How to  Effectively  Integrate  1:1   in the  Mathematics Classroom Jennifer Wathall
What is 1:1 ? Why / why not?  Rapid technological advancement  What the research says  How to effectively integrate 1:1
What is 1:1? 1:1 means putting a computer (laptop, tablet PC or any handheld device) into the hands of every student 1:1 means "anytime, anyplace technology for every student."  While many educators say that one-to-one computing is transforming education for the better, others say it's making the classroom teacher's job harder than ever. Some even believe that the emphasis on technology actually  prevents  students from learning.
 
Webolution
Webolution
1 Laptop for 1 Child Programme  With the rapid technological advancement in the world, educators have a duty to enhance the teaching and learning in their classrooms by incorporating learning technologies that not only stimulate learning but also give the learner deeper cognitive connections.
The Goals of 1:1 Programmes Around the World Improved academic achievement Digital equity Economic development Enhanced teaching leading to improved learning
What Impact Has 1:1 Had? Many schools world wide have adopted a 1:1 programme but what impact has this had on learning?  How do we effectively integrate a 1:1 programme in a mathematics classroom?
Objections to 1:1 “ Maths is for the most part still a paper-and-pencil activity when you’re learning it” “ The art of thinking is lost- You get an answer by just googling- where is the learning?” “ Our school has dropped out of 1:1 because we just do not have the funding and resources or knowledge to support this” “ 1:1 is a distraction for my students and they have become better at computer games”  “ There is no difference in our standardized test scores before and after we introduced our 1:1 programme” Seeing No progress, Some Schools Drop Laptops New York Times, May 2007.
The Research 1:1 can…. Improve learning through standardized test scores Increase student engagement Improve the economic viability of students (increasing student ability to survive in 21 st  c work environment) Close the digital divide by increasing technology literacy in all students Build 21 st  c skills such as critical thinking and sound reasoning, communication skills, information and visual literacy, scientific reasoning, productivity and creativity. “ Technology in Schools- What the research says” Charles Fadel, education Cisco system, 2006.
What Does The Research Say? The overwhelming weight of academic research points to the improvements in learning that are mediated by ubiquitous access to ICT resources. Studies show increased student engagement in learning and a shift in instructional practices of teachers to a more student centered,  problem based style  which is more demanding of Higher order thinking skills.  Overall, across all uses in all content areas, technology does provide a small, but significant, increase in learning when implemented with fidelity “ Technology in Schools- What the research says” Charles Fadel, Global Lead, Education, Cisco systems, 2006.
The 1:1 Learning Environment  Classroom technology should  enable  and  facilitate  the emphasis on the learning process.  “Outliers”  Valuable, appropriate use of laptops in the classroom can provide greater opportunities for feedback and student self assessment  There needs to be serious attention paid to leadership development, professional development for teachers, school culture, curricular redesign, and teacher preparation.
Outliers- The Secret to Success  Alan Schoenfeld maths professor at Berkley create computer programme to teach students how to calculate slope of a line. He asks subjects to find the slope of a vertical line through self discovery.
Renee  22 minutes!  Schoenfeld said it’s your attitude- your persistence and willingness to work hard for 22 minutes Space and time to explore  Appropriate use of 1:1 can help promote this inquiry based approach to learning and encourage students to explore the concepts and obtain the skills we are trying to teach
1:1 Dropouts- HOT skills Schools which have dropped 1:1 use LOT skills. Bloom’s taxonomy -remembering, understanding, and applying and this has resulted in no significant improvement in terms of standardized tests.  Using HOT skills such as analyzing, synthesizing, and creating when integrating 1:1 can utilize technological tools in a more appropriate fashion and improve learning.
Bloom’s Taxonomy Classification of Thinking
Animation Taxonomy
Successful 21st Century Learning Focus on 21st century skills, content knowledge and expertise Emphasize deep understanding rather than shallow knowledge using HOT skills Engage students with the real world data, tools and experts they will encounter in college, on the job, and in life; students learn best when actively engaged in solving meaningful problems
Bloom’s Taxonomy:  Enabling HOTS! Remember: Pythagoras’ Theorem  Understand: The squares of the sum of the two shorter sides in a RAT equals the square of the hypotenuse Apply: Know how to answer questions using Pythagoras’ Theorem  Analyze: Differentiate between when to use SOHCAHTOA and Pythagoras’ theorem  Evaluate: Assess whether your method and answer is reasonable and know how to interpret your answer Create: Compose a song, skit, poem, or video about one of the proofs of Pythagoras’ Theorem
Uses of Laptops in the Classroom LOT examples (remembering, understanding and applying) Research on internet to gather information and answer questions posed Use word processor to type up maths notes- instead of writing- type everything up! Use websites as instructional lessons to teach concepts  Using specialist software to demonstrate and tell students the answers
HOT skills Examples of HOT skills i.e. analyzing, evaluating and creating A) Use of specialist maths software to facilitate the learning process through inquiry based learning B) Use of webquests to problem solve and enable students to use critical thinking skills eg the birthday party  C) Use of multi media to engage and enable students to create their own projects D) Web 2.0 for collaboration both inside and outside the classroom includes 5 minute quizzes on a topic or collecting data through a survey and peer assessment through google
A) How to Use Specialist Software  Geogebra Autograph Geometer Sketch Pad  Scratch It doesn’t matter what you use it’s HOW you use it
Dynamic mathematics software that combines Geometry, algebra and calculus for teachers and students IT’s FREE
Student Directed Learning- HOT Skills Circle Theorems
Pre-Made Calculus Worksheets http://www.geogebra.org/en/examples/function_slope/function_slope1.html
Geogebra Resources http://www.geogebra.org/en/wiki/index.php/Main_Page
B) Webquests  A Webquest is an activity in which students utilize WWW resources to obtain information that is then used in a group project.  A maths webquest is a project which uses internet resources to obtain relevant data which is then analyzed and used in various mathematical exercises.  Most maths webquests involve work in cooperative groups where students work together in a constructivist setting to explore and understand mathematics.  Most math webquests involve reasoning and critical thinking by data collection on the Web and data analysis to use this information to reach conclusions or answer questions.  In other words HOT skills Maths webquests typically involve all five of the process standards in the NCTM Goals 2000: problem solving, reasoning, communication, connections, and representation.
 
Task Process Evaluation Resources Conclusion
Task 1 Task 2 Task 3 Task 4
 
 
Your Shopping List In this step you will compare prices for the following items: Cake Ingredients Punch Ingredients Hot Dogs, Hot Dog Rolls, Mustard, Soft drinks, Ice Cream Balloons, Party Hats, Party Favours Glasses, Forks & Spoons, Plates Table Cloth, Napkins
 
Inviting 25 people to the party .   In this section you are to visit websites to obtain the information you need. Decide which birthday invitation is best for you to send. You must include the following: Cost for Twenty-five Cards Cost of Stamps Total Cost
Making the Cake and Punch In this section you use the given recipe ingredients and prepare them for at least 25 guests. Also convert your units for all recipes to metric units!
Best Chocolate Cake  Serving size: 10 people 2 cups all-purpose flour 2 cups sugar 1/2 cup shortening 3/4 cup water 3/4 cup buttermilk 1 teaspoon baking soda 1 teaspoon salt 1 teaspoon vanilla 1/2 teaspoon baking powder 2 eggs 4 ounces unsweetened baking chocolate, melted and cooled
  Fudge Frosting Serving Size : 10 people   2 cups sugar 1/2 cup shortening 3 ounces unsweetened baking chocolate 2/3 cup milk 1/2 teaspoon salt 2 teaspoons vanilla
Find out a recipe for Tropical Punch and make sure you change you portions of each ingredients for 25 people.  
Your Shopping List In this step you will Compare prices for the following items: Cake Ingredients Punch Ingredients Hot Dogs, Hot Dog Rolls, Mustard, Soda, Ice Cream Balloons, Party Hats, Party Favours Glasses, Forks & Spoons, Plates Table Cloth, Napkins Your task is to create a shopping list of each item that you need to purchase and list how much it will cost you. Use the Online Shopping site to find the costs of each item.  Remember that you will have 25 guests at the party, so make sure you buy enough of each item. Figure that each person will eat two hot dogs.
Preparing your itemized bill for your friend’s mum. In this section you will create a table that lists each item that you purchased.  Below is an example of what should be included in your table . Item Cost per Item Number of items Total Cost  Orange juice $12.50 4 $48
Resources  Below are some websites you can use to help you www.wellcome.com.hk www.partyinvitations.com http:// www.hongkongpost.com /
Exemplary A Task 1:  Student quickly and efficiently finds and uses  information on the required internet sites. Student  accurately computes the required math involved. Task 2: Student Accurately converts the measurements in the provided recipes to suit the desired number of guests. Task 3: Student accurately and efficiently find the item prices and  correctly compute the required tax. Task 4: Student neatly and accurately display on a table the proper results needed to be presented.
Competent B Task 1:  Student finds and uses information on the required internet sites with little assistance. Student computes the required math involved with few errors and with little assistance. Task 2 : Student converts the measurements in the provided recipes to suit the desired number of guests with few errors and with little assistance. Task 3: Student finds the item prices and correctly compute the required tax with few errors and little assistance. Task 4: Student displays on a table the proper results needed to be presented with few errors and with little assistance.
Developing C Task 1:  Student finds and uses information on the required internet sites with assistance. Student computes the required math involved with some errors and with assistance. Task 2 : Student converts the measurements in the provided recipes to suit the desired number of guests with some errors and with assistance. Task 3: Student finds the item prices and correctly compute the required tax with some errors and assistance. Task 4: Student displays on a table the proper results needed to be presented with some errors and with assistance.
Emerging D Task 1:  Student finds and uses information on the required internet sites with much assistance. Student computes the required maths involved with many errors and with needed assistance. Task 2 : Student converts the measurements in the provided recipes to suit the desired number of guests with many errors and with needed assistance. Task 3: Student finds the item prices with many errors and needed assistance. Task 4: Student displays on a table the proper results needed to be presented with many errors and with needed assistance
Good Job! You completed the WebQuest  Assignment! As you can see, it takes a lot of effort to plan a birthday party and to make it a nice event. There were also a lot of mathematical skills required! Remember that, next time someone plans a party for you!
C) What is Multi Media? In general, multimedia includes a combination of different content forms such as text, audio, still images, animation, video, and interactivity. Multimedia can recorded and played, displayed or accessed by computerized and electronic devices and can also be part of a live performance.   Wikipedia Think, Pair and Share
It’s not about…. The Technology It’s about… The  Learning  of Mathematics and the Students!
The BIG Dryen (2003) : Pedagogy: Teacher-centred Andragogy: Learner-centred  Heutogogy: Learner-directed According to Ford (1997) Heutogogy is seen as an extension of andragogy incorporates self-directed learning and recognises the need for 'knowledge sharing' rather than 'knowledge hoarding.' 3
Multi Media Projects   Video- recording, editing and streaming Heutogogical student led projects
Pythagoras Proof
Students Teaching? We remember: 10% of what we read 20% of what we hear 30% of what we see 50% of what we see and hear 70% of what we discuss 80% of what we experience personally 90% of what we teach others
 
Chi Squared Test
SOHCAHTOA
The Quotient Rule Song “ The Quotient rule is driving me crazy The rule is simple Just remember, remember  Low dee hi, hi dee low and draw the line to square below You can easily solve this”
The Quotient Rule Song
Standard Deviation
D) Web 2.0  SurveyMonkey.com - to collect data Hot potato- online quizzes  Wordpress-  my  blog   Wetpaint, Ning- Wiki hosts  Islandschool google  online
  learning  Any form of technology  is a tool for more student centric, relevant, rigorous
It’s Not What You Use  It’s  HOW  You Use it!

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How to Integrate 1:1 effectively in the Mathematics Classroom

  • 1. How to Effectively Integrate 1:1 in the Mathematics Classroom Jennifer Wathall
  • 2. What is 1:1 ? Why / why not? Rapid technological advancement What the research says How to effectively integrate 1:1
  • 3. What is 1:1? 1:1 means putting a computer (laptop, tablet PC or any handheld device) into the hands of every student 1:1 means "anytime, anyplace technology for every student." While many educators say that one-to-one computing is transforming education for the better, others say it's making the classroom teacher's job harder than ever. Some even believe that the emphasis on technology actually prevents students from learning.
  • 4.  
  • 7. 1 Laptop for 1 Child Programme With the rapid technological advancement in the world, educators have a duty to enhance the teaching and learning in their classrooms by incorporating learning technologies that not only stimulate learning but also give the learner deeper cognitive connections.
  • 8. The Goals of 1:1 Programmes Around the World Improved academic achievement Digital equity Economic development Enhanced teaching leading to improved learning
  • 9. What Impact Has 1:1 Had? Many schools world wide have adopted a 1:1 programme but what impact has this had on learning? How do we effectively integrate a 1:1 programme in a mathematics classroom?
  • 10. Objections to 1:1 “ Maths is for the most part still a paper-and-pencil activity when you’re learning it” “ The art of thinking is lost- You get an answer by just googling- where is the learning?” “ Our school has dropped out of 1:1 because we just do not have the funding and resources or knowledge to support this” “ 1:1 is a distraction for my students and they have become better at computer games” “ There is no difference in our standardized test scores before and after we introduced our 1:1 programme” Seeing No progress, Some Schools Drop Laptops New York Times, May 2007.
  • 11. The Research 1:1 can…. Improve learning through standardized test scores Increase student engagement Improve the economic viability of students (increasing student ability to survive in 21 st c work environment) Close the digital divide by increasing technology literacy in all students Build 21 st c skills such as critical thinking and sound reasoning, communication skills, information and visual literacy, scientific reasoning, productivity and creativity. “ Technology in Schools- What the research says” Charles Fadel, education Cisco system, 2006.
  • 12. What Does The Research Say? The overwhelming weight of academic research points to the improvements in learning that are mediated by ubiquitous access to ICT resources. Studies show increased student engagement in learning and a shift in instructional practices of teachers to a more student centered, problem based style which is more demanding of Higher order thinking skills. Overall, across all uses in all content areas, technology does provide a small, but significant, increase in learning when implemented with fidelity “ Technology in Schools- What the research says” Charles Fadel, Global Lead, Education, Cisco systems, 2006.
  • 13. The 1:1 Learning Environment Classroom technology should enable and facilitate the emphasis on the learning process. “Outliers” Valuable, appropriate use of laptops in the classroom can provide greater opportunities for feedback and student self assessment There needs to be serious attention paid to leadership development, professional development for teachers, school culture, curricular redesign, and teacher preparation.
  • 14. Outliers- The Secret to Success Alan Schoenfeld maths professor at Berkley create computer programme to teach students how to calculate slope of a line. He asks subjects to find the slope of a vertical line through self discovery.
  • 15. Renee 22 minutes! Schoenfeld said it’s your attitude- your persistence and willingness to work hard for 22 minutes Space and time to explore Appropriate use of 1:1 can help promote this inquiry based approach to learning and encourage students to explore the concepts and obtain the skills we are trying to teach
  • 16. 1:1 Dropouts- HOT skills Schools which have dropped 1:1 use LOT skills. Bloom’s taxonomy -remembering, understanding, and applying and this has resulted in no significant improvement in terms of standardized tests. Using HOT skills such as analyzing, synthesizing, and creating when integrating 1:1 can utilize technological tools in a more appropriate fashion and improve learning.
  • 19. Successful 21st Century Learning Focus on 21st century skills, content knowledge and expertise Emphasize deep understanding rather than shallow knowledge using HOT skills Engage students with the real world data, tools and experts they will encounter in college, on the job, and in life; students learn best when actively engaged in solving meaningful problems
  • 20. Bloom’s Taxonomy: Enabling HOTS! Remember: Pythagoras’ Theorem Understand: The squares of the sum of the two shorter sides in a RAT equals the square of the hypotenuse Apply: Know how to answer questions using Pythagoras’ Theorem Analyze: Differentiate between when to use SOHCAHTOA and Pythagoras’ theorem Evaluate: Assess whether your method and answer is reasonable and know how to interpret your answer Create: Compose a song, skit, poem, or video about one of the proofs of Pythagoras’ Theorem
  • 21. Uses of Laptops in the Classroom LOT examples (remembering, understanding and applying) Research on internet to gather information and answer questions posed Use word processor to type up maths notes- instead of writing- type everything up! Use websites as instructional lessons to teach concepts Using specialist software to demonstrate and tell students the answers
  • 22. HOT skills Examples of HOT skills i.e. analyzing, evaluating and creating A) Use of specialist maths software to facilitate the learning process through inquiry based learning B) Use of webquests to problem solve and enable students to use critical thinking skills eg the birthday party C) Use of multi media to engage and enable students to create their own projects D) Web 2.0 for collaboration both inside and outside the classroom includes 5 minute quizzes on a topic or collecting data through a survey and peer assessment through google
  • 23. A) How to Use Specialist Software Geogebra Autograph Geometer Sketch Pad Scratch It doesn’t matter what you use it’s HOW you use it
  • 24. Dynamic mathematics software that combines Geometry, algebra and calculus for teachers and students IT’s FREE
  • 25. Student Directed Learning- HOT Skills Circle Theorems
  • 26. Pre-Made Calculus Worksheets http://www.geogebra.org/en/examples/function_slope/function_slope1.html
  • 28. B) Webquests A Webquest is an activity in which students utilize WWW resources to obtain information that is then used in a group project. A maths webquest is a project which uses internet resources to obtain relevant data which is then analyzed and used in various mathematical exercises. Most maths webquests involve work in cooperative groups where students work together in a constructivist setting to explore and understand mathematics. Most math webquests involve reasoning and critical thinking by data collection on the Web and data analysis to use this information to reach conclusions or answer questions. In other words HOT skills Maths webquests typically involve all five of the process standards in the NCTM Goals 2000: problem solving, reasoning, communication, connections, and representation.
  • 29.  
  • 30. Task Process Evaluation Resources Conclusion
  • 31. Task 1 Task 2 Task 3 Task 4
  • 32.  
  • 33.  
  • 34. Your Shopping List In this step you will compare prices for the following items: Cake Ingredients Punch Ingredients Hot Dogs, Hot Dog Rolls, Mustard, Soft drinks, Ice Cream Balloons, Party Hats, Party Favours Glasses, Forks & Spoons, Plates Table Cloth, Napkins
  • 35.  
  • 36. Inviting 25 people to the party .   In this section you are to visit websites to obtain the information you need. Decide which birthday invitation is best for you to send. You must include the following: Cost for Twenty-five Cards Cost of Stamps Total Cost
  • 37. Making the Cake and Punch In this section you use the given recipe ingredients and prepare them for at least 25 guests. Also convert your units for all recipes to metric units!
  • 38. Best Chocolate Cake Serving size: 10 people 2 cups all-purpose flour 2 cups sugar 1/2 cup shortening 3/4 cup water 3/4 cup buttermilk 1 teaspoon baking soda 1 teaspoon salt 1 teaspoon vanilla 1/2 teaspoon baking powder 2 eggs 4 ounces unsweetened baking chocolate, melted and cooled
  • 39.   Fudge Frosting Serving Size : 10 people   2 cups sugar 1/2 cup shortening 3 ounces unsweetened baking chocolate 2/3 cup milk 1/2 teaspoon salt 2 teaspoons vanilla
  • 40. Find out a recipe for Tropical Punch and make sure you change you portions of each ingredients for 25 people.  
  • 41. Your Shopping List In this step you will Compare prices for the following items: Cake Ingredients Punch Ingredients Hot Dogs, Hot Dog Rolls, Mustard, Soda, Ice Cream Balloons, Party Hats, Party Favours Glasses, Forks & Spoons, Plates Table Cloth, Napkins Your task is to create a shopping list of each item that you need to purchase and list how much it will cost you. Use the Online Shopping site to find the costs of each item. Remember that you will have 25 guests at the party, so make sure you buy enough of each item. Figure that each person will eat two hot dogs.
  • 42. Preparing your itemized bill for your friend’s mum. In this section you will create a table that lists each item that you purchased.  Below is an example of what should be included in your table . Item Cost per Item Number of items Total Cost Orange juice $12.50 4 $48
  • 43. Resources Below are some websites you can use to help you www.wellcome.com.hk www.partyinvitations.com http:// www.hongkongpost.com /
  • 44. Exemplary A Task 1: Student quickly and efficiently finds and uses  information on the required internet sites. Student accurately computes the required math involved. Task 2: Student Accurately converts the measurements in the provided recipes to suit the desired number of guests. Task 3: Student accurately and efficiently find the item prices and correctly compute the required tax. Task 4: Student neatly and accurately display on a table the proper results needed to be presented.
  • 45. Competent B Task 1: Student finds and uses information on the required internet sites with little assistance. Student computes the required math involved with few errors and with little assistance. Task 2 : Student converts the measurements in the provided recipes to suit the desired number of guests with few errors and with little assistance. Task 3: Student finds the item prices and correctly compute the required tax with few errors and little assistance. Task 4: Student displays on a table the proper results needed to be presented with few errors and with little assistance.
  • 46. Developing C Task 1: Student finds and uses information on the required internet sites with assistance. Student computes the required math involved with some errors and with assistance. Task 2 : Student converts the measurements in the provided recipes to suit the desired number of guests with some errors and with assistance. Task 3: Student finds the item prices and correctly compute the required tax with some errors and assistance. Task 4: Student displays on a table the proper results needed to be presented with some errors and with assistance.
  • 47. Emerging D Task 1: Student finds and uses information on the required internet sites with much assistance. Student computes the required maths involved with many errors and with needed assistance. Task 2 : Student converts the measurements in the provided recipes to suit the desired number of guests with many errors and with needed assistance. Task 3: Student finds the item prices with many errors and needed assistance. Task 4: Student displays on a table the proper results needed to be presented with many errors and with needed assistance
  • 48. Good Job! You completed the WebQuest Assignment! As you can see, it takes a lot of effort to plan a birthday party and to make it a nice event. There were also a lot of mathematical skills required! Remember that, next time someone plans a party for you!
  • 49. C) What is Multi Media? In general, multimedia includes a combination of different content forms such as text, audio, still images, animation, video, and interactivity. Multimedia can recorded and played, displayed or accessed by computerized and electronic devices and can also be part of a live performance. Wikipedia Think, Pair and Share
  • 50. It’s not about…. The Technology It’s about… The Learning of Mathematics and the Students!
  • 51. The BIG Dryen (2003) : Pedagogy: Teacher-centred Andragogy: Learner-centred Heutogogy: Learner-directed According to Ford (1997) Heutogogy is seen as an extension of andragogy incorporates self-directed learning and recognises the need for 'knowledge sharing' rather than 'knowledge hoarding.' 3
  • 52. Multi Media Projects Video- recording, editing and streaming Heutogogical student led projects
  • 54. Students Teaching? We remember: 10% of what we read 20% of what we hear 30% of what we see 50% of what we see and hear 70% of what we discuss 80% of what we experience personally 90% of what we teach others
  • 55.  
  • 58. The Quotient Rule Song “ The Quotient rule is driving me crazy The rule is simple Just remember, remember Low dee hi, hi dee low and draw the line to square below You can easily solve this”
  • 61. D) Web 2.0 SurveyMonkey.com - to collect data Hot potato- online quizzes Wordpress- my blog Wetpaint, Ning- Wiki hosts Islandschool google online
  • 62. learning Any form of technology is a tool for more student centric, relevant, rigorous
  • 63. It’s Not What You Use It’s HOW You Use it!