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Chapter 1. Elementary and Secondary Mathematics and Science Education

Teachers of Mathematics and Science

Among the many factors that influence student learning, teacher quality is believed to be one of the most crucial. Studies have found that various aspects of teachers and teaching make a significant difference in student performance (Boyd et al. 2008; Clotfelter, Ladd, and Vigdor 2007; Croninger et al. 2003; Darling-Hammond et al. 2005; Goe 2008; Guarino et al. 2006; Hanushek et al. 2005; Harris and Sass 2007; Nye, Konstantopoulos, and Hedges 2004; Wayne and Youngs 2003; Xue and Meisels 2004). To ensure that all classrooms are led by teachers who are effective in promoting student learning, the federal No Child Left Behind Act (NCLB) of 2001 mandates that schools and districts hire only "highly qualified" teachers, defining "highly qualified" in terms of state certification (excluding emergency, provisional, or temporary licenses),[7] a minimum of a bachelor's degree, and demonstrated subject area competence.[8]

This section examines indicators of teacher preparedness, experience, professional development, salaries, and working conditions. The major data source used here is the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99.[9] This longitudinal study followed students from kindergarten through eighth grade and collected data from students' teachers and schools as well as from the students and their families. When the cohort was in grades 5 and 8 (in 2004 and 2007, respectively), ECLS-K collected data from their teachers in each of the core academic subjects (i.e., reading/language arts, mathematics, and science), allowing researchers to distinguish teachers who taught mathematics and science from all other teachers.[10] Because the teacher information in ECLS-K was linked to the sampled students, the data enable analysis of whether students from different backgrounds and with different levels of prior achievement had equal access to high-quality and experienced teachers in their fifth and eighth grade mathematics and science classrooms. When possible, comparable data from the 2008 edition of Science and Engineering Indicators are either cited or included as complementary information about teachers of mathematics and science at the middle school and high school levels.

Teacher Quality

Researchers have often relied on indicators such as test scores (e.g., Praxis; see Gitomer 2007), education credentials, professional certifications, and teaching experience as proxies for teacher quality (Darling-Hammond 2000; Wayne and Youngs 2003). These indicators are relatively easy to measure and can be readily used to screen prospective candidates. They also align with the requirements for highly qualified teachers specified in NCLB. The following analysis examines the quality of mathematics and science teachers by focusing on the educational attainment, certification status, subject area preparation, and years of teaching experience of those who taught mathematics and science in public schools to fifth graders in 2004 and eighth graders in 2007.

Teacher quality is not limited to the characteristics examined here, however; it may include other important elements that are difficult or costly to measure, such as teachers' abilities to motivate students, manage the classroom, maximize instruction time, and diagnose and overcome students' learning difficulties. Current research on "teacher quality" is designed to yield measurable characteristics of teachers that are associated with student learning (Angrist and Guryan 2008; Boyd et al. 2008; Hill, Rowan, and Ball 2005; Goe 2008). This work is beginning and is expected to yield measures of teacher quality more directly related to student achievement than are the indicators examined here.

Formal Preparation
Teachers acquire a significant amount of subject knowledge and teaching skills through formal education and certification. Thus, teachers' level of educational attainment and type of professional certification provide some indication of how well teachers are prepared for their work.[11] Data on teachers' highest degree and certification status (regardless of the field in which the degree/certification was held) indicate that virtually all of them had at least a bachelor's degree. Nearly half also had a master's or higher degree, and a majority held a regular or advanced teaching certificate (NSB 2008).

Similar patterns are observed when the analysis focuses on how many students are taught mathematics and science by teachers with various levels of educational attainment and types of certification. For example, almost all public school fifth grade students in 2004 and eighth grade students in 2007 were taught mathematics and science by teachers who had attained a bachelor's or higher degree (regardless of the field in which the degree was earned), and about half of them were taught these two subjects by teachers with a master's or higher degree (appendix table 1-12 ). Furthermore, the majority of fifth and eighth grade students (90% and 84%, respectively) had teachers of mathematics and science with a regular or advanced teaching certificate (regardless of the field in which the certification was awarded).

Subject Area Preparation
Adequate subject matter knowledge and skills are critical for teachers to teach their subjects well (The Education Trust 2008; Goe 2008; Ingersoll 2003). NCLB mandates that all students be taught by teachers who not only are fully certified and possess at least a bachelor's degree, but also demonstrate competence in subject knowledge and teaching. In its 2007 policy recommendations regarding STEM education, the National Science Board (NSB) emphasized that STEM teachers should receive adequate STEM content knowledge that is aligned with what they are expected to teach (NSB 2007). Similarly, a report from the National Research Council of the National Academies (2007) advocated that teacher preparation and professional development programs focus on boosting teachers' knowledge of science, how students learn the subject, and methods and technologies that aid science learning for all. However, neither NCLB nor these reports' policy recommendations provide specific guidance or criteria regarding "adequate" preparation to teach mathematics and science at various grade levels.

While most states require those who teach mathematics and science at the high school level to have a degree or certification in their subject area, state laws and regulations regarding preparation of middle school teachers (eighth grade teachers fall in this group) vary, with some states allowing general education preparation and others requiring subject area preparation. As for elementary school teachers, who typically teach multiple subjects, most state policies consider teachers with a degree or certification in general elementary education to be "qualified" to teach elementary school mathematics and science (and other subjects), although some question whether elementary school teachers with general education preparation have sufficiently rigorous preparation for teaching mathematics and science (Greenberg and Walsh 2008).

Recent research efforts have focused on matching teachers' formal preparation (as indicated by degree major and certification field) with their teaching field to determine whether teachers have subject-specific preparation for the fields they teach (McGrath, Holt, and Seastrom 2005; Morton et al. 2008). Following this line of research, four levels of teachers' formal preparation for teaching mathematics and science at fifth and eighth grade levels were distinguished. In order of decreasing rigor of preparation, they are as follows:

  • In-field: Teachers who taught mathematics and had a degree and/or certificate in mathematics or mathematics education. Teachers who taught science and had a degree major and/or certificate in science or science education.
  • Related-field: Teachers who taught mathematics and had a degree and/or certificate in a field related to their teaching field (such as science, science education, computer sciences). This category is omitted for teachers of science in ECLS-K because these teachers were not asked about their degrees or certificates in specific science fields such as physics, chemistry, or biology.
  • General education: Teachers who taught mathematics or science and had a degree and/or certificate in general elementary or secondary education. Such teachers usually undergo some pedagogical training in mathematics and science.
  • Other: Teachers who taught mathematics or science but did not have a degree or certificate in their teaching field, a related field, or general elementary or secondary education.

In-field teaching in mathematics and science was less prevalent at lower grade levels than at higher grade levels. For example, in 2004, about 40% of fifth grade students in public schools were taught mathematics and science by in-field teachers (table 1-9 ; appendix table 1-13 ). Most students at this level (54%) had teachers with general education preparation. When students reached eighth grade in 2007, more than 80% of them had in-field teachers in their mathematics and science classes, and 9–10% were taught mathematics and science by teachers with general education preparation.

Similar patterns were also revealed using the teacher data from the 2003–04 and 2007–08 Schools and Staffing Survey (SASS).[12] In 2003, 53% of teachers of mathematics and 67% of teachers of science in public middle schools were teaching in field (table 1-10 ).[13] Partly reflecting the impact of NCLB on teacher qualifications, in-field mathematics teachers in public middle school increased to 64% in 2007, representing a significant 11 percentage point increase from 2003. Seventy percent of teachers of science in public middle schools were teaching in field in 2007, but this does not represent a significant increase from the 67% in 2003. In both years, between 27% and 38% of middle school teachers were teaching mathematics and science with general education preparation.

Moving up to the high school level, in-field teaching became more common. For example, in-field teaching in 2007 ranged from 82% of teachers of physical sciences and 88% of teachers of mathematics to 93% of teachers of biology/life sciences. The share of teachers with general education preparation declined to 3% or lower. Similar percentage ranges also were found among public high school mathematics and science teachers in 2003.

Teaching Experience
Experienced teachers are, generally, more effective than novices in helping students learn (Boyd et al. 2006; Clotfelter, Ladd, and Vigdor 2007; Hanushek et al. 2005; Harris and Sass 2008; Rice 2003; Rockoff 2004; Rowan, Correnti, and Miller 2002; Wayne and Youngs 2003). Overall, teachers with more than 3 years of teaching experience make up a large majority of the mathematics and science teaching force in public schools (NSB 2008; NCES 2007a). Likewise, between 82% and 88% of public school fifth and eighth grade students in 2004 and 2007 were taught mathematics and science by teachers with more than 3 years of teaching experience (appendix table 1-14 ). The majority of these students had teachers with 3 or more years of experience in the specific grade level or subject matter in question: 63%–65% of fifth grade students were taught mathematics and science by teachers with more than 3 years of experience in teaching fifth grade classes, and 76%–78% of eighth grade students had science and mathematics teachers who had taught their respective subject for more than 3 years.

Differences in Student Access to Qualified Teachers in Science and Mathematics
Access to better-qualified teachers was not equally distributed among students. In general, black and Hispanic students, students from less-educated and low-income families, and students with low levels of prior achievement had less access to teachers who were highly educated, fully certified, and had more experience and better preparation in the subject field than their counterparts (appendix table 1-12 , appendix table 1-13 , and appendix table 1-14 ). For example, fifth grade black and Hispanic students were less likely than their white peers to be taught mathematics by teachers with a master's or advanced degree (39% and 42% vs. 51%, respectively), a regular or advanced teaching certificate (86% and 85% vs. 92%), and more than 3 years of experience in teaching the fifth grade (48% and 58% vs. 68%) table 1-11 ). Students living in low-income families were less likely than their peers from higher-income families to be taught mathematics by teachers with a master's or advanced degree (35% vs. 50%, respectively). Also among fifth graders, a third of those in the lowest achievement quartile in grade 3 were taught mathematics by in-field teachers. In contrast, 41% of fifth graders in the top achievement quartile in grade 3 had such teachers.

In eighth grade, students whose mothers had not earned a high school diploma were less likely than those whose mothers had a bachelor's or higher degree to be taught science by teachers who had a master's or advanced degree (46% vs. 57%, respectively), a regular or advanced teaching certificate (79% vs. 87%), an in-field degree or certificate (84% vs. 93%), and more than 3 years of experience in teaching science (69% vs. 83%) (appendix tables 1-12, 1-13, and 1-14). Differences existed when looking at family income as well: eighth grade students from families with incomes below the poverty threshold were less likely than those from higher-income families to be taught science by teachers with a regular or advanced teaching certificate (79% vs. 86%, respectively), an in-field degree or certificate (84% vs. 89%), and more than 3 years of experience in teaching science (69% vs. 79%). In addition, 92% of students with high achievement in fifth grade were taught mathematics by in-field teachers, compared with 76% of those with low fifth-grade achievement who had such teachers.

Professional Development

Teachers rely on professional development to update their knowledge, sharpen their skills, and acquire new teaching techniques, all of which may enhance the quality of teaching and learning (Richardson and Placier 2001; Davis, Petish, and Smithey 2006). During the past decade, researchers have put significant effort into identifying features of high-quality professional development programs (Banilower et al. 2006; CCSSO 2008; Clewell et al. 2004; Desimone et al. 2002; Garet et al. 2001; Hawley and Valli 2001; Harris and Sass 2007; Heck, Rosenberg, and Crawford 2006; Penuel et al. 2007; Porter et al. 2000). They have come to general agreement that professional development is most effective if it

  • Focuses on subject content
  • Provides an intensive and sustained approach
  • Is presented in a format of teacher network, study group, mentoring, and coaching as opposed to a traditional workshop or conference
  • Is connected or related to teachers' daily work
  • Emphasizes a team approach and collaboration
  • Provides opportunities for active learning

When professional development is conducted in these ways, teachers are more likely to change their instructional practice, gain greater subject-matter knowledge, and improve their teaching (see, for example, the sidebar "Local Systemic Change Through Teacher Enhancement Program"). Consequently, there is increased potential for the professional development to have an effect on student achievement (Correnti 2007; Darling-Hammond and Youngs 2002; Wenglinsky 2002).

Evidence from the most recent national teacher survey in 2003–04 indicates that almost all mathematics and science teachers in public middle and high schools participated in some form of professional development activities during the school year (NSB 2008). However, the programs these teachers attended consisted mostly of short-term workshops, conferences, and training sessions. In general, teachers had less exposure to professional development with features identified by research as effective in bringing about positive changes in teaching practices.

Data from ECLS indicate that in 2004, the percentage of fifth graders whose teachers of mathematics and science reported that they had participated in staff development related to their subject content or pedagogy during the past school year was 73% and 53%, respectively (table 1-12 ). On average, teacher participants spent about 14 hours on subject-focused staff development during the entire school year. Furthermore, among students whose teachers participated in this staff development, about 40% had teachers rating this activity as very useful.

The 2007 TIMSS provides further evidence regarding the extent to which elementary school teachers participate in professional development in mathematics and science (Miller et al. 2009). In 2007, the percentage of fourth graders whose teachers participated in professional development on various aspects of mathematics during the previous 2 years ranged from 47% for assessment and 50% for pedagogy/instruction to 60% for mathematics content (figure 1-9 ). Participation in professional development relating to science was even lower among teachers of fourth graders: 24%–42% of students had teachers who participated in professional development on science content (42%), pedagogy/instruction (29%), and assessment (24%).

Teachers' Salaries

Adequate pay is important to attracting and retaining teachers (Guarino, Santibanez, and Daley 2006). Thus, policymakers often propose increasing teacher salaries to lower attrition and improve the quality of the teaching pool, arguing that if teachers could earn higher pay both when entering the profession and over time, stronger candidates would be drawn to teaching and more effective teachers might be retained (Johnson, Berg, and Donaldson 2005; Loeb and Reininger 2004; Stronge, Gareis, and Little 2006).

According to the latest annual teacher salary survey conducted by the American Federation of Teachers (AFT),[14] the average salary for all public K–12 teachers in 2006–07 was about $51,000 (AFT 2008). After adjustment for inflation, teacher salaries grew by 2.8% from 1996–97 to 2006–07. During this 10-year period, 18 states experienced declines in inflation-adjusted teacher salaries.

Using data from the Current Population Survey of the Bureau of Labor Statistics, Allegretto, Corcoran, and Mishel (2008) compared the weekly wages[15] of full-time public school teachers with those of people working in occupations requiring comparable education and skills, such as accountants, reporters, registered nurses, and computer programmers. [16] Their analyses showed that in 2006, full-time public school teachers earned 86% as much in weekly wages as did those in this set of comparable occupations. Furthermore, between 1996 and 2006, the gap in weekly wages between full-time teachers and those in comparable occupations widened from $7 to $153, in constant dollars (figure 1-10 ). A similar conclusion has been drawn about mathematics and science teachers—that is, their pay fell behind that of many professions with comparable educational backgrounds, and the gap widened substantially in recent years (NSB 2008).

Working Conditions

Poor working conditions can cause stress and dissatisfaction and may lead teachers to leave the teaching profession altogether (Hanushek, Kain, and Rivkin 2004; Hanushek and Rivkin 2007; Ingersoll 2001; Johnson, Berg, and Donaldson 2005). The working conditions that matter most to teachers include administrative leadership at their school, working relationships among colleagues, level of parental support, teaching loads, and student discipline problems (Guarino,Santibanez, and Daley 2006).

Most public middle and high school teachers have positive perceptions about their school conditions (NSB 2008). Such positive perceptions are also widely held among fifth and eighth grade students' teachers. In 2004, for example, for a large majority of fifth grade students (94%), the teachers who taught them mathematics and science felt accepted and respected by their school colleagues (appendix table 1-15 ). Large majorities of these students had teachers who believed that teachers in their schools were continually learning and seeking new ideas (86%);[17] that staff members had school spirit (81%) and agreed about the central mission of the school (75%); that school administrators knew the direction of the school and communicated it to staff (81%) and were supportive and encouraging (80%); and that parents were supportive of school staff (70%). Furthermore, relatively few students' teachers reported various learning and behavioral problems among students (12%–21%). Reports from eighth grade teachers were similar (appendix table 1-16 ), although eighth grade teachers were more likely than fifth grade teachers to report such problems as student misbehavior interfering with teaching (30% vs. 21%, respectively) and many children not being capable of learning (19% vs. 14%).

Positive perceptions of school conditions were less widely held among teachers of minority, socioeconomically disadvantaged, and low-achieving students. For example, fifth grade students whose mothers had less than a high school education were less likely than students whose mothers had a bachelor's or higher degree to have teachers who described parents in their school as "supportive" (61% vs. 82%, respectively) (figure 1-11 ). About 74% of fifth grade students from low-income families, compared with 81% of students from more financially advantaged families, had teachers reporting supportive school administrators. Compared with 17% of fifth grade white students, 33% of black students had teachers whose teaching was interrupted by child misbehavior. In addition, compared with 8% of high-achieving students, 18% of low-achieving students were taught mathematics and science by teachers who reported that many of their students were not capable of learning the materials they taught.


[7] Teaching certification is generally awarded by state education agencies to teachers who have completed specific requirements. These requirements vary across states but typically include completing a bachelor's degree, completing a period of practice teaching, and passing some type of formal tests. States also issue other types of certification besides regular or standard certification. For example, probationary certification is generally awarded to those who have completed all the requirements except for a probationary teaching period. Provisional or temporary certification is awarded to those who still have requirements to meet. Emergency certification is issued to those with insufficient teacher preparation who must complete a regular certification program to continue teaching (Henke et al. 1997).
[8] Specifically, NCLB defines a highly qualified elementary or secondary school teacher as someone who holds a bachelor's degree and full state-approved teaching certificate or license (excluding emergency, temporary, and provisional certificates) and who demonstrates subject-matter competency in each academic subject taught by having an undergraduate or graduate major or its equivalent in the subject; passing a test on the subject; holding a full teaching certificate in the subject; or meeting some other state-approved criteria. NCLB requires that newly hired elementary school teachers pass tests in subject-matter knowledge and teaching skills in mathematics, reading, writing, and other areas of the basic elementary school curriculum. Newly hired middle and high school teachers must either pass a rigorous state test in each academic subject they teach or have the equivalent of an undergraduate or graduate major or teaching certification in their fields.
[9] In previous editions, data from the National Center for Education Statistics' Schools and Staffing Survey (SASS) have been used to highlight various aspects of teachers and teaching. However, the 2007–08 SASS data were not available for analyses at the time this chapter was prepared.
[10] Typically, fifth grade teachers teach not only mathematics and science but also language arts, social studies, and other academic subjects and therefore cannot strictly be considered mathematics or science teachers. To refer to teachers who taught mathematics and science more accurately, the text uses such phrases as "teachers of mathematics and science," "teachers who taught mathematics and science," or "students who were taught mathematics and science by teachers" interchangeably.
[11] Alternatives to traditional teacher education have increased in number and scope. Among various alternative programs, Teach for America (TFA) is the most prominent one (Decker, Mayer, and Glazerman 2004). TFA is designed to recruit top graduates from some of the most competitive colleges to teach in the most challenging K–12 schools throughout the nation. Although TFA has been successful in attracting college graduates (e.g., from 2000 to 2003, the number of TFA applicants grew almost fourfold, from about 4,000 to 16,000) (Decker, Mayer, and Glazerman 2004), studies that have addressed the effectiveness of TFA teachers yielded mixed results from no to significant effects (Decker, Mayer, and Glazerman 2004; Kane, Rockoff, and Staiger 2006; Xu, Hannaway, and Taylor 2007).
[12] SASS teachers responded to a much longer list of possible fields for their degree major and certification than ECLS teachers, allowing more refined categorization of the variable. For more information about the definition of the subject area preparation variable in SASS, see the sidebar "In-Field and Out-of-Field Teaching" in the 2008 edition of Science and Engineering Indicators (NSB 2008).
[13] SASS collects data on teachers, whereas ECLS collects data on students, including data about those students' teachers. This difference may contribute to the different in-field teaching estimates in the two surveys. Another difference is that SASS includes all middle school teachers, whereas ECLS data refer only to those who teach eighth grade students.
[14] The Federation collects teacher salary data from each state's department of education.
[15] Because teachers' annual work schedules are different from those of other professions, these researchers compared wages earned for a week of work, rather than for the entire year. Critics of this method (e.g., Podgursky and Tongrut 2006) argue that the use of weekly wages to compare teachers with other workers may bias teacher earnings downward, in that teachers report a weekly wage that may be an annual salary divided over a full year rather than the partial year they actually work. To address this concern, Allegretto, Corcoran, and Mishel (2008) used several alternative methods to compare the salaries of teachers and other workers in their 2008 study and concluded that this bias is small.
[16] As part of the National Compensation Survey, the Bureau of Labor Statistics collects specific occupational skill information and rates each occupation on the level of skills required across 10 different dimensions (e.g., knowledge, complexity). Allegretto, Corcoran, and Mishel (2008) used the 6 most common occupations among the 16 identified as having skill ratings comparable to those of teachers to form the group of comparable occupations in their 2008 study. These 6 occupations are accountants, reporters, registered nurses, computer programmers, members of the clergy, and personnel officers, accounting for 83% of the employment in 16 occupations with skill ratings comparable to teaching.
[17] That is, 86% of fifth grade students had teachers of mathematics and science reporting this condition.

Science and Engineering Indicators 2010   Arlington, VA (NSB 10-01) | January 2010