*from Technology & Learning*

**Educators can turn to technology to help their students grasp difficult math concepts.**

Mathematics teachers at all levels of public school education want their students to understand and apply math concepts. When students use different technologies in the classroom, they will become engaged in meaningful learning that helps them to move from abstract ideas to hands-on applications. Students can "see" math concepts and manipulate those concepts quickly through technology.

**Elementary School**

**Online videos.** Watching online math videos can help elementary school students see and apply the geometry concept of patterns. The videos present many examples of patterns and non-patterns and allow the students to identify given examples.

**Students can use concept-mapping software on laptops to grasp how to represent numbers in various ways.**

**Videoconferencing.** One way students can learn to use representations is to communicate math through videoconferencing with another school. Participating schools can ask questions like How many students walk to school? Ride a bicycle to school? Get a ride from a parent or relative? Ride the bus? Each class answers the survey questions and creates an electronic spreadsheet, and then selects a graph to represent the information. The schools compare their graphs and talk about why they selected the specific graph to represent the information.

**Whiteboards.** Students can learn to analyze the characteristics and properties of two-dimensional geometric shapes through whiteboard activities. The students use the whiteboard to move and categorize the shapes by their angles and sides, a highly engaging and very visual learning activity.

**Collaborative Web projects.** An Internet-based collaborative grocery project is a great way to encourage kids to analyze and evaluate the mathematical thinking and strategies of other students. The hosting school starts by selecting five common foods, and then the classes from other states find their local prices and report back the information. Each class (or group within each class) creates math problems based on that information, ranging from the simple (How much does two gallons of milk and two loaves of bread from Ithaca cost?) to the more complex (What percent increase is the highest priced half gallon of ice cream compared to the lowest priced one?) The other class solves the problems and explains its thinking strategy. The problem-creating class verifies the answer and provides feedback and evaluation.

**Computers.** Students can create their own math problems based on understanding ways to represent numbers. They can form a percentage and decimal problem by creating 10 shapes of various types using Inspiration. For example, one student might make four blue squares, five red circles, and one yellow triangle. After all the students have created their math problems, the students go around the lab or laptops. They stop at each computer and write down the percent of the total for each type of shape and its decimal equivalent in their learning log. Each student shares the answers for his or her own problem.

**Middle School**

**Digital cameras.** Using a digital camera is one way students can connect mathematical concepts with the world at large. For example, they could take pictures of geometric shapes around the school—like a baseball field—to create their own math problems. A sample question, such as, If the school wants to fence in the baseball field, how much fencing would it take? can be answered by supplying the field's width and length dimensions. Questions can be posted to a class Web site or blog for other class-mates to answer.

**Word processing.** By pretending that they're part of an outer space team sent to gather data about Earth's vegetation, students can apply basic and advanced measurement concepts (and have some fun while they're at it). First they measure leaves to determine if they came from the same plant or different plants. Next they use a camera to document the samples. Finally, they use a word processor to send a report back to their commander giving the data, the pictures, and their professional analysis of the vegetation.

**Online.** Often online math sites contain student pretests and quizzes, such as applying the basic concepts of probability. However, many sites do not contain any constructive feedback if the student has an incorrect answer. For example, one site might repeat "No, try again" for every incorrect answer. That does not scaffold the problem to guide students toward understanding the math concept.

Math teachers can pretest their students' comprehension of a math standard, such as developing predictions that are based on data so that they can structure their next math unit for maximum effectiveness. If the teachers' district does not have an online quiz program, the teachers can use an online quiz or survey program such as Zoomerang to administer the quiz and report the results. The teachers pretest the standard in a comprehensive and in-depth manner to the highest level of thinking required by the standard. Based on the results, they refocus their unit to address the areas in which the class has the lowest scores.

**High School**

**Spreadsheets.** Few things inspire students more than the idea of having their own car. Educators can ask them to use math models to figure out how much it will cost for their dream vehicle. The students select their vehicle from an online car source, find its cost, check the interest rates from four banks, use a spreadsheet to calculate the interest on the car for three- and five-year periods, and determine the total cost of the vehicle including interest. Also, they determine how increasing the down payment impacts the interest and the total car cost.

**Graphing calculators.** When high school students use graphing calculators to apply transformations to mathematical situations, abstract quadratic equations become morphed into a visualized reality. Students play the "what if" game by changing the curve and instantly seeing the algebraic results.

**PowerPoint.**Sometimes students need to be guided through a complex process, such as the algebraic concept of polynomial long division. Teachers can create a step-by-step scaffolded presentation that not only shows each step but explains it through PowerPoint. That presentation could demonstrate how to avoid common mistakes in this division, and the teacher might choose to post it to the class Web site or blog. Before teachers create their own presentation, they can search for already created ones by putting "topic" plus ".ppt" in a search engine.

**Podcasts.** Some math classes synthesize their learning about concepts like functions by creating podcasts, but this tool can also be used by teachers and other professionals. Math teachers should analyze whether the topic can be understood by listening to an audio podcast or whether an enhanced or video podcast is a better learning experience for their students.

*Harry Grover Tuttle is an instructor/project manager at Syracuse University.*