Lee Honors College Senior Thesis Defense Amy Young October 28, 2011

 Fluency  What is fluency?  Efficient, appropriate, and flexible application of skills  Why is fluency important?  Assessment  What is the purpose of assessment?  Previous studies/research  Henry and Brown

 Rote memorization: written practice, flash cards, focused only on memorization and speed  Collections approach: seeing represented numbers as a group  Combinations of Ten: 1+9, 2+8, 3+7, 4+6, 5+5, 10+0

 After receiving small-group instruction on conceptual, meaningful ways to solve basic math fact problems involving combinations of ten and making ten strategies, do students have a better understanding of the meaning of mathematics and rely less on counting to determine answers to basic facts?

 St. Augustine Cathedral School  Student Interviews: Pre-assessment  Groups  Mini-Lessons  Student Interviews: Post-assessment  Sophistication: high or low based on how a student solves a problem  High: strategy, memorized recall  Low: counting, guessing, no answer

 Ten Frame  Quick Images  Tens Go Fish

This is an example of a double Ten Frame. The problem represented is 3+8. The students first represent the number 3 (or 8). Then they represent the 8 (or 3) on the second Ten Frame. The student then moves his chips to the Ten Frame containing 8 chips to make a complete Ten Frame (making a 10). The student can then easily see that the answer to 3+8 = 10+1 = 11.

Assessment Question Student Number AAAAAANAAAA 2AAAACAAAAA 3AAA DDDAAD 4AAAAAAAAAA 5ACACCAAAA 6AABACABAAA 7CACAACAAAA 8ABAACBAAAA Assessment Question Student Number AAAAAAAAAA 2CBBACAAAAA 3ACAACCABDA 4AACAAAAAAA 5CAACAAAAAD 6CBAACABAAD 7CACACAAAAA 8ABBDBAAAAA KEY A - CountingCorrect B - StrategyIncorrect C - MemorizedNo Answer D - Guess NA - No Answer

Student Number Assessment Questions 1AAAAAANAAAA10% AAAAAAAAAA80% 2AAAACAAAAA CBBACAAAAA100% 3AAANADDDAAD30% ACAACCABDA70% 4AAAAAAAAAA90% AACAAAAAAA70% 5ACACCAAAANA80% CAACAAAAAD70% 6AABACABAAA90% CBAACABAAD 7CACAACAAAA60% CACACAAAAA50% 8ABAACBAAAA90% ABBDBAAAAA70% KEY A - CountingCorrect B - StrategyIncorrect C - MemorizedNo Answer D - Guess NA - No Answer

Pre-AssessmentPost-Assessment

 Increased use of combinations of ten and making ten strategies  Increased willingness to attempt the tasks  Increased sophistication in strategies and accuracy

 Larger student sample  Control group  Different strategies  Subtraction  Application for upper grades

 Mrs. Gina Kling, thesis mentor  Committee Members: Dr. Jane Jane Lo, Mrs. Sharon Wade, Mrs. Vicki Kudwa  The Lee Honors College  St. Augustine Cathedral School  Western Michigan University Mathematics Department

Baroody, Arthur (2006):. “Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them.” Teaching Children Mathematics : “Grade 1 Mathematics: Operations and Algebraic Thinking”Common Core State Standards Initiative (2010). Henry, Valerie and Richard Brown (2008) “First-Grade Basic Facts: An Investigation Into Teaching and Learning of an Accelerated, High-Demand Memorization Standards” Journal for Research in Mathematics Education : 39(2) p Kling, Gina (2011). “Fluency with basic addition.” Teaching Children Mathematics: 18(2) p Mokros, Russell, & Economopoulos (1995). “Shouldn’t Students Memorize the Basic Math Facts?” Beyond Arithmetic : National Council of Teacher of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc. National Council of Teachers of Mathematics (2003). A Research Companion to Principles and Standards for School Mathematics. J.Kilpatrick, W. Martin, D. Schifter (Eds.). Reston, VA: National Council of Teachers of Mathematics, Inc. National Research Council (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. Thornton, Carol (1978). “Emphasizing Thinking Strategies in Basic Fact Instruction.” Journal for Research in Mathematics Education : 9(3), Wheatley & Reynolds (1999). “Thinking in Units.” Coming to Know Number: A Mathematics Activity Resource for Elementary Teachers : 9-15.