Critical Tasks of Reading: Fluency & Comprehension

Reading requires readers to successfully carry out two very different tasks: the ability to decode words fluently and comprehend the text.  Although fluency and comprehension are only two parts of a balanced literacy curriculum, they may very well be the two most important skills for reading success.  Each year school-age children across America are assessed of their ability to read fluently.  Running Records and Qualitative Reading Inventories (QRIs) have long been a source for fluency assessment, until 2001 when the University of Oregon established Dynamic Indicators of Basic Early Literacy (DIBELs).  Now a well known literacy test assessing students in more than 45 states, it still has its critics.  This article critiques the DIBELs assessment against similar tests of fluency, such as Running Records and QRIs, as a means of assessing and promoting fluency.  Furthermore, because fluency is in part a prerequisite to comprehension, this article will highlight the strategies most consistently recommended by experts in the field of literacy, in order to improve reader comprehension.

Fluency is “the ability to read accurately, quickly, effortlessly, and with appropriate expression and meaning” (Rasinski, 2005).  It is a necessary component of reading because it indicates that the reader has effortlessly decoded the words.  Successful text decoding is a precursor to comprehension.  As LaBerge and Samuels pointed  out in their 1974 theory of automaticity in reading, readers who must devote a sufficient amount of time and energy to decoding compromise the important task of making sense of the text; comprehension (Rasinski, 2005).  Thus comprehension is negatively affected by a lack of fluency and some researchers may argue that comprehension comes with fluency.  Regardless of whether fluency comes on its own or is a specific strategy that must be taught, one can not dispute that it is a building block of early literacy.

To assess a student’s fluency, timed reading tests are generally given, measuring two components: words correct per minute and reading fluency rate.  The words correct per minute is measured as a percentage of words read correctly from some total number of words, and reading fluency is determined as the number of words read correctly in a given time period, compared with published standards per grade level. The Institute for Literacy has defined  fluency testing as a calculated series of 1-minute tests. The National Reading Panel outlines a procedure for calculating fluency.  It begins with having the administrator select 2 or 3 grade leveled texts (regardless of the student’s instructional level) and have the student read each passage for exactly one minute. vThe administrator counts the number of words read during each test, and computes the average for the number of words read per minute.  Second, the administrator counts the number of words read incorrectly in each passage and computes the average number of errors per minute.  To calculate the average number of correct words read per minute (WCPM) the  administrator then subtracts the average number of errors read per minute from the average total number of words read per minute.  The WCPM rate should then be compared with published standards for fluency at the student’s current grade level (National Institute for Literacy, 2000). 

In 2001 federal funding used to support the No Child Left Behind Act opened the  Reading First Center on Teaching and Learning to support literacy education in Oregon schools.   From that committee the Dynamic Indicators of Basic Early Literacy (DIBELs) assessment was created.  Based on the five big ideas researched and supported by the National Reading Panel,  DIBELs assesses phonemic awareness, alphabetic principle, accuracy & fluency, vocabulary, and comprehension.  In the last 10 years DIBELs has become a household name in the world of early childhood literacy.  Now in it’s 6th edition, DIBELs is used widely across the country; at least 45 states include it as a measure of early childhood literacy skills, but its success does not come without critics (Center for Teaching and Learning, 2010).  DIBELs relies on a method of taking a median score versus a mean, perplexing some critics such as the New York State Education Department which questions “what is the advantage of taking the median score versus the average?”  (Center for Teaching and Learning, 2010).  DIBELs assesses oral reading fluency with a per-selected series of three 1-minute timed tests.   Students are given the text and told to begin reading, while they are timed and scored by an administrator. When 1 minute has passed students are told to stop reading.  The passages are scored for errors, and the total number of words read correctly is recorded as the score.  The median score from the three passages is then recorded as the child’s fluency score.  For example, if the student receives scores of 27, 36, and 25, the recorded score would be 27.  The Dynamic Measurement Group of the University of Oregon maintains that the median score is the most reliable estimate of a child’s performance.  Taking the median score minimizes error in measurement due to extraneous factors such as a child’s background knowledge or interest in particular passage.  Mean versus median is not the only topic of critique DIBELs has received as a method of assessing student fluency.  Miscues and errors in the DIBELs oral reading fluency assessment differs from running records, qualitative reading inventories, and other widely used fluency assessments.

  Running Records, created by reading remedial specialist, Marie M. Clay, assesses oral reading fluency in a way somewhat different from how DIBELs does.  The biggest difference is that DIBELs assess students at a grade level benchmark, whereas various running records can be administered to students regardless of their grade level.  Running Records seek to determine the child’s independent and instructional reading levels, which means a first grader can essentially be administered a fifth grade passage if it is at his independent reading level.  When the passages become too difficult for the child, the instructional level is determined and the test is concluded (Clay, 2000)   Running Records analyze six types of miscues, some are the same as DIBELs while others are vastly different.    While hesitations are not miscued in Running Records, nor are errors in the pronunciation or abbreviations, numerals,  and hyphenated words, there is some miscue analysis in Running Records not recordable as an error by DIBELs assessment.  Most obvious are that all self-corrections are recorded as errors in Running Records.  Similarly, repeated words are ignored and not marked as errors in DIBELs but do count against a student’s score in Running Records.  Substitutions are an additional kind of Running Record error that too is not mentioned in DIBELs oral reading fluency assessment.  A close look at another widely used fluency assessment, Qualitative Reading Inventories, provides another reason to question DIBELs fluency assessment measures.  Essentially, a student could read a single passage have three different administrators score them very differently depending on which fluency measure they were using (Leslie & Caldwell, 2000). 

Additionally, critics of DIBELs have questioned the fairness of the assessment of English Language Learner students and those with disabilities.  In 2008 the Oregon Reading First Center  addressed some the most frequent concerns aiming to dispel myths and rumors of DIBELs assessment.  The Oregon Reading First center proclaimed that DIBELs is an appropriate measure of students for whom English is a second language, unless the student is learning to read in another language.  Furthermore, Oregon Reading First stated that DIBELs is an appropriate measure for all students, even those with Individualized Educational Plans in literacy. The few exceptions are that DIBELs is not appropriate for students that are deaf, have severe disabilities, or have disabilities that affect their speech, such as stuttering, or oral paraxial (Center for Teaching & Learning, 2010).  Although fluency has been identified as an important ingredient in reading, it is only a part of the critical task of being able to read.  Decoding is one part, and comprehension is the other ingredient for success (Griffith & Rasinski, 2004).  Comprehension cannot rely on fluency alone however, it takes practice and skillful use of strategies that work.  There are effective strategies for reading comprehension that are widely recognized as suitable for teaching to young readers and/or less proficient readers in order to improve their comprehension.   Stephanie Harvey and Anne Goudvis, authors of Strategies that Work, have identified 6 key strategies for improving comprehension.  Their strategies, which are geared for K-8 students include activating background knowledge, questioning, visualizing and inferring, determining importance, and summarizing information (Harvey & Goudvis, 2000).   Harvey’s colleague, Debbie Miller,  highlights the same strategies in her book, Reading with Meaning, for the K-3 students.  Miller refers to visualizing as “creating mental images”, and stresses the importance of activating background knowledge through making connections.  Most primary teachers will confirm that their students are constantly making text to self connections, but had more difficulty making text-to-text and text-to-world connections (Miller, 2002).  Activation of background knowledge and making connections are on the forefront of Miller’s strategies for primary-age children, while with explicit instruction, modeling, and a gradual release of responsibility primary students can practice this and the other strategies on their own.   Fisher, Frey, and Lapp describe their experience observing and interviewing 67 nominated, and expert teachers in the field of literacy, who focused on the same reading comprehension strategies promoted by Harvey and Miller.  The findings of their study showed that teachers modeled their own thinking while students were primarily silent observers.  Teachers described their thinking and modeled multiples ways of thinking rather than focusing primarily on one strategy at a time. As one teacher commented, “we need to show students how to incorporate these things automatically and not artificially stop and summarize or question or whatever”. (Fisher, Frey, & Lapp, p. 550).   At the same time, teachers expressed that it is important to not use all of the strategies in their modeling.  In fact, Duke and Pearson assert that each mini-lesson should be kept brief, 10-15 minutes and then gradually move from a position in which the teacher assume all of the responsibility to a situation where the students assume all the responsibility.  This gradual release of responsibility allows the teacher use direct instruction through modeling, followed by guided practice of the strategy to a region of shared responsibility among students and teachers performing the comprehension technique (Duke & Pearson, 2002). To reiterate, DIBELs assesses students on a variety of areas of literacy, including initial sound fluency, letter naming recognition, nonsense word fluency, and oral reading fluency.  Oral reading fluency is the most effective DIBELs measure for assessing oral fluency. DIBELs assesses oral reading fluency at students’ grade level benchmark and compares their scores against benchmark standards.  DIBELs then suggests strategic or intensive interventions for less proficient readers.  In addition to the interventions suggested by DIBELs, comprehension monitoring strategies suggested by experts in the field of literacy, modeled through guided practice and a gradual release of responsibility promote increased comprehension when practiced regularly.  All of these parts of literacy contribute to a balanced and rich early learning environment that will prepare children for success in reading while providing teachers with the assessment tools to teach to where their students are at.

For More Information:

• • Center for Teaching and Learning. (2010). Official DIBELS homepage
  • Clay, M.M., (2000). Running records for classroom teachers. Heinmann.
  • Duke, N. K., & Pearson, D. (2002). Effective practices for developing reading comprehension. In A.E. Farstrup & S.J. Samuels, What research has to say about reading instruction (pp. 205-242). International Reading Association.
  • Fisher, D., Frey, N., & Lapp, D. (2008). Shared readings: modeling comprehension, vocabulary, text structures, and text features for older readers. The Reading Teacher, 61(7), 548-556.
  • Harvey, S., & Goudvis, A. (2000). Strategies that work. Stenhouse Publishers.
  • Leslie, L. & Caldwell, J. (2000). Qualitative reading inventories-3. Pearson Education.
  • Miller, D. (2002). Reading with meaning. Stenhouse Publishers.
  • National Institute for Literacy. (2000). Put reading first: the research building blocks for teaching children to read (PR/Award Number R305R70004). US Department of Education.
  • Rasinski, T. V., Padak, N. D., McKeown, C. A., Wilfong, L. G., Friedauer, J. A., & Heim, P. (2005). Is reading fluency a key for successful high school reading? Journal of Adolescent & Adult Literacy, 48 (1),

Parents Preparing Children for Success in Learning to Read and the Importance of Phonemic Awareness

The foundations of early literacy development begin at home. Children begin learning about literacy long before they are able to read. Although research suggests the literature rich environment in which children are raised varies considerably, it can be assumed that most parents, regardless of their approach to early education, hope their children will successfully learn to read, and some will make attempts to prepare their children for success in learning to read. This article will highlight just that, research based strategies parents can do to best prepare their young children for successfully learning to read. As an instructor of early education, it is the experience of the author of this article that phonemic awareness is one part of a balanced literacy program that is often misunderstood by parents. It is a skill that with early practice is essential for learning to read. Therefore, the explanation and importance of phonemic awareness will too be brought to light as a contributing skill for success in early literacy.

It is important to note the variety in type of literacy that occurs in homes. Although on may not realize it, literature appears everywhere. Literature is in the story a picture tells. Like the old saying goes, “a picture tells a thousand words”. Many children are fortune to experience the pleasure of being read to. Children who experience story time learn that print represents words, and words tell an account of something. Children may develop favorite stories and can expect these narratives to be the same each time they are read. Evidence of storytelling’s favorable impact on early literacy is undeniable. “Children who have had many and diver experiences in storybook reading do well on school-based measures of literacy” (Paratore, 57). However, not all children participate in story time experiences prior to a formal schooling experience. “There are other rich and varied literacy and language practices that are embedded in the fabric of children’s daily lives” (Paratore, 57). Though such practices may go unnoticed, a short list of everyday uses of literature and language appears quite impressive. Consider the following uses of everyday language: cutting coupons, reading roads signs, singing songs, filling out a form, cooking from a recipe, perusing the television guide, studying sports scores, balancing a budget, conversation, etc.

Unfortunately, socioeconomic status appears to parallel laying a literacy rich foundation for early literacy skills. “By the age of 3, children in poverty [are] already well behind their more affluent peers” according to a study by G. Wells, 1986 (Waskik and Bond, 63). On the basis of his study, Wells found that lower-income parents placed less value on literacy as evidenced by an absence of books in the home, and lack of rich language use. Not only do children in poverty have less access to literature materials, but their opportunities to converse with adults is 2x-3x lower than that of their middle-class counterparts. Therefore, providing a literacy rich learning environment in the home appears to require access to text, opportunities for read alouds, and meaningful conversation between child and adult.

“Reading aloud to children at home…is probably the most highly recommended activity for encouraging language and literacy” (Beck & McKeown, 2001). Read alouds strength brain development by forcing children to think about more than just the here and now. To make these experiences most effective for children, text must be challenging, and parents must engage in “text talk”, that is “getting children to think about what is going on in the story” (Freppon, p. 144, et al Beck & McKeown, 2001). Talking about text entails asking opened ended questions, activating background knowledge, making comparisons between text and text and/or text and real life, and explaining new vocabulary.

The key to preparing young children for success in learning to read is by providing read aloud experiences coupled with effective text talk. Although it may be relatively easy for middle class parents to provide read aloud experiences for their children, it is not as simple to engage in text talk that promotes language and literacy development. The most common read-aloud strategies are not the most effective. It takes practice on behalf of the parent and child. Use of open-ended questions allows children to construct meaning from what has been. Considering the following questions: “That character’s getting into trouble, isn’t he?” versus “What’s the character doing now?”, the latter probes the listener to construct meaning. Beck and McKeown suggest occasionally waiting to show pictures until after the reading has been discussed. Children often rely too heavily on pictures cues and can misconstrue basic story information when the content of the pictures is in conflict with the text (p 17). “Children need help in bringing background knowledge to bear in appropriate ways”, rather than simply recalling personal experiences, they need to be helped understand how their connection compares with the text. Parents also need to take advantage of the sophisticated vocabulary found in texts, by applying it in conversations with their children. Young children can handle challenging content (McKeown, 10).

In my experiences as an early education educator I have encountered numerous parents that have provided literacy strategies to help their children become successful readers. These parents provided read-aloud opportunities for their children and engaged in successful text talk. Moreover, the culture of their home was a rich literacy environment that included varieties of everyday text, early writing opportunities, singing, phonological activities (rhyming, knowledge of onset & rime), use of rich language, and letter recognition. Although their children knew the alphabet, could print their name, and recognize both upper and lowercase letters, time and time again parents have commented they wished they had spent more time on phonemic awareness. “Phonemes are the smallest units that make up spoken language. English consists of approximately 41-44 phonemes” (Ehri & Nunes). The letters of the English alphabet represent the phonemes in the spelling of words.

Phonemic awareness is a particularly difficult concept to understand. Whereas letter recognition simply implies being able to identify upper and lowercase letters in print, phonemic awareness relies entirely on listening to the units of sounds in spoken language. Many people confuse phonemic awareness with phonics, which is better explained as associating speech sounds with each corresponding letter. Phonemic awareness is difficult because there are more phonemes in the English language than there are letters in the alphabet. Many letter sounds blend together to form a single phoneme which is very difficult to distinguish because “there are no boundaries in speech marking where one phoneme ends and another begins”.

Phonemic awareness is essential for learning to read because of the sheer volume of words in our English language. Occasionally teachers run across a proficient early reader who appears to have mastered decoding, when in reality the students Has simply memorized a considerable amount of sight words. This system of reading may work for a few years, but eventually as the student encounter complex and richer vocabulary, without phonemic awareness skills the reader will fail to advance. While it is true that nearly 85% of the words adults read are sight words, the other 25% must be decoded or sounded out. For one to become a fluent reader, they must understand how to break works into smaller segments and break the code, so to speak.

“Phonemic awareness measured at the beginning of kindergarten is one of the best predictors of how well the child will learn to read during the first two years of school” (Paratore, 2001). Phonemic awareness is equally important in early literacy to write as it is to read. It’s no mystery that writing and reading go hand-in-hand. A beginning writer uses invented spelling by sounding out the smallest pieces of language (phonemes), and putting them into print (Yopp & Yopp, pg 131). The English language is much like a prescription. There is a prescribed spelling and pronunciation for each word dependent on the regularities of phonemes. Although some words with silent letters and unusual spellings defy the rules of the English language, most words can be decoded and spelled correctly simply by having a phonemic awareness and applying it to break words down to the smallest unit of sound.

To reiterate, the most important things parents can do to prepare their children for success in learning to read include providing read aloud experiences coupled with effective text talk. Effective text talk increases a child’s vocabulary and provides essential comprehension strategies such as answering opened ended questions, activating background knowledge, making comparisons between text and text and/or text and real life, and inferring main ideas. In part with providing a literacy rich home environment, parents might consider providing phonological experiences for their child, such as singing songs, playing rhyming games, and teaching children to identify onset and rime. In addition to learning letter names and basic sight word recognition, parents can provide phonics lessons for their children by teaching the sounds associated with each letter. Children who engage in early writing activities such as labeling pictures, and use of invented spellings are practicing phonemic awareness skills by sounding out words and breaking speech into the smallest units of sound for decoding purposes. All of these parts of literacy contribute to a balanced and rich early learning environment that will prepare children for success in school.

Getting What You Pay For: The Debate over Equality in Public School Expenditures

In response to the ongoing debate over equity in public school expenditures, a collection of data was recently compiled in attempt to shed light upon the argument of whether individual states and geographical regions are getting what they pay for.  Although some argue that finances to support public schools are spent disproportionately thereby yielding disproportionate levels of academic success among our nation’s students, others suggest money spent is statistically unrelated to student success rates.  In this dataset all of variables were collected from each state, and extracted from the Digest of Educational Statistics, where the primary purpose of the Educational Statistics publication is to provide prekindergarten through graduate school information on a variety of subjects related to public and private education, primarily compiled by the National Center for Education Statistics (NCES).

 

Frequency Distributions of the Dependent Variables

 

In this study, the independent variables include each of the 50 United States including the District of Columbia. In some investigations the four geographical regions of the U.S. are compared.  These regions include the West, Midwest, South, and Northeast.  A breakdown of the states included in each region is given later in this report.  The dependant variables in the continuous data include, but are not limited to: current expenditures per pupil in average daily attendance in public elementary and secondary schools, average pupil/teacher ratio in public elementary schools, estimated average annual salary of teachers in public education, and percent of students in elementary and secondary schools who are eligible for free or reduced-price lunch.  Figure 1 shows the frequency distribution of the current expenditures per pupil in average daily attendance in public elementary and secondary schools, 2005-2006.  Of the 51 states data was collected from, only one state spent less than $7,000.00 per pupil in average daily attendance and that was Utah at $5,960.00. Similarly, only one state spent more than $17,000.00 per pupil and that was the District of Columbia, spending $18,339.00 per pupil in average daily attendance in public school.

 

Figure 1. Expenditures per Pupil Histogram (thousands of dollars)

Results

Data analysis was compiled using numerous tabular and graphic tables available in Microsoft Office Excel, edition 2007. Figure 1. is a distribution of Expenditures per Pupil (raw scores) shown on the horizontal axis in thousands of dollars spent, with intervals of one thousand dollars along the abscissa. The ordinate indicates the frequency of occurrence by the independent variable, states, along the y axis.

Expenditure per pupil spending in the District of Columbia is an outlier, as indicated in Figure 2., a box plot of expenditures per pupil.  A five-number summary of the data in Figure 2. displays the dispersion of the data, highlighting the minimum and maximum of the data, median expenditure, and the lower (Q1) and upper (Q2) quartile of the data.  The expenditure per pupil for the District of Columbia at $18,339.00 falls beyond the Q2 and could be considered an outlier.

 

Figure 2. Expenditures per Pupil Box Plot

Distribution of Average Pupil / Teacher Ratio in Public Elementary Schools

Figures 3. and 4. display the distribution of the average pupil to teacher ratio in public elementary schools taken from the fall 2005 school year.

 

Figure 3. Average Pupil / Teacher Ratio in Public Elementary Schools Histogram

 

Figure 4.  Average Pupil / Teacher Ratio in Public Elementary Schools Box Plot

Figure 4. shows the corresponding box plot for average pupil / teacher ratio in public elementary schools.  Figure 4. shows the lower whisker, 10.8, is the lowest pupil to teacher ratio in the U.S. in Rhode Island.  The upper whisker score, 20.8, is the highest pupil to teacher ratio, in the state of California.  Utah’s pupil to teacher ratio of 22.8 to 1 is considered an outlier score.

 

 

 

Distribution of Estimated Annual Salary of Teachers in Public Elementary & Secondary Schools

Figures 5. and 6. illustrate the estimated annual salary of teachers in public elementary and secondary schools. The box plot below, show that there are no outliers in state’s wages among teachers.

 

Figure 5. Estimated Average Annual Salary of Teachers in Public Schools Box Plot, 2005-06.

 

 

Figure 6. Estimated Average Annual Salary of Teachers in Public Schools Histogram, 2005-06.

The state with the highest estimated salary is California, at an average of $61,372.00 annually. South Dakota pays its teacher’s the least in estimated annual salary at an average of $35,607.00.

Distribution of Percentage of Students Eligible for Free or Reduced-Price Lunch

 

            Figures 7. and 8. Display the percentage of elementary and secondary students eligible for free or reduced-price lunch.

 

Figure 7. Percent of Students Eligible for Free or Reduced Lunch Histogram

 

 

Figure 8. Percent of Students Eligible for Free or Reduced Lunch Box Plot

 

The data illustrated in the histogram shows that only one state has less than a quarter of its students qualifying for free or reduced-price lunch.  That state is New Hampshire, which has 17.70% of elementary and secondary students qualifying for free and reduced-price lunch.  The box plot shows that there are no outliers, and that the state with the highest percentage of free and reduced lunch qualifiers is Mississippi, with nearly 68%.

Frequency Distribution of Categorical Data

 

            Further statistical analysis was conducted to determine the frequency distribution of the aforementioned dependent variables, by the independent categorical regions. The four U.S. regions include the West, Midwest, South, and Northeast. A breakdown of the states included in each of the four regions is shown in Table 1.

West	Midwest	South	Northeast
Alaska	Illinois	Alabama	Connecticut
Arizona	Indiana	Arkansas	Maine
California	Iowa	Delaware	Massachusetts
Colorado	Kansas	D.C.	New Hampshire
Hawaii	Michigan	Florida	New Jersey
Idaho	Minnesota	Georgia	New York
Montana	Missouri	Kentucky	Pennsylvania
New Mexico	Nebraska	Louisiana	Rhode Island
Nevada	North Dakota	Maryland	Vermont
Oregon	Ohio	Mississippi
Utah	South Dakota	North Carolina
Washington	Wisconsin	Oklahoma
Wyoming		South Carolina
		Tennessee
		Texas
		Virginia
		West Virginia

Table 1. U.S. States by Region

Figure 9. is a box plot displaying the frequency distribution of current expenditures per pupil in average daily attendance in public elementary and secondary schools for the 2005-2006 school year.

 

Figure 9. Expenditures per Pupil by Region

 

Again, we see that the District of Columbia indicated as the 9th state, listed in alphabetical order, spends over $18,000.00 per pupil, creating an outlier score for the South region.  A closer look at the plot indicates the highest and lowest expenditures per region, as well as the upper and lower quartile for each.

            Figure 10. displays the average pupil to teacher ratio for students in public elementary schools categorized by region, fall 2005.

 

Figure 10. Pupil / Teacher Ratio in Elementary by Region

 

Comparing Figure 10. with Figure 4., Utah’s pupil to teacher ratio of 22.10 / 1, is no longer indicated as an outlier when categorized with like pupil to teacher ratios for the additional 12 states in the West region.  In Figure 10. our attention is drawn to the state of Virginia, number 47., in which the pupil to teacher ratio of 11.70 / 1 is considered low comparative to the South region’s other 16 states.

            Estimated annual teacher salary by region, 2005-2006, is shown in Figure 11.

Figure 11. Estimated Average Teacher Salary by Region

 

While Figure 5. showed no outliers scores in teacher salary nationwide, our attention is again drawn to the South region in Figure 11., where it is evident that three states have an unusually high estimated, annual teacher salary, comparative to other states within the same region. They are, the District of Columbia at an average of $60,526.00, Maryland at $55,738.00, and Delaware at $55,667.00.  Interestingly, Figure 9. showed that the District of Columbia had the hightest expenditure per pupil at an average of $18,339.00.  Figure 11. indicates that D.C. also pays its teachers the highest annual salary, on average.

Figure 12. Percent of Students Eligible for Free / Reduced Lunch by Region

 

At comparing categorical data within the four regions, Figure 12. illustrates the percentage of students in elementary and secondary public schools who are eligible for free or reduced-price lunch by region, 2006-2007. Again, Figure 8. merits a second look, where it is shown that nationwide there aren’t any outlier states with either high or low free or reduced lunch eligibilities.  However, a study of Figure 12. reveals that New Mexico (state 32), at nearly 61%, has a high percentage of students eligible for free or reduced lunch, compared to the remainder of the West region, which has a median percentage of eligible students under 40%.  Similarly, our attention is drawn to the Northeast, where New York (state 33), also has a much higher percentage of students eligible for free or reduced-price lunch at 43.5%.  Interestingly, the Northeast region also includes the state with the lowest percentage of student eligibility.  New Hampshire (state 30) has an estimated 17.7% eligibility for student free or reduced price lunch.

Statistical and Practical Significance

 

            Returning to the discussion of expendiures per pupil it can be assumed that since the distance between sucessive scale points are assumed to be equal, money spent is a scale of measurement provided in interval form.  Reflecting on the controversy of amount of money spent yielding higher or lower student success rates, and considering that the research includes the use of post-facto data, a hypothesis of difference requires testing.  The division of the United States into four regions necessitates the use of a one-way Analysis of Variance (ANOVA) or F Ratio statistical test.

Table 2. shows a source of variance for the dependent variable, current expenditures per pupil, per the four U.S. regions. The F ratio was calculated using the sum of the squares, or mean square. The F ratio of 9.75 helps with the goal of analysis of variance to detect the differences among MEANS. The between degrees of freedom (dfb) was calculated using the number of sample groups or regions (4) minus 1. The dfb = 3.  The within degrees of freedom (wdf) was calculated using the total number of scores or states (51) minus the number of groups or regions (4). The within degrees of freedom therefore equals 47.  Using the F ratio of variance between groups divided by the variance within groups, degrees of freedom = (3/48). A table of critical values of F compares the obtained value of F (9.75) with the critical value of F for the appropriate degrees of freedom. For the calculations completed, the column for 3df and the row for 47df intersect at two F values: 2.80 for an alpha level of .05 and 4.22 for an alpha level of .01. The null hypothesis is rejected when the obtained value of F is equal to, or greater than, the critical or table value of F.  Therefore, using a one-way ANOVA, a significant difference was found between the expenditures per pupil, per region.

Tests of Between-Subjects Effects
Dependent Variable: current expenditure per pupil in average daily attendance in public elementary and secondary schools 2005-06
Source	Type III Sum of Squares	df	Mean Square	F	p	Partial Eta Squared
region	120,097,648.80	3	40,032,549.60	9.75	.00	.38
Error	192,953,101.83	47	4,105,385.15
Total	5,752,870,321.00	51
Corrected Total	313,050,750.63	50

Table 2. Source of Variance Current Expenditures Per Pupil

 

            However, it is important to determine where the greatest differences in expenditures per pupil, per region came from. The between-group variance is large, but perhaps it is due to one region spending significantly more than the other regions. Perhaps two or more regions do not differ significantly in their expenditures per pupil at all. Tukey’s Honestly Significantly Difference (HSD) test can be used for this post-hoc comparison of regional spending.  Table 3. provides the data for the post-hoc multiple comparisons test of regional spending.

Multiple Comparisons
current expenditure per pupil in average daily attendance in public elementary and secondary schools 2005-06Tukey HSD
(I) region	(J) region	Mean Difference (I-J)	Std. Error	P	95% Confidence Interval
					Lower Bound	Upper Bound
West	Midwest	-660.49	811.12	.85	-2820.82	1499.83
	South	-475.96	746.52	.92	-2464.23	1512.31
	Northeast	-4356.52*	878.61	.00	-6696.60	-2016.45
Midwest	West	660.49	811.12	.85	-1499.83	2820.82
	South	184.53	763.94	1.00	-1850.14	2219.21
	Northeast	-3696.03*	893.46	.00	-6075.66	-1316.40
South	West	475.96	746.52	.92	-1512.31	2464.23
	Midwest	-184.53	763.94	.995	-2219.21	1850.14
	Northeast	-3880.56*	835.25	.000	-6105.17	-1655.96
Northeast	West	4356.52*	878.61	.00	2016.45	6696.60
	Midwest	3696.03*	893.46	.00	1316.40	6075.66
	South	3880.56*	835.25	.00	1655.96	6105.17
*. The mean difference is significant at the .05 level.

Table 3. Multiple Comparison Test of Expenditures Between Regions

 

            From the table, we learn that there are a number of mean differences significant at the .05 level between regional spending. Comparing the West with the Northeast there is a negative difference of $4,356.52 per pupil.  There is a negative difference in the Midwest of roughly $3,700.00 per pupil compared to what is spent per pupil in the Northeast. The South falls short of Northeast spending by roughly $3,880.00 per pupil. But perhaps the most significant mean difference is in the Northeast where at the .05 confidence interval, it can be said that the Northeast is outspending all of the other regions anywhere between $3,700.00 and $4,356,00 per pupil.

            It was determined in Figure 10. Virginia had a low pupil to teacher ratio. Figure 4. showed that Utah’s pupil to teacher ratio was quite high. Regionally comparative, Table 4. provides a look at how the West region has significantly higher pupil to teacher ratios: nearly 3 + students on the average compared to Midwest and Southern classrooms, and more than 5+ students in the West compared to Northeast classrooms. Similarly, compared to the Northeast, Southern classrooms have 2+ students more per teacher.  Overall, the West region has the highest pupil to teacher ratio, with more students assigned per classroom teacher than any of the other U.S. regions.

            With significantly higher pupil to teacher ratios in the West, and significantly higher expenditures per pupil in the Northeast,  annual teacher salaries, especially between these two regions warrant an investigation. Table 5. offers a multiple comparison difference between each of the 4 U.S. regions. Starting in the Northeast where student expenditures are high, annual teacher salaries are only significantly higher than their regional counterparts in the South. However, in Western states where pupil to teacher ratios are higher than all other regions teachers are earning annually an average of more than $6,640.00 less than teachers in the Northeast.  Teachers in the South also earn significantly less than their collegues in the Northeast.   The practical significance of these findings is limited however, as it would have been helpful to have data on cost of living in each region and average educational level of the teachers.

Multiple Comparisons
average pupil/teacher ratio Fall 2005Dunnett C
(I) region	(J) region	Mean Difference (I-J)	Std. Error	95% Confidence Interval
				Lower Bound	Upper Bound
West	Midwest	3.00*	.94	.19	5.81
	South	2.94*	.86	.40	5.49
	Northeast	5.07*	.94	2.23	7.92
Midwest	West	-3.00*	.94	-5.81	-.19
	South	-.06	.58	-1.78	1.67
	Northeast	2.08	.69	-.08	4.22
South	West	-2.94*	.86	-5.49	-.40
	Midwest	.06	.58	-1.67	1.78
	Northeast	2.13*	.58	.34	3.92
Northeast	West	-5.07*	.94	-7.92	-2.23
	Midwest	-2.080	.69	-4.22	.08
	South	-2.13*	.58	-3.92	-.34

Table 4. Multiple Comparison Test of Average Pupil / Teacher Ratio by Region

Multiple Comparisons
estimated average salary 2005-2006Tukey HSD
(I) region	(J) region	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
					Lower Bound	Upper Bound
West	Midwest	910.88	2594.81	.99	-6000.11	7821.88
	South	1506.03	2388.15	.92	-4854.55	7866.62
	Northeast	-6641.50	2810.72	.10	-14127.52	844.52
Midwest	West	-910.88	2594.81	.99	-7821.87	6000.11
	South	595.15	2443.89	1.00	-5913.89	7104.18
	Northeast	-7552.39	2858.22	.05	-15164.94	60.16
South	West	-1506.03	2388.15	.92	-7866.62	4854.55
	Midwest	-595.15	2443.89	1.00	-7104.18	5913.89
	Northeast	-8147.54*	2672.01	.02	-15264.15	-1030.92
Northeast	West	6641.50	2810.71	.10	-844.52	14127.52
	Midwest	7552.39	2858.22	.05	-60.16	15164.94
	South	8147.54*	2672.01	.02	1030.92	15264.15
Table 5. Multiple Comparison Test of Estimated Average Salary by Region

 

 

 

Additionally, it is necessary to take a look at the percentage of students eligible for free or reduced lunch, and how their data stacks up regionally. Figure 12.  provided a regional look at socioeconomic statuses; New Mexico, in the Western region, had the largest percentage of students eligible for free or reduced lunch, while New Hampshire, in the Northeast, had the lowest.  In the last multiple comparisons analysis, Table 6. presents evidence that the South has a significantly higher percentage of students eligible for free of reduced lunch than all other regions. In the Northeast, at the .05 confidence interval we see that there are significantly less students eligible for free or reduced lunch than in West and South, by as much as 19%.

Multiple Comparisons
% of students eligible for free/reduced lunch 2006-07Tukey HSD
(I) region	(J) region	Mean Difference (I-J)	Std. Error	P	95% Confidence Interval
					Lower Bound	Upper Bound
West	Midwest	5.14	3.20	.38	-3.38	13.66
	South	-9.57*	2.95	.01	-17.43	-1.70
	Northeast	9.79*	3.45	.03	.59	18.99
Midwest	West	-5.14	3.20	.38	-13.66	3.38
	South	-14.71*	2.95	.00	-22.58	-6.84
	Northeast	4.65	3.45	.54	-4.55	13.85
South	West	9.57*	2.95	.01	1.70	17.43
	Midwest	14.71*	2.95	.00	6.84	22.58
	Northeast	19.36*	3.23	.00	10.76	27.96
Northeast	West	-9.79*	3.45	.03	-18.99	-.59
	Midwest	-4.65	3.45	.54	-13.85	4.55
	South	-19.36*	3.23	.00	-27.96	-10.76
*. The mean difference is significant at the .05 level.

 

Table 6. Multiple Comparison Test of Percentage of Students Eligible for Free / Reduced Lunch

 

 

 

 

Regional Spending and its Relationship to Academic Success

 

            Thus far we have looked at how our nationa’s four regions compare with regard to educational spending. Data analysis has been provided for state and regional expenditures per pupil, average teacher salary, pupil to teacher ratios, and socioeconomic status of students between regions.  In attempt to shed light upon the controversy of spending and its association with student success, it is essential to compare the aforementioned data with standardized test scores. The Scholastic Apptitude Test (SAT), a college admissions assessment developed by the United States College Board scores college-bound students in three areas: math, verbal, and writing. Each section of the test is worth 800 points, and the maximum total score is 2400.  Depending upon the type of SAT test taken, the writing portion may or may not be included, thus a total maximum score of 1600 is also possible.  The SAT is a considered fair nationwide and should not present bias based on a student’s geographical region.

            Diagrams A. and B.. present average SAT scores for (A.) Math, and (B.) Verbal, 2005-2006.  Scatter plots of SAT scores versus expenditures per pupil, 2005-2006, are show below.  Diagram A. presents a weak negative correlation. There is some negative slope to the plot indicating that increased expenditures per pupil yield somewhat higher lower math SAT scores. This correlation is rather weak however, and shows almost as much zero correlation between the two variables.

 

Diagram A. Average Math SAT Scores versus Expenditures Per Pupil

 

Diagram B. provides more evidence of a negative correlation between expenditures per pupil and average verbal SAT scores.  The negative slope is still rather weak and further analysis must be computed to determine if in fact the correlation is negative, or whether there is zero correlation between SAT scores and expenditures per pupil.  The Correlation Coefficient, or Pearson r is an appropriate statistical test for determining a hypothesis of association between two measures of interval data.  Pearson r can be calculated using the raw data scores in Table 7.

 

Diagram B. Average Verbal SAT Scores versus Expenditures Per Pupil

Descriptive Statistics
	Mean	Std. Deviation	N
Expenditure/ pupil  (1000$)	10,327.78	2,502.20	51
SAT score 2005-06 (verbal)	534.94	37.80	51
SAT score 2005-06 (math)	540.59	37.46	51
SAT score 2005-06 (writing)	525.37	37.63	51

 

				verbal SAT score 2005-06		math SAT score 2005-06	writing SAT score 2005-06
Expenditure/ pupil 2005-06			Pearson r	-0.42**		-0.39**	-0.40**
			p	0.00		0.00	0.00
			n	51		51	51
Model	R	R Square	Std. Error of the Estimate
1	.39a	.16	34.79

 

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	601.42	20.88		28.80	.00
	Expenditure/ pupil 2005-06	-.01	.00	-.39	-3.00	.00
a. Dependent Variable: average math SAT score 2005-06Table 7.  Verbal and Math SAT Scores, Expenditures Per Pupil Raw Data

 

Mean math SAT scores are calculated as well as mean verbal, and the mean expenditures per pupil. Using the means the standard deviations can be determined and the data is plugged into the Pearson r equation. The value for the average math SAT score Pearson r = .39 

            To test for statistical correlation degrees of freedom must be obtained for the two variables. Degrees of freedom are calculated using the number of scores minus two. In the SAT math test, 51 scores were obtained, minus two, equals 49.  Using a table for the critical values of r for the Pearson correlation coefficient, the value of r at the .05 confidence interval is .268 and .372 at the .01 confidence interval.  The calculated value of r = .39 and is greater than the table r, thus we reject the null hypothesis, and determine there is statistical association between the two variables. The correlation between math SAT scores and expenditures per pupil is negative!  The same test of statistical significance is used with verbal SAT scores, and too is found to have a negative correlation. The r ratio for verbal SAT scores = .42 where the same number of samples (51) was obtained and r values for the .05 and .01 confidence intervals yield scores of .268 and .372

            It may be useful to determine if a correlation is present between SAT scores and pupil to teacher ratio.  Diagrams C. and D. provide scatter plots of verbal SAT scores, 2005-2006, versus the average pupil to teacher ratio, 2006.  Diagram C shows zero correlation between verbal SAT scores and pupil to teacher ratio. A glance at Diagram D provides the same evidence of zero correlation between math SAT scores and pupil to teacher ratio. Again, calculating the correlation coefficient may present evidence otherwise of either a positive or negative correlation between two of the variable data. 

 

Diagram C. Average Verbal SAT Scores versus Average Pupil / Teacher Ratio

 

 

Diagram D. Average Math SAT Scores versus Average Pupil / Teacher Ratio

Table 8. provides raw data for math and verbal SAT scores and pupil to teacher ratios.

Model	R	R Square	Std. Error of the Estimate
1	.03a	.00	38.16
Coefficientsa
Model				Unstandardized Coefficients			Standardized Coefficients	t	Sig.
				B		Std. Error	Beta
1	(Constant)			542.32		32.86		16.50	.00
	pupil/teacher ratio Fall 2006			-.49		2.14	-.033	-.23	.82
a. Dependent Variable: average verbal SAT score 2005-06

 

Model		R	R Square	Std. Error of the Estimate
1		.03a	.00	37.82
Coefficientsa
Model					Unstandardized Coefficients			Standardized Coefficients	t	Sig.
					B		Std. Error	Beta
1	(Constant)				546.76		32.57		16.79	.00
	average pupil/teacher ratio Fall 2006				-.41		2.12	-.03	-.19	.85
a. Dependent Variable: average math SAT score 2005-06

Table 8.  Verbal and Math SAT Scores, Pupil to Teacher Ratio

The number of subjects remain the same (51) – 2 = 49.  Using a table for the ecritical value of r at 49 degrees of freedom yeild values of .268 at the .05 confidence interval and .372 at the .01 confidence interval. The calculated r value = .03 for both math and verbal scores and that is smaller than the table r. Therefore, we must accept the null hypothesis and assume that pupil to teacher ratio has no significant correlation on both math and verbal SAT scores.

            Lastly,  comparing the socioeconomic status of students with their SAT scores may be practical for those wishing to argue that finances significantly impact student success rates. Diagrams E. and F. provide scatter plots for the percentage of students eligible for free or reduced lunch, 2006-2007, versus the math and verbal SAT scores, 2005-2006. A quick look at both scatter plots indicates zero correlation between average math or verbal SAT scores and students’ socioeconomic status.  However, raw data and calculating the product-moment correlation may prove otherwise. Using the data in Table 9.

 

Diagram E. Average Math SAT Scores versus percentage of students eligible for free / reduced lunch

the number of subjects remain the same (51) – 2 = 49.  Using a table for the critical value of r at 49 degrees of freedom yield values of .268 at the .05 confidence interval and .372 at the .01 confidence interval. The calculated r value = .08 for math and .02 for verbal scores and that is smaller than the table r. Therefore, we must accept the null hypothesis and assume that socioeconomic status has no significant correlation on both math and verbal SAT scores; or does it? 

 

Diagram F. Average Verbal SAT Scores versus percentage of students eligible for free / reduced lunch

Model	R	R Square	Std. Error of the Estimate
1	.08a	.01	37.80
Coefficientsa
Model				Unstandardized Coefficients			Standardized Coefficients	t	Sig.
				B		Std. Error	Beta
1	(Constant)			552.85		20.90		26.45	.00
	% of students eligible for free/reduced lunch 2006-07			-.292		.51	-.08	-.58	.57
a. Dependent Variable: average math SAT score 2005-06

 

Model	R	R Square	Std. Error of the Estimate
1	.02a	.00	38.19
Coefficientsa
Model				Unstandardized Coefficients			Standardized Coefficients	t	Sig.
				B	Std. Error		Beta
1	(Constant)			532.29	21.12			25.21	.00
	% of students eligible for free/reduced lunch 2006-07			.09	.51		.02	.17	.87
a. Dependent Variable: average verbal SAT score 2005-06

Table 9.  Verbal and Math SAT Scores, Percentage of Students Eligible for Free or Reduced Lunch

 

Conclusions

            Although all conclusions drawn from the analyses show a lack of positive correlation between financial spending and student success, no direct statement regarding cause and effect can be made. In other words, spending less money on student expenditures & teacher salaries and widening the ratio between pupils and teacher will not cause students to gain higher academic success. Although the data provides a possible hypothesis that more money spent in education correlates with lower levels of academic success, other hypotheses are at least possible. Perhaps a student who scores high on his SAT was encouraged to spend more time studying. Perhaps coming from a low socioeconomic background provides ambition for a child to spend more time studying.  Perhaps teachers with lower salaries are motivated to be highly qualified and teach better than do teachers who are already highly paid. It is important to note that although a relationship may exist, a direct statement on cause and effect cannot be made regarding any of the preceding relationships.