Practicing New Skills
Classroom examples of practicing new skills and procedures by applying understanding through carefully sequenced series of tasks.
Students perform at a higher level when teachers consistently use challenging tasks that encourage high-level thinking rather than procedural tasks (Rectanus, 2006). After synthesizing the substantial research on K-8 mathematics learning and cognitive psychology, the national Mathematics Learning Study Committee chose the term “mathematical proficiency” to describe successful mathematics learning. The Committee identified five interdependent strands that make a student mathematically proficient: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. The authors encourage practice embedded in problem solving. After students understand the meaning of a concept or procedure, practicing – to promote fluency – builds confidence and competence. Students who commit basic facts to memory and become computationally efficient are more likely to become successful problem solvers. Thus, automatizing mathematical procedures is justified when those procedures are regularly required to complete other tasks, such as basic multiplication combinations.
[Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Rectanus, C. (2006). So you have to teach math? Sound advice for grades 6-8 teachers. Sausalito, CA: Math Solutions.]
1. Games (elementary and middle school)
Students need frequent practice to learn new skills and procedures. Games are a great way to provide time for practice in early primary and intermediate classrooms. Students as young as kindergarten can practice number recognition with BINGO. Cribbage can be taught to second graders to reinforce addition facts. Teachers can reinforce multiples of five for all elementary students by teaching dominoes. Several games to develop number sense, including “Catch the Teacher,” “Greater/Fewer,” and “Moving Down the Road,” are described by Bender (2005).
http://teacher.scholastic.com/lessonrepro/lessonplans/grmagam.htm
See also:
Bender, W. N. (2005). Differentiating math instruction: Strategies that work for K-8 classrooms! Thousand Oaks, CA: Corwin Press.
Moscovich, I., & Brion, D. (2001). Probability games and other activities. New York, NY: Workman.
2. “Choice Time”/Math stations (elementary)
Students work on a variety of activities that focus on similar content. For example, in fourth through sixth grade, Volume Stations may include activities such as: creating a box with a volume of between 15 and 32 using graph paper; building a solid box using 36 cubes; and drawing the faces of a solid box that is 30 cubes. Ask how many ways you can build a solid box using 12 cubes, and how many cubes are needed to fill a box that is 10 by 3 by 4?
http://investigations.terc.edu/faqs/Choice_Time.cfm
3. Algebraic thinking
The activities and lessons on the NSDL Middle School Portal online resource range from introduction to the fundamentals of algebra to work on linear functions. These supplementary materials help students learn algebra through concrete models, visual representations, and interactive tasks.
http://msteacher.org/epubs/math/algebraic/introduction.aspx
4. NCTM Navigation Series (multiple grades)
Relevant for-purchase activities help students explore important ideas, make connections to deepen their understanding, and build fluency in procedures. Specific titles vary by grade level. Most come with CD-ROMs that include interactive programs and blackline masters.
http://my.nctm.org/eBusiness/ProductCatalog/productsview.aspx?id=110,