c math 2 claran einfeldt [email protected] [email protected] claran einfeldt [email protected] ...
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Senses on GeometrySenses on Geometry
Manipulative-based activities help students move from the Concrete to the Representationalto the Abstract
Manipulative-based activities help students move from the Concrete to the Representationalto the Abstract
Statistics for the AgesStatistics for the Ages
The Study of Statistics . . .Engages the learnerComes in many formsIs used to make decisionsAllows analysis of different
situations and claims
The Study of Statistics . . .Engages the learnerComes in many formsIs used to make decisionsAllows analysis of different
situations and claims
Calculators for Learning Mathematics
Calculators for Learning Mathematics
The calculator . . . Engages studentsEnhances their learningAdds motivationIs allowed on the ISAT Levels the playing field at the middle
level Enables the study of significant
mathematics
The calculator . . . Engages studentsEnhances their learningAdds motivationIs allowed on the ISAT Levels the playing field at the middle
level Enables the study of significant
mathematics
Teaching Algebra with Manipulatives
Teaching Algebra with Manipulatives
Algebra manipulatives can open the door for students to be successful . . .Computation with IntegersEvaluating ExpressionsWriting & Solving EquationsWorking with PolynomialsIntegrating with Geometry Concepts
Algebra manipulatives can open the door for students to be successful . . .Computation with IntegersEvaluating ExpressionsWriting & Solving EquationsWorking with PolynomialsIntegrating with Geometry Concepts
What is algebraic thinking or reasoning?
What is algebraic thinking or reasoning?
Forming generalizations from experiences with number and computation
Formalizing these ideas with the use of a meaningful symbol system
Exploring the concepts of patterns and functions
Forming generalizations from experiences with number and computation
Formalizing these ideas with the use of a meaningful symbol system
Exploring the concepts of patterns and functions
Van De Walle, Elementary and Middle School Mathematics: Teaching Developmentally
Linking Mathematics and Literature in a Meaningful
Way
Linking Mathematics and Literature in a Meaningful
Way Literacy and mathematics require
development of many of the same skills, including pattern recognition, classifying, organizing thoughts, and solving problems.
Literature can provide a means for mathematics and literacy skills to develop simultaneously as students read, write, listen, and talk about math.
Engagement with literature allows students to connect the abstract language of mathematics to their personal world in a natural way.
Literacy and mathematics require development of many of the same skills, including pattern recognition, classifying, organizing thoughts, and solving problems.
Literature can provide a means for mathematics and literacy skills to develop simultaneously as students read, write, listen, and talk about math.
Engagement with literature allows students to connect the abstract language of mathematics to their personal world in a natural way.
Deal or No Deal?Using Games for
Mathematics
Deal or No Deal?Using Games for
Mathematics
A game can provide the platform for students to be reflective about mathematical relationships. It is this reflective thought that promotes growth.
A game can provide the platform for students to be reflective about mathematical relationships. It is this reflective thought that promotes growth.
Words Matter in Mathematics
Words Matter in Mathematics
conversation understanding
Word Walls
vocabulary
Visual cuesSimilarities/differences
symbols
Illuminations© WebsiteIlluminations© Website
Activities92 online activitiesOrganized by
grade-bandLessons
521 lessonsOrganized by
grade-band and content strand
Activities92 online activitiesOrganized by
grade-bandLessons
521 lessonsOrganized by
grade-band and content strand
Standards NCTM Principles and
Standards Grade-band electronic
examples
Web Links 726 online resources Identified by an editorial
panel Organized by content
strand
Standards NCTM Principles and
Standards Grade-band electronic
examples
Web Links 726 online resources Identified by an editorial
panel Organized by content
strand
Making Probability Real with Simulations
Making Probability Real with Simulations
Using simulations:motivates interestprovides a level of concrete experiences leading to
later levels of abstractionaddresses misconceptions about probabilistic
situationsallows for the exploration of sophisticated
probability conceptsdevelops intuitive understanding of probability
concepts (e.g., the central tendency of large samples of data)
Using simulations:motivates interestprovides a level of concrete experiences leading to
later levels of abstractionaddresses misconceptions about probabilistic
situationsallows for the exploration of sophisticated
probability conceptsdevelops intuitive understanding of probability
concepts (e.g., the central tendency of large samples of data)
Five Instructional Practices that WORKFive Instructional
Practices that WORK1. Make Prime Time Count2. Create a language-rich
classroom3. Ensure Daily Residue4. Connect with Context5. Foster visualization
1. Make Prime Time Count2. Create a language-rich
classroom3. Ensure Daily Residue4. Connect with Context5. Foster visualization
Key elements of good questioning practicesKey elements of good questioning practices
Plan and collaborateEnsure rich tasks and a safe environment
Use questions to access understanding rather than find answer
Plan and collaborateEnsure rich tasks and a safe environment
Use questions to access understanding rather than find answer
Texas InstrumentsTexas Instruments
http://education.ti.com
For FREE Activities: click “Classroom Exchange”
For support programs:click “Funding, Research & Support”
http://education.ti.com
For FREE Activities: click “Classroom Exchange”
For support programs:click “Funding, Research & Support”
Texas InstrumentsTexas Instruments
Doug Harnish
Your IL and WI contact for product information, workshops, trainings, etc.
630-877-0085
Doug Harnish
Your IL and WI contact for product information, workshops, trainings, etc.
630-877-0085
Barbara Jo EvansEducational Consultant
Illinois**
Research tell us … The strongest predictor of earnings nine years
after graduation from high school is the number of mathematics classes the student has taken.
The odds that a student who enters college will complete a bachelor’s degree more than double if that student completed a mathematics course beyond Algebra II content.
Jobs that do not require a college degree, but will support a family and have the potential for advancement require mathematics content that is equivalent to Algebra II, as well as four years of English.
Research from…Improving Adolescent Mathematics,
Findings from Research
NWREL 2005
How Teachers Inspire …Although my school days are as
distant a memory to me as my first date, I can vividly recall a few magic moments in learning …
… from USA Today, 6/19/07
Not Lost … Just ExploringSome people choose to live their lives on quiet
avenues
While others find a place in the parade
Some like me … and Claran, and Sharon, and Tom, and Dean , and Linda, and Mary, and Nancy…are seekers
We take less traveled roads
Believing we can find a better way
Not lost … just ExploringAnd though we get discouraged, We won’t be
turning back
We have joy as our compass, and faith as our map …
I am not lost … I am exploringLife is an adventure worth enjoyingThough I may not know where I’m goingI am not lost … I am exploring
Inspire and Explore!
When your student say they are lost … Remember to tell them that they are NOT lost, but they ARE exploring!
Inspire yourselves and your students … to explore the magic world of mathematics.
Barbara Jo EvansEducational Consultant
Illinois
1. Students come to the classroom with preconceptions about how the world works.
2. To develop competence . . . Students must (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and (c) organize knowledge to facilitate retrieval and application.
3. A “metacognitive” approach to instruction can help students learn to take control.
1. Students come to the classroom with preconceptions about how the world works.
2. To develop competence . . . Students must (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and (c) organize knowledge to facilitate retrieval and application.
3. A “metacognitive” approach to instruction can help students learn to take control.
3 Principles of How People Learn
3 Principles of How People Learn
A Fish StoryA Fish Story
“I have been about the world – hopping here and there,” said the frog, “and I have seen extraordinary things.”
“Like what?” asked the fish.
“Birds”, said the frog mysteriously. and he told the fish about the birds,
“I have been about the world – hopping here and there,” said the frog, “and I have seen extraordinary things.”
“Like what?” asked the fish.
“Birds”, said the frog mysteriously. and he told the fish about the birds,
(birds) who had wings, and two legs, and many, many colors. As the frog talked, his friend saw the birds fly through his mind like large feathered fish.
(birds) who had wings, and two legs, and many, many colors. As the frog talked, his friend saw the birds fly through his mind like large feathered fish.
The frog continues with descriptions of cows,
which the fish imagines as black-and-white spotted fish with horns and udders . . .
The frog continues with descriptions of cows,
which the fish imagines as black-and-white spotted fish with horns and udders . . .
And Humans, which the fish imagines as fish walking upright
and dressed in clothing.
And Humans, which the fish imagines as fish walking upright
and dressed in clothing.
Leo Lionni’s Fish Is Fish © 1970. Copyright renewed 1998 by Leo Lionni. Random House Children’s Books a division of Random House, Inc.
Leo Lionni’s Fish Is Fish © 1970. Copyright renewed 1998 by Leo Lionni. Random House Children’s Books a division of Random House, Inc.
1
Build It concrete,
manipulative
3
Symbol It abstract symbolic4
Say It Write It
communications
2 Draw It representational
pictorial graphical
C. COLLABORATIONM. MATHEMATICSA. ACTIVITIES T. TIMEH. HAPPINESS2. FLEXIBILITY
C. COLLABORATIONM. MATHEMATICSA. ACTIVITIES T. TIMEH. HAPPINESS2. FLEXIBILITY
WHETHER YOU THINK YOU CANOR NOT
YOU ARE PROBABLY RIGHT
WHETHER YOU THINK YOU CANOR NOT
YOU ARE PROBABLY RIGHT
CLOSING AND DOOR PRIZESCLOSING AND DOOR PRIZES
QUESTIONSQUESTIONSFINAL
EVALUATIONSFINAL
EVALUATIONS