Subject Content Knowledge For The In Field Assessment Education Essay

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In 2002, teacher attrition rates and retention problems (Ingersoll, 2002) compounded the issue of out-of-field teachers, increasing the strain of meeting the requirements of placing a highly qualified teacher in every classroom (NCLB, 2001). In President Bush's 2006 State of the Union Address he pledged to create an additional 30,000 new mathematics and science teachers to correct for these shortages (Bush, 2006). Interestingly, in 2009 Ingersoll concluded that the teacher shortages were no longer the leading cause of the lack of high quality teachers but rather it was due to pervasive school staffing and management problems.  

Teacher shortages are still a major, however; several research studies have found that "highly qualified" teacher shortages has become an even greater concern (Blank, Langesen, Laird, DeMello, 2003; National Academy of Sciences, 2007; National Center for Education Statistics, 1997; Ingersoll, 2002; Rumberger, 1987; U.S. Department of Education, 2009). Sanders (2004) concluded that 57% of middle school students were taught by a teacher who had not earned enough college credits to declare a minor area of study in a related field;, 48% of middle school physical science students were taught by a teacher lacking a minor in a related field. More recently, a study by Schools and Trust (2008) found that teacher mis-assignments totaled 27% of the core courses in the nation's high-poverty schools. Mis-assignment is the assigning of a certified teacher to teach in a content area that he or she does not have an endorsement or major, and thus has insufficient content mastery. Alternatively, these teachers may be considered partially out-of field. Out-of-field assignments are still quite common. In each of the six years of data collection, Donaldson and Johnson (2010) found that anywhere from 57% to 74% of math teachers, 16% to 31% of social studies teachers, and 38% to 48% of science teachers lacked a major in the field they were teaching. Out-of-field assignments were most prevalent in the first one or two years of respondents' careers (Donaldson & Johnson, 2010).

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Despite a highly qualified status, if a teacher is mis-assigned or teaching completely out-of-field they are lacking the necessary training and knowledge needed to properly address the needs of the students. Filling the classroom with quality teachers remains a primary concern within the educational system. Having highly qualified teachers with knowledge and background in their content areas and strong supervision from content leaders and administrators is critical to the success of their students (Garner, 2007).

The National Council for Accreditation of Teacher Education has claimed that teacher quality represents "the parallel development of teaching knowledge that is specific to the content being taught, as well as general pedagogical knowledge" (Hattie, 2008). This research study examined the differences in teacher quality when teachers are outside their primary field of study. This measure of teacher quality represents a reflection of a teacher's subject content knowledge (SCK) and pedagogical content knowledge (PCK). The two knowledge domains of each teacher were measured both in math (in-field scores) and in science (out-of-field scores).

Hill, Rowan, and Ball (2005) found that teachers' mathematical knowledge was significantly related to student achievement gains. Furthermore, there are several studies that indicate teachers that have a degree majoring in mathematics are strongly associated with higher student achievement in high school and middle school (Aaronson, Barrow, & Sanders, 2007; Frome, Lasater, & Cooney, 2005: Goldhaber & Brewer, 2000: Monk, 1994; Wenglinsky, 2000, 2002). It has also been shown that teacher subject-area certification is consistently and strongly associated with high school and middle school student achievement (Cavalluzzo, 2004; Goldhaber & Brewer, 2000).

Several research studies exist, regarding either teacher effectiveness, teacher quality, or student achievement, each of which measure in some form or another both pedagogical content knowledge and subject content knowledge of the teachers (Hauk, Jackson, & Noblet, 2010; Saderholm,  Ronau, Brown, & Collins, 2010). Similarly, in this study the researcher measured the subject content knowledge and the pedagogical content knowledge of teachers as the determining measure of teacher quality. Specifically, middle school mathematics teachers' subject content knowledge and pedagogical content knowledge in mathematics were compared to their subject content knowledge and pedagogical content knowledge in physical science.

In this study 21 middle school mathematics teachers were given the Diagnostic Teacher Assessment of Mathematics and Science (DTAMS) Instrument for both mathematics (Algebraic Ideas Assessment) and Science (Physical Science Assessment). The DTAMS instrument has been shown to be both a valid and reliable survey designed to measure Subject Content Knowledge and Pedagogical Content Knowledge in math and science (Brown, McGatha, & Karp, 2006).

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Both Subject Content Knowledge and Pedagogical Content Knowledge have been used to measure teacher effectiveness and ultimately a measure of teacher quality (Ball, Thames, & Phelps, 2008; Hill, Ball, & Schilling; 2008; Manizade, 2007). Once both Subject Content Knowledge and Pedagogical Content Knowledge scores are established they were combined to form a measure for teacher quality. This was done for both in-field scores and out-of-field scores. After which the teacher quality scores for both in-field and out-of-field were directly compared to indicate the degree to which a teacher either gains or losses quality.

This research study addresses the question: What is the difference in quality of an in-field teacher compared to an out-of-field teacher - specifically in math as the in-field and science as the out-of-field content area?

Two characteristics that continue to surface when reviewing studies involving teacher effectiveness are the teachers' raw knowledge of the subject matter and their ability to transform that knowledge into an engaging lesson for students. These attributes of teacher effectiveness are more commonly referred to as subject content knowledge and pedagogical content knowledge. This study may offer a more direct comparison of a teacher's ability to use these traits outside their primary field of study. The outcomes of this study may prove to be significant to the professional development community at large. Furthermore, the results of this study may compliment an important research project, titled "Measures of Effective Teaching" (MET), sponsored by the Bill and Melinda Gates Foundation. Developed by researchers at Educational Testing Service (ETS) and the University of Michigan, the MET is designed to measure non-traditional aspects of knowledge specific to teaching.

The researcher administered both the mathematics portion (Algebraic Ideas) and the science portion (Physical Science) of the DTAMS survey, designed to measure both the pedagogical content knowledge as well as subject content knowledge, to certified middle school mathematics teachers. The surveys were then scored by the University of Louisville Center for Research in Mathematics and Science Teacher Development (CRMSTD) staff. The scores from the mathematics portion of the DTAMS were used as the baseline scores and referred to as the in-field scores. The scores from the science portion of the DTAMS were referred to as the out-of-field scores. The degree to which the in-field scores differ from the out-of-field scores indicated the expected change in a teacher's knowledge domains when teaching outside her primary field of study.

One of the primary limitations of this study stemmed from the size of the population. The assessment in this study was based on self-reported responses; however, it is expected that since the participants are professionals their responses were genuine. The population size is restricted for two reasons. First, each participant was expected to complete two surveys that took approximately one hour each. This was a time consuming task, and it was difficult to find enough middle school math teachers that were willing to participate. Secondly, each survey cost the researcher ten dollars to be evaluated by the trained scorers from The University of Louisville Center for Research in Mathematics and Science Teacher Development. It should be noted that the participants were strictly voluntary and were not compensated. Using trained scorers was necessary to assure the validity and reliability of the surveys.

Problem Background

It was reported that in 2000, 23% of public middle school students and 10% of public high school students received their education in mathematics by teachers without a major or certification in math education. These numbers are slightly greater when looking at private schools (Seastrom, Gruber, Henke, McGrath, & Cohen, 2002). Donaldson and Johnson (2010) found the numbers to be more disturbing. With six years of data collection, Donaldson and Johnson found that anywhere from 57% to 74% of math teachers, 16% to 31% of social studies teachers, and 38% to 48% of science teachers lacked a major in the field they were teaching.

With new statistical and analytical methods used by a wide range of researchers, evidence has been mounting that teacher quality can account for a large share of variance in student test scores (Boyd, Lankford, Loeb, Rockoff, & Wyckoff, 2008; Ferguson, 1991; Hanushek, 1996; Hanushek, Kain, & Rivkin, 2009; Rockoff, 2004). Quality teachers are essential to the success of any school program. The two most important attributes of a quality teacher is their subject content knowledge and their pedagogical content knowledge (Even, 1993; Hill, Rowan, & Ball, 2005; Ma, 1999; RAND, 2003).

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Teachers who have met the demanding standards of National Board Certification and those who have generated higher "value-added" student achievement gains are far less likely to teach economically disadvantaged and minority students (Cavalluzzo, 2004; Goldhaber & Anthony, 2004; Humphrey, Koppich, & Hough, 2005; Sanders & Rivers, 1996). As a result, high-poverty schools are more likely to be beset with teaching vacancies in math and special education, and much more likely to staff classrooms with out-of-field, inexperienced and less-prepared teachers. (Ingersoll, 2002; Mayer, Mullens, & Moore, 2002; Strizek, Pittsonberger, Riordan, Lyter, & Orlofsky, 2006).

The practice of hiring teachers to teach subjects that they are not qualified for is well documented and a serious detriment to the districts, the teachers and most importantly the success of the students. This is especially true in high minority and high poverty areas. The paucity in the literature occurs when attempting to quantify the degree to which an out-of-field teacher differs in abilities and strengths to teachers that remain within their primary field of study.

A few more recent studies have shown that a properly certified teacher who is teaching in their specific field of study contributes greatly to the success of their students. Out-of-field teachers are significantly less successful in increasing student achievement (Board of Regents, 2008). Research has also consistently and clearly pointed out that effective teaching is a highly significant factor affecting student achievement (Babu & Mendro, 2003; Hanushek, Kain, & Rivkin, 2009). Furthermore when it comes to effective teaching, research has found that teacher experience and subject content knowledge has consistently shown significant impact on student achievement (Gordon, Kane, & Staiger, 2006;  Rice, 2003; Hanushek, Kain, & Rivkin, 2009; Rockoff, May 2004). Effective teaching implies teachers have well-developed pedagogical content knowledge, yet this knowledge develops over time (Ball, Lubienski, & Mewborn, 2001; Grossman, 1990).

A growing number of research studies are attempting to flesh out a relationship between subject content knowledge and pedagogical content knowledge (Ball, 1990; Ball, Hill & Schilling, 2004; Ball, Thames, & Phelps, 2008; Hill, Ball, & Schilling, 2008; Ma, 1999; Manizade, 2007; Shulman, 1986; Thornton, 2004; Wilson, Shulman & Richert, 1987).

Shin, Koehler, Mishra, Schmidt, Baran, and Thompson (2009) demonstrated that the level of pedagogical content knowledge of a teacher contributes significantly toward effective teaching and student performance. Furthermore, there have been an increased number of research studies attempting to operationalize the measure of teacher's pedagogical content knowledge by way of a paper pencil system or online survey (Ball, 2003; Kromrey & Renfrow, 1991; Shin et al., 2009).

Saderholm, Ronau, Brown, and Collins (2010) have recently contributed to the search for teacher quality by validating the Diagnostic Teacher Assessment in Mathematics and Science (DTAMS) mathematics assessments for middle-school teachers. The reliability and validity of the DTAMS assessments were initially established by utilizing expert question writing teams and reviewers as well as reviewing national standards for content. DTAMS measures both subject content knowledge and pedagogical content knowledge in several math and science topics. These topics are directly related to teacher quality and student achievement.

There were two distinct (DTAMS) assessments that were utilized in this study. The in-field (mathematics) DTAMS Algebraic Ideas assessment measured memorized knowledge, conceptual understanding, higher-order thinking, and pedagogical content knowledge. The out-of-field (science) Physical Science assessment measured declarative knowledge, scientific inquiry and procedures, schematic knowledge, pedagogical content knowledge, and science, technology, and society knowledge (Brown, McGatha, & Karp, 2006).

Purpose of the Study

This study was designed to measure the change in a teacher's subject and pedagogical attributes if they were to teach outside of her field of study. By understanding the degree to which a teacher's knowledge domains change when teaching just outside of their primary field of study, educators and administrators would have a more clear understanding as to the effects an out-of-field teacher may have on his or her students. More specifically, this study focused in on two closely related fields, mathematics and physical science. This offers an exceptional insight as to the unique differences in both subject content and pedagogical content knowledge that an out-of-field teacher would have in the education of students. These differences could serve as a yard stick for administration and policy makers as they consider the issue of hiring out-of-field teachers and ultimate success or failure of their students and schools.

It has been well established that not only is the quality of the teacher the single most important schooling factor predicting student outcomes (Ferguson 1998; Goldhaber 2002; Goldhaber, 1999; Hanushek, 1999), but that "the quality of a teacher can make the difference of a full year's learning growth" (Hanushek, 1992, p.8). Furthermore, many researchers and educators agree that a combination of both subject content knowledge and pedagogical content knowledge are the primary attributes of a quality teacher (Ball & Bass, 2000; Ma, 1999; Rowland, Martyn, Barber & Heal, 2000; Shulman 1986, 1987, 1996).

Research Questions

This research is designed to answer several questions. First, how much subject content knowledge is gained or lost when a middle school mathematics teacher teaches outside his/her field in physical science?

H1: Middle school teachers certified to teach mathematics will show a decrease in subject content knowledge when they teach outside of their field, physical science.

H1a: Middle school teachers certified to teach mathematics will show no significant change in subject content knowledge when they teach outside of their field, physical science.

H1b: Middle school teachers certified to teach mathematics will show an increase in subject content knowledge when they teach outside of their field, physical science.

The other important yet distinct knowledge domain that must be considered is the pedagogical content knowledge of the teacher. This was done by answering the question, how much pedagogical content knowledge is gained or lost when a middle school mathematics teacher teaches outside his/her field in physical science?

H2: Middle school teachers certified to teach mathematics will show a decrease in pedagogical content knowledge when they teach outside of their field, physical science.

H2a: Middle school teachers certified to teach mathematics will show no significant change in pedagogical content knowledge when they teach outside of their field, physical science.

H2b: Middle school teachers certified to teach mathematics will show an increase in pedagogical content knowledge when they teach outside of their field, physical science.

Finally, the last set of questions combines the measurements for both subject and pedagogical content knowledge to determine an overall effect on teacher quality. By viewing both knowledge domains as equal contributors to the overall measure of a teacher quality we can determine the general effect (increase or decrease) that middle school mathematics teachers who teach outside of the field (physical science) may experience. What is the overall effect on teacher quality when a middle school mathematics teacher teaches outside his/her field in physical science?

H3: The overall quality of middle school teachers certified to teach mathematics will decrease when they teach outside of their field, physical science.

H3a: The overall quality of middle school teachers certified to teach mathematics will show no significant change when they teach outside of their field, physical science.

H3b: The overall quality of middle school teachers certified to teach mathematics will increase when they teach outside of their field, physical science.

Limitations and Delimitations

The population used in this study was its primary limitation. The sample of participants included 21 teachers that were certified to teach middle school mathematics in Illinois. The researcher administered both the Algebraic Ideas Survey (DTAMS) and the Physical Science Survey (DTAMS). Each survey took about 60 minutes to complete. A commitment of two hours of the participants' time was a large request; this limited the number of participants willing to respond to this study. The surveys were then sent to the University of Louisville Center for Research in Mathematics and Science Teacher Development (CRMSTD) for analysis by the researcher of this study. The analysis included a comparison of both subject content knowledge and pedagogical content knowledge of the teachers for both in-field (mathematics) and out-of-field (physical science). The results of this comparison addressed directly the research questions found in this study.

Distinct advantages and disadvantages occur that are indicative of a descriptive research design. This study specifically targets the relationship between in-field scores and out-of-field scores making a correlational analysis an appropriate foundation. A correlational analysis lent itself naturally in seeking relationships between subject content knowledge, pedagogical content knowledge and among the related demographics. However, no matter how significant the correlation, causation cannot be inferred due to possible influence of unchecked extraneous variables.

Several statistical methods were implemented so as to counter the influence certain specific variables may have on the results of this study. These variables include age, experience, educational history, and socio-economic work environment.

Finally, it is important to note that respondents were not given the opportunity for clarification of survey questions nor did they have an opportunity to explain their interpretation of the question. Misconstrued questions often times led to an inappropriate response when in fact the participant may very well have a clear and strong understanding of the subject or variable characteristics being measured.

Definition of Terms

In this research study, it is particularly important to explicitly define any key terms. In the following section the primary key terms are defined.

Subject Content Knowledge for the Out-of-Field Assessment

Declarative Knowledge:  This knowledge is solely based on facts and definitions. Teachers with this knowledge have the skills to perform rote algorithmic tasks that are essential to solving problems. The ability to recall facts, rules, scientific laws and definitions is a crucial component in teaching (Brown, McGatha, & Karp, 2006).

Scientific Inquiry and Procedures:  Scientific procedures and approaches represent the knowledge type that allows for the ability to recognize the elements of scientific inquiry such as identifying questions for scientific inquiry, design and conduct scientific investigations and experiments, use appropriate data collection and analysis techniques, the ability to think critically about the data and to make logical conclusions and explanations (Brown, McGatha, & Karp, 2006).

Schematic Knowledge:  Schematic knowledge represents a more in-depth understanding of the nature of scientific concepts, principles and related phenomenon. Teachers with this knowledge can effectively compare and contrast various scientific properties and characteristics and can explain limits and the evolution of current scientific knowledge (Brown, McGatha, & Karp, 2006).

Science, Technology, and Society Knowledge (STS): This knowledge allows teachers to bridge the gap between the scientific community and its influences on society as a whole. Teachers were able to demonstrate a thorough understanding of the role that human needs play in the development and application of science as well as a historical and global perspective of how scientific discoveries have impacted society. It is the nature by which science, technology, society, and current environments interact and evolve as a single entity (Brown, McGatha, & Karp, 2006).

Subject Content Knowledge for the In-Field Assessment

Memorized Knowledge: This is most closely related to the previously mentioned declarative knowledge in the previous assessment. This is knowledge that is based upon applying the skills and algorithms necessary for accurate computation. This is not conceptual by nature nor is it a measure of problem solving abilities. Teachers with this knowledge can perform computations involving various algorithms, definitions, and a recollection of facts (DTAMS, 2006).

Conceptual Understanding: This knowledge corresponds most closely to Schematic Knowledge for the science assessment, wherein it represents the knowing and understanding why. Teachers with this knowledge have the ability to make connections between mathematical topics and to see the general relationship that uniquely binds these topics into universal concepts (Brown, McGatha, & Karp, 2006).

Problem Solving and Reasoning: This knowledge represents the tactical knowledge needed to deduce what is important mathematical information in non-standard math problems, and know how and why one can apply different mathematical approaches to find solutions to an array of applications (Brown, McGatha, & Karp, 2006).

Pedagogical Content Knowledge

Pedagogical Content Knowledge: Lee Shulman coined the phrase "pedagogical content knowledge" in 1985 and perhaps defines it best in his own words (Shulman, 1987, p. 13):

[Pedagogical Content Knowledge is the ability to] elucidate subject matter in new ways, reorganize and partition it, clothe it in activities and emotions, in metaphors and exercises, and in examples and demonstrations, so that it can be grasped by students.

Additionally, pedagogical content knowledge "represents a class of knowledge that is central to teachers' work and that would not typically be held by non-teaching subject matter experts or by teachers who know little of that subject" (Marks, 1990, p. 9).

For this study the term Pedagogical Content Knowledge most closely reflected the following definition from the Diagnostic Teacher Assessment in Mathematics and Science: This knowledge represents strategic knowledge for mathematics teaching-"knowing when, where, and how to best teach mathematics" (Brown, McGatha, & Karp, 2006, p. 1). Once again these assessments concentrated on the use of pedagogical content knowledge in the correction of student misconceptions about mathematics. Teachers with this knowledge can satisfy two criteria: recognize the students' misconceptions, and describe the most effective ways to teach particular mathematical concepts using the most powerful analogies, illustrations, examples, explanations, experiments, and demonstrations.

Middle School Teachers

For the purposes of this study middle school teacher is defined as any teacher certified to teach sixth, seventh, and eighth grade.

Significance of the Study

Teachers in high poverty, high minority schools are more likely to be less experienced, less educated, teaching on emergency permits or waivers, and teaching subjects for which they are not qualified (Carroll, Reichardt & Guarino, 2000; Darling-Hammond, 2002; Goe, 2002; Hanushek, Kain, O'Brien, & Rivkin, 2005; Ingersoll, 2002; Lankford, Loeb, & Wyckoff, 2002; Marvel, Lyter, Peltola, Strizek, & Morton, 2007; Peske & Haycock, 2006; Scafidi, Sjoquist, & Stinebrickner, 2007; Useem & Farly, 2004). Mathematics and science, in particular, are typically targeted as fields most suffering from shortages (Grissmer & Kirby, 1992, 1997; Liu & Ramsey, 2008; Murnane et al., 1991; National Commission on Mathematics and Science Teaching, 2000; Weiss & Boyd, 1990). In fact, numerous high-profile reports from organizations including the National Academy of Sciences (2006), the National Research Council (2002), and the US Department of Education (2002) have directly tied mathematics and science teacher shortages to the quality of educational performance and, in turn, to the future well-being of the economy and the security of the nation.

Although many middle school administrators may feel it necessary to utilize teachers in areas for which they are under-qualified, this study may indicate the risks to student achievement based on an out-of-field policy. Research has consistently pointed to effective teaching as the most significant factor affecting student achievement (Babu & Mendro, 2003; Manizade, 2007; Rivkin, Hanushek, & Kain, 2005). This study is significant to further the understanding of the benefits and/or risks of using out-of-field teachers in a middle school science class.

Echoing the educational need for quality teachers, the research community including the Research and Development (RAND) Mathematics Study Panel of 2003 had called for increasing standards for teacher preparation programs (RAND, 2003).

This study would offer some insight as to the direct and distinct difference in teacher quality when considering a placement of an out-of-field teacher into a classroom that they are not fully prepared to teach.

Conclusion

Gains in student achievement are, more often than not, accredited to the quality of the teacher. Loopholes in the hiring practices of quality teachers have led to an increase in out-of-field teachers in the classroom. In chapter 1 it was stated that researchers commonly view teacher quality as a combination of both subject content knowledge and pedagogical content knowledge. The purpose of this research was to measure the difference in teacher quality between in-field and out-of-field teachers. The results of this study are significant in that it contributes to the broader understanding of how out-of-field teacher impact education.

Chapter one is an overview of the research that was performed; an introduction to the background of the problem, purpose of the study, research questions with hypotheses, definition of key terms, limitations of the study, and the importance of the study. In the following chapters, there is a review of the relevant research related to this study, an explanation of the methods employed, data analysis with an explanation of the results, and a discussion of how the results could be applied.