The Math Forum @ Drexel: Technology Enhances
Problem Solving and Assessment
presented by Suzanne Alejandre & Cynthia Lanius

NCTM 2006 Annual Meeting and Exposition
Asking Questions - Generating Solutions

Session 670 in St. Louis, Missouri
Friday, April 28, 2006, from 1:00 pm to 2:30 pm
America's Center - 262 (capacity: 50)

Introduction

What is a tPoW?

 

Let's do math!

Balloon Booths - Scale the size of a hot air balloon so you can make it fit through a narrow passage and hit a nail to pop it.

How might technology enhance or detract from students' mathematical understanding?

 

Traffic Jam Activity - Find the fewest number of moves for the ten people to end up on the opposite side from where they started. Kinesthetic experience (people), manipulative (plastic people), technology (Java applet)

What is the advantage of using one method over another?

 

Explore tPoW Selection

Building a House

What are the largest number of cubes to make the house? What's the smallest number of cubes?

 

Counterfeit Coins

Find the fewest number of weighings that will identify which of the nine coins is counterfeit.

 

Galactic Exchange II

Using a vending machine (Java applet) determine the relative values of the coins used on the planet Orange.

 

How Many Cubes?

Given the front view and side view of some cubes, students are asked what the larget number of cubes can be used to make the arrangement and what the smallest number of cubes would be.

 

Million Penny Project

Students use a spreadsheet to show when they will have collected their million pennies.

 

Miranda and the Rookie

Use a spreadsheet to compare salaries of the star basketball player and the rookie.

 

Munching Bugs

Use the Sam the Chameleon applet to learn more about the coordinate plane.

 

Patio Stones

How many stones did Kathy need to buy to pave an area in her yard?

 

Tangrams

Use an interactive applet to discover some of the relationships among the pieces in a set of Tangrams.

 

Temperature Change

Use the given information to find the temperature.

 

Train Trouble

How fast is the train moving to allow Herman and Sheila to each escape the tunnel?

 

Types of Triangles

Students use a GSP sketch or an interactive web page to drag and manipulate four triangles. They identify one of each type: scalene, isosceles, equilateral, and right.

 

Let's Submit

Temperature Change submission

Hints and Answer Checks

Student Sample Solutions

Scoring Rubric and Scoring Grid

 

Questions for Discussion:

How engaging are the problems? Are they at the right level of rigor for your students? Will they challenge students? What learning goals will they help achieve?

 

How might communication (reading, writing, talking, and explaining) around the problem enhance or detract from students' mathematical understanding?

 

What kinds of support will you and your students need to solve the problems and use the technologies effectively? How can we best deliver that support?

 

Resources to Browse with Internet Access:

List of Technology Problems of the Week

Math Tools
      Getting Started
      Navigating Math Tools

 

Notes of Appreciation

Thank you to Joel Duffin of the National Library of Virtual Manipulatives (NLVM), Utah State University for his assistance and permission to use the Space Blocks, Coin Problem, Tangrams, Pattern Blocks, and Color Chips Java applets.

 

Thank you to the Freudenthal Institute, Utrecht, The Netherlands, for their assistance and permission to use the Building houses with side views Java applet.

 

Thank you to George Reese and Pavel Safronov of MSTE, a division of the College of Education at the University of Illinois at Urbana-Champaign, for their assistance and permission to use the Chameleon Java applet.