Where's the math?
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The document describes two math activities observed in a grade 9 classroom using TI-Nspire handheld devices. The first activity involved students working textbook problems using paper, the board, and their devices. The second used a digital document on average life expectancies, with students graphing and taking notes on their devices. Key locations where work was recorded are identified for each lesson part. The configurations of different activities are compared and described as either primarily digital or paper-based. Material relationships between teacher, technology, textbooks and students are mapped.
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Where's the math?
- 1. Where’s the math? Thomas Hillman University of Gothenburg
- 3. Theory Socio-cultural Socio-technical A. Technologies are co-constructions of both developers and users B. Humans and technology both act in networks of social activity C. Learning is tool mediated activity
- 4. Theory Socio-cultural C Socio-technical B A A. Technologies are co-constructions of both developers and users B. Humans and technology both act in networks of social activity C. Learning is tool mediated activity
- 6. Technological Context • Handheld • CAS/Non-CAS • Integrated mathematical environment • Computer software...
- 8. Interviews • Teachers who regularly use TI-Nspire as part of their practice • Reflecting different teaching experiences/approaches • Focused on teaching background, goals and perceptions of the role of technology in their practices • Grade 9 students within the teachers classes
- 9. Observation • 5 consecutive observation sessions in each teacher’s classroom • Suburban secondary school in Ontario • Grade 9 Academic • Student ownership of TI-Nspire • Video-recorded • Single camera focused on teacher practice with multiple microphones...
- 11. Data Analysis • Created content logs & transcriptions • Drawing on Interaction Analysis procedures • Identified perceived adaptions to socio-technical relationships from interviews • Used to orient analysis of observational videos • Mapped the formation & adaption of socio-technical ensembles in the classrooms from observational videos • Organized data in Transana • Created descriptive keywords across data sets
- 13. Socio-technical Configurations Teacher IWB Blackboard Textbook Paper & Pencil Students Handheld
- 14. Basic Lesson Form Lesson Part Activity Preparation Presentation/Modeling Reading Tasks Conjecturing Solutions Verifying Conjectures Practice Small-group Sharing Checking Answers Recording Answers Whole-class Sharing Checking Answers Evaluation Recording Answers Collection
- 15. 2 Activities with TI-Nspire • Textbook Activity • Exponent laws • e.g. (x2)(x6) • Digital Document Activity • Graphing data and modeling linear relationships • Average male/female life expectancy
- 17. Textbook Activity Teacher Blackboard Handheld Students Textbook Paper & Pencil
- 19. Textbook Activity Lesson Part Activity Key Inscription Location(s) Preparation Presentation/Modeling Blackboard Reading Tasks Textbook Conjecturing Solutions Paper & Pencil Verifying Conjectures Handheld (CAS) Practice Small-group Sharing Handheld (CAS) Paper & Pencil Checking Answers Handheld (CAS) Recording Answers Paper & Pencil Whole-class Sharing Blackboard Checking Answers Handheld (CAS) Evaluation Recording Answers Paper & Pencil Blackboard Collection Paper & Pencil Paper/Blackboard Digital
- 20. Textbook Activity Lesson Part Activity Key Inscription Location(s) Preparation Presentation/Modeling Blackboard Reading Tasks Textbook Conjecturing Solutions Paper & Pencil Verifying Conjectures Handheld (CAS) Practice Small-group Sharing Handheld (CAS) Paper & Pencil Checking Answers Handheld (CAS) Recording Answers Paper & Pencil Whole-class Sharing Blackboard Checking Answers Handheld (CAS) Evaluation Recording Answers Paper & Pencil Blackboard Collection Paper & Pencil Paper/Blackboard Digital
- 21. Textbook Activity Lesson Part Activity Key Inscription Location(s) Preparation Presentation/Modeling Blackboard Reading Tasks Textbook Conjecturing Solutions Paper & Pencil Verifying Conjectures Handheld (CAS) Practice Small-group Sharing Handheld (CAS) Paper & Pencil Checking Answers Handheld (CAS) Recording Answers Paper & Pencil Whole-class Sharing Blackboard Checking Answers Handheld (CAS) Evaluation Recording Answers Paper & Pencil Blackboard Collection Paper & Pencil Paper/Blackboard Digital
- 23. Digital Document Activity IWB Teacher Handheld Students
- 25. Digital Document Activity Lesson Part Activity Key Inscription Location(s) Preparation Presentation/Modeling IWB (emulator) Tasks Handheld (notes pages) Conjecturing Solutions Handheld (data & graphing) Verifying Conjectures Handheld (data & graphing) Practice Small Group Sharing Handheld (data & graphing) Checking Answers --- Recording Answers Handheld (data & graphing + notes) Whole-class Sharing IWB (emulator) Checking Answers --- Evaluation Recording Answers IWB/Handheld (following along) Collection Digital Document Paper/Blackboard Digital
- 26. Digital Document Activity Lesson Part Activity Key Inscription Location(s) Preparation Presentation/Modeling IWB (emulator) Tasks Handheld (notes pages) Conjecturing Solutions Handheld (data & graphing) Verifying Conjectures Handheld (data & graphing) Practice Small Group Sharing Handheld (data & graphing) Checking Answers --- Recording Answers Handheld (data & graphing + notes) Whole-class Sharing IWB (emulator) Checking Answers --- Evaluation Recording Answers IWB/Handheld (following along) Collection Digital Document Paper/Blackboard Digital
- 27. Digital Document Activity Lesson Part Activity Key Inscription Location(s) Preparation Presentation/Modeling IWB (emulator) Tasks Handheld (notes pages) Conjecturing Solutions Handheld (data & graphing) Verifying Conjectures Handheld (data & graphing) Practice Small Group Sharing Handheld (data & graphing) Checking Answers --- Recording Answers Handheld (data & graphing + notes) Whole-class Sharing IWB (emulator) Checking Answers --- Evaluation Recording Answers IWB/Handheld (following along) Collection Digital Document Paper/Blackboard Digital
- 29. Comparing Configurations Lesson Part Activity Key Inscription Location(s) Preparation Present/Model Blackboard IWB (emulator) Reading Tasks Textbook Handheld Conjecturing Paper & Pencil Handheld Verifying Handheld Handheld Practice Sharing Handheld P&P Handheld Checking Handheld --- Recording Paper & Pencil Handheld Sharing Blackboard IWB (emulator) Checking Handheld --- Evaluation Recording Paper & Pencil Handheld Collection Paper & Pencil Handheld/PC Paper/Blackboard Digital
- 30. Comparing Configurations Lesson Part Activity Key Inscription Location(s) Preparation Present/Model Blackboard IWB (emulator) Reading Tasks Textbook Handheld Conjecturing Paper & Pencil Handheld Verifying Handheld Handheld Practice Sharing Handheld P&P Handheld Checking Handheld --- Recording Paper & Pencil Handheld Sharing Blackboard IWB (emulator) Checking Handheld --- Evaluation Recording Paper & Pencil Handheld Collection Paper & Pencil Handheld/PC Paper/Blackboard Digital
- 31. Comparing Configurations Lesson Part Activity Key Inscription Location(s) Preparation Present/Model Blackboard IWB (emulator) Reading Tasks Textbook Handheld Conjecturing Paper & Pencil Handheld Verifying Handheld Handheld Practice Sharing Handheld P&P Handheld Checking Handheld --- Recording Paper & Pencil Handheld Sharing Blackboard IWB (emulator) Checking Handheld --- Evaluation Recording Paper & Pencil Handheld Collection Paper & Pencil Handheld/PC Paper/Blackboard Digital
- 32. Primarily Digital Teacher IWB Blackboard Textbook Students Handheld
- 33. Primarily Digital Teacher IWB Blackboard Textbook Students Handheld
- 34. Primarily Digital Teacher IWB Blackboard Textbook Students Handheld
- 35. Primarily Paper & Pencil Teacher IWB Blackboard Textbook Paper & Pencil Students Handheld
- 36. Primarily Paper & Pencil Teacher IWB Blackboard Textbook Paper & Pencil Students Handheld
- 37. Primarily Paper & Pencil Teacher IWB Blackboard Textbook Paper & Pencil Students Handheld
- 38. Key Material Relationships Teacher IWB Blackboard Textbook Paper & Pencil Students Handheld
- 39. Key Material Relationships Teacher IWB Blackboard Textbook Paper & Pencil Students Handheld
- 40. Key Material Relationships Teacher IWB Blackboard Textbook Paper & Pencil Students Handheld
- 41. Key Material Relationships Teacher IWB Blackboard Textbook Paper & Pencil Students Handheld
- 42. Computer Lab → Key Material Relationships Homework Teacher IWB Blackboard Textbook Tests & Exams Manipulatives Paper & Pencil Students Handheld Worksheets
Editor's Notes
- Aims:\nTrace the ways the introduction of a handheld technology shapes socio-technical networks in mathematics classrooms\nIdentify key relationships in terms of locations of mathematical activity & in particular inscriptions\n\nsocio-genetic perspective - in situ - development and use (today focused on use)\n
- Technologies are co-constructions of both developers and users\nScience & Technology Studies\nTools are not finished when first created\nTools slowly emerge as they shape users and users shape them\n\nHumans and technology both act in networks of social activity\nActor-network theory\nAll actors (actants) are analytically symmetrical\nThe capacity to act is not located in any individual entity either but instead emerges from interactions\nFocus on the negotiations between human and non-human actors\n\nLearning is tool mediated activity\nSociocultural theory\nLearning is socioculturally situated, distributed and embodied activity\nLearning always involves mental and/or material tools\n\nShaffer & Clinton toolforthoughts\n\n\n
- Technologies are co-constructions of both developers and users\nScience & Technology Studies\nTools are not finished when first created\nTools slowly emerge as they shape users and users shape them\n\nHumans and technology both act in networks of social activity\nActor-network theory\nAll actors (actants) are analytically symmetrical\nThe capacity to act is not located in any individual entity either but instead emerges from interactions\nFocus on the negotiations between human and non-human actors\n\nLearning is tool mediated activity\nSociocultural theory\nLearning is socioculturally situated, distributed and embodied activity\nLearning always involves mental and/or material tools\n\nShaffer & Clinton toolforthoughts\n\n\n
- Technologies are co-constructions of both developers and users\nScience & Technology Studies\nTools are not finished when first created\nTools slowly emerge as they shape users and users shape them\n\nHumans and technology both act in networks of social activity\nActor-network theory\nAll actors (actants) are analytically symmetrical\nThe capacity to act is not located in any individual entity either but instead emerges from interactions\nFocus on the negotiations between human and non-human actors\n\nLearning is tool mediated activity\nSociocultural theory\nLearning is socioculturally situated, distributed and embodied activity\nLearning always involves mental and/or material tools\n\nShaffer & Clinton toolforthoughts\n\n\n
- Technologies are co-constructions of both developers and users\nScience & Technology Studies\nTools are not finished when first created\nTools slowly emerge as they shape users and users shape them\n\nHumans and technology both act in networks of social activity\nActor-network theory\nAll actors (actants) are analytically symmetrical\nThe capacity to act is not located in any individual entity either but instead emerges from interactions\nFocus on the negotiations between human and non-human actors\n\nLearning is tool mediated activity\nSociocultural theory\nLearning is socioculturally situated, distributed and embodied activity\nLearning always involves mental and/or material tools\n\nShaffer & Clinton toolforthoughts\n\n\n
- Technologies are co-constructions of both developers and users\nScience & Technology Studies\nTools are not finished when first created\nTools slowly emerge as they shape users and users shape them\n\nHumans and technology both act in networks of social activity\nActor-network theory\nAll actors (actants) are analytically symmetrical\nThe capacity to act is not located in any individual entity either but instead emerges from interactions\nFocus on the negotiations between human and non-human actors\n\nLearning is tool mediated activity\nSociocultural theory\nLearning is socioculturally situated, distributed and embodied activity\nLearning always involves mental and/or material tools\n\nShaffer & Clinton toolforthoughts\n\n\n
- Technologies are co-constructions of both developers and users\nScience & Technology Studies\nTools are not finished when first created\nTools slowly emerge as they shape users and users shape them\n\nHumans and technology both act in networks of social activity\nActor-network theory\nAll actors (actants) are analytically symmetrical\nThe capacity to act is not located in any individual entity either but instead emerges from interactions\nFocus on the negotiations between human and non-human actors\n\nLearning is tool mediated activity\nSociocultural theory\nLearning is socioculturally situated, distributed and embodied activity\nLearning always involves mental and/or material tools\n\nShaffer & Clinton toolforthoughts\n\n\n
- Technologies are co-constructions of both developers and users\nScience & Technology Studies\nTools are not finished when first created\nTools slowly emerge as they shape users and users shape them\n\nHumans and technology both act in networks of social activity\nActor-network theory\nAll actors (actants) are analytically symmetrical\nThe capacity to act is not located in any individual entity either but instead emerges from interactions\nFocus on the negotiations between human and non-human actors\n\nLearning is tool mediated activity\nSociocultural theory\nLearning is socioculturally situated, distributed and embodied activity\nLearning always involves mental and/or material tools\n\nShaffer & Clinton toolforthoughts\n\n\n
- Technologies are co-constructions of both developers and users\nScience & Technology Studies\nTools are not finished when first created\nTools slowly emerge as they shape users and users shape them\n\nHumans and technology both act in networks of social activity\nActor-network theory\nAll actors (actants) are analytically symmetrical\nThe capacity to act is not located in any individual entity either but instead emerges from interactions\nFocus on the negotiations between human and non-human actors\n\nLearning is tool mediated activity\nSociocultural theory\nLearning is socioculturally situated, distributed and embodied activity\nLearning always involves mental and/or material tools\n\nShaffer & Clinton toolforthoughts\n\n\n
- Technologies are co-constructions of both developers and users\nScience & Technology Studies\nTools are not finished when first created\nTools slowly emerge as they shape users and users shape them\n\nHumans and technology both act in networks of social activity\nActor-network theory\nAll actors (actants) are analytically symmetrical\nThe capacity to act is not located in any individual entity either but instead emerges from interactions\nFocus on the negotiations between human and non-human actors\n\nLearning is tool mediated activity\nSociocultural theory\nLearning is socioculturally situated, distributed and embodied activity\nLearning always involves mental and/or material tools\n\nShaffer & Clinton toolforthoughts\n\n\n
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- Classic activity. Work handed in on note paper afterwards\n
- Latour inscriptions. Law & Moll fluid spaces\n\nMixed paper & pencil and digital...\n1. Constant translation between paper & pencil and CAS representations\nLed to focus on procedure during class-time.\n2. Checking answers on CAS instead of back of book or teacher - unpacking possible\nChanged relationship to teacher - mathematical authority\n
- Latour inscriptions. Law & Moll fluid spaces\n\nMixed paper & pencil and digital...\n1. Constant translation between paper & pencil and CAS representations\nLed to focus on procedure during class-time.\n2. Checking answers on CAS instead of back of book or teacher - unpacking possible\nChanged relationship to teacher - mathematical authority\n
- Latour inscriptions. Law & Moll fluid spaces\n\nMixed paper & pencil and digital...\n1. Constant translation between paper & pencil and CAS representations\nLed to focus on procedure during class-time.\n2. Checking answers on CAS instead of back of book or teacher - unpacking possible\nChanged relationship to teacher - mathematical authority\n
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- Assignment distributed and collected digitally. Digital notetaking.\nAverage male and female life expectancy.\nFind point where they meet. \nDiscussion of linear model vs likely reality.\n
- All digital but...\n1. In many cases conjecturing and verifying isn’t readily visible\n2. Checking answers not really observed - mathematical authority of tool - implicit vs explicit\nBut... Feedback loop sped up. Access to concepts instead of focus on procedure.\n\n
- All digital but...\n1. In many cases conjecturing and verifying isn’t readily visible\n2. Checking answers not really observed - mathematical authority of tool - implicit vs explicit\nBut... Feedback loop sped up. Access to concepts instead of focus on procedure.\n\n
- All digital but...\n1. In many cases conjecturing and verifying isn’t readily visible\n2. Checking answers not really observed - mathematical authority of tool - implicit vs explicit\nBut... Feedback loop sped up. Access to concepts instead of focus on procedure.\n\n
- See difference in inscription locations...\n1. Relationship between location of tasks and media for preparation\n2. Relationship between student recording location & shared space\n\n\n
- See difference in inscription locations...\n1. Relationship between location of tasks and media for preparation\n2. Relationship between student recording location & shared space\n\n\n
- See difference in inscription locations...\n1. Relationship between location of tasks and media for preparation\n2. Relationship between student recording location & shared space\n\n\n
- See difference in inscription locations...\n1. Relationship between location of tasks and media for preparation\n2. Relationship between student recording location & shared space\n\n\n
- See difference in inscription locations...\n1. Relationship between location of tasks and media for preparation\n2. Relationship between student recording location & shared space\n\n\n
- See difference in inscription locations...\n1. Relationship between location of tasks and media for preparation\n2. Relationship between student recording location & shared space\n\n\n
- See difference in inscription locations...\n1. Relationship between location of tasks and media for preparation\n2. Relationship between student recording location & shared space\n\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- Two key relationships from which the broader socio-technical configurations unfold.\n1. Primarily digital\nTI-Nspire acts in a secondary partner role\nSituated by teacher as mathematical expert e.g. Ask the calculator the answer\nExplicit mathematical authority\nEmphasis on translations between representations\n\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- 2. Primarily paper & pencil\nSituated as mathematical ‘power tool’ for offloading computational and representational tasks\nEmphasis on speeding up procedures and dealing with concepts\nImplicit mathematical authority\n
- Tendency to stay within a representational form\nPaper & pencil - Blackboard\nHandheld - IWB\nThis key relationship constrains other possible socio-technical interactions in the classroom\nWithout IWB, handheld may not become a central location of mathematical activity etc\n1. Textbook may no longer used to check answers. Maybe not used at all - implications for what is taught, how teachers decide on activities\n2. Teacher role as guide changes\n3. Students ability to create a computational/representational library external memory with capabilities beyond a notebook\n4. Others: Worksheets, Manipulatives, Homework, Tests & Exams, Computer Lab, etc...\n
- Tendency to stay within a representational form\nPaper & pencil - Blackboard\nHandheld - IWB\nThis key relationship constrains other possible socio-technical interactions in the classroom\nWithout IWB, handheld may not become a central location of mathematical activity etc\n1. Textbook may no longer used to check answers. Maybe not used at all - implications for what is taught, how teachers decide on activities\n2. Teacher role as guide changes\n3. Students ability to create a computational/representational library external memory with capabilities beyond a notebook\n4. Others: Worksheets, Manipulatives, Homework, Tests & Exams, Computer Lab, etc...\n
- Tendency to stay within a representational form\nPaper & pencil - Blackboard\nHandheld - IWB\nThis key relationship constrains other possible socio-technical interactions in the classroom\nWithout IWB, handheld may not become a central location of mathematical activity etc\n1. Textbook may no longer used to check answers. Maybe not used at all - implications for what is taught, how teachers decide on activities\n2. Teacher role as guide changes\n3. Students ability to create a computational/representational library external memory with capabilities beyond a notebook\n4. Others: Worksheets, Manipulatives, Homework, Tests & Exams, Computer Lab, etc...\n
- Tendency to stay within a representational form\nPaper & pencil - Blackboard\nHandheld - IWB\nThis key relationship constrains other possible socio-technical interactions in the classroom\nWithout IWB, handheld may not become a central location of mathematical activity etc\n1. Textbook may no longer used to check answers. Maybe not used at all - implications for what is taught, how teachers decide on activities\n2. Teacher role as guide changes\n3. Students ability to create a computational/representational library external memory with capabilities beyond a notebook\n4. Others: Worksheets, Manipulatives, Homework, Tests & Exams, Computer Lab, etc...\n
- Tendency to stay within a representational form\nPaper & pencil - Blackboard\nHandheld - IWB\nThis key relationship constrains other possible socio-technical interactions in the classroom\nWithout IWB, handheld may not become a central location of mathematical activity etc\n1. Textbook may no longer used to check answers. Maybe not used at all - implications for what is taught, how teachers decide on activities\n2. Teacher role as guide changes\n3. Students ability to create a computational/representational library external memory with capabilities beyond a notebook\n4. Others: Worksheets, Manipulatives, Homework, Tests & Exams, Computer Lab, etc...\n
- Tendency to stay within a representational form\nPaper & pencil - Blackboard\nHandheld - IWB\nThis key relationship constrains other possible socio-technical interactions in the classroom\nWithout IWB, handheld may not become a central location of mathematical activity etc\n1. Textbook may no longer used to check answers. Maybe not used at all - implications for what is taught, how teachers decide on activities\n2. Teacher role as guide changes\n3. Students ability to create a computational/representational library external memory with capabilities beyond a notebook\n4. Others: Worksheets, Manipulatives, Homework, Tests & Exams, Computer Lab, etc...\n
- Tendency to stay within a representational form\nPaper & pencil - Blackboard\nHandheld - IWB\nThis key relationship constrains other possible socio-technical interactions in the classroom\nWithout IWB, handheld may not become a central location of mathematical activity etc\n1. Textbook may no longer used to check answers. Maybe not used at all - implications for what is taught, how teachers decide on activities\n2. Teacher role as guide changes\n3. Students ability to create a computational/representational library external memory with capabilities beyond a notebook\n4. Others: Worksheets, Manipulatives, Homework, Tests & Exams, Computer Lab, etc...\n
- Tendency to stay within a representational form\nPaper & pencil - Blackboard\nHandheld - IWB\nThis key relationship constrains other possible socio-technical interactions in the classroom\nWithout IWB, handheld may not become a central location of mathematical activity etc\n1. Textbook may no longer used to check answers. Maybe not used at all - implications for what is taught, how teachers decide on activities\n2. Teacher role as guide changes\n3. Students ability to create a computational/representational library external memory with capabilities beyond a notebook\n4. Others: Worksheets, Manipulatives, Homework, Tests & Exams, Computer Lab, etc...\n