Making Math Success Happen

The Best of Learning and Leading With Technology on Mathematics

Ivan W. BaughAnne Raymond

ISTE Publications

Making Math Success Happen closely examines the use of technology in the teaching of

mathematics – BEYOND USING A GRAPHING

CALCULATOR.

The text is organized around the NCTM Standards:

• Process Standards– Communication: Do mathematicians communicate?– Connections: Does mathematics relate to other

curriculum content?– Problem Solving: Why is everything in mathematics a

problem?– Reasoning and Proof: Are the results really evident?– Representation: Are pictures worth a thousand

words?

And the NCTM Technology Principle: “Technology is essential in teaching and learning mathematics; it influences the

mathematics that is taught and enhances student’s learning.

• As essential tools for teaching and learning, calculators and computers:– provide visual images of mathematical ideas– facilitate organizing– compute efficiently and accurately

• Further, when such tools are available students can focus more on mathematical process, such as decision making, reasoning and problem solving.

And the ISTE Technology Standards for students which are

centered around the six categories:

• Basic operations and concepts• Social, ethical, and human isues• Technology productivity tools• Technology communications tools • Technology research tools• Technology problem-solving and decision-

making tools

And the ISTE Technology Standards for teachers which are

centered around the six categories:

• Technology operations and concepts• Planning and designing learning

environments and experiences• Teaching, learning, and the curriculum• Assessment and evaluation• Productivity and professional practice• Social, ethical, legal, and human issues

It is particularly important to ponder these issues when planning lessons

that integrate technology into the mathematics pedagogy because

appropriate technology should be a TOOL that encourages discourse

and establishes an engaging learning environment.

When students engage in mathematical problem solving,

particularly when using technology as a tool for solving problems, they

become mathematically empowered and gain a confidence that students may never achieve in

a traditional mathematics classroom.

This will require a significant philosophical change for many

mathematics educators. They must stop teaching as they

were taught and start teaching in a manner that enables students to

master the concepts.

Text Layout:

• Conversation: Ann and Ivan introduce each NCTM standard

• Theory into Practice: Ideas for incorporating the standard

• Insight: Reflections on the standard

• Articles: Field tested activities/lessons

Chapter 1: Communication

• Pictures express more than a thousand words

• NETS Communication Standard 4 – Technology Communication tools:– Students use telecommunications to

collaborate, publish, and interact with peers, experts, and other audiences

– Students use a variety of media and formats to communicate information and ideas effectively to multiple audiences

Assigned Readings

• NCTM Conference – Anyone interested?

NCTM Position Paper – Technology in the Learning and Teaching of Mathematics

• Technology is an essential tool for teaching and learning mathematics effectively: it extends the mathematics that can be taught and enhances student’s learning

• Teachers must be prepared to serve as knowledgeable decision makers in determining when and how their students can use these tools most effectively– Examples:

• Square roots• Logs• Factoring

NCTM Position Paper – Calculators in the Education of Youth

• NCTM recommends the integration of calculators into the school mathematics program AT ALL GRADE LEVELS

• Skill in estimation, both numerical and graphical, and the ability to determine if a solution is reasonable are essential elements for the effective use of calculators

In-Class ActivityBottles and Beyond

• Skills– Measurement– Graphing– Drawing

• Software– MS Draw– MS Excel

Summary

• Insert your lesson plan

• Expansions:– Hot tub graphs– Popcorn graphs– As the caterpillar crawls– Match the graph – Student generated data– Assignment – from the handout

Additional Activities

• The Spreadsheet – Absolutely Elementary– Offers ideas for enhancing spreadsheet presentations

• Journaling with a Database– Offers ideas for writing journals

• Teaching Students to Communicate Mathematically– Offers organizational techniques for mathematics

communications

• ANY OF THESE MAY BE USED AS A GUIDE FOR YOUR END OF SEMESTER PROJECT

Chapter 2 - Connections

• Mathematicians turned artist:– Lewis Carroll – Alice in Wonderland– Art Garfunkel – Simon and Garfunkel

• Artists turned mathematicians:– M.C. Escher – geometric drawings– Benjamin Bennaker – architech of

Washington D.C.

NCTM Standard - Connections Instructional program from pre-kindergarten through grade 12 should enable all students to:

• Recognize and use connections among mathematical idesa

• Understand how mathematical ideas interconnect and build on one another

• Recognize and apply mathematics in contexts outside of mathematics (commonly overlooked!)

NETS Standard – Technology Research Tools

• Students use technology to locate, evaluate and collect information from a variety of sources (web searching techniques to be discussed later)

• Students use technology tools to process data and report results

• Students evaluate and select new information resources and technological innovations based on the appropriateness to specific tasks

NOWHERE does the math content become secondary – rather through making connections while learning skills, students associate the skills with daily life and better internalize

them for future use

Assigned ReadingISTE Standards

• www.iste.org

• http://cnets.iste.org.index2ns.html

Activity – State Representatives

• Skills:– Collect data from the WWW

• http://www.census.gov/prod/2001pubs/c2kbr01-2.pdf

– Formulas in Excel– Analyze results in writing

• Software– WWW– MS Excel– MS Word

Summary

• Insert your lesson plan

• Expansions:– Search for any other allocation methods – Which method(s) work best for your home

state?– Increase/decrease the population of your

home state and examine the effect on the allocation to the remaining states.

ActivityLeonard’s Proportions

• Skills:– Measurement– Data entry– Formulas – proportions

• Software:– MS Excel

• Student Data Sheet

Summary

• Insert your lesson plan• Expansions:

– Search for additional data on the golden section (AKA The golden ration or the golden number)

– Search for a biography of Leonardo Da Vinci (a good resource for the History of Math course)

– Applications of the golden ration in Geometry (to be explored later using different software)

Chapter 3 – Problem Solving

Calls for reform repeatedly include the need to improve the teaching and learning of mathematics by engaging students in

more problem-solving tasks

George Polya

• Understand the problem– Examine the information, Identify the question

• Devise a Plan– Make a list, Draw a picture, Guess and check

• Carry out the plan– Modify as needed

• Look back– Make sure the answer is reasonable

NCTM Standard

• Build new mathematical knowledge through problem solving

• Solve problems that arise in mathematics and other contexts

• Apply and adapt a variety of appropriate strategies to solve problems

• Monitor and reflect on the process of mathematical problem solving

NET-S Standard

• Students use technology resources for solving problems and making informed decisions

• Students employ technology in the development of strategies for solving problems in the real world

Two important issues

• Via technology, “problem solving can focus on more real-life issues and on the process of problem solving…rather than the complicated mathematical computations.

• Rather than teaching students about problem solving, educators need to think about teaching students via problem solving. (Masingila, Lester, and aymond, 2001)

Guess and Check Method

• Page 79 of the text – Problems on ticket sales and temperature conversion– Using the spread sheet – page 79 of text– Using a sequence and list on TI 83– Using y-variables on TI 83