intermath professional and cognitive development through problem solving and technology

InterMathProfessional and Cognitive Development through Problem Solving and Technology

http://www.intermath-uga.gatech.edu/

Evan GlazerLearning and Performance Support Laboratory

University of [email protected]

http://www.arches.uga.edu/~eglazer/NECC2001.html

Overview My Background About InterMath Professional Development Cognitive Development Teachers’ Activities


Background Doctoral Candidate in IT at UGA


Baptism Bulldawg Style

Background

Doctoral Candidate in IT at UGA InterMath - problem solving with

TEMIs.


Under the direction of Jim Wilson and others http://www.intermath-uga.gatech.edu/

Background Doctoral Candidate in IT at UGA InterMath - problem solving with

TEMIs. Taught high school mathematics in

Glenview, Illinois


You might be a “real” teacher if... You grade papers in the car, during commercials, in

faculty meetings, in the bathroom, and (at the end of the six weeks) have been seen grading in church.

You have a disjointed neck from writing on boards without turning your back on the class.

You are written up in medical journals for the size and elasticity of your kidneys and bladder.


You might be a “real” teacher if... You have been timed gulping down a full lunch in 2

minutes, 18 seconds. Master teachers can eat faster than that.

You know it is better to seek forgiveness than to ask permission.

You buy Excedrin and Advil at Sam's.

You know secretaries and custodians run the school


You might be a “real” teacher if... You hear the heartbeats of crisis; always have time

to listen; know you teach students, not just a subject; and you are absolutely non-expendable.


Background

Doctoral Candidate in IT at UGA InterMath - problem solving with


Glenview, Illinois Web-based development since

1993.


Background Doctoral Candidate in IT at UGA InterMath - problem solving with


Glenview, Illinois Web-based development since 1993 I have a passion for working with

kids, teaching, learning, mathematics, and running


Mathematicians have the unique talent of determining howfast they are running, and how much faster they need to runby the end of the race in order to set a personal record.

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.


Unflattering portrait:How one child perceives mathematicians

Source: http://www.thetimes.co.uk/article/0,,2-61352,00.html

Background Doctoral Candidate in IT at UGA InterMath - problem solving with TEMIs. Six years of teaching high school

mathematics in Illinois Web-based development since 1993 I have a passion for working with kids,

learning, mathematics, and running Research and writing interests include

communities of practice and technology integration.


Available September 1, 2001Greenwood Publishing

About InterMath What is InterMath? Who is involved in InterMath? What is the rationale for InterMath? What are the goals of InterMath?

About InterMathProfessional DevelopmentCognitive Development http://www.intermath-uga.gatech.edu/

What is InterMath? A five year, NSF-funded Internet-based

professional development project A community of middle school

mathematics teachers and administrators

An effort to strengthen teachers’ conceptual understanding

A program that uses technology to explore problem solving situations

About InterMath•What is InterMath?•Who is involved?•Rationale•Goals

Professional DevelopmentCognitive Development http://www.intermath-uga.gatech.edu/


Professional DevelopmentCognitive Development

A Sad Excuse for Problem Solving



A Consequence of Bad Problems

Who is Involved? LPSL - UGA (Hannafin, Wilson)

Research scientists, SMEs, Web and curriculum developers CEISMC - Georgia Tech (Ohme)

Web designers and technical support Workshop Participants

Middle school teachers/administrators and instructors at UGA, Kennesaw State, Valdosta State, and state INTECH centers.




Rationale for InterMath New approaches to teaching and

learning



Learning over the Past 50 years



Teaching Math in 1950:

A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price.

What is his profit?





A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit?





A logger exchanges a set "L" of lumber for a set "M" of money. The cardinality of set "M" is 100. Each element is worth one dollar. Make 100 dots representing the elements of the set "M". The set "C", the costof production contains 20 fewer points than set "M". Represent the set "C" as a subset ofset "M" and answer the following question: What is the cardinality of the set "P" of profits?





A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20.

Your assignment: Underline the number 20.





By cutting down beautiful forest trees, a logger makes $20. What do you think of this way of making a living? Topic for class participation after answering the question:

How did the forest birds and squirrels feel as the logger cut down the trees?





A company outsources all of its loggers. The company claims that contracting workers will Ultimately save them on expenses for benefits and salaries when demand for their product is down. The union requests that you take a closer look at historical employment, salary, benefits, and contracting data located on the web.

Was outsourcing a good move? Use a cognitive tool like a spreadsheet or simulation to develop and support your reasoning.


learning



Resilient and pervasive beliefs about teaching mathematics

Insufficient content background in teacher training programs


Is this what mathematics teaching is about?




learning Insufficient content background in

teacher training programs Resilient and pervasive beliefs

about teaching mathematics



Escalating demands for teachers and little support


Teacher Support




learning Insufficient content background in

teacher training programs Resilient and pervasive beliefs

about teaching mathematics Escalating demands for teachers

and little supportAbout InterMath•What is InterMath?•Who is involved?•Rationale•Goals


Difficulty attaining learning standards


Georgia Test Scores



The Truth



Compared to the Nation



“Georgia drops to 50th in nation in SAT scores” “State Board of Education's goal of reaching a 1,000 mean score by 2001 is all but dead.” -Savannah Morning News


Goals for InterMath Promote innovative practices Revitalize teaching by modeling

and applying innovative approaches

Support reform of mathematics teaching and learning

Establish a human and technological support infrastructure


Professional DevelopmentCognitive Development http://www.intermath-uga.gatech.edu/

Professional Development Participant Selection Workshop Procedures Our Use of Technology Additional Contributions


Participant Selection

Underserved schools will receive priority Schools where mathematical technologies

are available Teams of middle-school teachers and

administrators

About InterMathProfessional Development

•Participant Selection•Workshop Procedures•Use of Technology•Additional Contributions

Cognitive Development http://www.intermath-uga.gatech.edu/

“If you can teach middle school, then you can teach anyone.”



Cognitive Development

Workshop Procedures 100 hours of training

45 hour workshop, 55 hour “follow along” development course

Development of portfolio using a web page Write-ups of investigations Development of technology lessons

Ongoing support system Human (experts, community) Electronic (listserv, bulletin board, email) Documents (tutorials, guides)




InterMath’s Use of Technology




…does not focus on finding answers.

InterMath’sUse of Technology

Cognitive tool for building ideas, organizing thinking, solving problems, and exploring patterns

Multiple technologies promote multiple representations

Provides new learning opportunities About InterMath

Professional Development•Participant Selection•Workshop Procedures•Use of Technology•Additional Contributions


Additional Contributions

Evolving database of investigations Teacher resources and lesson

plans Discourse through electronic

communitiesAbout InterMathProfessional Development




Rationale of Workshop Activities Workshop Content Investigations Teacher’s Activities


Rational of Workshop Activities Intrinsically motivating

Appropriate level of challenge Appeal to curiosity Learner control Realistic applications

Ownership of learning Open-ended exploration Generative extensions of

investigations

About InterMathProfessional DevelopmentCognitive Development

•Rationale of Workshop Activities•Workshop Content•Investigations•Teacher’s Activities

Workshop Content 14 topics under four categories

Algebra Geometry Number Concepts Data Analysis

Adapted investigations from MTMS Support materials

Guides and tutorials Database of solutions


•Rationale of Workshop Activities•Workshop Content•Investigations•Teacher’s Activities http://www.intermath-uga.gatech.edu/



Multiple cases can be investigated using technology. Pre-Algebra students can rely on technology to investigate the situation. The investigation promotes generalizability or can be used as a springboard for further exploration. Multiple methods can be used to explore the situation. Multiple solutions are possible. The investigation is easy to start exploring. The investigation can be modified for use in a middle school classroom.


Investigation Criteria

Sample Investigation



Choose two numbers. Add them together and form a Fibonacci-like sequence, starting with your first two numbers, and ending with a total of ten numbers. For example, if your first two numbers are 3 and 5, then your third number is 8 (3+5), your fourth number is 13 (8+5), your fifth number is 21 (8+13), and so on. Determine a relationship using the seventh term and sum of the terms of your sequence. Is this true for every sequence of this nature? Explain.





To make a pen for his new pony, Ted will use an existing fence as one side of the pen. If he has ninety-six meters of fencing, what are the dimensions of the largest rectangular pen he can make?

(Source: Mathematics Teaching in the Middle School,

Nov-Dec 1994).





Quadrilateral ABCD is a rectangle with length to width in the ratio of 3 : 2. AN and BM arebisectors of angle A and angle B, respectively. What is the ratio of the area of the shaded regionto the area of ABCD? Explain your solution.


Teacher Write-Up



Determining which method to use in solving this problem intrigued me. My students have been studying rotations, dilations, and reflections usinga coordinate graph and triangles. This seemed a good opportunity for me to show them how these movements could be used to solve a problem….

Creating Investigations What are some issues?



Support Familiarity with software Motivation Prior knowledge Use of technology Structure and hints Self and Peer-evaluation

Teacher Lessons



Your employer has put you in charge of the packaging for a new promotional item. If children send in 10 proofs of purchase along with $1.95 to cover shipping, they will receive a box of 125 cubic centimeters of SLIME! The packaging for the slime should be in the shape of a rectangular prism for easy mailing. What dimensions should you give this package?

Problem created by Kim Seay, Dacula Middle School

A Reflection



... it's a different story to hear [from a teacher] "hey, I did this in my classroom, and the kids did awesome with it, and you should see what they did" than to hear somebody stand up at a lecture and they say this is how you should teach cause kids will do this and kids will do that. Um, a lot of stuff sounds good in theory, but you think, oh yeah, well how is that going to happen? You know, how could you do that? ... I think that since I have been able to do some of it, and been able to get the type of reactions from the kids, that makes me want to tell people, you know, and show people, here you can do this and it's really good.

Teacher Lessons



The bases on a baseball field are 90 feet apart and form right angles. The pitcher’s mound is 60 ft and6 inches from home plate. If the third baseman isthrowing the ball to the first baseman, should the pitcher duck his head if he is standing on the mound?

Problem created by Peggy Reigle, Athens Academy

Next Steps What we have achieved (years 1-2)

Design and development of workshop investigations and website

Workshops in Athens/Atlanta Teacher development of write-ups and lesson

plans What we plan to achieve (years 3-5)

Implementation of workshops at various sites around Georgia

Ongoing support system of resources, tools, and people

Our Challenge Ahead Our goal is to empower teachers with skills and strategies to use technology in a manner where mathematics is explored, learned, and applied in meaningful, useful, and resourceful ways.

However, if we train teachers to use technology solely based on our vision without being aware of their learning and pedagogical needs, we may be in for an unpleasant and unfortunate surprise...


http://www.arches.uga.edu/~eglazer/NECC2001.html

intermath professional and cognitive development through problem solving and technology

Documents

ugaintermath problem

taught high school mathematics

illinoiswebbased development

real teacher

goals of intermath

communities of practice

personal record

technology integration