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  • Share some math examples with you <br />
  • Share some math examples with you <br />
  • Share some math examples with you <br />
  • Share some math examples with you <br />
  • Share some math examples with you <br />
  • Share some math examples with you <br />
  • Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007 <br />
  • Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007 <br />
  • Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007 <br />
  • Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007 <br />
  • Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007 <br />
  • Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007 <br />
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  • My new moniker is <br />
  • My new moniker is <br />
  • My new moniker is <br />
  • My new moniker is <br />
  • My new moniker is <br />
  • My new moniker is <br />
  • My new moniker is <br />
  • My new moniker is <br />
  • My new moniker is <br />
  • My new moniker is <br />
  • NCTM has a vision of what math teaching should be like. It is stated in its principles and standards <br />
  • NCTM has a vision of what math teaching should be like. It is stated in its principles and standards <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • So what’s so special about a turtle drawing pictures?Why did this MIT professor and a lot other people including Alan kay inventor the personal computer and negroponti who is sharing affordable laptops with 3rd world countries got so excited about it? <br /> <br /> I heard SP called the father of Logo speak at TC at the time his book mindstorms came out while I was doing my graduate work there. He talked about his passion for gears and how they impacted his attitude towards learning math and becoming a mathematician. He wanted to help others particularly children capture that feeling about ideas and learning. <br /> <br /> His curriculum were open-ended microworlds computer based learning learning environments <br /> In that process of engaging with these microworlds where powerful ideas are imbedded inside of neat phenomenon so that Learning formal ideas becomes more concrete. <br /> <br /> (For example in the Jinx we will see the power of variables) <br /> <br /> <br /> <br />
  • Here’s Seymour in 1983 being shown a Logo microworld by a young student who said he did it in the second grade. The turtles here are dynamic. They take on motion and shapes all directed by the student. Watch for Seymour’s wow response and the student says neat! <br /> --------- <br /> follow up with an example from Microworlds EX or scratch!!!! <br /> <br />
  • Here’s Seymour in 1983 being shown a Logo microworld by a young student who said he did it in the second grade. The turtles here are dynamic. They take on motion and shapes all directed by the student. Watch for Seymour’s wow response and the student says neat! <br /> --------- <br /> follow up with an example from Microworlds EX or scratch!!!! <br /> <br />
  • But it wasn’t just the concern about the expense of computers, Math scores were comparing poorly with other nations and NCTM was concerned about this as well as the sorry state of math scores. In response to building criticism of the vagueness of their message they launched C & E standards for school mathematics in 1989 It included a reference to technology that was well buried in the document. <br />
  • But it wasn’t just the concern about the expense of computers, Math scores were comparing poorly with other nations and NCTM was concerned about this as well as the sorry state of math scores. In response to building criticism of the vagueness of their message they launched C & E standards for school mathematics in 1989 It included a reference to technology that was well buried in the document. <br />
  • But it wasn’t just the concern about the expense of computers, Math scores were comparing poorly with other nations and NCTM was concerned about this as well as the sorry state of math scores. In response to building criticism of the vagueness of their message they launched C & E standards for school mathematics in 1989 It included a reference to technology that was well buried in the document. <br />
  • But it wasn’t just the concern about the expense of computers, Math scores were comparing poorly with other nations and NCTM was concerned about this as well as the sorry state of math scores. In response to building criticism of the vagueness of their message they launched C & E standards for school mathematics in 1989 It included a reference to technology that was well buried in the document. <br />
  • But it wasn’t just the concern about the expense of computers, Math scores were comparing poorly with other nations and NCTM was concerned about this as well as the sorry state of math scores. In response to building criticism of the vagueness of their message they launched C & E standards for school mathematics in 1989 It included a reference to technology that was well buried in the document. <br />
  • When Seymour saw what NCTM was doing he wrote.... <br /> <br /> Standards going in right direction.. but are much too conservative and I think they (quote) <br />
  • When Seymour saw what NCTM was doing he wrote.... <br /> <br /> Standards going in right direction.. but are much too conservative and I think they (quote) <br />
  • When Seymour saw what NCTM was doing he wrote.... <br /> <br /> Standards going in right direction.. but are much too conservative and I think they (quote) <br />
  • When Seymour saw what NCTM was doing he wrote.... <br /> <br /> Standards going in right direction.. but are much too conservative and I think they (quote) <br />
  • Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. » <br /> http://my.nctm.org/standards/document/chapter2/index.htm <br /> “Students can learn more mathematics more deeply with the appropriate and responsible use of technology… In mathematics-instruction programs, technology should be used widely and responsibly, with the goal of enriching students’ learning of mathematics.” (NCTM, 2000 p. 25) <br /> <br />
  • Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. » <br /> http://my.nctm.org/standards/document/chapter2/index.htm <br /> “Students can learn more mathematics more deeply with the appropriate and responsible use of technology… In mathematics-instruction programs, technology should be used widely and responsibly, with the goal of enriching students’ learning of mathematics.” (NCTM, 2000 p. 25) <br /> <br />
  • Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. » <br /> http://my.nctm.org/standards/document/chapter2/index.htm <br /> “Students can learn more mathematics more deeply with the appropriate and responsible use of technology… In mathematics-instruction programs, technology should be used widely and responsibly, with the goal of enriching students’ learning of mathematics.” (NCTM, 2000 p. 25) <br /> <br />
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  • The message is that technology is important. Like making it be required on the test. <br /> Life after Papert included Sketchpad and spreadsheets as well as microworlds! <br /> <br />
  • The message is that technology is important. Like making it be required on the test. <br /> Life after Papert included Sketchpad and spreadsheets as well as microworlds! <br /> <br />
  • The message is that technology is important. Like making it be required on the test. <br /> Life after Papert included Sketchpad and spreadsheets as well as microworlds! <br /> <br />
  • The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon. <br />
  • The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon. <br />
  • The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon. <br />
  • The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon. <br />
  • The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon. <br />
  • The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon. <br />
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  • Try A & C here. I'm good at dividing!!!!! <br />
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  • Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?) <br /> <br /> Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch <br />
  • Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?) <br /> <br /> Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch <br />
  • Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?) <br /> <br /> Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch <br />
  • Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?) <br /> <br /> Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch <br />
  • Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?) <br /> <br /> Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch <br />
  • Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?) <br /> <br /> Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch <br />
  • Do we have time for the A&C - multiply? and A&C - add? <br />
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  • The powerful idea - the variable! <br />
  • The powerful idea - the variable! <br />
  • The powerful idea - the variable! <br />
  • The powerful idea - the variable! <br />
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  • In 1990 I became interested in power of story telling for the teaching of math. One of the first examples that got me excited was a movie that I saw back in 1970 called the Weird Number. It was about an event that happened in a very unusual town somewhere “on this side of the mountains”. The inhabitants were all rational numbers. One day there was a robbery at a bakery and someone stole a part of a loaf of bread. The thief was 2/3. However the sheriff was not able to capture the culprit because he wore a disguise. Can you spot him in the photo above? If you did you know more about how 2/3 disguises himself than any of the other numbers in the photo. <br /> <br />
  • In 1990 I became interested in power of story telling for the teaching of math. One of the first examples that got me excited was a movie that I saw back in 1970 called the Weird Number. It was about an event that happened in a very unusual town somewhere “on this side of the mountains”. The inhabitants were all rational numbers. One day there was a robbery at a bakery and someone stole a part of a loaf of bread. The thief was 2/3. However the sheriff was not able to capture the culprit because he wore a disguise. Can you spot him in the photo above? If you did you know more about how 2/3 disguises himself than any of the other numbers in the photo. <br /> <br />
  • In 1990 I became interested in power of story telling for the teaching of math. One of the first examples that got me excited was a movie that I saw back in 1970 called the Weird Number. It was about an event that happened in a very unusual town somewhere “on this side of the mountains”. The inhabitants were all rational numbers. One day there was a robbery at a bakery and someone stole a part of a loaf of bread. The thief was 2/3. However the sheriff was not able to capture the culprit because he wore a disguise. Can you spot him in the photo above? If you did you know more about how 2/3 disguises himself than any of the other numbers in the photo. <br /> <br />
  • In 1990 I became interested in power of story telling for the teaching of math. One of the first examples that got me excited was a movie that I saw back in 1970 called the Weird Number. It was about an event that happened in a very unusual town somewhere “on this side of the mountains”. The inhabitants were all rational numbers. One day there was a robbery at a bakery and someone stole a part of a loaf of bread. The thief was 2/3. However the sheriff was not able to capture the culprit because he wore a disguise. Can you spot him in the photo above? If you did you know more about how 2/3 disguises himself than any of the other numbers in the photo. <br /> <br />
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  • Last part of video. <br />
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  • How did this happen? I have no idea? In fact, this really simulates the real world. <br />
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Keynote presents Keynote presents Presentation Transcript

  • The famous Jinx Puzzle, Measuring the Earth, Shooting Globs and other Classroom adventures
  • The famous Jinx Puzzle, Measuring the Earth, Shooting Globs and other Classroom adventures
  • The famous Jinx Puzzle, Measuring the Earth, Shooting Globs and other Classroom adventures
  • The famous Jinx Puzzle, Measuring the Earth, Shooting Globs and other Classroom adventures
  • The famous Jinx Puzzle, Measuring the Earth, Shooting Globs and other Classroom adventures http://DMCpress.org
  • BEFORE
  • BEFORE Ihor Charischak
  • BEFORE Ihor Charischak Mathematics Project Manager
  • BEFORE Ihor Charischak Mathematics Project Manager Stevens Institute of Technology Center for Innovation in Engineering & Science Education
  • BEFORE Ihor Charischak Mathematics Project Manager Stevens Institute of Technology Center for Innovation in Engineering & Science Education
  • BEFORE Ihor Charischak Mathematics Project Manager Recently Retired.... Stevens Institute of Technology Center for Innovation in Engineering & Science Education
  • Truman Retires
  • NOW
  • NOW Ihor Charischak
  • NOW Ihor Charischak Proprietor
  • NOW Ihor Charischak Proprietor Dynamic Classroom Press
  • NOW Ihor Charischak Proprietor h Dynamic at M Classroom Press
  • NOW Ihor Charischak Proprietor h Dynamic at M Classroom Press http://DMCpress.org
  • Council for Technology in Math Education
  • Council for Technology in Math Education
  • Council for Technology in Math Education http://CLIME.org
  • Technology in Math Education
  • Technology in Math Education Three Visions
  • Vision #1
  • Mindstorms: Falling Love with Math
  • Mindstorms: Falling Love with Math
  • Mindstorms: Falling Love with Math
  • Mindstorms: Falling Love with Math Microworlds: Environments for learning
  • Mindstorms: Falling Love with Math Microworlds: Environments for learning Powerful Ideas
  • Mindstorms: Falling Love with Math Microworlds: Environments for learning Powerful Ideas Neat Phenomenon
  • Mindstorms: Falling Love with Math Microworlds: Environments for learning Powerful Ideas Neat Phenomenon Father of LOGO
  • Mindstorms: Falling Love with Math Microworlds: Environments for learning Powerful Ideas Neat Phenomenon Father of LOGO
  • Mindstorms: Falling Love with Math Microworlds: Environments for learning Powerful Ideas Neat Phenomenon Father of LOGO Turtle: an object to think with
  • 1989
  • 1989 National Council of Teachers of Mathematics (NCTM)
  • 1989 National Council of Teachers of Mathematics (NCTM) Curriculum & Evaluation Standards for School Mathematics (1989)
  • 1989 National Council of Teachers of Mathematics (NCTM) Curriculum & Evaluation Standards for School Mathematics (1989)
  • 1989 National Council of Teachers of Mathematics (NCTM) Curriculum & Evaluation Standards for School Mathematics (1989)
  • “I think they [the Standards] are going in the right direction but they are incredibly conservative, from my point of view. But again, I’d make reservation that if one has to work within the framework for schools as they are and curriculum as it is, maybe there isn’t very much room for making radical change. One of the ways in which the council is conservative is that it does not make full use of a computer -based construction of learning. I think the would have done much better if they had originally integrated Logo in their proposals. But there is no question that an imaginative Logo-using teacher wants to follow these Standards can do it better with Logo.” Seymour Papert
  • “I think they [NCTM] would have done much better if they had originally integrated Logo in their proposals.”
  • Vision #2 in 2000
  • Vision #2 in 2000
  • 6 Pr inciple s
  • 6 Pr inciple s •Equity
  • 6 Pr inciple s •Equity •Curriculum
  • 6 Pr inciple s •Equity •Curriculum •Teaching
  • 6 Pr inciple s •Equity •Curriculum •Teaching •Learning
  • 6 Pr inciple s •Equity •Curriculum •Teaching •Learning •Assessment
  • 6 Pr inciple s •Equity •Curriculum •Teaching •Learning •Assessment •Technology
  • Technology Principle p.26
  • Technology Principle p.26 “Teachers should use technology to enhance their students' learning opportunities by selecting or creating mathematical tasks that take advantage of what technology can do efficiently and well—graphing, visualizing, and computing. […]
  • Technology Principle p.26 “Teachers should use technology to enhance their students' learning opportunities by selecting or creating mathematical tasks that take advantage of what technology can do efficiently and well—graphing, visualizing, and computing. […] Spreadsheets, dynamic geometry software, and computer microworlds are useful tools for posing worthwhile problems….”
  • Vision #3
  • Vision #3 The Dynamic Classroom
  • Vision #3 The Dynamic Classroom
  • Vision #3 The Dynamic Classroom Microworlds: Environments for learning
  • Vision #3 The Dynamic Classroom Microworlds: Environments for learning Powerful Ideas
  • Vision #3 The Dynamic Classroom Microworlds: Environments for learning Powerful Ideas Neat Phenomenon
  • Knowledge Domains
  • Knowledge Domains Community of Powerful ideas
  • Knowledge Domains Community of Powerful ideas Resources
  • Knowledge Domains Community of Powerful ideas Resources Curriculum
  • Knowledge Domains Community of Powerful ideas Resources Curriculum Environment
  • Knowledge Domains Community of Powerful ideas Resources Math Learning Curriculum Environment
  • Knowledge Domains Community of Powerful ideas Resources Math Learning Curriculum Pedagogy Environment
  • Knowledge Domains Community of Powerful ideas Resources Math Learning Curriculum Teaching Environment
  • Knowledge Domains Community of Powerful ideas Resources Math Learning Curriculum Teaching Environment Assessment
  • Knowledge Domains Community of Powerful ideas Resources Math Learning The Dynamic Curriculum Teaching Classroom! Environment Assessment
  • The Activities
  • The Activities (in Story form)
  • The Activities (in Story form) Average Traveler
  • The Activities (in Story form) Average Traveler The Famous Jinx Puzzle
  • The Activities (in Story form) Average Traveler The Famous Jinx Puzzle Measuring the Earth
  • The Activities (in Story form) Average Traveler The Famous Jinx Puzzle Measuring the Earth Great Green Globs Contest Let’s begin...
  • Story #1 The Road sign Problem
  • Story #1 The Road sign Problem
  • A Student’s Guide to Problem Solving
  • A Student’s Guide to Problem Solving Rule 1: If at all possible, avoid reading the problem. Reading the problem only consumes time and causes confusion.
  • A Student’s Guide to Problem Solving Rule 1: If at all possible, avoid reading the problem. Reading the problem only consumes time and causes confusion. Rule 2: Extract the numbers from the problem in the order in which they appear. Be on the watch for numbers written in words
  • A Student’s Guide to Problem Solving Rule 1: If at all possible, avoid reading the problem. Reading the problem only consumes time and causes confusion. Rule 2: Extract the numbers from the problem in the order in which they appear. Be on the watch for numbers written in words Rule 3: If rule 2 yields three or more numbers, the best bet for getting the answer is adding them together.
  • A Student’s Guide to Problem Solving Rule 1: If at all possible, avoid reading the problem. Reading the problem only consumes time and causes confusion. Rule 2: Extract the numbers from the problem in the order in which they appear. Be on the watch for numbers written in words Rule 3: If rule 2 yields three or more numbers, the best bet for getting the answer is adding them together. Rule 4: If there are only two numbers that are approximately the same size, then subtraction should give the best results.
  • Rule 5: If there are only two numbers in the problem and one is much smaller than the other, then divide the smaller in to the larger if it goes evenly. Otherwise multiply.
  • Rule 5: If there are only two numbers in the problem and one is much smaller than the other, then divide the smaller in to the larger if it goes evenly. Otherwise multiply. Rule 6: if the problem seems like it calls for a formula, pick a formula that has enough letter to use all the numbers given in the problem.
  • Rule 5: If there are only two numbers in the problem and one is much smaller than the other, then divide the smaller in to the larger if it goes evenly. Otherwise multiply. Rule 6: if the problem seems like it calls for a formula, pick a formula that has enough letter to use all the numbers given in the problem. Rule 7: Never, never spend too much time solving problems. Remember the best student in mathematics is the one who get to the bottom of the page first. This set of rules will get you through even the longest assignments in more than ten minutes with very little thinking.
  • Most common responses:
  • Most common responses: the total should be 6,122
  • Most common responses: the total should be 6,122 There’s should be a comma between the
  • Most common responses: the total should be 6,122 There’s should be a comma between the 1 and 8 in 1802
  • Most common responses: the total should be 6,122 There’s should be a comma between the 1 and 8 in 1802 The answer should have some kind of units.
  • One of the problems on the NAEP secondary mathematics exam, which was administered to a stratified sample of 45,000 students nationwide, was the following: An army bus holds 36 soldiers. If 1128 soldiers are being bused to their training site, how many buses are needed?
  • One of the problems on the NAEP secondary mathematics exam, which was administered to a stratified sample of 45,000 students nationwide, was the following: An army bus holds 36 soldiers. If 1128 soldiers are being bused to their training site, how many buses are needed?
  • •Seventy percent of the students who took the exam set up the correct long division and performed it correctly. However, the following are the answers those students gave to the question of quot;how many buses are needed?quot;:
  • •Seventy percent of the students who took the exam set up the correct long division and performed it correctly. However, the following are the answers those students gave to the question of quot;how many buses are needed?quot;: •29% said...quot;31 remainder 12quot;
  • •Seventy percent of the students who took the exam set up the correct long division and performed it correctly. However, the following are the answers those students gave to the question of quot;how many buses are needed?quot;: •29% said...quot;31 remainder 12quot; •18% said...quot;31quot;
  • •Seventy percent of the students who took the exam set up the correct long division and performed it correctly. However, the following are the answers those students gave to the question of quot;how many buses are needed?quot;: •29% said...quot;31 remainder 12quot; •18% said...quot;31quot; •23% said...quot;32quot;, which is correct.
  • •Seventy percent of the students who took the exam set up the correct long division and performed it correctly. However, the following are the answers those students gave to the question of quot;how many buses are needed?quot;: •29% said...quot;31 remainder 12quot; •18% said...quot;31quot; •23% said...quot;32quot;, which is correct. •30% did not do the computation correctly.
  • •Seventy percent of the students who took the exam set up the correct long division and performed it correctly. However, the following are the answers those students gave to the question of quot;how many buses are needed?quot;: •29% said...quot;31 remainder 12quot; •18% said...quot;31quot; •23% said...quot;32quot;, which is correct. •30% did not do the computation correctly. •It's frightening enough that fewer than one-fourth of the students got the right answer. More frightening is that almost one out of three students said that the number of buses needed is quot;31 remainder 12quot;. [our emphasis]
  • Story #2 The Famous Jinx Puzzle
  • Story #2 The Famous Jinx Puzzle Pick a Number (1 to 10)
  • Story #2 The Famous Jinx Puzzle Pick a Number (1 to 10) Add 11
  • Story #2 The Famous Jinx Puzzle Pick a Number (1 to 10) Add 11 Multiply by 6
  • Story #2 The Famous Jinx Puzzle Pick a Number (1 to 10) Add 11 Multiply by 6 Subtract 3
  • Story #2 The Famous Jinx Puzzle Pick a Number (1 to 10) Add 11 Multiply by 6 Subtract 3 Divide by 3
  • Story #2 The Famous Jinx Puzzle Pick a Number (1 to 10) Add 11 Multiply by 6 Subtract 3 Divide by 3 Add 5
  • Story #2 The Famous Jinx Puzzle Pick a Number (1 to 10) Add 11 Multiply by 6 Subtract 3 Divide by 3 Add 5 Divide by 2
  • Story #2 The Famous Jinx Puzzle Pick a Number (1 to 10) Add 11 Multiply by 6 Subtract 3 Divide by 3 Add 5 Divide by 2 Subtract the original number
  • 13
  • 13 Jinx Calculator
  • Powerful Idea
  • Powerful Idea X
  • Powerful Idea X Flash demo Jinx Lesson
  • Story #3 Fraction Darts
  • Story #3 Fraction Darts The object of the Fraction Darts challenge is to quot;popquot; balloons located on a number line between 0 and 1. The darts are quot;thrownquot; by entering a number in fractional form.  Here is a glimpse of a game in progress. Two darts (7/8 and 3/4) have been thrown so far. Notice that 3/4 is too small and 7/8 is too big. What is your next throw?
  • Story #3 Fraction Darts The object of the Fraction Darts challenge is to quot;popquot; balloons located on a number line between 0 and 1. The darts are quot;thrownquot; by entering a number in fractional form.  Here is a glimpse of a game in progress. Two darts (7/8 and 3/4) have been thrown so far. Notice that 3/4 is too small and 7/8 is too big. What is your next throw? Go to Game
  • The trouble with Fractions
  • The trouble with Fractions A fraction is a single number with a specific value rather than two independent whole numbers. It can be represented as:
  • The trouble with Fractions A fraction is a single number with a specific value rather than two independent whole numbers. It can be represented as: -> part of a single whole or a set
  • The trouble with Fractions A fraction is a single number with a specific value rather than two independent whole numbers. It can be represented as: -> part of a single whole or a set -> a quotient of integers
  • The trouble with Fractions A fraction is a single number with a specific value rather than two independent whole numbers. It can be represented as: -> part of a single whole or a set -> a quotient of integers -> a measure i.e. a number on a number line
  • The trouble with Fractions A fraction is a single number with a specific value rather than two independent whole numbers. It can be represented as: -> part of a single whole or a set -> a quotient of integers -> a measure i.e. a number on a number line -> a ratio of two integers
  • The trouble with Fractions A fraction is a single number with a specific value rather than two independent whole numbers. It can be represented as: -> part of a single whole or a set -> a quotient of integers -> a measure i.e. a number on a number line -> a ratio of two integers -> as a decimal
  • The trouble with Fractions A fraction is a single number with a specific value rather than two independent whole numbers. It can be represented as: -> part of a single whole or a set -> a quotient of integers -> a measure i.e. a number on a number line -> a ratio of two integers -> as a decimal -> as a percentage
  • Story #2 continued
  • Story #2 continued Number Town
  • Story #2 continued Number Town
  • Story #2 continued Number Town A scene from this summer’s blockbuster movie The Weird Number. Do you recognize 2/3 the star of the movie? He often wears a disguise.
  • Story #2 continued Number Town A scene from this summer’s blockbuster movie The Weird Number. Do you recognize 2/3 the star of the movie? He often wears a disguise. http://ciese.org/ciesemath/number_town.html
  • Story #2 continued Number Town A scene from this summer’s blockbuster movie The Weird Number. Do you recognize 2/3 the star of the movie? He often wears a disguise. http://ciese.org/ciesemath/number_town.html
  • http://ciese.org/math/elizabeth/stevesiracusa.html
  • Mr. Siracusa's Class - We Are Family!
  • Mr. Siracusa's Class - We Are Family! I’m 2/3. I live between 1/2 and 3/4.
  • Mr. Siracusa's Class - We Are Family! I’m 2/3. I live between 1/2 and 3/4.
  • “...Of course, many children memorize how to perform the mumbo-jumbo and manage to get an A but because they don’t understand what they are doing once the test is over they revert back to not knowing how to add fractions. If the meaning was there they would remember. Just how successful a person is in mastering school mathematics is largely a matter of how much meaning they can construct for the symbols manipulated and the operations performed on them. The problem many people have with school arithmetic is that they never get to the meaning stage; it remains forever an abstract game of formal symbols...” The Math Instinct – Why you are a Mathematical Genius by Keith Devlin – page. 248
  • Story #4 The Pizza Server Mystery
  • Story #4 The Pizza Server Mystery
  • Story #4 The Pizza Server Mystery Web version
  • 10.00
  • 10.00 11.05
  • 10.00 11.05 12.10
  • 10.00 11.05 12.10 13.15
  • T P 10.00 11.05 0 10 1 11.05 2 12.10 3 13.15 12.10 13.15
  • T P 10.00 11.05 0 10 1 11.05 2 12.10 3 13.15 12.10 13.15
  • T P 10.00 11.05 0 10 1 11.05 2 12.10 3 13.15 12.10 13.15
  • T P 10.00 11.05 0 10 1 11.05 2 12.10 3 13.15 12.10 13.15
  • T P 10.00 11.05 0 10 1 11.05 2 12.10 3 13.15 12.10 13.15
  • T P 10.00 11.05 0 10 1 11.05 2 12.10 3 13.15 P=1.05T+10 12.10 13.15
  • Toppings Small Medium Large Family 0 $6.00 $10.00 $13.00 $18.00 1 $6.80 $11.05 $14.75 $20.50 2 $7.60 $12.10 $16.50 $23.00 3 $8.40 $13.15 $18.25 $25.50 4 $9.20 $14.20 $20.00 $28.00 5 $10.00 $15.25 $21.75 $30.50
  • Toppings Small Medium Large Family 0 $6.00 $10.00 $13.00 $18.00 1 $6.80 $11.05 $14.75 $20.50 2 $7.60 $12.10 $16.50 $23.00 3 $8.40 $13.15 $18.25 $25.50 4 $9.20 $14.20 $20.00 $28.00 5 $10.00 $15.25 $21.75 $30.50
  • Toppings Small Medium Large Family 0 $6.00 $10.00 $13.00 $18.00 1 $6.80 $11.05 $14.75 $20.50 2 $7.60 $12.10 $16.50 $23.00 3 $8.40 $13.15 $18.25 $25.50 4 $9.20 $14.20 $20.00 $28.00 5 $10.00 $15.25 $21.75 $30.50
  • Toppings Small Medium Large Family 0 $6.00 $10.00 $13.00 $18.00 1 $6.80 $11.05 $14.75 $20.50 2 $7.60 $12.10 $16.50 $23.00 3 $8.40 $13.15 $18.25 $25.50 4 $9.20 $14.20 $20.00 $28.00 5 $10.00 $15.25 $21.75 $30.50
  • Toppings Small Medium Large Family 0 $6.00 $10.00 $13.00 $18.00 1 $6.80 $11.05 $14.75 $20.50 2 $7.60 $12.10 $16.50 $23.00 3 $8.40 $13.15 $18.25 $25.50 4 $9.20 $14.20 $20.00 $28.00 5 $10.00 $15.25 $21.75 $30.50
  • Toppings Small Medium Large Family 0 $6.00 $10.00 $13.00 $18.00 1 $6.80 $11.05 $14.75 $20.50 2 $7.60 $12.10 $16.50 $23.00 3 $8.40 $13.15 $18.25 $25.50 4 $9.20 $14.20 $20.00 $28.00 5 $10.00 $15.25 $21.75 $30.50
  • Toppings Small Medium Large Family 0 $6.00 $10.00 $13.00 $18.00 1 $6.80 $11.05 $14.75 $20.50 2 $7.60 $12.10 $16.50 $23.00 3 $8.40 $13.15 $18.25 $25.50 4 $9.20 $14.20 $20.00 $28.00 5 $10.00 $15.25 $21.75 $30.50
  • 6 $10.00 15.25 $21.75 $30.50 7 $10.00 15.25 $21.75 $30.50 8 $10.00 15.25 $21.75 $30.50
  • 6 $10.00 15.25 $21.75 $30.50 7 $10.00 15.25 $21.75 $30.50 8 $10.00 15.25 $21.75 $30.50
  • 6 $10.00 15.25 $21.75 $30.50 7 $10.00 15.25 $21.75 $30.50 8 $10.00 15.25 $21.75 $30.50
  • Powerful Idea:
  • Powerful Idea: Graphs tell stories.
  • Powerful Idea: Graphs tell stories. (It’s not always just connect the dots.)
  • Powerful Idea: Graphs tell stories. (It’s not always just connect the dots.) Good Question with graph related problems:
  • Powerful Idea: Graphs tell stories. (It’s not always just connect the dots.) Good Question with graph related problems: What stories are being told here?
  • Powerful Idea: Graphs tell stories. (It’s not always just connect the dots.) Good Question with graph related problems: What stories are being told here? (See Graphs Related to Events)
  • Activity #5
  • Activity #5 How Round is the Earth? Inquiring Minds want to Know... Find out how it was done in 200 BC!
  • You Tube Version
  • You Tube Version
  • You Tube Version
  • You Tube Version
  • You Tube Version
  • You Tube Version
  • You Tube Version
  • You Tube Version
  • You Tube Version
  • You Tube Version
  • You Tube Version
  • You Tube Version
  • You Tube Version
  • How round was the Pizza?
  • On my way to Sketchpad
  • Website
  • Website Reports
  • Website Reports Video2
  • Story #6 The Great Green Globs Contest
  • Story #6 The Great Green Globs Contest
  • Switch to Game
  • Guillermo’s Big Score
  • 63
  • 63
  • 64
  • 64
  • y= 5.2 sin(5.4x) + .8x + 2
  • 66
  • 66
  • Part 3 - The Debriefing
  • Part 3 - The Debriefing or what did we learn today?
  • Powerful Ideas
  • Powerful Ideas Road Sign - Making Sense
  • Powerful Ideas Road Sign - Making Sense Darts - Numbers are masters of disguise
  • Powerful Ideas Road Sign - Making Sense Darts - Numbers are masters of disguise Pizza - Graphs tell stories
  • Powerful Ideas Road Sign - Making Sense Darts - Numbers are masters of disguise Pizza - Graphs tell stories Jinx Puzzle - Power of the variable
  • Powerful Ideas Road Sign - Making Sense Darts - Numbers are masters of disguise Pizza - Graphs tell stories Jinx Puzzle - Power of the variable Globs - Algebra can be addicting!
  • Barry Fishman writes:
  • Barry Fishman writes: quot;... Based on my own research and experience, and the research of many colleagues in the learning sciences and related fields, I firmly believe that technology can transform teaching and learning environments and help students achieve beyond what is possible without the support of technology.
  • Barry Fishman writes: quot;... Based on my own research and experience, and the research of many colleagues in the learning sciences and related fields, I firmly believe that technology can transform teaching and learning environments and help students achieve beyond what is possible without the support of technology. It is a tremendous challenge to translate knowledge about teaching with technology from schools that are currently doing extraordinary things—both on their own and in the context of school improvement projects into knowledge that is broadly usable by the majority of schools.
  • Barry Fishman writes: quot;... Based on my own research and experience, and the research of many colleagues in the learning sciences and related fields, I firmly believe that technology can transform teaching and learning environments and help students achieve beyond what is possible without the support of technology. Nonetheless, it is a key challenge that must be met in order to employ technology effectively in school improvement efforts...”
  • Take The Fishman Challenge: From Extraordinary to Ordinary CLIME | council for technology in math education http: clime.org Dynamic Math Classroom Press & Blog http://DMCpress.org
  • The End