Practicing Patterns

Interactive Web tools support math learning and skill practice that matters

Mr. Marcos teaches fourth grade at a neighborhood school. Recently the student population has begun to grow as older apartments in the area are converted to subsidized housing for low-income families. This has changed the school's demographics as well and staff are now more aware of the needs of diverse learners.

A recent math pre-test of students showed the broadest range of abilities in the class he's seen in his 12 years of teaching. He realizes he will need to differentiate instruction, and to find effective strategies to use with his students.

Implementing Research-Based Strategies

In previous years he concentrated on skill practice and memorization at the beginning of the school year. He learned that mastery of skills takes place over time, and that students need time practicing new skills in a variety of applications and in different contexts. Compressing practice into the beginning of the year does not allow students to adapt the new information to their growing conceptual understanding.

He needed to spread out practice over the entire school year, building toward mastery over time.

• When students practice a skill, they reach approximately 48 percent accuracy after only the first four practice sessions. It"s not until students have practiced a new skill about 24 times that they reach 80 percent accuracy. Mastery occurs with practice that is spread out over time (Anderson, 1995; Newell & Rosenbloom, 1981).
• Understanding reaches a "halfway point" relatively quickly, but then slows and continues to increase only incrementally (Marzano, Pickering, & Pollock, 1999).
• Teaching concepts and skills in isolation weakens students' ability to make connections to their ideas, experiences, and other subjects (Bransford, Brown, & Cocking, 1999).

Marcos designed a plan for practice that allows students to create links between their personal experiences and mathematics, as well as other content areas. To plan his next math unit he selected the goal of "Understanding Patterns". ("represent and analyze patterns, using words, tables, and graphs". He found that this goal is required across the math, science, and social studies standards for fourth grade.

Technology Supporting Success

Aware that many national education organizations develop online resources, Marcos found a handful of interactive Web sites that support math and science with online tools for students. He planned the unit around those most appropriate for his students.

Marcos decided to build the class's weekly visits to the computer lab around math learning. He constructed a schedule for the 75 minute block that creates repeat opportunities for practice throughout the year. During the first 15 minutes students practiced the concept learned the previous week. The next 15 minutes he modeled the new lesson or activity, and then students worked together for 30 minutes. (His students worked in pairs because there were only 18 computers.) The final 15 minutes were spent writing. He asked students to write about the math they had learned, and describe how it connected to their world.

Computer Lab Schedule

To use the time in the computer lab as a curriculum "anchor point" grounding the students in the mathematical concept, he used simulations, challenges, and resources he found on the Web, and connected them to specific content areas. Each week he found a different online resource and used it to support his students' understanding of patterns.

For example, he chose an interactive online calculator from the NCTM Illuminations Web site to develop an activity for students to practice creating number patterns. An online tool for Morse Code helped students learn patterns in language and code. A "Pattern Generator" provided students opportunities to experiment and practice pattern development with images. Each student could experiment and learn at his or her own pace, and throughout the year the various approaches and activities would provide a wide range of experiences for the range of student abilities.

The visual representations helped students demonstrate and model understanding, and the interactive tools helped them practice and apply new concepts at their own pace. Using technology helped Marcos provide his diverse learners with ample experiences in many formats to practice.