, the researcher worked within the described structure of levels for each particular task. The measure of agreement between the principal researcher and the co-marker was 92%. Throughout the coding process, the consistency of the SOLO Model was also established via consultation between researcher and co-marker when rare difficulties occurred with categorisation of particular responses. This was particularly necessary in transitional cases. Overall, the following measures ascertained coding reliability for the SOLO model. 338 Appendices APPENDIX E PLAIN LANGUAGE STATEMENT / CONSENT FORM Dear Parent / Guardian, I am currently completing a Ph. D at the University of New England. As part of this program I am undertaking a study to investigate students' growth and understanding in Geometry. The focus of the study is to be on Years 8 to 12 students in Armidale High Schools. The purpose of this letter is to request your permission to include your son/daughter/ward as a participant in the study. The study, which has the support of the Principal of the school, is designed in such a way that disruption to the normal school process will be minimal. It will consist of each student being interviewed on one occasion for approximately 40 minutes. At a later date each student will also be required to complete some pen and paper tasks. The interviews will be audiotaped for later analysis but there will be complete confidentiality for both students and schools with the use of pseudonyms where necessary. All records will be held within the Centre of Cognitive Research in Learning and Teaching (CRiLT). The title of the project is "An investigation of students' understanding of class inclusion concepts in Geometry." Associate Professor John Pegg from the Department of Curriculum Studies, UNE, will also be involved in the study. Participation by your son/daughter/ward is entirely voluntary and he/she will not be penalised for not wishing to be involved. It is also possible for the participant to withdraw consent and discontinue participation at any time. If you have any concerns or enquiries you can contact me (Ph 73 5073), Assoc. Prof. John Pegg (Ph 73 5070) or the Principal for further information. If you are willing to allow your son/daughter/ward to participate could you please complete the attached consent form and return it to the school. If your son / daugter / ward is selected at random as a participant, a letter will be sent to you before the commencement of interviews. Should you have any complaints concerning the manner in which this research is conducted, please contact the Ethics Committee at the following address: The Secretary Human Research Ethics Committee Research Services University of New England Armidale, NSW 2351 Telephone: (067) 73 2352 Facsimile (067) 73 3543 Yours Faithfully, Penelope Serow Ph. D Student Principal 339 Appendices Student Consent I, (the participant) have read the information concerning the study and any questions I have asked have been answered to my satisfaction. I agree to participate in this activity, realising that I may withdraw at any time. I agree that research data gathered for this study may be published, provided my name is not used. Student Signature Date Parent /Guardian Consent I, (parent/guardian) have read the information concerning the study and any questions I have asked have been answered to my satisfaction. I give permission for my son/daughter/ward to be a participant in this study, realising that my child may withdraw at any time. I agree that research data gathered for this study may be published, provided my child' s name is not used. Parent / Guardian Signature Date Acute angle Obtuse angle II? '‘■ Right angle ' II --\ 340 Appendices APPENDIX F RELATIONSHIPS AMONG TRIANGLES TASK ANALYSIS A student's response concerning the relationships among triangles could include one of three sets of triangle relationships and the reasons for these links. The three sets of relationships, which could be identified and justified, are based on similar features, independent triangle-type classes, and triangle-type classes involving class inclusion. Set 1: Relationships based on similar features There are three types of features upon which students could link triangles, namely, angle types (Figure F.1), side lengths and angle sizes (Figure F.2), and symmetry (Figure F.3). a) Angle Types In Figure F.1 triangles are linked on one of three angle types. A student would select a feature and then link triangles that are seen to contain that feature. Figure F.1 Angle-type triangle classes b) Sides and/or Angles In Figure F.2 the triangles are linked based on the properties associated with equality of sides and/or angles. The alternatives are three sides/angles equal, two sides/angles equal, and no sides/angles equal. Three sides and/or three angles equal. Two sides and/or two angles equal. A No sides and/or no angles equal. 341 Appendices Figure F.2 Relationships based on equality sides and/or angles c) Symmetry In Figure 4.3 the existence of symmetry is the defining feature. Here there are three possibilities, which are three axes of symmetry, one axis of symmetry, and no axes of symmetry. Figure F.3 Relationships based on symmetry Set 2: The establishment of three triangle-type classes, namely, scalene, isosceles, and equilateral (Figure F.4). Set 3: The relationships among the triangle types incorporate the notion of class inclusion (Figure F.5). N I I/ Scalene II? ...X A /Isosceles .„.„,.,.._ A Equilateral 342 Appendices Figure F.4 Triangle type classes In Figure F.4 the triangles are linked based on properties, such as equality of sides/angles, and/or the number of axes of symmetry. These combine to establish an identified and independent class of triangles. Figure F.5 Class inclusion incorporating triangle-type relationships 343 Appendices The equilateral triangle is a subset of the isosceles class of triangles. This relationship exists because the equilateral triangle is seen to include in its list of properties, the properties of an isosceles triangle, i.e., two sides/two angles equal and one axis of symmetry. Overall, the task analysis provides a number of expected outcomes that might be considered plausible possibilities. Of interest is whether students provide these possibilities, whether there is some sequencing of the responses in terms of development, and the nature of the thinking that accompanies the responses. I I-t Two sets of equal sides. I Opposite sides equal I I I I 1? II -1 1 /1 / All sides equal. Adjacent sides equal. 344 Appendices APPENDIX G RELATIONSHIPS AMONG QUADRILATERALS TASK ANALYSIS It is necessary to consider all possible elements of a response addressing the relationships between the six quadrilaterals focused upon in the interview, prior to coding into groups. A response concerning the relationships among quadrilaterals include two sets of relationships and the reasons for these links. These being: Set 1: Relationships based on similar properties In Figures G.1, G.2, G.3, G.4, and G.5, the quadrilaterals are linked based on the properties associated with equality of sides, equality of angles, symmetry, diagonals, and parallelism. a) Sides Figure G.1 Relationships based on side properties. 1 I II 1? II All angles equal / or four right angles. Opposite angles equal. II 1? II 1 I -1 I Four axes of symmetry. /I At least two axes of symmetry / / At least one axis of symmetry. No axes of symmetry. I I 1? II I 1 I II 7? II -1 I I 345 ? Appendices b) Angles Figure G.2 Relationships based on angle properties c) Symmetry Figure G.3 Relationships based on symmetry properties d) Diagonals I II 1? 1 1 Equal diagonals. I I / / ? /1 I Diagonals meet at right angles. Diagonals bisect each other. / / Ii I II 1? I IIi II I I / >> Opposite sides parallel. At least one pair of parallel sides. 346 Appendices Figure G.4 Relationships based on diagonal properties e) Parallelism Figure G.5 Relationships based on parallelism. Set 2:? The establishment of three quadrilateral classes involving subsets with justification for each class based on properties such as sides, angles, symmetry, and diagonals (Figure 5.6). The three classes include; a) Rectangle b) Rhombus c) Parallelogram 347? Appendices Figure G.6 Quadrilateral classes involving subsets 348 Appendices APPENDIX H QUADRILATERAL PROPERTIES TASKS CONTEXTUAL GROUPINGS Student Square Parallelogram Rhombus Scott 3 3 2 Jason 2 2 3 Brendan 1 2 2 Kathy 2 3 3 Louise 3 2 3 Narelle 2 3 3 Peter 2 3 2 Andrew 2 2 3 Arthur 3 2 3 Alice 2 2 3 Megan 3 2 2 Ellen 2 3 2 Nathan 1 2 2 Adam 2 2 2 Allan 1 2 2 Frances 2 2 2 Suzanne 1 2 1 Tracy 2 2 2 Cameron 2 3 3 Michael 2 2 3 David 1 2 2 Beth 1 3 2 Dianne 2 3 2 Jenny 2 3 3 349 Appendices APPENDIX I SOLO RESPONSE CODINGS FOR STUDIES 1, 2, AND 3 ID 1. Tri 2. Quad 3. E • u 4. Isos 5. S • u 6. Para 7. Rhom Scott 101 M2/R2 (CS) M2 (CS) Ul (F) Ul (F) Ul (F) R2 (CS) U2 (CS) Jason 102 R2 cat 1 (CS) M2 (CS) Ul (F) Ul (F) M1 (F) R1 (F) M2 (CS) Kathy Narelle 106 Ri (CS) Ri (CS) M2 (CS) M2 (CS) R2 (CS) R2 (CS) U2 (CS) Arthur 109 U2 cat 1(CS) M2 (CS) M2 (CS) Ul (F) R2 (CS) Ul (F) M2 (CS) Cameron 119 R2 cat 1 (CS) U2 (CS) Ul (F) Ul (F) Mi (F) M1 (F) Ul (F) Michael 120 R2 cat 2 (CS) R2 (CS) Ul (F) M2 (CS) Ml (F) R2 (CS) Ul (F) David 121 R1 (F) R1 (F) Ul (F) Ul (F) U2 (CS) U2 (F) R2 (CS) Jenny Ul (F) Scott 1 Ul (F) Jason 1 U2 (F) Brendan 1 MI (F) Kathy 14 Ul (F) Louise 1 Ul (F) Narelle 206 R1 (F) R2 (CS) M1 (F) U2 (F) M1 (F) Ul (F) M1 (F) Peter 207 R2 (CS) M2 (CS) U1/M1 (F) M2 (CS) M1 (F) Ul (F) MI (F) Andrew 208 M2 (CS) R2 (CS) R1 (F) Ui (F) M1 (F) M1 (F) M1 (F) Arthur 209 R2 (CS) M2/R2 (CS) Ul (F) Ul (F) M1 (F) R1 (CS) Mi (F) Alice EMI Ellen 210 M2 (CS) M2 (CS) U2 (F) U2 (F) M1 (F) Ml (F) R2 (CS) 211 R2 (CS) R2 (CS) M2 (CS) Ul (F) R2 (CS) M2 (CS) Ul (F) 212 M2 (CS) R2 (CS) U1/M1 (F) U2 (CS) R2 (CS) U2 (CS) R2 (CS) 350 Appendices APPENDIX J RASCH ANALYSIS CODING ID 1. Tr i 2.Quad 3.Equ 4.Isos 5.Squ 6.Para 7.Rhom Scott 101 3 3 5 5 5 4 2 Jason 102 4 3 5 5 6 7 3 Brendan 103 3 8 4 3 4 6 6 Kathy 104 4 3 3 4 2 6 3 Louise 105 3 3 4 4 5 5 6 Narelle 106 1 1 3 3 4 4 2 Peter 107 2 3 5 2 5 4 5 Andrew 108 3 3 3 5 4 6 3 Arthur 109 2 3 3 5 4 5 3 Alice 110 3 3 1 3 5 3 6 Megan 111 3 2 6 5 4 4 5 Ellen 112 2 3 1 2 3 4 5 Nathan 113 5 7 3 3 6 7 8 Adam 114 8 7 5 4 6 6 6 Allan 115 4 4 6 5 6 6 4 Frances 116 4 1 3 8 5 3 3 Suzanne 117 3 3 3 3 5 3 5 Tracy 118 2 1 5 5 6 5 4 Cameron 119 4 2 5 5 6 6 5 Michael 120 4 4 5 3 6 4 5 David 121 7 7 5 5 2 8 4 Beth 122 4 3 5 4 5 7 8 Dianne 123 6 4 3 4 4 5 4 Jenny 124 4 4 1 5 3 5 5 Scott 201 4 4 8 6 7 8 5 Jason 202 8 8 8 8 6 8 8 Brendan 203 3 8 8 5 8 8 6 Kathy 204 3 3 5 8 5 5 5 Louise 205 3 4 6 6 6 6 5 Narelle 206 7 4 6 8 6 5 6 Peter 207 4 3 5 3 6 5 6 Andrew 208 3 4 7 5 6 6 6 Arthur 209 4 3 5 5 6 1 6 Alice 210 3 3 8 8 6 6 4 Megan 211 4 4 3 5 4 3 5 Ellen 212 3 4 5 2 4 2 4 Key: 1=R1(CS), 2=U2(CS), 3=M2(CS), 4=R2(CS), 5=U1(F), 6=M1(F), 7=R1(F), 8=U2(F)