Cecil Thompson

Omega Graduate School

Prof. Sean Taladay, Ed.D

May 25, 2024

Assignment #2 – Developmental Readings

Create Developmental Readings from seminal sources and scholarly peer - reviewed journal articles.

Review instructions for Assignment #3, the course essential elements, and course readings to identify selections of books and journals to create entries.

Refer to the " Student Guide to Developmental Readings " in the General Helps

folder for updated information on sample comments, the grading rubric, and key

definitions related to developmental readings.

N.B.: 1. Below, I have highlighted all quotes in RED. Everything else is in indirect speech.

2. The old rubric asked for a minimum of 8 sources and 25 comments. The new rubric

does not mention a required number of sources or comments. What is the

requirement?

Please forgive the lengthy illustrations I’ve used to support my points.

Source: 1

Ogundimu, Charles O. (2014). Does the mode of entry into teaching matter in teacher-

retention? A discrete-time survival analysis modeling of New York City public school

teachers. Columbia University (PhD).

Comment: Teaching Fellows’ Program and teacher attrition

Quote/Paraphrase: In this introduction of Ogundimu’s dissertation, a level 2 heading, written in italics, poses the question, “Why is the study of NYCTF [New York City Teaching Fellow] retention important?” The answer to that question resides in The Purpose statement of the dissertation. He writes that The Purpose of the “…dissertation is to critically examine and compare the retention of beginning teachers from the TFP [Teaching Fellows’ Program] in NYC (TFs) [teaching fellows] with the retention of teachers who entered teaching in New York City through the traditional route” (Ogundimu, (2014, p.7).

Essential Element: NYC DOE teacher-attrition rates between “Teaching Fellows” (TF) and “Non-Teaching Fellows” (NTF).

Additive/Variant: The above question posed, in the introductory part of the dissertation, is actually exemplary of how one can effectively lead cut a pathway into the presentation of the Purpose statement in order to develop an argument for the Significance of the major research or proposal.

Contextualization: It seems to me that this position of Ogundimu’s, in part at least, is a reasonable extension of our years (his and mine) of ongoing discussions about the state and quality of public education. In some ways, our verbal exchanges about the structure of the public education under NYC DOE for decades, had found one of the possible logical outlet into his 2014 dissertation entitled, “Does the Mode of Entry into Teaching Matter in Teacher Retention? A Discrete-Time Survival Analysis Modeling of New York City Public School Teachers.”

Ogundimu and I had discussed at length how many of the troublesome issues swirling around public education in the city had to do with an archaic crumbling instructional system, ill-suited to the time. Back then, he felt that the politicians’ educational philosophy was the right move to reform public education. DOE’s plan was to break up the large, often historically renoun schools into mini-schools, while, at the same time, it would drastically reduce public school funding in order to promote government subsidized charter schools, and voucher programs that allowed children, whose family opting for “school choice”, to use government monies to attend religious schools.

But, when Ogundimu moved on to become assistant principal, and later (a very successfully) school principal, he began to appreciate my perspective on the question of what the matter really was with the NYC DOE education philosophy. Back in the day, the political talk was that the teachers were not “smart” enough, and so the system should throw loads of money in to sweeten the pot so as to encourage “high powered” professionals in teaching. Hence, this was the birth of the Teaching Fellows’ Program. They only had to pass the State Content Specialty Exam, and over several years they would need to pass the other exams; a master’s degree paid for by DOE, to boot. If the goal was to improve teacher-quality and reduce the rate of teacher-attrition, did it work. According to Ogundimu’s research the latter, at least, did not work.

Comment: Rationale for the Dissertation?

Quote/Paraphrase: In his dissertation, Ogundimu informs us that his Rationale “. . . poses five questions that ask how to test the claim of TF longevity, the acclaimed superiority of TFs, and to determine if the time they remain in teaching has had a positive effect on the students” (Ogundimu, 2014, p.7). It goes on to examine the conditions under which TF quits. Then, it looks at the conditions under which teachers who came in through the traditional teacher recruitment (TTR) channels usually quit. The logical next step proposed in the dissertation was to examine “. . . .whether [hiring of the] TF has shown any improvement in the teacher recruitment by the NYC Department of Education (DOE)” (Ogundimu, 2014, p.8).

Essential Element: How the Ogundimu dissertation came about—Rational?

Additive/Variant: In summing up the Rationale for this research, Ogundimu cracks open a door, from the onset, to allow the reader a glimpse of the justification for the dissertation in the title, itself, by way of the words, “Does the mode of entry into teaching matter in teacher-retention?” (Ogundimu).

Contextualization: I spent my last twenty-two years as a NYC DOE appointed teacher of Mathematics at Jane Addams High School in the South Bronx. I did so as a teacher holding triple New York State Certifications in the areas of English, Mathematics, and School District Administrator (SDA). Because Jane Addams was primarily an academic trade school with Business, Nursing, Cosmetology, and Tourism, it also needed state certified teachers in these vocational subject areas along with those of us who were teaching standard academic subjects.

Charles Ogundimu came in initially as a state-certified business teacher. But because of the natural intersection among business, mathematics and school administration, Ogundimu had the qualification to get himself certified in those two additional areas, as well, and began teaching a split program in Mathematics and Business before changing school to become an assistant principal, and later, a principal. Over the years, even before he had completed the doctorate at Columbia University, we spoke quite a bit about how high levels of student performance are achieved and maintained. He always insisted that while the continuing education of DOE teachers have been pretty much on track, teacher attrition remained the most destruction factor against DOE student education and advancement.

I saw it differently. To me, the DOE had never done enough to maintain the balance between the races of the students and those of their teachers. I saw the shortage and shrinkage of Black and Hispanic teachers as part of DOE’s failure to recognize the power of teachers as racial role-models. Ogundimu wrote a dissertation that addressed the question, not in opposition to my primary hypothesis, but as a precursor to it. When I pose the question, “thought” by many New York City public school students, “Why doesn’t my teacher look like me?” I am seeking to address a part of the question Ogundimu posed in the title of his dissertation.

3. Comment: Ogundimu’s Working Hypotheses

Quote/Paraphrase: Five Working Hypotheses are presented. Ogundimu refers to all five of them as hypotheses even though none of the first four is presented in a form that contains anything resembling “independent” and “dependent” variables. The first of these is in the form of a “nullified” statement. It states that, “Teaching Fellows [TFs] do not have a higher retention rate than None Teaching Fellows.” The fifth of these states that “The Teaching Fellow’s Program [TFP] has changed the dynamics of teacher recruitment in NYC public school system”. This latter one comes closest to a hypothesis (Ogundimu, 2014, p.12).

Essential Element: The difference between research questions and Hypotheses

Additive/Variant: It has long been standard practice for anyone doing scholarly

research to predicate their research, either on research “questions”, or “hypotheses”. That there is a clear difference between the two predicates—research questions or hypotheses—do not make one any less acceptable than the other. The difference between the two has to do with whether or not the one carries, in it, an independent variable and a dependent variable, which, through the relationship between the two variables, tells us “What we think the prediction will be?” Yet, only two of Ogundimu’s five “hypotheses” meet the criteria to be classified as hypotheses rather than research questions (Richard G. Trefy Library).

Contextualization: In my dissertation research, my primary research hypothesis states that, “Black NYC public school 12 graders, for whom 20% or less of their teachers are not of the same race, tend not to aspire to teaching or any of the professional.”

Comment: The Significance of Ogundimu’s dissertation

Quote/Paraphrase: “Why is the study of NYCTF retention important? In context with the problem and purpose of the research, this is clearly about significance. For this reason, I refer to the text: ‘The economic implications of high school dropouts, as well as potential individual and societal benefits have been well documented’ (Belfield & Levin, 2007)” (Ogundimu, 2014, p. 12).

Essential Element: Beyond the retention of Teaching Fellows

Additive/Variant: This segment of the introduction of the Ogundimu dissertation addresses the negative personal, economic and social impact of a failed school system. But the fact that this dissertation is placing the burden of investigating, and fixing the problem solely on the study and fixing of the problems with “NYCTF retention” is only one step in the right direction. Another step might be the conduction of research into the DOE deliberate motion toward an increasingly dangerous segregated school system and how to curb it.

Contextualization: Ogundimu and I had discussed at length how many of the troublesome issues swirling around public education in the city had to do with an archaic crumbling instructional system ill-suited to the changing times. Back then, he felt that the politicians’ educational philosophy of breaking up the large, often historically renown schools into mini-schools, while, at the same time, drastically reducing public school funding in order to promote government subsidized charter schools, and voucher programs that allowed children, whose family opting for “school choice”, to use government monies to attend religious schools.

My position, then, was that these policies were effectively designed to skim off from the top, the brightest and most teachable students. That means that they were selectively placing the crem de la crem of the city K-12 population into the mini-schools, the charter schools, and the “church” based schools. By design, the traditional public schools were being left with the least teachable students, grossly inadequate supplies, and a tremendous problem with “teacher-burnout”. Of course, these schools would naturally be posting lower passing rates on standardized tests, as well as lower graduation rates. And, in the end, what this would mean was that New York City DOE’s school segregated plan, at all levels, was firmly in place.

Comment: Teacher Retention v. Attrition

Quote/Paraphrase: Through careful review of Hanushek’s and Pace’s (1995) research on the question of who become teachers, during the 1980s, it is brought out that the highest percentage of students most likely to complete teacher training programs was White females. Further, they found that students closer to the top of their class tended not to select education majors. Along with that, many would-be teachers, at the time, found state certification examinations and other school district requirements impassible impediments to entry into the teaching profession. In looking at the several steps to be taken in trying to transition from high school into the teaching profession, Vagas et al. (2001), poses four questions: “ ‘Who graduates from high school?’; (2) ‘Who enters college?’; (3) ‘Who obtains a B.A.?’; and (4) ‘Who enters teaching?’ (Ogundimu, 2014, pp. 15- 16).” All of the answers to these questions lead into corollaries that necessitate further research questions on whether there would have been any need for a racially diverse teaching force and how that need would connect to high school completion by minorities and students of color (Ogundimu).

Essential Element: Who teaches and why?

Additive/Variant: Much of this research that Ogundimu draws on about who become teachers and why, goes back fifteen years before being referenced in his dissertation at Columbia University, in 2014. Due to the fifteen year gap, the answers to those questions from that earlier time might no longer have been relevant, then, and certainly not today. But what it does is that it describes a condition then that might well be a useful indicator of a pattern that almost always occurs.

Contextualization: The central thesis of the Ogundimu dissertation states that the answer to “who becomes teacher and why” is at the heart of the problem of teacher-attrition in NYC DOE public schools, and teacher-attrition is at the heart of student failure. In his study, the two main competing forms of teacher-entry into the classroom, over the last two decades, are held up and compared in accordance with their respect longevity. Although Ogundimu, by all appearance, is a proponent of the idea that “teaching conditions predict teacher turnover in certain states” (Loeb, & Darling-Hammond, 2005), he elaborates but little on the notion that a racially unequal public school system such as the NYC DOE, is, by itself, exemplary of one of main conditions that spawns teacher turnover on a mammoth scale. Bound within that central angle of the New York City segregated public school system, the subtended arc of racial inequity—bearing in it just a spate of children of color taught by a dearth of teachers who look like them—continues to swirl into a vicious cycle of an ever-dwindling population of teachers-of color.

In such a cycle as this, where children of color are taught mostly by White teachers, and more and more White teachers are deciding to leave the classroom than teach in neighborhood of color, the candle is being burnt from both ends. Since NYC’s K-12 public school children of color tend to have few teacher-role models who look like them, they tend to see themselves as something less than college material or future professionals (especially as teachers). The fact that the Ogundimu dissertation does not delve into this area of teacher attrition is fine. For it is probably beyond the scope of his research. But mine is probably a viable extension; how teaching conditions predict teacher turnover in certain states (Loeb, & Darling-Hammond, 2005).

Source: 2

Loeb, Susanna; Darling-Hammond, Linda and Luezak, John (2005). How teaching conditions

predict teacher-turnover in California schools. Peabody Journal of Education, 80(3)

44-70. Taylor & Francis, Ltd., Accessed: March 8, 2016

http://www.jostor.org/stable/3497042.

Comment: Part demography play in teacher turnover

Quote/Précis: Susanna Loeb et al. (2005) suggest that a good many of the instances where teaching conditions have been presaging teacher-turnover appears to fall within the frame of demography, large class sizes, shortage of materials and supplies, schools with multi-tracking systems, as well as schools containing problematic teaching facilities. But, the highest rates of predicted teacher-turnover is said to fall most frequently within the broad swarth of demographic conditions such as “racial composition and proportions of low-income students” (Loeb et al, 2005, pp.44-45).

Essential Element: The impact of demography on teacher turnover from the vantage point of the Black teacher.

Additive/Variant: This segment suggests that researchers have found indicators that point to “demography” as the prime predicate for prompting teachers to quit or transfer. But, even so, the claim that most teachers quit or transfer because they do not wish to teach children belonging to minority groups, implies an even more deeply indelible stain in the American educational system that is contributing to the ever-swelling demand for teachers over the shrinking supply.

Based on the research, it is quite probable that a teacher who finds himself or herself assigned to a classroom of Blacks, Hispanics, Muslims, or something else, may choose to leave the profession because he or she just cannot get reassigned. If that is the case, it would be that such a teacher would have to be harboring certain negative stereotypic notions about these groups that he or she is assigned to teach. First, one logical conclusion would be that the teacher is White. And second, such a problem arising from the Colored children White teacher dynamics could not have been restricted to the teacher alone. But, whatever the source of the problem, the nature of it would definitely be demographic, in the largest sense.

What this suggests, at length, is that this particular teacher quit-transfer problem may not even have existed if that teacher was not, once upon a time, a child of segregated classrooms. The fact that such a person who had once been “socially” miseducated is now a teacher, and one who finds it necessary to quit because of the miseducation he or she had, begs the question, why does not the educational system in America just fix it? Did Brown v. Board of Education not go far enough?

So far, neither have the various Boards of Education around the country not only invested enough time and money into resisting Brown, but that Brown, itself, did not go far enough. In addition, many Boards of Education have tried not to enforce laws that should have been treated as the nexus to Brown. If Title VII of the Civil Rights Act of 1964, a whole decade after Brown, were treated as an addendum to Brown, a good part of the teacher quit-transfer rate could be curtailed, even after the fact. The fact being that even though the miseducation of innocent little White children turned teachers might not be remediable, it does not have to cause them to quit teaching. What this means is that the Board of Education in question could clamp down on the demographic triggers to the teacher quit-transfer problem by simply hiring more teachers of color.

Contextualization: Back in the 1980s, The City of Buffalo, New York and New York City were the only two cities in the State to require a string of examinations for a person with a bachelor’s degree and the professional (education) course requirement to become an “appointed” teacher. During the 1983-’84 school year, while I was still taking the examinations to become a fully appointed teacher of English, I took a position as a “regularly assigned” TPD English teacher at Evander Childs High School. At the time, the school had a student-population of approximately 4,000 (nycargo.orghttp://schools.Nyc.gov/SchoolPortals/

11x425/defaulthtm).

At that time, the school had Mrs. Kathrine Kelly, an African American assistant principle, as the supervisor of their Special Education Department. Conveniently, then, Black teacher-hires were usually shunted off into the Special Education Department unless they had been directly appointed into the school by the Board. Since I was not an appointed teacher, as such, I was routinely dumped into the Special Education Department. I was given five classes in a Math and English split program teaching learning-disabled students. In face-to-face direct contact with these students, their supposed handicapping condition did not seem as physically apparent as my prejudice had led me to expect. What was particularly “special” about this portion of the Evander Child’s student population was that truancy was rampant.

One day, shortly after the bell had just sounded, Mr. Kline, the principal, and Mrs. Kelly made an unannounced entrance into my classroom. Each, armed with a clipboard and a pen, had come in at what I thought was a most propitious time. They had come in upon what I had planned to be a dramatic unwrapping of the first of a five-lesson interdisciplinary “English” unit, with Geometry and syllogistic reasoning intertwined. That lesson was supposed to be one more step in the preparation of my students for the New York Regents Competency Test (RCT) in Writing.

The two stayed in my class for the entire period. The bell rang and they got up and left the room. But in leaving, he handed me a note summoning me to a Post Observation Conference (POC) in his office at the end of my school day.

From the beginning of the POC, Mr. Klein went immediately into attack mode. Speaking with prideful disdain, he said, “I’m a well-educated man, and I didn’t understand any of what you were teaching.” He went on to advise me that my job with that level of Special Education students was “just to teach them enough to get by and let them go”. Surprisingly, throughout the conference, Mrs. Kelly said nothing. A couple of days later, I received a “U-rating” in my mailbox; it was signed by both of them.

In June, one of the girls in the English class had passed the RCT Writing Exam and the other two girls came pretty close to passing as well. Together with that, seven students in my math class (a class of ten), passed the RCT Math. This level of performance among the Special Ed population at Evander Childs High was simply unheard of.

Over the next couple of weeks, toward the end of the school year, Mrs. Kelly’s attitude to me had morphed into something that was very unlike that of her usual, polite self. She would walk back and forth past me in the hallways as if I were “The Invisible Man”. She no longer said the usual, “Good Morning, Mr. Thompson!” Nor did she give that occasional jocular nod upon any of our transitional encounters. And yet, the sudden changed attitude in her toward me did not fire me up to contemplate a probable cause in any meaningful way until I had that rude awakening on that day in which I physically responded to the Board’s letter summoning me to the Hiring Hall at 65 Court St.

There we sat—thirty something of us—waiting patiently in the Hiring Hall. After five minutes or so had elapsed, a person egressed out of a door from the inner office. The entrant into the Hall, a Black man of average build and height, introduced himself as Rufus Thomas—no prefix, no pretentious titles. He spoke briefly about the process and gave each of us a list of schools that were relatively close to our homes from which to pick.

I went over and said quietly to him, “I don’t need to pick one; I’ll stay at Evander Childs High School.”

He pulled me aside and said brusquely, perhaps even a bit out of character, “I’d already spoken to Mr. Klein. He said he didn’t want you there.”

That was hurtful! But it made me realize that I had overstepped by getting Black Special Ed students to pass the RCT Writing and Math while there were mainstream students who did not pass them. I went quietly back to my seat as he asked the group whether anyone who qualified wanted to be appointed through the “Ethnic Preference” program. I asked him what was meant by “Ethnic Preference”. He explained that because some schools under BOE have been trying to keep ethnic minority teachers (Blacks, Hispanics, etc.) out, the BOE had devised this system to try to counter that by using “Ethnic Preference”. He warned, however, that anyone who chooses “Ethnic Preference” could wind up in a school that might try to “discontinue” his or her licence during the three-year probationary period. I picked Christopher Columbus High School from the list.

Columbus High was approximately half a mile down the road in a southerly direction from Evander Childs High School. It had a student population of approximately 2,000 students, which made it slightly smaller than Evander Childs High School.

As I entered the building, I met an African American man who was just leaving the building. He volunteered the fact that he was a gym teacher, and said, “Welcome! I’m the only one of us, here.”

The day was a “Faculty Professional Development” day. It was just after lunch. After that brief encounter, I went directly to the security officer at the desk and told him who I was and what my business was. He led me into the second office on the right front corner of the building. He, then, introduced me to the principal, Mrs. Rosa and returned to his post. She expressed surprise at the BOE had sent me to be appointed in her school and advised me to report to the Bronx branch office of the BOE’s Hiring Hall.

The following day, I went to the Bronx branch of the Hiring Hall. I was fast realizing that “Ethnic Preference” was an empty ploy. It was just a smoke screen blown out in order to give the unsuspecting ethnic minority teaching force, a false sense of the Board’s commitment to providing the children with equal representation among school faculty, by race. But, did I succeed in becoming the second of two Black teachers at Christoper Columbus High School. The way it turned out, was that the hour I spent at Columbus that day was the sum total of my regular teaching activity at Christopher Columbus High School.

In time, I would find that my brief stint at Evander Childs High School and my one hour BOE appointment in Christoper Columbus High School had given me a tiny glimpse into the tonal quality and temperament of the real New York City Board of Education; and what that experience portended for me over the next 30 years as a Black teacher vying for the chance to teach children who look just like me in the New York City BOE (DOE).

Comment: Market Forces on teacher quit-transfer rate

Quote/Paraphrase: Researchers have been looking at the teacher quit-transfer rate from the point of view of how the behavior of the teacher labor market forces negatively impacts the education of students in certain demography. Some of these researchers are claiming that the negative effect from the increase in teacher turnover appears to leave its worse scars “more or less among advantaged population of students” (Lankford, Loeb & Wyckoff, 2002; National Commission on Teaching and America’s Future [NCTAF], 1996,2003).

Essential Element: How Disadvantaged minority students predict teacher turnover rate.

Additive/Variant: These economic factors are thought to paint a clear picture of the workings of specific labor market forces around teacher quit-transfer rates. In this situation, there is a twist that might well have sprung from the fact that “advantaged” students in the New York City public school system are not, to any noteworthy extent, a reflection of the public school population, in the main. Ostensibly, the post-1990s teaching-force of New York City DOE has not shown much of a significant upward tick in teacher quit-transfers rates out of these largely minority, “disadvantaged” (public) schools into “advantaged” (private) schools the way these authors suggest they are occurring on a national scale. What we have seen is that the Guiliani-Bloomberg system of carving up the city’s 80% “disadvantaged” student population into the “more advantaged” and the “less advantaged” students through the voucher system, coupled with charter and mini-schools did what it was meant to do. It was not meant to address a teacher quit-transfer problem, but, ironically, to create a more segregated school system.

In those years, however, we have only seen the teacher quit-transfer problem go from “disadvantaged” (public schools) to “advantaged” (private schools) in ways that cause the very same teachers to suffer drastic pay cuts and loss of benefits. By this fact, then, one would expect to find some evidence that, even though many well-meaning school systems are working overtime to stem the tide of teacher quit-transfer rates, there are always parts of the issue of teacher loss that are tethered to the questions of what is meant by well “qualified teachers” and what methods of intervention are being used by politicians to bring “disadvantaged” children up to par with “advantaged” ones. For, although the New York State teacher certification requirements seem meant to halt the teacher quit-transfer rate in its effort to guarantee that the best qualified teachers are available for socially and economically “disadvantaged” students, the results of their actions have worked to the contrary.

Contextualization: The New York City DOE has remained steadily, an extremely diverse school system of a largely “disadvantaged” (80%) population of Black and Latino children. In the 1990s, Mayor Guiliani publicly aired his concern over the comparatively low level performance of New York City (K-12) students when pitted against that of students at the same levels around the world. He had pretty much theorized, off the cuff, that the poor academic performance of the City’s children was due chiefly to the poor quality of teachers unlike the “high” quality of teachers in private (parochial and religious) school systems around the city. As a teacher in the DOE system, at the time, I was bothered by the fact that, not only was the mayor’s theory a classic example of sophistry, but it was the kind of thinking that would engender a false positive errant response. This, while appearing to be part of a vital part of the fix for the city’s teacher-supply problem, it was actually an exacerbation of the problem created by education polices from the very top. Within the teaching community, the Guiliani-Bloomberg “logic” became the running joke of the time.

In 2001, No Child Left Behind came in vogue but was not put into effect in the city until sometime about 2005. So, meantime, “in the spring 2002, NYC was said to employ 12,400 teachers who only had temporary licenses” (NYSED). But, eventually, these teachers with so-called, “Temporary Provisional Teachers” (TPTs) licenses were put on the chopping block for removal from the DOE employment payroll. It meant that many of these teachers who were still not able to pass the New York State Teacher Certifying Exams turned to local private schools or left the system altogether.

Comment: Absence of teacher of color

Quotes/Paraphrase: Loeb et al (2005) calls attention to Shen’s comparative examination of why teachers quit schools or just simply switch profession. He claims to have found that, on the average, teachers do quit their schools because of issues with pecuniary recompense, poor teaching conditions, and a whole range of students’ characteristics issues (race, etc.), including the extent to which the level of student-preparation and skill impede the teachers’ effort to deliver the instruction (Boyd, Lankford, Loeb & Wyckoff, in press). But, at the same time, a number of studies about quitters had “found that teachers leave schools with larger proportions of low-income and minority students at higher rates than [they do from] other schools” (Shen, 1997). Still, other researchers have been able to trace patterns in which the best teacher tend to be the ones transferring “out of high-minority schools into schools with fewer minority” (e.g., Carroll, Reichardt & Guarino, 2000; Scafidi, Sjoquist & Stinebrickner, 2002). (Loeb et al, p.45).

Essential Element: Why is there a high quit transfer rate among top teachers?

Additive/Variance: It goes without saying that there are good teachers and bad teachers. Therefore, it may be assumed that among the several reasons why the problem of teacher-turnover exists at such a startling rate is that some teachers are just not up to snuff. In such cases, many of the weaker teachers are weeded out of the educational system in short shrift, by being “U-rated” out of the job or removed for failure to meet the qualification criteria. If it serves any useful purpose for top teachers to receive high ratings, it must be that school systems are trying to identify and retain the “best” teachers so that they can be put in the trenches where students are considered to be most “disadvantaged”, and are thus, most at risk. Yet, the research is showing that teachers who are considered to be among the brightest and the best are the very ones “leav[ing] schools with larger proportions of low-income and minority students at higher rates than” those leaving schools of which the student population comprises mostly of “advantaged” young people.

Contextualization: In the feverish rush to engineer and put in place the Guiliani-Bloomberg public education model, New York City had effectively hatched a scheme whereby children from within the general public school population (mostly disadvantaged minorities) who had demonstrated special aptitude for the professions were screened for admission into the new specialized magnet and charter schools. Through this strategy, the bulk of “hard to teach” children, some of whom have special learning needs, and others with social-emotional issues, remained in the old educational setting. Many of these teachers, struggling at wit’s end to try and find a way to execute lesson plans, to no avail, soon chose early retirement, or decide to take a walk.

At the same time, a relatively the small percentage of Black and Hispanic children were allowed to participate in the voucher lottery program had a subliminal effect on the increase in the teacher quit-transfer rate. To me, this latter (beginning in the late 1990s) was Mayor Guiliani’s test run of a plan to privatize public education with government funding. This went a long way toward the “excessing” of less senior appointed teachers, as well as the issuance of “pink slippings” of TPTs.

Source: 3

Kalaian, Sema A; Kasim, Rafa M. (2014 Mar). A meta-analytic review of studies of the

effectiveness of small-group learning methods on statistics achievement. Journal of Statistics Education. Alexandria 2(1) 1-19. [Method]

Doi: 10. 1080/10691898.2014.11889691

Comment: Teacher dominated instruction v. Student Centered instruction

Quote/Paraphrase: “Table 1 lists 10 ‘effect sizes’ extracted from the 9 statistics primary studies including the meta-analytic review” (Klain et al, p.9). In this descriptive tabulation, the authors did a statistical comparison among ten of the small student-centered learning groups with the same number of lecture-centered groups. They, then, described the interval over which the groups were compared, and the “effect-size” of the groups analyzed, but the result does not favor either set (p.9).

Essential Element: Using “effect-size”, etc., to determine whether instruction through multiple small student-centered groups is more effective than that through a single large teacher-centered group instruction.

Additive/Variant: By using a table of varying numbers of samples from the small-group learning models and the large group learning models reviewed, there is not one instant where a set of results presented by the authors has an effect-size of one or greater. For instance, Table 1 showed that Borresen (1990), who has the largest sample on the table, a sample of 100 small groups and the same number of lecture groups. The table also showed that this was done over a total of forty-five hours, and the result, in terms of “effect size,” was 0.71 (71%). The problem is that this was not a positive integral effect size. As it turns out, Borrensen’s result was pretty much standard. For, beside the fact that one researcher came out with a decisive negative effect-size, none of the others had an effect size of n 1. So, the researchers quite rightly reported that the result as to the effectiveness of small group student- centered instruction over large group lecture-type instruction was decidedly inconclusive.

Contextualization: Frankly, in my thinking there is a bit of circumnavigation going on in which the effort of researchers to base their research results on “effect size” has proven to be, at best, a demonstration that they have been masterly inactive. If it were left to me, I would have done a “pretest-instruction-post-test” with fifty groups from each category and be done with it. From personal experience, I have found that certain “content-topics” are more effectively imparted in large group, teacher-dominated setting for the majority of the lesson. However, where this kind of instruction delivery is most successful where the “instructional objective” assessment and reinforcement reverts to multiple small groups culminating activities.

Source: 3

Bala, Jyoti. (2016 Nov). Contribution of SPSS in social sciences research. 7(6) (Special Issue)

International Journal of Advance Research in Computer Science.

www.ijjarcs.inform.

Comment: Using SPSS software

Quote/Paraphrase: In recent years, researchers have been accumulating a tremendous lot of knowledge from surveys and empirical processes. And now, in the wake of the new burst of information technology advancements, computers have become invaluable to researchers in every area of research. Because of the rapid rate of creation of computer applications in the area of social research, social scientists have been able to tap into what would ordinarily have been among the hidden, if not inaccessible, complexities of man’s nature and his social organizations. Consequently, social scientists have come to rely upon the computer for just about every aspect of research involving human society. Just like the scores of general-purpose codes and the compatible hardware that are being churned out of the heads of Silicone Valley coders, and other such geeks, billions of lines of special purpose codes are also being etched into storage devices to advance the research objectives of scientists in their various specialized fields. The Statistical Package for the Social Sciences (SPSS), although widely used by researchers in diverse fields, justifiably became the all-purpose specialized software for social scientists. The need for statisticians to possess the facility to respond to difficult research questions about society with ponderous mathematical calculations is fast becoming a thing of the past. The SPSS is now supplying answers to the most enigmatic questions about society with a couple of clicks on a keyboard (Bala, 2016, p. 250).

Essential Element: Why should social scientists use Statistical Package for the Social Sciences (SPSS).

Additive/Variant: The Statistical Package for the Social Sciences is perhaps a bigger deal than novice researchers, as I am, are able to confirm. However, I am sure that there are many other statistical software being written to help statisticians solve research problems without the need for cumbersome mathematical skills than that needed in decades past.

Contextualization: Over at least the last twenty-five years, school districts have been requiring that high school mathematics teachers use the TI-83 Calculator to teach logarithms, statistics, and other sub-mathematical disciplines and functions that are programmed into it. The examinations prepared by the various boards of Regents and Advance Placement boards have long required the use of the TI-83 for their examinations. So, although teaching the use of the TI-83 has become an imperative for the Teacher of Mathematics, viz., Statistics. Although the SPSS has not yet been included into the statistical part of the high school mathematic curriculum, I believe it is just a matter of time.

Comment: The brief history of SPSS

Quote/Paraphrase: The Statistical Package for the Social Sciences was first written in 1968, by Norman H. Nie, Dale H. Bent, and C. Hadlai Hull as a statistical research tool specifically for analytic work in the social sciences. SPSS has been upgraded three times in 47 years. It is a software program with numerous subprograms, capable of reading data from questionnaire. It always begins with definitions of variables, graduating to bivariate tests, correlations, nonparametric tests, and so on. Next, upon the heels of the identification of the variables, comes the quantification, or measurement of the variables. Thus, numbers are assigned to nominal variables, and the likes. Although the researcher need not be a mathematician to be able to use the SPSS effectively, he or she must be facile with the statistical underlayment of mathematical concepts upon which the software program rests (Bala, p. 251).

Essential Element: The versatility of SPSS software in social science research

Additive/Variant: I still believe that, while researchers may be passing their statistical problems on to specialists who are armed with dependable software, in the field of statistics, the statistician, himself, should be armed with the pertinent back-up mathematical skills despite the availability of software such as SPSS, just in case.

Contextualization: There is good reason why I have been careful to teach both the manual mathematics, including derivation of formulas and attendant algorithms, along with the calculator skills. I suspect that as with the TI-83, there are also special skills one needs to learn in order to be able to use and teach the Statistical Package for the Social Sciences at the highest level of proficiency.

Comment: Use of SPSS with different participant design

Quotes/Paraphrase: How is SPSS serviceable to the statistician in solving problems for researchers? After the quantification of the variables, the scales of measurement are itemized, ranging from “nominal”, “ordinal,” “interval,” to the “ratio scale”. Following this is the Study Design. The first one is called, “between-participants (unrelated) design,” and the other is the known as, “within-the-participant (related) design.” The first has to do with a comparison between two or more groups. The second design has to do with using the same sample repeatedly to measure different things. In addition, the same thing could be measured repeatedly. Of course, if there are two or more independent variables, the study could be subject to a “mixed-design”—the two different variables being used as a related design and an unrelated design. The researcher’s job is to lay the foundation for his analysis on the basis of variables, measures, and study design.

Essential Element: The application of SPSS between-participants (unrelated) design,” and “within-the-participant (related) design.”

Additive/Variant: It is obviously necessary for variables to be quantified since some, such as nominal and ordinal variables, do not naturally exist as part of the body of the quantitative data that are collected. This article, in its service as a medium by which to describe the use of technology to perform the statistical tasks, has unveiled for us a sensible grasp of what is meant by “study design”.

Contextualization: To illustrate the concept of what may be called an “unrelated study design”, 60 adults between the ages of twenty-five and thirty could be selected at random. In the beginning, they would all be tested for COVID-19 and come out negative. Once done, the sample would be divided into two halves. The first (experimental half) group of thirty will be given the J & J vaccine. Meanwhile, the second (control) group will be given a placebo. This is an example of the “unrelated” or, the “between-participant” study-design. After two weeks, and an exit test result of 100% negative, the participants will be released.

To illustrate the second type of study-design known as the “related” or, “within-participant” study-design, a sample of thirty will be selected from a similar population. These would be domiciled in a semi-quarantined common hotel-living facility together. They would be expected to prepare their own meals so that they would not come in contact with any outsider once indoors. However, they would be allowed to continue all their usual outdoor activities while wearing a mask. After two weeks, they would again be tested. Once the test result is negative for the pandemic, the participants are release. The same group will be asked to remain in the living facility for two more weeks. This time they were asked to not wear masks for outdoor activities. In the end, they would again be tested. This time, 30% of them would test positive and 20% of those who are testing positive would wind up being hospitalized.

Comment: SPSS—The process

Quote/Paraphrase: Here, the case is being made about how to set off the research as soon as the values are assigned to the variables. The data is loaded into the SPSS. This will be the most time-consuming part of the process. The cursor from the mouse is put on the “Menu”; it clicks on the variable of choice, followed by a click on “Run!” SPSS then reads the cases, does the analysis, and spits out the results. All the results are then sent to a dialogue box named, “SPSS Viewer.” “. . . . SPSS is a desktop and larger computer-based quantitative analysis package . . . [it] can perform many data management and statistical [analytical]. . . tasks with base SPSS, a researcher can manage data with case selection file reshaping and creating derived data. A metadata dictionary is stored with the data statistical analysis tasks that can be performed with the base package include the generation of descriptive statistics, bivariant statistics, prediction of numerical outcomes, and prediction of identifying groups. Although SPSS is very popular with social science researchers, its ease of unsend-add-on modules allows it to operate as a cross disciplinary software package” (Bala, p. 252).

Essential Element: How to use SPSS

Additive/Variant: In this segment, instruction for the use of SPSS actually takes us through use of the software technology for the standard research process. This segment begins with the “Menu” and continues to where there is a command to “Run”. I would think that since the results of the analyses that follow the command to run are sent to the dialogue box, SPSS Viewer, the program does probably have some way to provide the researcher or the statistician with a way of viewing the results so that he or she will be able to make some corrections. The fact that it does the two important functions of “data management” and “statistically analysis”, is just about everything that is needed.

Contextualization: I am not conversant with the SPSS, but I think that it ought to be a software that provides plenty of “descriptive statistics” along with all the alpha- numeric outputs. From my familiarity with the TI-83, I must applaud it for being a complete statistical tool that produces results in graphs, histograms, etc., as well as numeric results.

Comment: Using SPSS; then what!

Quote/Paraphrase: “SPSS has a Command syntax language (CSL), Macro Language (CYL), and two types of View” (Bala). It has a programmable pull-down menu is with 4GL. Its Command Syntax Language (CSL) is programmable with functions that facilitate reducibility and simplification of repetitive tasks, and manipulation of complex data, while doing analyses. Through its macro linguistic system, programmers are able to write language subroutines as well as complete programs. Both forms possess the ability to perform graphical operational interfaces with “two views which can be toggled by clicking on either of the two tabs on the left” (Bala, p. 252 –’53). SPSS can engage in two-way linguistic exchanges (reading and writing data) in ASCII texts, while also making spreadsheets and databases. It is also able to make tables via ODBC and SQL. “The proprietary output can be exported to text or Microsoft Word, PDF, Excel and other formats. Alternatively, output can be captured as data (using OMS command), as text, tab-delimited text, PDF, XLS, HTML, XML, variety of graphs” (Bala, p. 252). Its limitations are its inability to import csv files with variables in in the proper numerical format for SPSS (pp. 252-’53).

Essential Element: SPSS’ broad ability to facilitate programming, data manipulation on spreadsheet, etc., along with graphic interpretation of data, and exportation of its files to Word, etc.

Additive/Variant: It appears from this final section suggests that the SPSS is loaded with functions and assets, some of which I have little or no knowledge. But it does seem as though this section answers my some of my earlier questions, especially that about descriptive statistics. Further, it does appear to allow the researcher or statistician to write “code” into what is presented as the results that are produced. As it states, Macro Language can be used to write language subroutines as well as full scale programs.

Contextualization: All I can say, is that my knowledge of the vast array of functions and data management capabilities boasted by SPSS is well beyond my scant knowledge of technical computer software. I have to conclude that if my experience with the TI-83 and my half-forgotten skill in the manipulating of formulas and spreadsheets on MS Excel is anything, it certainly pales in comparison to what SPSS has to offer. My only question is, “How soon can SPSS be introduced as a statistics software course in high schools?”

Source: 4

Andrews, Douglas M. (1999 Aug). The American statistician. Journal of Statistics

Education, Alexandria, 53(3), 291. [Statistical Reasoning & Method for pedagogical purposes]

Comment: Review of Statistics Book

Quote/Paraphrase: This article is a Douglas Andrews review of the book, Statistical Reasoning and Methods by Richard A. Johnson and Cam Wah Tsui. Andrews points out that the book is actually an attempt to tie together a statistical bundle of loose ends from an earlier book entitled, Statistics: Principles and Methods. The original book was written by Johnson and Bhattachary in 1987. According to Andrews, Johnson and Tsui have, in this new book, written a follow-up text to illuminate the chapters on variance analysis, multiple regression, and non-parametrics. They have instead compressed categorical inferences and inferences for one and two proportions into a single chapter dealing with analysis of count-data. He says that in this work, they were responding to a public outcry that statistics education should place emphasis on statistical reasoning over calculations, which can now be left to computers. The idea is that this version should include actual examples of learning data, student projects and exercises. But, since most of this material is lifted straight out of the previous text, this book has neither changed focus nor orientation (Bala, p. 290).

Essential Element: Book review dealing with variance analysis, multiple regression, and non-parametric data analysis.

Additive/Variant: The criticism, here, is being leveled mainly against what the reviewer sees as an unnecessary over-use of mathematical formulas and algorithms to solve statistics problems related to variance, multiple regression, and non-parametrics. The position is based on the fact that most solutions to statistical problems only require a few data entries. The problem is that when the computer is doubtful, how do you check or fix it without resorting to statistical formulae and algorithm?

Contextualization: Some years ago, my PSA (prostate specific antigen) began to edge up. I looked at my multiple myeloma m-protein and PSA and thought that both of them seemed to have been moving up and down in synchronicity. I decided to treat the m-protein as an independent variable (x) and the PSA as the dependent variable (y). I did the calculations manually using the Pearson r—a massive formula. The coefficient turned out to be .86 (86%). I could not believe it. I felt I may have made a mistake, so I tried it on the computer for verification. The computer result was the same. I then used the Kapa/Lambda ratio from the light chain proteins on the myeloma cells as the x and the PSA as the y. The correlation coefficient was .85 (85%). And, once again, I tried the computer for verity. The result was identical. These were high correlations, and because of that, my doctors were able to make better decisions on the treatment choices.

Comment: Averting the Mathematical Complications

Quote/Paraphrase: Although the authors have done well by inserting the randomizing of samples, Andrews, in his review of the book, still considered it top-heavy in favor of mathematical calculations. He says that far too much of the book is devoted to probability, random variables, and binomial distribution. The authors confessed that “only the first nine chapters can be covered in a single semester. . . . [which] would end the course after inference for a single mean which would leave out inference for two means and for proportions” (p. 290) as well as linear regression. The authors further suggested that the chapter on bivariant description be skipped “if student projects are not a priority”. To this, Andrews complains that the section on design, being thus eliminated in the more recent edition, excluded scatter plot and correlation, too (Bala, p. 290).

Essential Element: Reviewing a statistics textbook that seeks to teach statistics by minimizing the tedium of mathematical calculation.

Additive/Variant: The case here is the same as that made in the segment immediately above, only that this time the practical meaning of probability and binomial distribution cannot be fully appreciated without demonstrating a sense of difference between probability and combination. Further, the “descriptive” appreciation of correlation and situations that involve “mean-proportion” requires submersion in the very mathematical forms that Andrews would rather have excised from Johnson’s second book. The mathematical formulas, calculations and descriptions make it possible for the student to think statistics rather than just receive answers from computer software outputs.

Contextualization: Recently, I saw the movie, Hidden Figures, and what it demonstrated to me was that, even in the age of computer technology all the way to artificial intelligence, the human ability to find solutions to the “novel” problem where machines fail, is undeniable. In this time when “computer pirates” are hacking into life sustaining computer systems, if no one knows how to do the math, how can we stop the hack?

Comment: The book’s conceptual appreciation of statistics

Quote/Paraphrase: “The best feature of the book is the inclusion of ‘statistical reasoning boxes’ in which the author briefly describes how statistical thinking is used in a concrete context. Unfortunately, the 13 boxes are marginalized and just a handful of pages are devoted to normal and residual plots” (Bala, p.290). While, at the same time, precious little energy has been exerted on setting straight incorrect interpretations, and on elaborating on the proper uses and the common abuses of statistical tools. Most of the workbook style activities require that students simply find numerical results or create visual displays, with little demand for genuine analysis and insight based on the calculations and displays. A few computer exercises are appended to the end of most chapters. Though a tiny bit of these appears to be more flashy than “7.34: use of MINITAB to find mean and standard deviation for the dataset in table 4” (Bala). Certainly, computer results are included so as to help students learn the-activity section of the book (Bala, p.290).

Essential Element: Criticisms of the author’s insufficient emphasis on statistical misconceptions and in proper use of statistical tools.

Additive/Variant: Here, Andrews attacks ironically supports the exact point he opposed earlier in his review. He says that not enough effort is expended on exercises that help students of statistics to develop the ability to understand the correct and incorrect interpretations and on the common abuses of statistical tools.

Of course, this is not surprising since this book has done more to tone down the hard mathematics of the other book. I suspect that this section has done much to tone down this, the most necessary aspect of what the student workbook in statistics is all about—doing the math.

Contextualization: In my personal struggle with multiple myeloma (cancer of the bone marrow), and now, prostate cancer, I have had to do some of the statistical heavy lifting—the math—in helping to guide my treatment. I helped make decisions based on high correlation coefficients and the likes. But I did so with full awareness of what the numbers really meant. In drawing conclusions about correlation, one has to be aware of the rule that, “Correlation is not causation.” But even so, we must also know that correlation, like probability, ranges from 0 to 1 (or 0% to 100%).

We also know that 0 is an impossibility and 1 is a certainty. So, the closer our correlation is to 1 is the closer it is to a certainty, hence to causation.

Comment: A textbook on research design

Quote/Paraphrase: Andrews applauded the student-projects near the close of each of the eight chapters but found the quantity of projects rather skimpy. The first two projects pushed students “to think about sampling and experimental design”. The third prompted them to generate sample distribution by repeat sampling. The projects, in the last five of the eight chapters, are meant to push students to hurriedly specify their designs, then move on to calculations of tests and confidence intervals while disregarding exploratory data analysis, “except for the advice to ‘include a graphical display’ in one of the projects” (Bala, 2016, p. 290).

Essential Element: This has to do with how the statistical review the

textbook on statistics highlights the necessary elements and the order through which scholarly research design should unfold.

Additive/Variant: As the reviewer walks us through a book on a book, which most of us have never read, we begin to hear more and more about what should have been pruned and what should have been spruced when it comes to student follow-up activities based on the instruction on statistics throughout the book. If what Andrews claims is true, the book has neglected student reinforcement activities in critical areas in parametrics, descriptive statistics and meaningfulness.

Contextualization: Parametric and descriptive statistics help to make statistics meaningful in a way that computer applications do not. If we are able to look at correlation in terms of a line drawn through points on a scatterplot, we should be able to give tangibility of how perfectly or imperfectly the points fit or do not fit. But once we say line, we must think of the rate of change. We are thinking of regression. And in the world where things happen, we think of them happening on an arc or a line. When the physicist talks about his inclined plane, he can make predictions about where something on the inclined plane will be at a certain point at

a certain time. In analytic geometry we think of a line as having a specific slope (m)

and an intercept of (b). Ex. 1: y= mx + b (Line). Ex.2: m = Y1 – Y2. (Slope).

X1 – X2

In linear regression, where you will have a large number of independent and dependent variables drawn from the sample, the slope is:

m = n (xy) – ( x)( y)

n ( x2) – ( x )2

Comment: The student’s “Cliff Notes” type of workbook

Quote/Paraphrase: As Andrews sees it, the authors appeared to have veered from the stated purpose in the book. He said that their stated goal was to foster active collaborative learning but instead they have focused on having students perform experiments and collect data (p. 191).

Essential Element: Why does a textbook on statistics should have a companion workbook.

Additive/Variant: The Douglas Andrews’ article is the only link we have to the book, Statistical Reasoning and Methods by Richard A. Johnson and Cam Wah Tsui. So, we are forced to take Andrews’ word for it. This means that as a textbook for undergraduate statistics students, there is need for the authors to create a student activity supplement or a separate accompanying workbook.

Contextualization: Based on Douglas Andrews’ review, if I had written that book for students, I know exactly what I would do.

Source: 5

Natiliia, Byshevets; Lolita, Denysova; Oksana, Shynkaruk; et al.(2019). Using the method of

mathematical statistics in sports and educational research of masters in physical

education and sport. Journal of Physical Education and Sport, suppl, 3(19), 1030-

1034. Doi:10. 7752/jpes.2019.s3148.

Comment: Educational research

Quote/Paraphrase: According to the author, the more scientific advancements there are, is the more progressive social transformation there will be. As contemporary statistical activities follow their natural course of data collection and analysis, together with the identification of correlational relationships, new trends are being formed in the area of pedagogical research. Thus, the viability of hypotheses that are being presented by researchers, in their attempt to find answers to problems related to the education of children, is constantly being weighed and sifted in order to determine their level of validity. For that reason, the application of statistics to empirical data is a vital part of the teaching and the performing of scientific activity (p. 1030).

Essential Element: The application of statistics to education as a subset of social science.

Additive/Variant: We see science in terms of that final product of applied human ingenuity that eventually leads to greater ease and culturally improvement. And so, as the author suggests, the more scientific advancements there are, the more progressive the social transformations. With that, little thought is given to the fact that in order for science to put its finishing touches on the product that comes out of it, there is need to bring the statistician in, to test the viability and effectiveness of the product before it is adapted into a cycle of usefulness. Hence, the scientific implements and actions around us are the results of proven hypotheses—sometimes written down, thought of, or, at other times, just spoken. The only important fact that exists in the teacher-student interaction over a lesson in statistics is a pragmatic one.

Contextualization: Whenever I teach mathematics, including statistics, I intertwine the basic rules of pedagogy with , but I always remain focused on my goal to realize a pragmatic outcome. In New York, the forces that be expect the teacher to teach the entire lesson by means of the Socratic method and in the midst of the process, the whole thing unfolds like a series of hypotheses and the attendant tests results at a certain level. In the end, students must demonstrate the skills acquired, the knowledge of concepts taught, and a sense of how they are applied.

Comment: How to gather and analyze data for education

Quote/Paraphrase: At the present time, a significant amount of theoretical and practical analyses of data are being gathered. Today, a vast cache of automated methods of statistical computation has been developed (Shelamov, 2010). In the natural, as well as in the social sciences, the proper gathering of data for the conduction of scientific studies has been among the most important actions taken during research activity. But, in the areas of human centered studies, namely, in sports and pedagogical research, the large majority of relevant data can only be gathered by way of questionnaire polling. in studying humans, it must be realized that the researcher in dealing with data that may not be quantifiable. For that reason, he must realize that he might not be able to verify the level of confidence as to the objectivity of the results (Yates, 1934; McNemar Quinn, 1948, Karuskal 1952) (npn).

Essential Element: The difficulty with hypothesis testing and other statistical tools affecting the sampling of humans.

Additive/Variant: When we study human behavior or characteristics such as race, gender, anger, happiness, and so on, we are usually dealing with normative data. This kind of data may be assigned numbers, even though such numbers do not have quantifiable values. For example, the questionnaire could ask the respondent to enter 1 for African-American; 2 for Caucasian, and so forth. If it is a study for breast cancer research and it is meant to screen only African-American women whose mothers were, either North Carolinian or South Texan, and numbers are assigned to all categories, a total numerical value would be required within a certain range.

Contextualization: I wrote a thesis for an MS degree at CCNY in the year 2000. In it, I created what I called the “Thompson College Fit” (TCF) instrument. The TCF used the Likert scale as its base. On the left, from top to bottom, there are 15 statements. The first of the statements is, “Changes in financial aid package;” the twelfth is, “Feeling academically unprepared;” and, the fifteenth is, “Proud to be a student at this college.” The numeric choices from left to right are 100, 89, 79, 69, and 59. While, their verbal descriptions for each of the five values, in respective order, from left to right, are: “None,” “Seldom,” “Sometimes,” “Often,” and “Very Often.”

If student A were to picked, “None” (100) for all fifteen statements, he would

score 1500 or 100%. The inference, then, would be that A’s college choice was a

perfect fit for him. On the other hand, if student B selected “very Often” for all

fifteen statements, his score would be 885 out of a possible 1500. That would be a

TCF rate of 59%. Since the New York State Education Department and the Board of

Regents have set the minimum passing rate for examinations and other activities at

65%, student B would have failed the TCF. The conclusion would, then, be that the

college student B had chosen was an absolute misfit for him.

Comment: Testing the sample

Quote /Paraphrase: When conducting research in the field of sports or education, certain criteria are usually applied, each, having its own conditions and limitations (Lackin, 1990; Denysova, 2011- 2012; Dennysova, Shynkaruk, Usychenko, 2018). Although these criteria are inclined to malfunction, especially in terms of the volume of essential data, from time to time, they are still frequently being kept in used to solve various types of sports and education research problems. The widespread use of these criteria appears, in multiple ways, to be related to the fact that source-data can be measured on all of the scales (normative, etc.). Through these criteria, samples of both dependent and independent variables can be extracted (Sysa, 2010) (Natiliia et al, 2019, p. 1030).

For instance, one criterion among this lot is the -test. This test is used to compare two samples (independent or related samples). When in use, it measures the frequency of the effect, and how such effect serves to determine the “differences between the particles of both samples in which the effect was received” (Paragina, 2016) (Natiliia et al, p. 1031).

These days, -tests are rarely used to validate results of data involving human subjects as one would expect in sports and childhood education. Neither is much literature available to show that computer technology is being utilized to test hypotheses where physical education and sports are concerned (Naftiliia et al, p. 1031).

Essential Element: The -tests: When and what it does.

Additive/Variant: Obviously, it is quite difficult, if not impossible to analyze data about human beings in numerical ways. To begin with, if the researcher’s hypothesis has to do with Novak Djokovic’s passion for tennis or a particular student’s intrinsic motivation for learning statistics, he might be hard put to test it objectively.

Contextualization: I might be mistaken in my thinking about the appropriateness of

choosing one research or another. My thinking is that there is a place for the objective study of sadness, joy, sports and educational aptitude and interest. I believe that if we were to try to pile in all the tests, etc., that belong to quantitative research as well as those belonging to qualitative research, we would find that enough of elements belong to both that should make them operate like intersecting sets.

Comment: Vindicating the use of the Fisher -tests

Quote/Precis: According to the authors, the intent of this segment of the article is

to justify the universal application of Fisher -test criteria in research involving

physical culture and sports. The methods used are aimed at the analysis, and the

systematization of scientific literature, as well as the generalization of scientific,

educational, and practical education. During the questionnaire polling, the data from

human subjects are presented in the nominal scale. By using this scale, the

researcher can only infer the level at which values are. Even though the nominal

scale is used, the amount of objects involved can be quantified (Ashykhmina, 2009);

(Naftiliia et al, pp. 1031-1032).

Essential Element: How versatile is the -tests?

Additive/Variant: We understand that certain tools and tests appear to be more naturally custom-tailored to one type of research method over another. But even so, some tools, tests, and instruments fall in the overlap section of the different sets of research methods. It is said that Fisher -test criteria can be applied universally to different methods.

Contextualization: I have never studied the nature or use of the -test criteria nor had to learn it for imparting statistics to my math students. Perhaps I will be able to secure information about the nature and use of the Fisher -test criteria from the reading recommended. So far, I have not seen any reference to it in the readings or videos.

Comment: A combined use of the -test and the F-test

Quote/Paraphrase: “The purpose of the article is to justify the universal application of the -test criteria in scientific research in physical culture and sports” (Byshavets, npn). Having accepted the versatility of the -test, the author calls attention to the fact that the test exhibits some restrictions when applied to an ensemble of particles. He suggests that it is here that the F-test becomes helpful. In the questionnaire, numbers are assigned to the objects in a manner that is consistent with the rules. The data in the nominal scale are placed under their respective labels. If the numerical assignments are done in respect to the amount of objects under their respective labels, most experimental data can be quantified (Ashykhmina, 2009). In this scale, comparing and contrasting the different values, only allows the researcher to determine the levels at which each type of data belong. When the F-test is brought into play, the researcher can then visualize the scaled data in terms of angles within the range of all angles within a half-turn

(Naftiliia et al, p. 1030).

So, an F-test is appropriately defined as angular. The first particle (P) can be

written as one of the angles from 0o to 180o. if the researcher gets to where he can say “there is an effect”, and that effect can then be presented as an angle within that half-turn range in the following manner 0 n 180. The angles are calculated as 1 and 2 by use of the formula. Based on the set of rules, the initial data are plugged into the MS Excel table and the experimental values of the angles were calculated by means of a formula and the particles of the samples Pi should produce an observable effect. “The analysis of literary sources showed that the specialists presented methods of applying nonparametric criteria (Arkhipova, 2009) and described application of an -test in psychological and pedagogical researches” (Rudenko, 2012) (Naftiliia et al, 2019, p.1031).

“However, nowadays, methods of test of personal data, in particular an -test, are not widely used as basis of validity and effectiveness of results in sports and pedagogical research. The question of automating its use in the field of physical education and sport is not sufficiently covered in literary sources” (p. 1032).

Essential Element: How do we combine the use of with the use of the F-test whose interval is in angle measure.

Essential Element:

Additive/Variant: In this segment of the article, it is suggested that there is a way to use the -test to uncover the effect that an independent variable has on a dependent variable. The implication is that the test is supposed to show the effect from the independent variable in terms of linearity or curve-linearity, if you will. My thinking is that if the line of regression is horizontal, the slope would be zero, and a zero slope would make the effect tantamount to nil. Also, it seems that where there are multiple independent variables, the -test is not adequate, so the F-test comes into play. The problem is that the rules provided as the means by which to perform these tests are not coherent in my estimation. There obviously needs to be more mathematical clarity in the rules and a clear algorithmic path to follow.

Contextualization: Throughout this article, I have looked for a clear, workable “definition” in the form of an equation or a formula, to no avail. The phi-test formula below is one example of a formula the author could have used (Wikipedia). Clearly, the formula is an irrational expression with a “Chain Rule” principle (syllogistic) as is shown:

= . ad – bc .

(a + b)(c +d)(a + c)(b + d)

There has to be a dichotomy of variables in which at least one is nominal, such as light/dark, truth/lie, etc. Working Day broken down into night and day. Night: a =12, c = 10; Day: b =14, d = 18, So,

= . (12)(18) – (14)(10) .

(12)+ (14)(10)+(18)(12) + (10)(14)+(18)

= . 216 –140 . . 76 . 76 .

[(26)(28)(22)(32)] = (512512 = 715.8 = 0.106175

Granting that the numerical values I offered here are arbitrary, the result that comes out of the phi-test at 0.106 or 11% is a very weak positive effect. In the case of the F-test, summation of the variables could be done as indicated below (Wikipedia):

Y = 0 + 1 X1 + 2 X2 + 3 X3 + I

Kruschke, John K; Liddell, Torrin, M. (2018 Feb). The Bayesian new Statistics: Hypothesis testing,

estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic Bulletin & Review; New York. 25(1), 178-206.

Doi: 10. 3758/s13423-016-1221-4

Comment: Estimates by quantifiable immunity

Quote/Paraphrase: A distinct difference exists between the use of traditional hypothesis-testing tools and those tools of estimation done by means of “quantifiable uncertainty”. And, today, as the winds of change push researchers away from the older algorithms of hypothesis testing toward newer processes done under the more newly coined generalized sobriquet, “The New Statistics,” has become a thing of wide acceptance (Cumming, 2014). Secondly, there is a marked distinction between the “Frequentist” and the Bayesian techniques in hypothesis- testing as well as in the estimation of confidence intervals (CI). This article also addresses the way the Bayesian method is used in meta-analyses, randomizing control trials, and power analyses. With this, there is a shift away from null hypothesis significance testing (NHST) toward “estimation based on effect sizes, confidence intervals, and meta-analysis” (Cumming, 2014, p. 7) (Kruschke 2018 et al, p. 179).

Essential Element: The paradigm shift from NHST to The New Statistics involving effect size, confidence interval, and meta-analyst in the effort to achieve “quantifiable uncertainty”.

Additive/ Variant: At last, we are here in a highly technological age where mathematics and the magical outcomes form specialized algorithms are king. Yet, analysts are settling for statistical predictions resting on viable proofs of the uncertainty principle.

Contextualization: Even I am becoming satisfied with the notion that once the central tendency and the standard deviations have succumbed to the usual mathematical algorithms, a distribution curve skewed, or not, may lead the way to guestimates that are worth their weight in the game of predictive analysis. That is something that can be made quite graphic, and hence, something teaching of an abstraction by way of concretizing.

Comment: Nonparametric v parametric statistics

Quote/Paraphrase: In data analysis, formal mathematical models are used to describe data and their parameters. For instance, a shower head could be tilted in a manner that causes the water (data) to be sprayed out at a certain inclination. We could treat the angled spray and the type of spray-pattern created by the setting of the nozzle as the two parameters. So, the data observed are manipulated to fit the appropriate mathematical machine to which its parameters are set. In this case, the object is to come up with other settings of the parameters that simulate the empirical data (p.179).

Likewise, if we decide to measure the intelligence quotients (IQ) of a group of people, we could make a histogram of the scores—one that has a single mode and is symmetric—one that could be translated into a bell curve. The mean and the scale, or the standard deviation, would thus be the parameters. By comparing these two parameters with the angling of the spray from the nozzle, and by setting the type of spray-action set by the control knobs, we are able to obtain a sense of how these IQ scores could be similarly manipulated to work in a mathematical machine that is aptly suited for generating normally distributed data (Kuschke et al., 2018, p. 179).

Essential Element: How nonparametric data can be collected and organized to compare with parametric data.

Additive/Variant: The situation with the shower head must first be seen as a purely geometrical one. And, as such, a number of geometrical adjustments can be made that simulates what was originally observed. The simulations could be one in which angles and spray adjustments could be set randomly to suit the height and comfort of the person using the shower. Or, it could be set in random similarity by proportion. This latter adjustments of the angle and spray would be more practical for people of different sizes and comfort levels, and a better suited comparison to the IQ parameters of mean and standard deviation. In this respect, we are using the word “similarity” in a non-mathematical as well as a mathematical way.

Contextualization: If the original angling of the shower head were at a forty-five degree angle and the spray was set at a dilation of 10 inch-diameter at floor- contact, they could be adjusted to a 40o angle and a 8.9 inch-dilation. This is a mean-proportional (x1: y1 = x2 :y2) relationship that makes it perfectly “similar” to the original 45o : 10 ratio. Otherwise, the angle and spray-dilation parameters could be disproportionately paired as they would naturally be in a practical situation. When we compare this to IQ scores of a random sample, of let us say, 20 people in a population, you would expect the sample to range probably from 90 to 140. That would make it possible to find central tendency and standard deviation.

Comment: Frequentist approach

Quote/Précis: According to Kruschke et al (2018), it is that intrinsic logic in the mathematical model that enables the analyst to determine the properties of the parametric descriptions. The analyst is able to choose whichever of a number of models he favors. He may choose to perform one of the typical hypothesis-tests on the parameter values or he may choose to estimate the values of the parameters by way of the “uncertainty principle”. Through the Bayesian method of hypothesis-testing, one could extrapolate the probability that the mean (µ) will fall between 99 and 101, given the empirical data. Inversely, the frequentist method relies upon the sampling distributions of imaginary data. This type of data is said to be at the very heart of finding the p-values and confidence intervals. The p-value has to be computed through the normal process of t-test utilization, if p < .05, the null hypothesis will be thrown out. But, to begin with, in order to do the test, some collected data have to be summed up as a t. A single group of data, “t = (y - µ 0)/(s/VN), where y is the sample mean, µ0 is the mean of the null hypothesis, sigma (s) is the sample standard deviation, and N is the sample size” (Kruschke et al, p. 180) must be harvested. What the frequentist seeks is to show how improbable it would be to obtain a t if the null hypothesis were true and if the data were collected the way they usually are when an actual research is being conducted. Truly, all the frequentist needs in order to reject the null hypothesis, is a very low probability. “Therefore, the probability is the rate of committing a false alarm (also known as a ‘Type 1 error), and the goal of the decision threshold (usually set at 0.05) is to limit false alarms to that [level of] frequency” (Kruschke et al, p. 180).

Essential Element: Using the Frequentist approach to determine that the probability of obtaining a false positive of the -value is 99% or less only in absolute values.

Additive/Variant: I cannot say that I understand why the mean would fall specifically between 99 and 101 if it is based on observed data. Also, even if the process is going to be carried out by estimation, I would think that the probability would not fall outside the bounds of zero and one.

Contextualization: After reading the entire article of 24 pages, I have noted that this is the only segment in which it is suggested that probability could exist beyond the certainty of 1.0 or 100%. I cannot see how I would teach it.

Comment: The use of repeated sampling

Quote/Précis: The authors insist that the reiteration of randomized sampling of the null hypothesis will continue to churn out the samples in similar fashion to that occurring with the real data samples. And so, for each simulated sample that comes out, the statistician computes a summary statistic that matches the one computed for the actual data samples. The distribution of randomly produced summary values, then, constitutes the simulated values along with a few other chanced values which rarely appear. Any samples among these “chanced values” are assessed as being a very unlikely product of the hypothesis, and so the hypothesis related to these rare outcomes is rejected. This type of rare outcome, being a simulated rather than being an actual outcome, is the p-value (Kruschke et al.,p. 180).

A p-value is defined thus, “For a set of actual data, let T (D actual) be a descriptive summary value of the data, such as a t-statistic” (Kruschke et al., p. 181) If the actual data were sampled by certain test-stop-test procedure denoted by I, the p-value is:

p value = p (T (D simulated) > T (D actual) | µ , I ), for such situations in which T (D simulated) “are the descriptive summary of simulated data sampled from a hypothetical population characterized by parameter value µ according to the same stopping and testing intentions, I, as the actual data” (Kruschke et al., p. 180).

Normally, the p-value is considered to be the standard value by which the null hypothesis is tested, and when the model-parameter, µ, turns out to be zero, or to whatever miniscule value, it is indicative of “no effect”. So, it stands to reason that whenever a p-value is used to determine the null-hypothesis (µ0), the process is aptly referred to as a “null-hypothesis significance test”—NHST (Kruschke et al, pp. 180-82).

Essential Element: Using repeated random sampling to mirrors the actual population and achieve NHST.

Additive/Variant: Naturally, if we accept the premise that the probability that an event (p) must fall somewhere within the interval 0 < p < 1, we must also accept the conclusion that p = 0 is not merely improbable, but “impossible”. And, by the same token, a probability of 1 is not merely a highly probable chance of occurrence, but an “absolute certainty”. With that 0.5 is the midpoint from which the chance of an event may progress toward significant or insignificance. Yet, different types of events have different thresholds of significance. So then, if the p-value comes out to be as far below the conventional threshold as p < .05, the null hypothesis will be rejected.

Contextualization: When forecasting the weather, meteorologists do not ordinarily predict the chance of any impending weather condition on a scale that is bound at the bottom by zero and sealed at the top by one, but on the percentage scale from zero to 100. If the meteorologist has determined that tomorrow’s Yankee-Tiger game will be washed out, he will post a prediction of absolute certainty as to the probability of rain, not as the number one, but as a 100% chance of rain. At the other end of the scale, there is no numerical difference if the probability that it will rain tomorrow is given as the number zero or 0% because both are absolutely impossible and offers no degree of significance. But, while a 0.05 probability that it will rain, which is a 5% probability of rain, suggests that there could still be some rain, a p-value of 0.05 is so far below the threshold that could uphold a null hypothesis for which the effect size is so minute that it has to be rejected.

Comment: The process of elimination at work.

Quote/Paraphrase: Kruschke et al (2019) tell us that the Bayesian analysis reassigns credibility in a one-to-one correspondence with a set of matching possibilities. Sherlock Homes appeared to have anticipated the Bayesian process in his words: “When you have anticipated the impossible, whatever remains, however improbable, must be the truth” (Doyle, 1890). To illustrate the point, he identified a string of suspects; then, after collecting new evidence, he assigned degrees of suspicion to those not eliminated by the “improbability rejection rule”. Once those who belonged to the low probability group are eliminated, the suspicion list is narrowed down to the most highly improbable (Kruschke et al., 2019, p.183).

The analysis begins with “a space of possible parameter values” that abound

within a descriptive data model quite the way that it would in a Frequentist analysis. The amount of belief in the parameter values, after ignoring the data, is known as the prior distribution. So, the amount of belief-exhibited while accounting for the data, is called a posterior distribution. “The exact re-allocation of credibility across parameter value [sic] are provided by the mathematics of Bayes’ rule” (Kruschke et al, p.183).

Individuals are asked whether they agree with a particular policy. Each

respondent is treated as if he or she is being randomly sampled to indicate that the probability of the positive response is the parameter value being represented by the unknown variable, Q. The realization is that all of these parameter values fall within the interval of 0 < Q < 1. The analysis begins with “a space of possible parameter values” that abound, not with the amount of belief one puts into the parameter values, while ignoring the data, is known as the “prior distribution”. While the amount of belief-exhibited by one after the data have been collected is called a “posterior distribution”. “The exact reallocation of credibility across parameter value [sic] are provided by the mathematics of Bayes’ rule” (Kruschke et al., p.183).

Let us say, that workers are asked whether they agree with a particular policy. Each respondent is treated as if he or she is being randomly sampled to indicate the probability of the positive (yes) response as the parameter value being represented by the unknown variable, Q. The realization is that all of these parameter values fall within the interval, 0 < Q < 1. Using the Bayesian model, the goal is to re-allocate credibility to the values in the interval except for those values that are not consistent with the data. To begin with, values of Q are harvested by the process of “prior distribution” so that the number of positive responses (z) are extracted from the total (N) number of responses. Credibility is, then, reallocated to the “Yesses” (z/N) that coincide with what is actually observed in the data.

Next, some of the small values of theta are, naturally, inconsistent with a good many of the positive responses in the data. And so, the small values of theta have “low posterior credibility”. Using the Bayesian model, the goal is to re-allocate credibility to the values that are bound in the interval with the exception of those values that are not consistent with the data. To begin with, values of Q are harvested by the process of “prior distribution”. The number of positive responses (z) are extracted from the total (N) number of responses. Credibility, is, then, reallocated to the “Yesses” (z/N) which coincide with what is actually observed in the data. As it happens, some of the small values of theta are inconsistent with a good many of the positive responses in the data; and so, the small values of theta have low posterior credibility. Because the actual data is accounted for, the “posterior distribution” begins to take form and the level of credibility is elevated. As the posterior distribution spreads out, the “uncertainty” of the small parameter values becomes more evident. Since the highest “density interval” (HDI) bunches up where Q < 1 is, it contains parameter values of higher probability density progresses from high to higher. The values outside of Q < 1, included within 0 < Q progress from low to lower, and therefore, these fell within the realm of uncertainty and are very likely to be improbable (Kruschke et al., pp. 182-’84).

Essential Element: How low distribution is separated from high distribution to isolate “uncertainty”.

Additive/Variant: Simply, Bayesian analysis comes closer to pure inferential logic than Frequentist analysis does. It is a method of hypothesis testing done by the “process of elimination”; beautiful!

Contextualization: Twenty teachers (N) of a high school senior-class are asked whether the entire class will satisfy the graduation requirement this year. Sixteen of them (z) responded in the affirmative. The proportion of those who responded positively is z/N, which gives us an actual numerical setup of 16/20. The Greek letter, Q (theta) is used to represent the probability of the positive responses and Q null represents the null hypothesis which, at 0.5, serves as the fulcrum of the null hypothesis itself. The sample is picked intermittently to ensure some degree of randomization until a total of 20 teachers were selected. The p-value (0.05) becomes the set-up for the probability that simulates z/N and would be as extreme or even more extreme than the actual z/N moving in either direction away from the null hypothesis. In which case, the Qnull, on both sides, would be rejected. The p-value by itself would not help us to come up with an “estimated magnitude of the parameter” (EMP).

By turning to the frequentist model, we can seek to find the “maximum likelihood estimate” (MLE). And, as such, the MLE of Q would be the actual z/N, which would sets up the actual ratio, 14/18 = 0.80. This would also be the modal value as well as being pretty close to the median value. In frequentist method, we represent the uncertainty of the estimated parameter value by first coming up with a confidence interval (CI). If we make the confidence interval 95%, all the parameter values within it would be safe from rejection, but those value outside would not be. Using the posterior distribution, the uncertainty of the estimate should be evident in the breadth of its spread. However, with one standard deviation to the right of the mean (µ), any assumed certainty of the p-value indicated by Q < 1 on the outside right toward the upper bound would be rejected. Thirty-four percent on the left of the mean, at approximately 0.5 would render all values moving toward 0.0 highly uncertain. To fully illustrate this, it would be necessary to present it visually in the form of a normal distribution curve.

Works Cited

Andrews, Douglas M. (1999 Aug). The American statistician. Journal of Statistics

Education. Alexandria. 53(3), 291

Bala, Jyoti. (2016 Nov). Contribution of SPSS in social sciences research. International Journal of

Advance Research in Computer Science. 7(6) (Special Issue).

www.ijjarcs.inform.

Hardwickes, Tom E; Goodman, Steven N. (2020, Oct). PloS One; San Francisco. Vol. 15(10).

e239598. doi: 10: 1371/journal.pone. 0239598.

Kalaian, Sema A; Kasim, Rafa M. (2014 Mar). A meta-analytic review of studies of the

effectiveness of small-group learning methods on statistics achievement. Journal of Statistics Education. Alexandria 2(1), 1-19

Doi: 10. 1080/10691898.2014.11889691.

Kirby, Berends, & Naftel, 1999); how teaching conditions predict teacher turnover in certain

states (Loeb, & Darling-Hammond, 2005); These findings confirm that the notion of creating a racially diverse school system.

Kruschke, John K; Liddell, Torrin M. (2018 Feb). The Bayesian new Statistics: Hypothesis testing,

estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic Bulletin & Review; New York. 25(1), 178-206.

Doi: 10. 3758/s13423-016-1221-4.

Loeb, Susanna; Darling-Hammond, Linda and Luezak, John (2005). How teaching conditions

predict teacher-turnover in California schools. Peabody Journal of Education, 80(3)

44-70. Taylor & Francis, Ltd., Accessed: March 8, 2016

http://www.jostor.org/stable/3497042.

Natiliia, Byshevets; Lolita, Denysova; Oksana, Shynkaruk; et al.(2019 May). Using the method of

mathematical statistics in sports and educational research of masters in physical education and sport. Journal of Physical Education and Sport, suppl. 3(19), 1030-1034. doi:10. 7752/jpes.2019.s3148.

Ogundimu, Charles O. (2014). Does the mode of entry into teaching matter in teacher-

retention? A discrete-time survival analysis modeling of New York City public school

teachers. Columbia University (PhD).

Magnet June 30, 2020, US Supreme Court Espinoza v. Montana Dep of Revenue. Art X, sec 6, free exercise clause

Schools National Center for Ed Stats (2013) 14.7% in private sch.

“Some educational policies and practices boast average academic achievement even as the broaden educational inequalities” (e.f. Args, Rees & Brewer 1996.

NYC School Choice Scholarship Program $1,400 private voucher (Mayer et al. 2002). Studies showed almost no effect on math and reading.(p.4). K-4.

Public School Review. Dec 08, 2023. Grace Chen. NYC. Schools: Most Segregated in Nation.

UCLA’s Civil Rights Project