10. BEFORE
Ihor Charischak
Mathematics Project Manager
11. BEFORE
Ihor Charischak
Mathematics Project Manager
Stevens Institute of Technology
Center for Innovation
in Engineering & Science
Education
12. BEFORE
Ihor Charischak
Mathematics Project Manager
Stevens Institute of Technology
Center for Innovation
in Engineering & Science
Education
13. BEFORE
Ihor Charischak
Mathematics Project Manager Recently
Retired....
Stevens Institute of Technology
Center for Innovation
in Engineering & Science
Education
39. Mindstorms: Falling Love with Math
Microworlds: Environments for learning
Powerful Ideas
Neat Phenomenon
40. Mindstorms: Falling Love with Math
Microworlds: Environments for learning
Powerful Ideas
Neat Phenomenon
Father of LOGO
41. Mindstorms: Falling Love with Math
Microworlds: Environments for learning
Powerful Ideas
Neat Phenomenon
Father of LOGO
42. Mindstorms: Falling Love with Math
Microworlds: Environments for learning
Powerful Ideas
Neat Phenomenon
Father of LOGO
Turtle: an object to think with
48. 1989
National Council of Teachers of
Mathematics (NCTM)
Curriculum & Evaluation Standards
for School Mathematics (1989)
49. 1989
National Council of Teachers of
Mathematics (NCTM)
Curriculum & Evaluation Standards
for School Mathematics (1989)
50. 1989
National Council of Teachers of
Mathematics (NCTM)
Curriculum & Evaluation Standards
for School Mathematics (1989)
51.
52. “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
53. “I
think they [NCTM] would
have done much better if
they had originally integrated
Logo in their proposals.”
67. 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. […]
68. 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….”
101. 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.
102. 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
103. 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.
104. 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.
105.
106. 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.
107. 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.
108. 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.
115. Most common responses:
the total should be 6,122
There’s should be a comma between the
1 and 8 in 1802
116. 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.
117.
118.
119.
120. 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?
121. 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?
122.
123. •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;:
124. •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;
125. •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;
126. •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.
127. •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.
128. •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]
140. Story #2
The Famous Jinx Puzzle
Pick a Number (1 to 10)
Add 11
Multiply by 6
141. Story #2
The Famous Jinx Puzzle
Pick a Number (1 to 10)
Add 11
Multiply by 6
Subtract 3
142. Story #2
The Famous Jinx Puzzle
Pick a Number (1 to 10)
Add 11
Multiply by 6
Subtract 3
Divide by 3
143. Story #2
The Famous Jinx Puzzle
Pick a Number (1 to 10)
Add 11
Multiply by 6
Subtract 3
Divide by 3
Add 5
144. 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
145. 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
155. 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?
156. 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
159. 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:
160. 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
161. 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
162. 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
163. 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
164. 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
165. 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
170. 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.
171. 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
172. 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
190. “...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
228. Powerful Idea:
Graphs tell stories.
(It’s not always just connect the dots.)
229. Powerful Idea:
Graphs tell stories.
(It’s not always just connect the dots.)
Good Question with graph related problems:
230. 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?
231. 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)
287. Powerful Ideas
Road Sign - Making Sense
Darts - Numbers are masters of disguise
Pizza - Graphs tell stories
288. Powerful Ideas
Road Sign - Making Sense
Darts - Numbers are masters of disguise
Pizza - Graphs tell stories
Jinx Puzzle - Power of the variable
289. 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!
292. 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.
293. 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.
294. 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...”
295.
296.
297.
298. 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
Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007
Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007
Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007
Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007
Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007
Hello, my name is Ihor Charischak. This was my previous life up until September 30, 2007
My new moniker is
My new moniker is
My new moniker is
My new moniker is
My new moniker is
My new moniker is
My new moniker is
My new moniker is
My new moniker is
My new moniker is
NCTM has a vision of what math teaching should be like. It is stated in its principles and standards
NCTM has a vision of what math teaching should be like. It is stated in its principles and standards
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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?
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.
His curriculum were open-ended microworlds computer based learning learning environments
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.
(For example in the Jinx we will see the power of variables)
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!
---------
follow up with an example from Microworlds EX or scratch!!!!
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!
---------
follow up with an example from Microworlds EX or scratch!!!!
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.
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.
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.
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.
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.
When Seymour saw what NCTM was doing he wrote....
Standards going in right direction.. but are much too conservative and I think they (quote)
When Seymour saw what NCTM was doing he wrote....
Standards going in right direction.. but are much too conservative and I think they (quote)
When Seymour saw what NCTM was doing he wrote....
Standards going in right direction.. but are much too conservative and I think they (quote)
When Seymour saw what NCTM was doing he wrote....
Standards going in right direction.. but are much too conservative and I think they (quote)
Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. »
http://my.nctm.org/standards/document/chapter2/index.htm
“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)
Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. »
http://my.nctm.org/standards/document/chapter2/index.htm
“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)
Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. »
http://my.nctm.org/standards/document/chapter2/index.htm
“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)
The message is that technology is important. Like making it be required on the test.
Life after Papert included Sketchpad and spreadsheets as well as microworlds!
The message is that technology is important. Like making it be required on the test.
Life after Papert included Sketchpad and spreadsheets as well as microworlds!
The message is that technology is important. Like making it be required on the test.
Life after Papert included Sketchpad and spreadsheets as well as microworlds!
The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon.
The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon.
The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon.
The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon.
The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon.
The DC is where the curriculum is Microworlds oriented where powerful ideas are embedded in neat phenomenon.
Try A & C here. I'm good at dividing!!!!!
Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?)
Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch
Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?)
Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch
Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?)
Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch
Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?)
Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch
Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?)
Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch
Surprising there was one answer that didn’t appear. Can’t use calculators on NAEP test (What is NAEP?)
Oh I forgot, there was one more PS technique that is used. It is the called the Costello effect. Watch
Do we have time for the A&C - multiply? and A&C - add?
The powerful idea - the variable!
The powerful idea - the variable!
The powerful idea - the variable!
The powerful idea - the variable!
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.
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.
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.
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.
Last part of video.
How did this happen? I have no idea? In fact, this really simulates the real world.