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Teacher Interventions-To-Go Series
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School-Wide Strategies for Managing...
MATHEMATICS

Mathematics instruction is a lengthy, incremental process that spans all grade levels. As children begin formal schooling in kindergarten, they develop ‘number sense’, an intuitive understanding of foundation number concepts and relationships among numbers. A central part of number sense is the student’s ability to internalize the number line as a precursor to performing mental arithmetic. As students progress through elementary school, they must next master common math operations (addition, subtraction, multiplication, and division) and develop fluency in basic arithmetic combinations (‘math facts’). In later grades, students transition to applied, or ‘word’, problems that relate math operations and concepts to real-world situations. Successful completion of applied problems requires that the student understand specialized math vocabulary, identify the relevant math operations needed to solve the problem while ignoring any unnecessary information also appearing in that written problem, translate the word problem from text format into a numeric equation containing digits and math symbols, and then successfully solve. It is no surprise, then, that there are a number of potential blockers to student success with applied problems, including limited reading decoding and comprehension skills, failure to acquire fluency with arithmetic combinations (math facts), and lack of proficiency with math operations. Deciding what specific math interventions might be appropriate for any student must therefore be a highly individualized process, one that is highly dependent on the student’s developmental level and current math skills, the requirements of the school district’s math curriculum, and the degree to which the student possesses or lacks the necessary auxiliary skills (e.g., math vocabulary, reading comprehension) for success in math. Here are some wide-ranging classroom (Tier I RTI) ideas for math interventions that extend from the primary through secondary grades.

Jim's Recommended Internet Resources for...
MATHEMATICS

A-Plus Flashcard Maker. You can create math fact flashcards online. Customize your flashcards by type of number operation or even enter your own values to create individual flashcards. ||Report Broken Link

Ask Dr. Math.. Dr. Math is an online math tutorial service, maintained by Drexel University, Philadelphia, PA. Students can browse a large archive of math questions and answers and post their own questions as well. This tutorial site never closes! ||Report Broken Link

Cognitive Strategies in Math. This site presents several thinking strategies that students can learn to master math computation and applied math problems. It is sponsored by the Special Education Department, University of Nebraska-Lincoln. ||Report Broken Link

Math Central. Billing itself as ‘an Internet service for mathematics students and teachers’, this site contains math teaching resources, a forum to post math questions, and a challenging ‘math problem of the month.’ Math Central is sponsored by the University of Regina, Saskatchewan, Canada. ||Report Broken Link

Math Worksheet Generator. Sponsored by Intervention Central, this free site allows users to create math computation worksheets and answer keys for addition, subtraction, multiplication, and division. Use the Worksheet Generator to make math worksheets to use with students who need to build fluency with math facts. ||Report Broken Link

Numberfly: Early Math Fluency Probes. Numberfly is a free application from Intervention Central that allows educators to create CBM progress-monitoring probes of 3 types that assess students' developing numeracy skills: Quantity Discrimination, Missing Number, and Number Identification. This application also includes instructions for administering and scoring these early math assessments, as well as suggestions for using Early Math Fluency Probes in a school-wide RTI Universal Screening. ||Report Broken Link

Teacher2Teacher. Sponsored by Drexel University, Philadelphia, PA, Teacher2Teacher describes itself as “a resource for teachers and parents who have questions about teaching mathematics.” Participants can browse archived math teaching questions by level (elementary, secondary), pose their own teaching questions, and take part in on-line discussions on math instruction topics of interest. ||Report Broken Link

References

Armendariz, F., & Umbreit, J. (1999). Using active responding to reduce disruptive behavior in a general education classroom. Journal of Positive Behavior Interventions, 1(3), 152-158.

Baxter, J. A., Woodward, J., & Olson, D. (2005). Writing in mathematics: An alternative form of communication for academically low-achieving students. Learning Disabilities Research & Practice, 20(2), 119–135.

Bryan, T., & Sullivan-Burstein, K. (1998). Teacher-selected strategies for improving homework completion. Remedial & Special Education, 19, 263-275.

Carnine, D. (1997). Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 130-141.

Caron, T. A. (2007). Learning multiplication the easy way. The Clearing House, 80, 278-282.

Chard, D. (n.d..) Vocabulary strategies for the mathematics classroom. Retrieved November 23, 2007, from http://www.eduplace.com/state/pdf/author/chard_hmm05.pdf

Cooke, L B. & Adams, V. M. (1998). Encouraging "math talk" in the classroom. Middle School Journal, 29(5), 35-40.

Hawkins, J., & Brady, M. P. (1994). The effects of independent and peer guided practice during instructional pauses on the academic performance of students with mild handicaps. Education & Treatment of Children, 17 (1), 1-28.

Hong, E., Sas, M., & Sas, J. C. (2006). Test-taking strategies of high and low mathematics achievers. Journal of Educational Research, 99(3), 144-155.

Lambert, M. C., Cartledge, G., Heward, W. L., & Lo, Y. (2006). Effects of response cards on disruptive behavior and academic responding during math lessons by fourth-grade urban students. Journal of Positive Behavior Interventions, 8(2), 88-99.

Montague, M. (1997). Cognitive strategy instruction in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 164-177.

Montague, M., Warger, C., & Morgan, T. H. (2000). Solve it! Strategy instruction to improve mathematical problem solving.. Learning Disabilities Research & Practice, 15, 110-116.

Pólya, G. (1957). How to solve it (2nd ed.). Princeton University Press: Princeton, N.J.

Rhymer, K. N., Skinner, C. H., Jackson, S., McNeill, S., Smith, T., & Jackson, B. (2002). The 1-minute explicit timing intervention: The influence of mathematics problem difficulty. Journal of Instructional Psychology, 29(4), 305-311.

Skinner, C. H., Pappas, D. N., & Davis, K. A. (2005). Enhancing academic engagement: Providing opportunities for responding and influencing students to choose to respond. Psychology in the Schools, 42, 389-403.

Van Essen, G., & Hamaker, C. (1990). Using self-generated drawings to solve arithmetic word problems. Journal of Educational Research, 83, 301-312.

Van Garderen, D. (2006). Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities. Journal of Learning Disabilities, 39, 496-506.

Williams, K. M. (2003). Writing about the problem solving process to improve problem-solving performance. Mathematics Teacher, 96(3), 185-187.

Woodward, J. (2006). Developing automaticity in multiplication facts integrating strategy instruction with timed practice drills. Learning Disability Quarterly, 29, 269-289.

Zrebiec Uberti, H., Mastropieri, M. A., & Scruggs, T. E. (2004). Check it off: Individualizing a math algorithm for students with disabilities via self-monitoring checklists. Intervention in School and Clinic, 39, 269-275.

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