Research for TechQuest Project

Research for TechQuest Project: A Compelling Mathematical Dilema

I was amazed at how much information I found on the topic of math fact fluency. Quite frankly, growing up, I just thought that it was something the teachers did to torture us. I thought it was old school teaching to emphasize drill and practice of math facts. Timed math facts tests and “star charts” posted on the wall for everyone to see who the math geniuses of the group were tormented me throughout grade school. Now that I am a teacher and I can see the negative effects on students when they do not have automaticity and fluency when solving math problems I am researching the very topic I was so intimidated by and frustrated with while growing up. I do have to say that we have come a long way in this area and hopefully there are only a limited number of actual “star charts” posted in classrooms for everyone to see each others rankings.
As I began the research I first wanted to make sure that I had a valid concern that was backed up by research. I had seen first-hand, time and time again, that students in grades fifth through eighth were struggling through more difficult math concepts and multi-step problems if they didn’t have automatic math fact recall. Unfortunately, this is a much bigger problem than I had originally thought. So fortunately, there is a lot of research about it.
I started off my search by looking for journal articles and studies to support my theory that a deficit in math fact recall will negatively affect a student’s math ability in the middle school grades and beyond. I started off by using the MSU Libraries on line. This was incredibly helpful. By just searching “math facts fluency” through a ProQuest basic search I was able to locate hundreds of articles that related to my topic. However, a lot of these results were just software suggestions or other non-essential topics that I wasn’t looking for. Then I did some more advanced searches with the subject of education and teaching math fact fluency. I was also able to search for current articles by including date parameters. I did not realize the “math wars” that have been going on for decades around this subject. I was able to tab and save research through the MSU library site on twelve different resources that all directly related to the validity of my TechQuest topic. I have listed four of the best resources I found through MSU Libraries below. I have also gone to the source and linked the title of each article to the full online version or the ProQuest link.

The New York Times:
Report Urges Changes in Teaching Math

• After hearing testimony and comments from hundreds of organizations and individuals, and sifting through a broad array of 16,000 research publications, the panelists shaped their report around recent research on how children learn.

• For example, the report found it is important for students to master their basic math facts well enough that their recall becomes automatic, stored in their long-term memory, leaving room in their working memory to take in new math processes.

• ''For all content areas, practice allows students to achieve automaticity of basic skills -- the fast, accurate and effortless processing of content information -- which frees up working memory for more complex aspects of problem solving,'' the report said.

• Dr. Faulkner, a former president of the University of Texas at Austin, said the panel ''buys the notion from cognitive science that kids have to know the facts.''

Lewin, T. (2008, March 14). Report urges changes in teaching math. New York Times, section A; Column O; National Desk; Page 17.



The Wall Street Journal:
Arithmetic Problem: New Report Urges Return to Basics in Teaching Math; Critics of 'Fuzzy' Methods Cheer Educators' Findings; Drills without Calculators; Taking Cues from Singapore

• The nation's math teachers, on the front lines of a 17-year curriculum war, are getting some new marching orders: Make sure students learn the basics.

• In a report to be released today, the National Council of Teachers of Mathematics, which represents 100,000 educators from prekindergarten through college, will give ammunition to traditionalists who believe schools should focus heavily and early on teaching such fundamentals as multiplication tables and long division.

• The council's advice is striking because in 1989 it touched off the so-called math wars by promoting open-ended problem solving over drilling. Back then, it recommended that students as young as those in kindergarten use calculators in class.

John Hechinger. (2006, September 12). Arithmetic Problem: New Report Urges Return to Basics In Teaching Math; Critics of 'Fuzzy' Methods Cheer Educators' Findings; Drills Without Calculators; Taking Cues From Singapore. Wall Street Journal (Eastern Edition), p. A.1. Retrieved April 5, 2010, from ABI/INFORM Global. (Document ID: 1125933101).



Phi Delta Kappan:
Endless Ping-Pong Over Math Education

The reason cited by many critics for U.S. students' having fallen below the ridiculous "first in the world" declaration of Goals 2000 is that they don't learn the fundamentals. Math reforms, they say, focus too much on learning through applied practice and not enough on learning through necessary rote methods. This was the basis of the "math wars" in California several years ago.

Anne C Lewis. (2005). Endless Ping-Pong Over Math Education. Phi Delta Kappan, 86(6), 420-421. Retrieved April 5, 2010, from Research Library Core. (Document ID: 796601741).


Education Week:
Panel Calls for Systematic, Basic Approach to Math; Federal advisory group's proposals may reignite debate on 'broken' content and instruction

• Nearly two years in the making, the report went through 90 drafts, with its members wrestling over major recommendations and individual words and phrases. It was approved unanimously at the panel's final meeting, held March 13 at Longfellow Middle School here in a suburb of the nation's capital.

• The 90-page document calls for the math curriculum to be streamlined in pre-K-8, a strategy it calls putting "first things first." Students need to be grounded in both the effortless, automatic recall of simple procedures and in the acquisition of broader problem-solving skills. Too often, those skills are wrongly presented as incompatible, the report says.

• At various points, the authors also allude to the enduring philosophical battles over how to teach the subject--commonly referred to as "the math wars." Those disputes tend to pit those who argue that students should be grounded more firmly in simple math procedures against others who advocate a more conceptual approach to teaching and learning.

• "Debates regarding the relative importance of these aspects of mathematical knowledge are misguided," the report says. "These capabilities are mutually supportive, each facilitating the learning of the other."

Sean Cavanagh. (2008, March). Panel Calls for Systematic, Basic Approach to Math:Federal advisory group's proposals may reignite debate on 'broken' content and instruction. Education Week, 27(28), 1,12. Retrieved April 5, 2010, from Research Library Core. (Document ID: 1454317041).

My next research stop was to the U.S. Department of Education website (Ed.gov) to search for more related information there. I found The Final Report of the National Mathematics Advisory Panel. This is a very interesting report that all math and elementary teachers should read. It really backs up my theory.

U.S. Department of Education:
The Final Report of the National Mathematics Advisory Panel

• To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem solving skills. Debates regarding the relative importance of these aspects of mathematical knowledge are misguided. These capabilities are mutually supportive, each facilitating learning of the others. Teachers should emphasize these interrelations; taken together, conceptual understanding of mathematical operations, fluent execution of procedures, and fast access to number combinations jointly support effective and efficient problem solving.

• Computational proficiency with whole number operations is dependent on sufficient and appropriate practice to develop automatic recall of addition and related subtraction facts, and of multiplication and related division facts. It also requires fluency with the standard algorithms for addition, subtraction, multiplication, and division.

• Research on instructional software has generally shown positive effects on students’ achievement in mathematics as compared with instruction that does not incorporate such technologies. These studies show that technology-based drill and practice and tutorials can improve student performance in specific areas of mathematics.

After my surfing and searching through Google I also found this great website called the Center for Implementing Technology in Education. They have an entire research center you can search for relevant information. I found a great research paper related to my TechQuest.

Center for Implementing Technology in Education:
Technology Supported Math Instruction for Students with Disabilities: Two Decades of Research and Development.

• A variety of technologies are available to enhance students’ mathematical competency by building their declarative, procedural, and conceptual knowledge. The remainder of this paper will review these technologies. This review will be guided by the NCTI Mathematics Matrix found at http://www.citeducation.org/mathmatrix. The matrix identifies six purposes of technology use for supporting student mathematical learning, including (1) building computational fluency;…

• Declarative knowledge is developed through technologies that help build computational fluency.
The research on computational fluency suggests that the ability to fluently recall the answers to basic math facts is a necessary condition for attaining higher-order math skills. The rationale for this thinking is that all human beings have a limited information-processing capacity. That is, an individual simply cannot attend to too many things at once. Grover Whitehurst, the Director of the Institute for Educational Sciences (IES), noted this research during the launch of the federal Math Summit (2003):

Cognitive psychologists have discovered that humans have fixed limits on the attention and memory that can be used to solve problems. One way around these limits is to have certain components of a task become so routine and over-learned that they become automatic.

• The implication for mathematics is that some of the sub-processes, particularly basic facts, need to be developed to the point that they are done fluently and automatically. If this fluent retrieval does not develop, then the development of higher-order mathematics skills—such as multiple-digit addition and subtraction, long division, and fractions—may be severely impaired (Resnick, 1983). Indeed, studies have found that lack of math fact retrieval can impede participation in math class discussions (Woodward & Baxter, 1997), successful mathematics problem-solving (Pellegrino & Goldman, 1987), and even the development of everyday life skills (Loveless, 2003). And rapid math-fact retrieval has been shown to be a strong predictor of performance on mathematics achievement tests (Royer, Tronsky, Chan, Jackson, & Merchant, 1999).

• While the research cited above highlights the importance of math fact fluency, the computation capabilities of American students might well be diminishing. Tom Loveless of the Brookings Institute has reviewed responses to select items on the NAEP and concluded that performance on basic arithmetic facts declined in the 1990s (2003). More emphasis needs to be placed on developing rapid, effortless, and errorless recall of basic math facts.

I decided to search using Bing next. I searched for “research math computation fluency”. I found a great research project on FASTT Math and I even emailed the two teachers that implemented it. I am waiting to hear back from them to see if I can site some of their findings. This is the same program I was going to try and use.
What Is the Relationship Between Fluency and Automaticity through Systematic Teaching with Technology (FASTT Math) and Improved Student Computational Skills?
Patty Lehner; Virginia Beach City Public Schools; November 30, 2008

FASTT Math
I have streamlined my focus and I have discovered that trying to recreate the wheel is not necessary. My original goal was to implement my idea using free resources and websites with a math log; however, I am now seeing the advantages to using one database or program to implement my TechQuest. The ability for a program to interpret student ability and customize a program for each individual is critical for long term success. There were a number of programs I came across while conducting my research.

One of the programs that I continued to see over and over again was FASTT Math (Fluency and Automaticity through Systematic Teaching with Technology). I found different research studies that have been done using this program and they all seem to have had success. Some of the research I found to support the use of FASTT Math I have listed below.

This is a basic overview of the FASTT Math idea: Using FASTT Math (Fluency and Automaticity through Systematic Teaching with Technology), struggling students, grades 2 – up, develop fluency with basic math facts in addition, subtraction, multiplication, and division. The software moves beyond traditional drill and practice to assess each student's level and to provide a continuously adaptive program that increases fluency in customized, 10-minute daily sessions. FASTT Math also includes prescribed print activities for those students who need additional instruction in the conceptual foundation of numbers and operations.

Product Features
• Research-based and validated • Authored by Ted Hasselbring and Laura Goin • Students practice basic facts in addition, subtraction, multiplication, or division • Customized course of study for each student, based on individual assessments • Frequent, short practice sessions • Choice of two fact ranges: 0-9 or 0-12 • Generates customized worksheets for additional practice • 12 detailed performance and usage reports at the student, class, grade, and school levels for teachers and administrators • Teacher’s Guide with assessments and lesson plans • Fact Fluency Foundations Guide with age-appropriate activities for counting, number concepts, and computation strategies • Bilingual — switch easily between English and Spanish • Meets guidelines for universal accessibility and Meets State and National Standards

Students will:
Learn basic facts in addition, subtraction, multiplication, and division; Be able to recall facts from memory; Develop fluency with multi-digit problems in each operation; Gain the foundation necessary for success in higher-order problem
solving.
For more information or to request an evaluation version or a research report call Tom Snyder Productions at (800)342-0236 or log on to http://www.tomsnyder.com/

Research to back up the FASTT Math program:
The following excerpt is taken from Technology Supported Math Instruction for Students with Disabilities: Two Decades of Research and Development.

Developing Fluency in Math Delayed Children using Technology
To counteract the problem described above, educators have turned to technology with varying degrees of success to help students achieve fluency in math facts. Although it seems intuitive that using technology in a drill-and-practice format helps students develop the declarative fact knowledge, evidence suggests that this is not the case. In an early study by Hasselbring, Goin, and Sherwood (1986), it was found that computerized drill and practice was ineffective in developing declarative fact knowledge in students with math difficulty. The identified problem was that typical drill-and-practice software was designed in such a way that students were practicing “procedural counting” strategies instead of developing the ability to recall facts from memory. As a matter of fact, even studies that report reduced response latencies as a result of the use of computerized drill and practice could not demonstrate that facts were being retrieved from memory, only that procedural counting time was reduced (Christensen & Gerber, 1990; Pellegrino & Goldman, 1987).
As a result of this research, Hasselbring and Goin (2005) developed an intervention paradigm called FASTT (Fluency and Automaticity through Systematic Teaching with Technology) designed to assist students in the development of declarative fact knowledge. The FASTT approach has been used successfully to develop mathematical fluency. It appears that the key to making the retrieval of basic math facts fluent is to first establish a mental link between the facts and their answers which must be stored in long term memory. FASTT embodies several unique design features to help develop these relationships. These 7 features include the following:

1. Identification of fluent and non-fluent facts;
2. Restricted presentation of non-fluent information;
3. Student generation of problem/answer pairs;
4. Use of "challenge times;"
5. Spaced-presentation of non-fluent information;
6. The appropriate use of drill-and-practice; and
7. Computer monitoring of student performance.
Each of the above features has been incorporated into a software program, called FASTT Math (2005) designed specifically to develop declarative fact knowledge.

There is a FASTT Math Research Foundation site that shows all kinds of interesting statistics and research that has been conducted on this program. Of course, this is also the same site you can order from so it is always important to keep that in mind.

Again, I refer to the study done by two teachers that I have emailed and hope to hear back from.
What Is the Relationship Between Fluency and Automaticity through Systematic Teaching with Technology (FASTT Math) and Improved Student Computational Skills?
Patty Lehner; Virginia Beach City Public Schools; November 30, 2008

Research Summary
Overall, I found more than enough information to help me with my TechQuest. Honestly, I could have done research for weeks. I will admit than I am one to use Google too often and not expand my search. I am so glad I used so many different search engines and methods this time. Yes, there was some overlap but honestly I found new and exciting references in each location! The MSU Libraries were probably the most helpful in keeping my search focused and on target so I didn’t have to weed through tons of “junk”. I was disappointed with my EduHound search. There were some references to testing results; however, most of the sites were linking me to math teaching ideas and websites that were more about classroom tools and tips.
Based on the research I have conducted I think that I have a very valid problem of practice and a good start to helping solve the problem using technology. Some of the barriers and complications to conducting this TechQuest will be the costs and access to a classroom since I am currently a building substitute teacher. I have decided to write this up as a proposal for future implementation in a school I hope to be working in next year.