View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by University of Minnesota Digital Conservancy AUTOMATICITY OF BASIC MATH FACTS: THE KEY TO MATH SUCCESS? THESIS Presented in Partial Fulfillment of the Requirements for The Master of Education Degree in the College of Education and Human Service Professions By Carmel E. DeMaioribus University of Minnesota Duluth 2011 Committee Signatures: Chair Member Graduate Program Director AUTOMATICITY OF BASIC MATH FACTS 11 ABSTRACT Despite a concerted effort by policy makers and educators to improve U.S. math education, student math scores remain unimpressive. In exploring possible reasons for this, this study examined the role that basic math fact automaticity plays in math success, where automaticity is defined as the ability to recall facts with speed and accuracy at an unconscious level. Information processing theory posits that automaticity frees up cognitive resources for more complex processes, and should therefore be an important part of learning math. To investigate this, basic multiplication fact fluency levels of a group of college students were determined by a timed math probe. These same students also completed a short survey assessing their attitudes and high school math achievements. The students’ levels of fluency as demonstrated on the math probe were then compared to their reported math attitudes and achievements. Relationships between levels of fluency and math attitude and achievement were noted. The most interesting finding, however, was the lack of basic multiplication fact automaticity in 90% of the college students tested. The implications of this lack of automaticity present an interesting subject for future study. AUTOMATICITY OF BASIC MATH FACTS 111 TABLE OF CONTENTS Chapter One: Introduction............................................................................................ 1 Research Problem and Purpose.....................................................................................1 Research Questions....................................................................................................... 3 Background....................................................................................................................3 Setting........................................................................................................................... 4 Assumptions.................................................................................................................. 4 Scope of the Study........................................................................................................ 5 Definitions..................................................................................................................... 6 Summary....................................................................................................................... 6 Chapter Two: Literature Review...................................................................................8 U.S. Math Education Today..........................................................................................8 Mathematical Learning in Children............................................................................10 Automaticity................................................................................................................12 Why Students Do Not Develop Automaticity............................................................ 14 Summary ....................................................................................................................16 Chapter Three: Methodology......................................................................................17 Research Questions.....................................................................................................17 Participants..................................................................................................................17 Research Design..........................................................................................................18 Data Collection............................................................................................................19 Treatment of Data....................................................................................................... 20 Summary ....................................................................................................................21 Chapter Four: Results and Discussion........................................................................22 Results......................................................................................................................... 22 Fluency........................................................................................................................22 Achievement............................................................................................................... 23 Attitude........................................................................................................................23 Discussion .................................................................................................................. 24 Fluency and Achievement...........................................................................................25 Fluency and Attitudes................................................................................................. 26 Analysis.......................................................................................................................27 Summary ....................................................................................................................29 Chapter Five: Summary and Conclusions.................................................................. 30 Significant Findings....................................................................................................30 Educational Implications ........................................................................................... 31 AUTOMATICITY OF BASIC MATH FACTS iv Recommendations for Future Research......................................................................32 Conclusion.................................................................................................................. 34 References................................................................................................................... 35 Appendix A: Survey................................................................................................... 44 Appendix B: Math Probe............................................................................................ 45 Appendix C: Information Sheet for Research............................................................ 46 Appendix D: Percentage of Students in Each Fluency Tier.......................................47 Appendix E: Data Sorted by Number of Correct Answers........................................ 48 Appendix F: Math Achievement by Fluency Tier......................................................51 Appendix G: Math Attitude by Fluency Tier............................................................. 52 Appendix H: Fluency Levels Within Majors............................................................. 53 AUTOMATICITY OF BASIC MATH FACTS CHAPTER ONE Introduction College students have graduated from high school and have been accepted to college, but do they really know their multiplication tables? This is not an idle question. With alarming frequency, college professors have noted with shock and dismay how ill- prepared their incoming students are (Alsup, 2005; Latterell, 2005; National Science Foundation, 2006; Sanoff, 2006; Wilson, 2007). This is particularly vexing because many school districts have increased both the requirements and the rigor of their secondary math programs in recent years. Greater numbers of high school students are now taking more math at higher levels (Reys, Dingman, Nevels, & Teuscher, 2007). What, then, accounts for this discrepancy between the increased emphasis on math and the lack of commensurate results? In the public realm, discussions about math education by politicians and business people have concentrated on ways to enable students graduating from American schools to be competitive in STEM (Science, Technology, Engineering, and Mathematics) fields (Heritage Foundation, 2009; National Governor’s Association, 2008; National Science Foundation, 2006; U.S. Department of Education, 2008). To this end, there has been additional pressure from policy-makers and administrators to teach more math to students before they graduate from high school. But perhaps the focus should not be on how much math is taught before graduation, but rather how solid the foundations of math are. Research Problem and Purpose Research has shown that higher level math requires automaticity of basic math facts, where automaticity is defined as the ability to recall basic math facts with speed AUTOMATICITY OF BASIC MATH FACTS 2 and accuracy at an unconscious level (Baroody, Bajwa, & Eiland, 2009; Cumming & Elkins, 1999; Poncy, Skinner, & Jaspers, 2006; Verschaffel, Luwel, Torbeyns, & VanDooren, 2009; Woodward, 2006). It is usually assumed that because students have progressed through the primary grades, they have achieved automaticity of basic math facts. However, this may not be true in many cases. There is a dearth of data on whether or not students actually achieve automaticity in American schools, and