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Here s How& 63 Richelle (Rikki) Blair Lakeland Community College Kirtland, Ohio Email: rblair@ncweb.com AMATYC Annual Conference Phoenix, AZ November, 2002 (C5  0JZ@Agenda:Introduction Research - Learning and Algebra Looking at Classroom Activities Discussion What makes a good activity? YOUR Classroom Reflection |[d [   $ F11:00-11:20 11:20-11:35 11:35-11:50 11:50-11:55 11:55-Noon>G)  AClassroom Goals:  Achieve these goals in a student-centered classroom: Greater academic achievement (content). Favorable attitudes toward learning and mathematics. Increased persistence in mathematics courses. ZZZ(ZZ5ZZ.ZZ _ .f"6Variables Contributing to Student Academic Achievement g#2Matching Learning and Teaching Styles (4 Clusters)$3% h%%Matching Learning and Teaching Stylesi&What can faculty do?The problem is not that faculty/student styles are mismatched. The failure to work out potential conflicts and misunderstandings undermine student learning. Helping students become aware of their learning styles can be empowering and assist in stretching their capabilities.J?ZZ^ZZvZ]#MEANINGFUL LEARNING (UNDERSTANDING)$$ /To UNDERSTAND something means to assimilate it into an appropriate schema. Meaningful learning is learning in which students are actively involved in integrating, or linking, new concepts and skills into an already existing conceptual framework, not simply accumulating isolated facts and procedures.BMddd0"^(MEANINGFUL LEARNING&  is characterized by evidence that the learner: claims to have learned something new; can articulate what it is they think they have learned, with some degree of clarity and accuracy; can demonstrate formation of links with an existing framework that the learner already possesses; has experienced a change from insecurity to confidence. Clarke, D., Helme, S., and Kessel, C. (1996) j/#5/"%b#"3"  EHow People LearnNew developments in the science of learning emphasize the importance of helping people take control of their own learning. All new learning involves transfer based on previous learning. (page 41) Bransford, Brown, and Cocking (eds). How People Learn  Brain, Mind, Experience, and School. National Academy Press, Washington, DC, 1999, www.nap.edu.{ZZZ4ZZ%   % 6  < F How People Learn3Active student learning activities shown to increase the degree to which students transfer learning to new settings. Teachers must draw out and work with pre-existing understandings that students bring with them. (Bransford, page 19) Social opportunities positively affect motivation. (Bransford, page 49)uuHu_  2$ N8Connecting Knowledge: Memorize each list in 10 seconds:$9!$EHT ATC NRA OERV HTE GDO.$ The Cat Ran Over The Dog.$R Reflection:If new information doesn t connect to current knowledge, the concepts roll off like water off a duck s back. :8r[JSources of Student Difficulty in Transitioning from Arithmetic to Algebra: bZZZZZZZX-Research-Based Algebra: Student Difficulties8Recognizing the  = symbol as an equivalence relation, rather than an instruction  to get an answer. Understanding multiple uses of variables: To represent unknowns; As objects to show relationships between quantities; As arbitrary objects in an algebraic structure; To describe patterns and create equations. Kieran, C. (1992). The Learning and Teaching of School Algebra. In Grouws, D.A. (ed). Handbook of Research on the Mathematics Teaching and Learning (pp. 390-419). Reston, VA: National Council of Teachers of Mathematics.fZZ*ZZZg*^ = I d Looking at Classroom ActivitiesFind the other attendees with the same playing card. Introduce yourselves. Review the 4 Classroom Activities in your group (about 2-3 minutes per activity). Rate the activities on a scale from 1 to 5 (5 = excellent)._.Rating Classroom Activities: (5= Excellent)$/ ZSymbols and Notations What IS Algebra anyway? Interpreting Graphs Which Answer is Correct? =1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 DClassroom ActivitiesO What makes a classroom activity successful? When would a lecture be better?4, Pc What is CL?Cooperative Learning  structured systematic instructional strategy in which groups work toward a common goal.o[ (Collaborative Learning  unstructured process in which participants define problems, develop procedures, and produce socially constructed knowledge.e! In reality:dMost small group learning activities are a mix of cooperative and collaborative learning activities.J Why use CL in Mathematics?Meta-analysis of research on 39 undergraduate science, mathematics, engineering, and technology courses demonstrated: Greater academic achievement, More favorable attitudes towards learning, Increased persistence Compared with traditionally taught counterparts. Springer, Stanne, Donovan.  Effects of Small-Group Learning on Undergraduates in Science, Mathematics, Engineering, and Technology: A Meta-Analysis. Review of Educational Research, Spring 1999, Vol. 69, No. 1, pp.21-51.v_3v_  3      )  K Why use CL in Mathematics?Results of meta-analysis showed positive effects of small-group learning significantly greater for members of underrepresented groups (women, African Americans, and Latinos). (Springer, page 40)JZUZ) L Why use CL in Mathematics?zThe learning process requires some sort of cognitive restructuring, or elaboration, of material. One of the most effective means of elaboration is explaining the material to someone else. Some theorists believe that too much structure on a task involving higher-order thinking skills is dysfunctional because it impedes conceptually oriented interactions. (Springer, page 25)a[` [ U Reflection:kReflection is a key element to learning. Kemp, R. Psychology of Learning Mathematics. N)ZCZ+$  "  I .How can you make your classroom an active one?Short classroom activities that engage students: Pre-planned activities Textbook problems Discussion problems Use timing tools. Plan in advance. Seize the teaching moment.P1=>1=> M(When should we use classroom activities?6When they make sense. Be sure to consider differences in students learning styles. Open the door to student opportunities to communicate mathematically.>>FO Reflection:It s hard to change. No one wants change except a wet baby. (, ,S Reflection:tWhat idea would you like to remember from today s session?\Thank you for attending.wPlease complete the blue Evaluation and Reflection form and the AMATYC Evaluation Form. Leave both with the presider._x`Strengths and Weaknesses:ZSymbols and Notations What IS Algebra anyway? Interpreting Graphs Which Answer is Correct?  /QVjklmnopq r s t u v ` 33PP` 3333` ___MMM` 13` 333fpKNāvI` j@v۩ῑ΂H` Q_{>?" dd@,?n<d@ `7 `2@`7``2 n?" dd@   @@``PR    @ ` ` p>>     (    <u") @   TPyd"z) @   <||" @   T~d"] @   Nԁ"<E# @   <"@hw @   C x쇸?d?" @   64 "   T Click to edit Master title style! !$  0\ "/  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     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Bradenton, FL: Academic Success Press, Inc., page 20.i 2i  ` C ArC:\My Documents\Presentations\Variables Stud Achieve.jpgI H ` 0޽h ? 3333   xpd(  dr d S dJ    J n T d #"& op=@T  )d Z|J ??T z2Role Modeling Sharing Experiences Teacher Coaching33 @`  (d ZdPH ??T y1Lectures Exams/Grades Emphasized Teacher Centered22 @` %d ZH ??R [Teaching Methods: @` $d Zп ??R [Teaching Methods: @`* #d ZPJ ?? R 6Teaching Style: Personal Model Expert Formal Authority0'' @` "d ZJ ?? R 'Teaching Style: Expert Formal Authority0 @`% !d ZJ ??  1Learning Style: Participant Dependent Competitive0"" @`%  d ZJ ??  1Learning Style: Dependent Participant Competitive0"" @` d ZhJ ?? Q Cluster 2   @` d ZO ?? Q Cluster 1   @`B *d Zo??B 0d Zo??TTB 1d Zo??B 2d T1 ??TB 3d Zo??B Rd Zo??B Sd Zo?? B Ud Zo?? B Wd Zo?? RB Zd Zo?? RB \d Zo??RB _d Zo??RB ad Zo??TB dd Zo??TB fd Zo??TTB md T1 ??  B qd T1 ?? {d T O ??f0` Grasha, A.F. (1996). Teaching with style: A practical guide to enhancing learning& , Pittsburgh: Alliance Publishers.u 2u H d 0޽h ? 3333h   8p(  px p c $hO    O n [ 8p #"& op^@[ p Z'H ??[ >Independent Study Practicum Small Group Teams Student Journals?? @` p Zd$O ??[ =Case Studies Laboratory Projects Open Discussions Simulations>> @` p Z-O ??R [Teaching Methods: @` p Zt/O ??R [Teaching Methods: @`B p Z7O ?? R ,Teaching Style: Delegator Facilitator Expert0  @`%  p ZHO ?? R 1Teaching Style: Facilitator Personal Model Expert0"" @`+  p Z4RO ??  7Learning Style: Independent Collaborative Participant0(( @`)  p Z[O ??  5Learning Style: Collaborative Participant Independent0&& @`  p Z8eO ?? Q Cluster 4   @`  p ZfO ?? Q Cluster 3   @`B p Zo??B p Zo??[[B p Zo??B p T1 ??[B p Zo??B p Zo??B p Zo?? B p Zo?? B p Zo?? RB p Zo?? RB p Zo??RB p Zo??RB p Zo??[B p Zo??[B p Zo??[[B p T1 ??  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Blairic108Microsoft PowerPointoso@ g@@%f@oq G!g   .& &&#TNPP2OMi & TNPP &&TNPP    - "-- !-- "-&U&dO33--- !B"e---&5dO&--ZZ- $5d?d?5- $?dIdI?- $IdOdOI---&&&&![--- !B!!---&>[&--F- $>HH>- $HRRH- $R[[R---&&&&,&--&&- $ - $ - $- $(- $(2- $2<cc- $<F==- $F$P- $P$,X $X,,X&&& "- & $,,&Kttb&-&& &&-&&-&&- $ - $ - $- $(- $(2- $2<cc- $<F==- $F$P- $P$,X $X,,X&- --&&--- !U2---&&--- $##!!!- $#--#%%%- $-77-)))- $7AA7,,,- $AKKA000- $KUUK444- $U__U888- $_ii_<<<- $issi@@@- $s}}sEEE- $}}JJJ- $MMM- $RRR- $WWW- $\\\- $```- $eee- $jjj- $nnn- $sss- $xxx- $~~~- $- $  - $  - $- $''- $'11'- $1;;1- $;EE;- $EOOE- $OYYO- $YccY- $cmmc- $mwwm- $ww- $- $- $- $- $- $- $- $- $- $- $- $- $- $  - $  - $!!- $!++!- $+55+- $5??5- $?II?- $ISSI- $S]]S- $]gg]- $gqqg- $q{{q- ${{- $- $- $ $- $ $- $---&&&--N-- - @"Tahoma- 33. 2 XYOU"*'. 33"--Y-33-  33X 33.2 Can Have a #!(. 33.2 XDynamic Algebra (!2 # !!. 33.2 IX Classroom.#  2. 33.2 X Heres How( ( ,0.--e l- - 33@"Tahoma-  .(2 x Richelle (Rikki) Blair       . ..2 Lakeland Community College       . .2 (Kirtland, Ohio    .@"Tahoma-  .2 Email:  . .2 9rblair@ncweb.com     . "- -:@"Tahoma- .+2 AMATYC Annual Conference    . .2 5> Phoenix, AZ   . .2 L-November, 2002    .--  "System-&TNPP &0DTimes New Roman9bb0bWo 0@DSymbolew Roman9bb0bWo 0 a.  @n?" dd@  @@``   @FL FG       #$## #   " "&# !$9'% %&'()*+,-./0123456789:;<=>?@h2$pH$l9\s_2$(vt{|!n.;+$2$Y]Dse8)2$ب ֌{ 8a2$ɦ{y  #E&2$ 98(?.k2$?3iIuI32$N'7<62$A 0UٹMtv.E@$2$v#G4^4"n_$2$.7ESnu|^McR$^)֗-MzV}g 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@89 :  uʚ;2Nʚ;g4*d*d0brp@ pp<4!d!d 0b:b<4dddd 0b:b<4BdBd 0b:bg4*d*d0bTpp pp___PPT9zr2? -O =4TjYOU Can Have a Dynamic Algebra Classroom. Here s How& 63 Richelle (Rikki) Blair Lakeland Community College Kirtland, Ohio Email: rblair@ncweb.com AMATYC Annual Conference Phoenix, AZ November, 2002 (C5  0JZ@Agenda:Introduction Research - Learning and Algebra Looking at Classroom Activities Discussion What makes a good activity? YOUR Classroom Reflection |[d [   $ F11:00-11:20 11:20-11:35 11:35-11:50 11:50-11:55 11:55-Noon>G)  AClassroom Goals:  Achieve these goals in a student-centered classroom: Greater academic achievement (content). Favorable attitudes toward learning and mathematics. Increased persistence in mathematics courses. ZZZ(ZZ5ZZ.ZZ _ .f"6Variables Contributing to Student Academic Achievement g#2Matching Learning and Teaching Styles (4 Clusters)$3% h%%Matching Learning and Teaching Stylesi&What can faculty do?The problem is not that faculty/student styles are mismatched. The failure to work out potential conflicts and misunderstandings undermine student learning. Helping students become aware of their learning styles can be empowering and assist in stretching their capabilities.J?ZZ^ZZvZ]#MEANINGFUL LEARNING (UNDERSTANDING)$$ /To UNDERSTAND something means to assimilate it into an appropriate schema. Meaningful learning is learning in which students are actively involved in integrating, or linking, new concepts and skills into an already existing conceptual framework, not simply accumulating isolated facts and procedures.BMddd0"^(MEANINGFUL LEARNING&  is characterized by evidence that the learner: claims to have learned something new; can articulate what it is they think they have learned, with some degree of clarity and accuracy; can demonstrate formation of links with an existing framework that the learner already possesses; has experienced a change from insecurity to confidence. Clarke, D., Helme, S., and Kessel, C. (1996) j/#5/"%b#"3"  EHow People LearnNew developments in the science of learning emphasize the importance of helping people take control of their own learning. All new learning involves transfer based on previous learning. (page 41) Bransford, Brown, and Cocking (eds). How People Learn  Brain, Mind, Experience, and School. National Acade  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~1Root EntrydO)oq-@PicturesxCurrent UserSSummaryInformation(|#PowerPoint Document(=DocumentSummaryInformation8bWo 0"DTahomaew Ro<b9bb0bWo 0" DWingdingsRo<b9bb0bWo 00DTimes New Roman9bb0bWo 0@DSymbolew Roman9bb0bWo 0 a.  @n?" dd@  @@``  x ?FL FG       #$## #   " "&# !$9'% %&'()*+,-./0123456789:;<=>?h2$pH$l9\s_2$(vt{|!n.;+$2$Y]Dse8)2$ب ֌{ 8a2$ɦ{y  #E&2$ 98(?.k2$?3iIuI32$N'7<62$A 0UٹMtv.E@$2$v#G4^4"n_$2$.7ESnu|^McR$^)֗-MzV}g 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@89 :  uʚ;2Nʚ;g4*d*d0brp@ pp<4!d!d 0b:b<4dddd 0b:b<4BdBd 0b:bg4+d+d0blp@ pp___PPT9zr2? -O =4TjYOU Can Have a Dynamic Algebra Classroom. Here s How& 63 Richelle (Rikki) Blair Lakeland Community College Kirtland, Ohio Email: rblair@ncweb.com AMATYC Annual Conference Phoenix, AZ November, 2002 (C5  0JZ@Agenda:Introduction Research - Learning and Algebra Looking at Classroom Activities Discussion What makes a good activity? YOUR Classroom Reflection |[d [   $ F11:00-11:20 11:20-11:35 11:35-11:50 11:50-11:55 11:55-Noon>G)  AClassroom Goals:  Achieve these goals in a student-centered classroom: Greater academic achievement (content). Favorable attitudes toward learning and mathematics. Increased persistence in mathematics courses. ZZZ(ZZ5ZZ.ZZ _ .f"6Variables Contributing to Student Academic Achievement g#2Matching Learning and Teaching Styles (4 Clusters)$3% h%%Matching Learning and Teaching Stylesi&What can faculty do?The problem is not that faculty/student styles are mismatched. The failure to work out potential conflicts and misunderstandings undermine student learning. Helping students become aware of their learning styles can be empowering and assist in stretching their capabilities.J?ZZ^ZZvZ]#MEANINGFUL LEARNING (UNDERSTANDING)$$ /To UNDERSTAND something means to assimilate it into an appropriate schema. Meaningful learning is learning in which students are actively involved in integrating, or linking, new concepts and skills into an already existing conceptual framework, not simply accumulating isolated facts and procedures.BMddd0"^(MEANINGFUL LEARNING&  is characterized by evidence that the learner: claims to have learned something new; can articulate what it is they think they have learned, with some degree of clarity and accuracy; can demonstrate formation of links with an existing framework that the learner already possesses; has experienced a change from insecurity to confidence. Clarke, D., Helme, S., and Kessel, C. (1996) j/#5/"%b#"3"  EHow People LearnNew developments in the science of learning emphasize the importance of helping people take control of their own learning. All new learning involves transfer based on previous learning. (page 41) Bransford, Brown, and Cocking (eds). How People Learn  Brain, Mind, Experience, and School. National Academy Press, Washington, DC, 1999, www.nap.edu.{ZZZ4ZZ%   % 6  < F How People Learn3Active student learning activities shown to increase the degree to which students transfer learning to new settings. Teachers must draw out and work with pre-existing understandings that students bring with them. (Bransford, page 19) Social opportunities positively affect motivation. (Bransford, page 49)uuHu_  2$ N8Connecting Knowledge: Memorize each list in 10 seconds:$9!$EHT ATC NRA OERV HTE GDO.$ The Cat Ran Over The Dog.$R Reflection:If new information doesn t connect to current knowledge, the concepts roll off like water off a duck s back. :8r[JSources of Student Difficulty in Transitioning from Arithmetic to Algebra: bZZZZZZZX-Research-Based Algebra: Student Difficulties8Recognizing the  = symbol as an equivalence relation, rather than an instruction  to get an answer. Understanding multiple uses of variables: To represent unknowns; As objects to show relationships between quantities; As arbitrary objects in an algebraic structure; To describe patterns and create equations. Kieran, C. (1992). The Learning and Teaching of School Algebra. In Grouws, D.A. (ed). Handbook of Research on the Mathematics Teaching and Learning (pp. 390-419). Reston, VA: National Council of Teachers of Mathematics.fZZ*ZZZg*^ = I d Looking at Classroom ActivitiesFind the other attendees with the same playing card. Introduce yourselves. Review the 4 Classroom Activities in your group (about 2-3 minutes per activity). Rate the activities on a scale from 1 to 5 (5 = excellent)._.Rating Classroom Activities: (5= Excellent)$/ ZSymbols and Notations What IS Algebra anyway? Interpreting Graphs Which Answer is Correct? =1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 DClassroom A      !"#$%&'()*+./023456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~ctivitiesO What makes a classroom activity successful? When would a lecture be better?4, Pc What is CL?Cooperative Learning  structured systematic instructional strategy in which groups work toward a common goal.o[ (Collaborative Learning  unstructured process in which participants define problems, develop procedures, and produce socially constructed knowledge.e! In reality:dMost small group learning activities are a mix of cooperative and collaborative learning activities.J Why use CL in Mathematics?Meta-analysis of research on 39 undergraduate science, mathematics, engineering, and technology courses demonstrated: Greater academic achievement, More favorable attitudes towards learning, Increased persistence Compared with traditionally taught counterparts. Springer, Stanne, Donovan.  Effects of Small-Group Learning on Undergraduates in Science, Mathematics, Engineering, and Technology: A Meta-Analysis. Review of Educational Research, Spring 1999, Vol. 69, No. 1, pp.21-51.v_3v_  3      )  K Why use CL in Mathematics?Results of meta-analysis showed positive effects of small-group learning significantly greater for members of underrepresented groups (women, African Americans, and Latinos). (Springer, page 40)JZUZ) L Why use CL in Mathematics?zThe learning process requires some sort of cognitive restructuring, or elaboration, of material. One of the most effective means of elaboration is explaining the material to someone else. Some theorists believe that too much structure on a task involving higher-order thinking skills is dysfunctional because it impedes conceptually oriented interactions. (Springer, page 25)a[` [ U Reflection:kReflection is a key element to learning. Kemp, R. Psychology of Learning Mathematics. N)ZCZ+$  "  I .How can you make your classroom an active one?Short classroom activities that engage students: Pre-planned activities Textbook problems Discussion problems Use timing tools. Plan in advance. Seize the teaching moment.P1=>1=> M(When should we use classroom activities?6When they make sense. Be sure to consider differences in students learning styles. Open the door to student opportunities to communicate mathematically.>>FO Reflection:It s hard to change. No one wants change except a wet baby. (, ,S Reflection:tWhat idea would you like to remember from today s session?\Thank you for attending.wPlease complete the blue Evaluation and Reflection form and the AMATYC Evaluation Form. Leave both with the presider._x`Strengths and Weaknesses:ZSymbols and Notations What IS Algebra anyway? Interpreting Graphs Which Answer is Correct?  /,QVjklmnopq r s t u vwxyz{|}~    T$(  Tr T S 4O    O r T S O / O H T 0޽h ? 3333^   00(  0r 0 S O    O r 0 S O /+  O r 0 S dO   O H 0 0޽h ? 3333p    @(  r  S O    O r  S ؘO /  O   S ZH   O  H  0޽h ? 3333p    PP(  Px P c $ܤO    O x P c $O  O x P c $TO   O H P 0޽h ? 3333   `\(  \x \ c $O    O ~ \ s *O /  O  \ C A C:\Program Files\Common Files\Microsoft Shared\Clipart\cagcat50\PE01561_.wmf0H \ 0޽h ? 3333   p$(  r  S  0 (  X  C F   L  S L @  L `Use what we know from research to help us present mathematical concepts and design lesson plans.aaH  0޽h ? ̙33  0  (  X  C F   L  S L @  L  H  0޽h ? ̙33 0 0(  X  C F   L  S L @  L  H  0޽h ? ̙33 0 @(  X  C F   L  S L @  L  H  0޽h ? ̙33 0 P(  X  C F   L  S 0L @  L  H  0޽h ? ̙33! 0 `(  X  C F     S D @    H  0޽h ? ̙33  0 p(  X  C F     S  @    H  0޽h ? ̙33  0 (  X  C F     S \ @    H  0޽h ? ̙33  0 (  X  C F     S  @    H  0޽h ? ̙33 0 (  X  C F     S x @    H  0޽h ? ̙33  0 (  X  C F   H  S  H 4 rblair@ncweb.comJ/ 0|DArialew Ro<b9bb0bWo 0"DTahomaew Ro<b9bb0bWo 0" DWingdingsRo<b9bb0bWo 0 Z՜.+,D՜.+,    jOn-screen ShowhomereeF $ArialTahoma WingdingsTimes New RomanSymbolBlends6YOU Can Have a Dynamic Algebra Classroom. Heres HowAgenda:Classroom Goals: 7Variables Contributing to Student Academic Achievement3Matching Learning and Teaching Styles (4 Clusters)&Matching Learning and Teaching StylesWhat can faculty do?$MEANINGFUL LEARNING (UNDERSTANDING)MEANINGFUL LEARNING isHow People Learn How People Learn9Connecting Knowledge: Memorize each list in 10 seconds: Reflection:KSources of Student Difficulty in Transitioning from Arithmetic to Algebra:.Research-Based Algebra: Student Difficulties Looking at Classroom Activities/Rating Classroom Activities: (5= Excellent)Classroom Activities What is CL? In reality:Why use CL in Mathematics?Why use CL in Mathematics?Why use CL in Mathematics? Reflection:/How can you make your classroom an active one?)When should we use classroom activities? Reflection: Reflection:Thank you for attending.Strengths and Weaknesses:  Fonts UsedDesign Template Slide Titles 8@ _PID_HLINKSAhmailto:rblair@ncweb.com)_bRichelle M. BlairRichelle M. Blairmy Press, Washington, DC, 1999, www.nap.edu.{ZZZ4ZZ%   % 6  < F How People Learn3Active student learning activities shown to increase the degree to which students transfer learning to new settings. Teachers must draw out and work with pre-existing understandings that students bring with them. (Bransford, page 19) Social opportunities positively affect motivation. (Bransford, page 49)uuHu_  2$ N8Connecting Knowledge: Memorize each list in 10 seconds:$9!$EHT ATC NRA OERV HTE GDO.$ The Cat Ran Over The Dog.$R Reflection:If new information doesn t connect to current knowledge, the concepts roll off like water off a duck s back. :8r[JSources of Student Difficulty in Transitioning from Arithmetic to Algebra: bZZZZZZZX-Research-Based Algebra: Student Difficulties8Recognizing the  = symbol as an equivalence relation, rather than an instruction  to get an answer. Understanding multiple uses of variables: To represent unknowns; As objects to show relationships between quantities; As arbitrary objects in an algebraic structure; To describe patterns and create equations. Kieran, C. (1992). The Learning and Teaching of School Algebra. In Grouws, D.A. (ed). Handbook of Research on the Mathematics Teaching and Learning (pp. 390-419). Reston, VA: National Council of Teachers of Mathematics.fZZ*ZZZg*^ = I d Looking at Classroom ActivitiesFind the other attendees with the same playing card. Introduce yourselves. Review the 4 Classroom Activities in your group (about 2-3 minutes per activity). Rate the activities on a scale from 1 to 5 (5 = excellent)._.Rating Classroom Activities: (5= Excellent)$/ ZSymbols and Notations What IS Algebra anyway? Interpreting Graphs Which Answer is Correct? =1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 DClassroom ActivitiesO What makes a classroom activity successful? When would a lecture be better?4, Pc What is CL?Cooperative Learning  structured systematic instructional strategy in which groups work toward a common goal.o[ (Collaborative Learning  unstructured process in which participants define problems, develop procedures, and produce socially constructed knowledge.e! In reality:dMost small group learning activities are a mix of cooperative and collaborative learning activities.J Why use CL in Mathematics?Meta-analysis of research on 39 undergraduate science, mathematics, engineering, and technology courses demonstrated: Greater academic achievement, More favorable attitudes towards learning, Increased persistence Compared with traditionally taught counterparts. Springer, Stanne, Donovan.  Effects of Small-Group Learning on Undergraduates in Science, Mathematics, Engineering, and Technology: A Meta-Analysis. Review of Educational Research, Spring 1999, Vol. 69, No. 1, pp.21-51.v_3v_  3      )  K Why use CL in Mathematics?Results of meta-analysis showed positive effects of small-group learning significantly greater for members of underrepresented groups (women, African Americans, and Latinos). (Springer, page 40)JZUZ) L Why use CL in Mathematics?zThe learning process requires some sort of cognitive restructuring, or elaboration, of material. One of the most effective means of elaboration is explaining the material to someone else. Some theorists believe that too much structure on a task involving higher-order thinking skills is dysfunctional because it impedes conceptually oriented interactions. (Springer, page 25)a[` [ U Reflection:kReflection is a key element to learning. Kemp, R. Psychology of Learning Mathematics. N)ZCZ+$  "  I .How can you make your classroom an active one?Short classroom activities that engage students: Pre-planned activities Textbook problems Discussion problems Use timing tools. Plan in advance. Seize the teaching moment.P1=>1=> M(When should we use classroom activities?6When they make sense. Be sure to consider differences in students learning styles. Open the door to student opportunities to communicate mathematically.>>FO Reflection:It s hard to change. No one wants change except a wet baby. (, ,S Reflection:tWhat idea would you like to remember from today s session?\Thank you for attending.wPlease complete the blue Evaluation and Reflection form and the AMATYC Evaluation Form. Leave both with the presider._x`Strengths and Weaknesses:ZSymbols and Notations What IS Algebra anyway? Interpreting Graphs Which Answer is Correct?  /,QVjklmnopq r s t u vwxyz{|}~ 0 B: (    0l&M P%  M B*   0l  % M D* d  c $ ?9 K  M  0  @) M RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  6 P   B*   6h    D* H  0޽h ? ̙33 H(    0 P%   B*   0\  %  D*   6J P   B*   6 ʸ   O D* H  0޽h ? ̙33N   `(  `r ` S 0J    J " ` T̺J ?? @ hNolting, P.D. (1998). Math Study Skills Workbook. Bradenton, FL: Academic Success Press, Inc., page 20.i 2i  ` C ArC:\My Documents\Presentations\Variables Stud Achieve.jpg@H ` 0޽h ? 3333   xpd(  dr d S dJ    J n T d #"& op=@T  )d Z|J ??T z2Role Modeling Sharing Experiences Teacher Coaching33 @`  (d ZdPH ??T y1Lectures Exams/Grades Emphasized Teacher Centered22 @` %d ZH ??R [Teaching Methods: @` $d Zп ??R [Teaching Methods: @`* #d ZPJ ?? R 6Teaching Style: Personal Model Expert Formal Authority0'' @` "d ZJ ?? R 'Teaching Style: Expert Formal Authority0 @`% !d ZJ ??  1Learning Style: Participant Dependent Competitive0"" @`%  d ZJ ??  1Learning Style: Dependent Participant Competitive0"" @` d ZhJ ?? Q Cluster 2   @` d ZO ?? Q Cluster 1   @`B *d Zo??B 0d Zo??TTB 1d Zo??B 2d T1 ??TB 3d Zo??B Rd Zo??B Sd Zo?? B Ud Zo?? B Wd Zo?? RB Zd Zo?? RB \d Zo??RB _d Zo??RB ad Zo??TB dd Zo??TB fd Zo??TTB md T1 ??  B qd T1 ?? {d T O ??f0` Grasha, A.F. (1996). Teaching with style: A practical guide to enhancing learning& , Pittsburgh: Alliance Publishers.u 2u H d 0޽h ? 3333h   8p(  px p c $hO    O n [ 8p #"& op^@[ p Z'H ??[ >Independent Study Practicum Small Group Teams Student Journals?? @` p Zd$O ??[ =Case Studies Laboratory Projects Open Discussions Simulations>> @` p Z-O ??R [Teaching Methods: @` p Zt/O ??R [Teaching Methods: @`B p Z7O ?? R ,Teaching Style: Delegator Facilitator Expert0  @`%  p ZHO ?? R 1Teaching Style: Facilitator Personal Model Expert0"" @`+  p Z4RO ??  7Learning Style: Independent Collaborative Participant0(( @`)  p Z[O ??  5Learning Style: Collaborative Participant Independent0&& @`  p Z8eO ?? Q Cluster 4   @`  p ZfO ?? Q Cluster 3   @`B p Zo??B p Zo??[[B p Zo??B p T1 ??[B p Zo??B p Zo??B p Zo?? B p Zo?? B p Zo?? RB p Zo?? RB p Zo??RB p Zo??RB p Zo??[B p Zo??[B p Zo??[[B p T1 ??  B p T1 ??H p 0޽h ? 3333 0 0B(  ^  S 9 K   O  c $HFJ @)  O 8Emphasize the need to help our students MAKE the cognitive CONNECTIONS of new mathematics concepts to old ones& To make them stick!H  0޽h ? ̙33 0 @((  ^  S 9 K   H  c $H @)  H  H  0޽h ? ̙33| 0 <4P(  ^  S 9 K   M.  c $P M @)  M Model and active classroom, using tools, like playing cards, a timer, and horn. Review Research  quickly to leave time to talk together I even set the timer on myself! Look at activities, etc& .. H  0޽h ? ̙33+ 0 `{(  ^  S 9 K   L  c $JL @)  L qADo you agree that these are worthy goals and ones that you share?BBH  0޽h ? ̙33" 0 p (  ^  S 9 K   M  c $BM @)  M What we do in the classroom DOES matter& Helping students feel comfortable and open to learning is also important.ttH  0޽h ? ̙33# 0 H(  ^  S 9 K   L  c $-L @)  L >There are many ways to look at Learning Styles and Teaching Styles. (526,000 hits on a web search) Grasha clustered them in these four groups. Along with a matching Teaching Style and appropriate Teaching Methods.,E!mH  0޽h ? ̙33% 0 ((  ^  S 9 K   L  c $bL @)  L  H  0޽h ? ̙33\& 0 (  ^  S 9 K   L  c $ tL @)  L POur job is to help the student understand themselves& make sure we understand our own strengths and weaknesses& and be flexible enough to adapt to a given situation.6rH  0޽h ? ̙33v 0 6.(  ^  S 9 K   L(  c $ȡL @)  L To accomplish our goals, we need to know what Meaningful Learning is& .GGH  0޽h ? ̙33 0 (  ^  S 9 K   L  c $Recent research tells us that& &  H  0޽h ? ̙33t 0 4,(  ^  S 9 K   L&  c $L @)  L Cover right half& . Take 15 seconds to memorize& Uncover right half.FFH  0޽h ? ̙33 0 ((  ^  S 9 K   L  c $dL @)  L  H  0޽h ? ̙33 0 KC(  ^  S 9 K   L=  c $D~L @)  L Introduce yourself to your neighbor and compare your responses to #1 on the blue survey. Set timer for 2 minutes. Set timer for 4 minutes and record responses H  0޽h ? ̙33J 0  (  ^  S 9 K   L  c $L @)  L `Use what we know from research to help us present mathematical concepts and design lesson plans.aaH  0޽h ? ̙33  0  ((  ^  S 9 K   L  c $L @)  L  H  0޽h ? ̙33 0 0((  ^  S 9 K   L  c $L @)  L  H  0޽h ? ̙33 0 @((  ^  S 9 K   L  c $L @)  L  H  0޽h ? ̙33 0 P((  ^  S 9 K   L  c $0L @)  L  H  0޽h ? ̙33! 0 `((  ^  S 9 K     c $D @)    H  0޽h ? ̙33  0 p((  ^  S 9 K     c $ @)    H  0޽h ? ̙33  0 ((  ^  S 9 K     c $\ @)    H  0޽h ? ̙33  0 ((  ^  S 9 K     c $ @)    H  0޽h ? ̙33 0 ((  ^  S 9 K     c $x @)    H  0޽h ? ̙33  0 ((  ^  S 9 K   H  c $P "Vf0jk!$M'#*S,.0B35t7T94;=>@BDtFTH4JLM%NOI( P> H 4 rblair@ncweb.comJ/ 0|DArialew Ro<b9bb0bWo 0"DTahomaew Ro<b9bb0bWo 0" DWingdingsRo<b9bb0bWo 00DTimes New Roman9bb0bWo 0@DSymbolew Roman9bb0bWo 0 a.  @n?" dd@  @@``   @FL FG       #$## #   " "&# !$9'% %&'()*+,-./0123456789:;<=>?@h2$pH$l9\s_2$(vt{|!n.;+$2$Y]Dse8)2$ب ֌{ 8a2$ɦ{y  #E&2$ 98(?.k2$?3iIuI32$N'7<62$A 0UٹMtv.E@$2$v#G4^4"n_$2$.7ESnu|^McR$^)֗-MzV}g 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@89 :  uʚ;2Nʚ;g4*d*d0blp@ pp<4!d!d 0b:b<4dddd 0b:b<4BdBd 0b:bg4*d*d0bTpp pp___PPT9zr2? -O =4TjYOU Can Have a Dynamic Algebra Classroom. Here s How& 63 Richelle (Rikki) Blair Lakeland Community College Kirtland, Ohio Email: rblair@ncweb.com AMATYC Annual Conference Phoenix, AZ November, 2002 (C5  0JZ@Agenda:Introduction Research - Learning and Algebra Looking at Classroom Activities Discussion What makes a good activity? YOUR Classroom Reflection |[d [   $ F11:00-11:20 11:20-11:35 11:35-11:50 11:50-11:55 11:55-Noon>G)  AClassroom Goals:  Achieve these goals in a student-centered classroom: Greater academic achievement (content). Favorable attitudes toward learning and mathematics. Increased persistence in mathematics courses. ZZZ(ZZ5ZZ.ZZ _ .f"6Variables Contributing to Student Academic Achievement g#2Matching Learning and Teaching Styles (4 Clusters)$3% h%%Matching Learning and Teaching Stylesi&What can faculty do?The problem is not that faculty/student styles are mismatched. The failure to work out potential conflicts and misunderstandings undermine student learning. Helping students become aware of their learning styles can be empowering and assist in stretching their capabilities.J?ZZ^ZZvZ]#MEANINGFUL LEARNING (UNDERSTANDING)$$ /To UNDERSTAND something means to assimilate it into an appropriate schema. Meaningful learning is learning in which students are actively involved in integrating, or linking, new concepts and skills into an already existing conceptual framework, not simply accumulating isolated facts and procedures.BMddd0"^MEANINGFUL LEARNING is characterized by evidence that the learner: claims to have learned something new. can articulate what it is they think they have learned, with some degree of clarity and accuracy. can demonstrate formation of links with an existing framework that the learner already possesses. has experienced a change from insecurity to confidence. Clarke, D., Helme, S., and Kessel, C. (1996) l,"5,"%b#"3"  EHow People LearnNew developments in the science of learning emphasize the importance of helping people take control of their own learning. All new learning involves transfer based on previous learning. (page 41) Bransford, Brown, and Cocking (eds). How People Learn  Brain, Mind, Experience, and School. National Academy Press, Washington, DC, 1999, www.nap.edu.{ZZZ4ZZ%   % 6  < F How People Learn3Active student learning activities shown to increase the degree to which students transfer learning to new settings. Teachers must draw out and work with pre-existing understandings that students bring with them. (Bransford, page 19) Social opportunities positively affect motivation. (Bransford, page 49)uuHu_  2$ N8Connecting Knowledge: Memorize each list in 10 seconds:$9!$EHT ATC NRA OERV HTE GDO.$ The Cat Ran Over The Dog.$R Reflection:If new information doesn t connect to current knowledge, the concepts roll off like water off a duck s back. :8r[JSources of Student Difficulty in Transitioning from Arithmetic to Algebra: bZZZZZZZX-Research-Based Algebra: Student Difficulties8Recognizing the  = symbol as an equivalence relation, rather than an instruction  to get an answer. Understanding multiple uses of variables: To represent unknowns; As objects to show relationships between quantities; As arbitrary objects in an algebraic structure; To describe patterns and create equations. Kieran, C. (1992). The Learning and Teaching of School Algebra. In Grouws, D.A. (ed). Handbook of Research on the Mathematics Teaching and Learning (pp. 390-419). Reston, VA: National Council of Teachers of Mathematics.fZZ*ZZZg*^ = I d Looking at Classroom ActivitiesFind the other attendees with the same playing card. Introduce yourselves. Review the 4 Classroom Activities in your group (about 2-3 minutes per activity). Rate the activities on a scale from 1 to 5 (5 = excellent)._.Rating Classroom Activities: (5= Excellent)$/ ZSymbols and Notations What IS Algebra anyway? Interpreting Graphs Which Answer is Correct? =1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 DClassroom ActivitiesO What makes a classroom activity successful? When would a lecture be better?4, Pc What is CL?Cooperative Learning  structured systematic instructional strategy in which groups work toward a common goal.o[ (Collaborative Learning  unstructured process in which participants define problems, develop procedures, and produce socially constructed knowledge.e! In reality:dMost small group learning activities are a mix of cooperative and collaborative learning activities.J Why use CL in Mathematics?Meta-analysis of research on 39 undergraduate science, mathematics, engineering, and technology courses demonstrated: Greater academic achievement, More favorable attitudes towards learning, Increased persistence Compared with traditionally taught counterparts. Springer, Stanne, Donovan.  Effects of Small-Group Learning on Undergraduates in Science, Mathematics, Engineering, and Technology: A Meta-Analysis. Review of Educational Research, Spring 1999, Vol. 69, No. 1, pp.21-51.v_3v_  3      )  K Why use CL in Mathematics?Results of meta-analysis showed positive effects of small-group learning significantly greater for members of underrepresented groups (women, African Americans, and Latinos). (Springer, page 40)JZUZ) L Why use CL in Mathematics?zThe learning process requires some sort of cognitive restructuring, or elaboration, of material. One of the most effective means of elaboration is explaining the material to someone else. Some theorists believe that too much structure on a task involving higher-order thinking skills is dysfunctional because it impedes conceptually oriented interactions. (Springer, page 25)a[` [ U Reflection:kReflection is a key element to learning. Kemp, R. Psychology of Learning Mathematics. N)ZCZ+$  "  I .How can you make your classroom an active one?Short classroom activities that engage students: Pre-planned activities Textbook problems Discussion problems Use timing tools. Plan in advance. Seize the teaching moment.P1=>1=> M(When should we use classroom activities?6When they make sense. Be sure to consider differences in students learning styles. Open the door to student opportunities to communicate mathematically.>>FO Reflection:It s hard to change. No one wants change except a wet baby. (, ,S Reflection:tWhat idea would you like to remember from today s session?\Thank you for attending.wPlease complete the blue Evaluation and Reflection form and the AMATYC Evaluation Form. Leave both with the presider._x`Strengths and Weaknesses:ZSymbols and Notations What IS Algebra anyway? Interpreting Graphs Which Answer is Correct?  /,QVjklmnopq r s t u vwxyz{|}~   p($(  (r ( S  PJ    J r ( S PJ p J H ( 0޽h ? 3333   rj(  r  S lJ    J r  S TJ /+  J   c Ar D:\PFiles\MSOffice\Clipart\standard\stddir1\AN01109_.wmf@ pl JH  0޽h ? 3333rPR^0PHI( P> H 4 rblair@ncweb.comJ/ 0|DArialew Ro<b9bb0bWo 0"DTahomaew Ro<b9bb0bWo 0" DWingdingsRo<b9bb0bWo 00DTimes New Roman9bb0bWo 0@DSymbolew Roman9bb0bWo 0 a.  @n?" dd@  @@``   @FL FG       #$## #   " "&# !$9'% %&'()*+,-./0123456789:;<=>?@h2$pH$l9\s_2$(vt{|!n.;+$2$Y]Dse8)2$ب ֌{ 8a2$ɦ{y  #E&2$ 98(?.k2$?3iIuI32$N'7<62$A 0UٹMtv.E@$2$v#G4^4"n_$2$.7ESnu|^McR$^)֗-MzV}g 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@89 :  uʚ;2Nʚ;g4*d*d0blp@ pp<4!d!d 0b:b<4dddd 0b:b<4BdBd 0b:bg4*d*d0bTpp pp___PPT9zr2? -O =4TjYOU Can Have a Dynamic Algebra Classroom. Here s How& 63 Richelle (Rikki) Blair Lakeland Community College Kirtland, Ohio Email: rblair@ncweb.com AMATYC Annual Conference Phoenix, AZ November, 2002 (C5  0JZ@Agenda:Introduction Research - Learning and Algebra Looking at Classroom Activities Discussion What makes a good activity? YOUR Classroom Reflection |[d [   $ F11:00-11:20 11:20-11:35 11:35-11:50 11:50-11:55 11:55-Noon>G)  AClassroom Goals:  Achieve these goals in a student-centered classroom: Greater academic achievement (content). Favorable attitudes toward learning and mathematics. Increased persistence in mathematics courses. ZZZ(ZZ5ZZ.ZZ _ .f"6Variables Contributing to Student Academic Achievement g#2Matching Learning and Teaching Styles (4 Clusters)$3% h%%Matching Learning and Teaching Stylesi&What can faculty do?The problem is not that faculty/student styles are mismatched. The failure to work out potential conflicts and misunderstandings undermine student learning. Helping students become aware of their learning styles can be empowering and assist in stretching their capabilities.J?ZZ^ZZvZ]#MEANINGFUL LEARNING (UNDERSTANDING)$$ /To UNDERSTAND something means to assimilate it into an appropriate schema. Meaningful learning is learning in which students are actively involved in integrating, or linking, new concepts and skills into an already existing conceptual framework, not simply accumulating isolated facts and procedures.BMddd0"^MEANINGFUL LEARNING is characterized by evidence that the learner: claims to have learned something new. can articulate what it is they think they have learned, with some degree of clarity and accuracy. can demonstrate formation of links with an existing framework that the learner already possesses. has experienced a change from insecurity to confidence. Clarke, D., Helme, S., and Kessel, C. (1996) l,"5,"%b#"3"  EHow People LearnNew developments in the science of learning emphasize the importance of helping people take control of their own learning. All new learning involves transfer based on previous learning. (page 41) Bransford, Brown, and Cocking (eds). How People Learn  Brain, Mind, Experience, and School. National Academy Press, Washington, DC, 1999, www.nap.edu.{ZZZ4ZZ%   % 6  < F How People Learn3Active student learning activities shown to increase the degree to which students transfer learning to new settings. Teachers must draw out and work with pre-existing understandings that students bring with them. (Bransford, page 19) Social opportunities positively affect motivation. (Bransford, page 49)uuHu_  2$ N8Connecting Knowledge: Memorize each list in 10 seconds:$9!$EHT ATC NRA OERV HTE GDO.$ The Cat Ran Over The Dog.$R Reflection:If new information doesn t connect to current knowledge, the concepts roll off like water off a duck s back. :8r[JSources of Student Difficulty in Transitioning from Arithmetic to Algebra: bZZZZZZZX-Research-Based Algebra: Student Difficulties8Recognizing the  = symbol as an equivalence relation, rather than an instruction  to get an answer. Understanding multiple uses of variables: To represent unknowns. As objects to show relationships between quantities. As arbitrary objects in an algebraic structure. To describe patterns and create equations. Kieran, C. (1992). The Learning and Teaching of School Algebra. In Grouws, D.A. (ed). Handbook of Research on the Mathematics Teaching and Learning (pp. 390-419). Reston, VA: National Council of Teachers of Mathematics.fZZ*ZZZg*^ = I d Looking at Classroom ActivitiesFind the other attendees with the same playing card. Introduce yourselves. Review the 4 Classroom Activities in your group (about 2-3 minutes per activity). Rate the activities on a scale from 1 to 5 (5 = excellent)._.Rating Classroom Activities: (5= Excellent)$/ ZSymbols and Notations What IS Algebra anyway? Interpreting Graphs Which Answer is Correct? =1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 DClassroom ActivitiesO What makes a classroom activity successful? When would a lecture be better?4, Pc What is CL?Cooperative Learning  structured systematic instructional strategy in which groups work toward a common goal.o[ (Collaborative Learning  unstructured process in which participants define problems, develop procedures, and produce socially constructed knowledge.e! In reality:dMost small group learning activities are a mix of cooperative and collaborative learning activities.J Why use CL in Mathematics?Meta-analysis of research on 39 undergraduate science, mathematics, engineering, and technology courses demonstrated: Greater academic achievement, More favorable attitudes towards learning, Increased persistence Compared with traditionally taught counterparts. Springer, Stanne, Donovan.  Effects of Small-Group Learning on Undergraduates in Science, Mathematics, Engineering, and Technology: A Meta-Analysis. Review of Educational Research, Spring 1999, Vol. 69, No. 1, pp.21-51.v_3v_  3      )  K Why use CL in Mathematics?Results of meta-analysis showed positive effects of small-group learning significantly greater for members of underrepresented groups. (women, African Americans, and Latinos). (Springer, page 40)JZUZ) L Why use CL in Mathematics?zThe learning process requires some sort of cognitive restructuring, or elaboration, of material. One of the most effective means of elaboration is explaining the material to someone else. Some theorists believe that too much structure on a task involving higher-order thinking skills is dysfunctional because it impedes conceptually oriented interactions. (Springer, page 25)Ja[g U Reflection:kReflection is a key element to learning. Kemp, R. Psychology of Learning Mathematics. N)ZCZ+$  "  I .How can you make your classroom an active one?Short classroom activities that engage students: Pre-planned activities Textbook problems Discussion problems Use timing tools. Plan in advance. Seize the teaching moment.P1=>1=> M(When should we use classroom activities?6When they make sense. Be sure to consider differences in students learning styles. Open the door to student opportunities to communicate mathematically.>>FO Reflection:It s hard to change. No one wants change except a wet baby. (, ,S Reflection:tWhat idea would you like to remember from today s session?\Thank you for attending.wPlease complete the blue Evaluation and Reflection form and the AMATYC Evaluation Form. Leave both with the presider._x`Strengths and Weaknesses:ZSymbols and Notations What IS Algebra anyway? Interpreting Graphs Which Answer is Correct?  /,QVjklmnopq r s t u vwxyz{|}~   $(  r  S J    J r  S lJ /` J H  0޽h ? 3333   $(  r  S TO    O r  S O / O H  0޽h ? 3333   $(  r  S pO    O r  S ,O / O H  0޽h ? 3333r*K fRXz >Root EntrydO){0-PicturesxCurrent User-SummaryInformation(|#      !"#$%&'()*+./23456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~1 itles 8@ _PID_HLINKSAhmailto:rblair@ncweb.com%_b Jim Roznowski M. Blair