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The Role of Subject-Matter Content in Teacher Preparation: An International Perspective for Mathematics

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Title: The Role of Subject-Matter Content in Teacher Preparation: An International Perspective for Mathematics
Language: English
Authors: Schmidt, William H., Burroughs, Nathan A., Cogan, Leland S., Houang, Richard T.
Source: Journal of Curriculum Studies. 2017 49(2):111-131.
Availability: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 21
Publication Date: 2017
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Secondary Education
Elementary Education
Secondary Education
Higher Education
Postsecondary Education
Descriptors: Teacher Education, International Education, Educational Policy, Comparative Analysis, Teacher Education Programs, Mathematics Instruction, Teacher Surveys, Elementary Secondary Education, Mathematics Teachers, Elementary School Teachers, Secondary School Teachers, Achievement Tests, International Assessment, Mathematics Tests, Foreign Countries, Mathematics Achievement, Science Tests, Science Achievement, Preservice Teachers
Assessment and Survey Identifiers: Trends in International Mathematics and Science Study
DOI: 10.1080/00220272.2016.1153153
ISSN: 0022-0272
Abstract: International comparative studies in education provide a fresh perspective on K-12 education policy by enabling countries to learn from each other's approaches. The recently conducted Teacher Education and Development Study--Mathematics provides a worldwide lens by which to examine the role of subject-matter in the preparation of US teachers of mathematics for primary and lower secondary students. More specifically, a previous study looking at the international top-performing teacher preparation programmes identified a common set of learning experiences (topics/content) related to mathematics. This empirically derived international benchmark is used in this paper to examine the quality of the mathematics preparation of future US teachers in various university and college programmes.
Abstractor: As Provided
Number of References: 37
Entry Date: 2017
Accession Number: EJ1132575
Database: ERIC
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  Value: <anid>AN0121905065;b9j01apr.17;2019Feb14.14:15;v2.2.500</anid> <title id="AN0121905065-1">The role of subject-matter content in teacher preparation: an international perspective for mathematics. </title> <p>International comparative studies in education provide a fresh perspective on K-12 education policy by enabling countries to learn from each other's approaches. The recently conducted Teacher Education and Development Study—Mathematics provides a worldwide lens by which to examine the role of subject-matter in the preparation of US teachers of mathematics for primary and lower secondary students. More specifically, a previous study looking at the international top-performing teacher preparation programmes identified a common set of learning experiences (topics/content) related to mathematics. This empirically derived international benchmark is used in this paper to examine the quality of the mathematics preparation of future US teachers in various university and college programmes.</p> <p>Keywords: Teacher education (mathematics); teacher education curriculum; international education (teacher); educational policy</p> <p>The preparation of new teachers is an important issue of interest to government and policy-makers around the world. This is evidenced by the participation of over 30 countries in the 2013 Teaching and Learning International Survey (TALIS) conducted by the Organisation for Economic Co-operation and Development (OECD). One finding from that study was that in all countries, teachers whose formal education included training in the content, pedagogy and classroom practices of the subjects they teach reported feeling better prepared to teach (p. 37, OECD, [<reflink idref="bib24" id="ref1">24</reflink>]). In this paper, we examine this issue in greater depth drawing upon the Teacher Education and Development Study—Mathematics (TEDS-M) recently conducted in 16 countries which provides a worldwide lens for examining the role of subject-matter and its related pedagogy in the formal preparation of teachers of mathematics for primary and lower secondary students. In addition, we report on a follow-up study of the US TEDS-M sample of future teachers after they had begun teaching to explore the longer term relationship of their formal teacher preparation opportunities to learn (OTL) to teacher self-efficacy.</p> <hd id="AN0121905065-2">Background</hd> <p>An influential vein of research suggests that teachers play a key role in the quality of schooling. As a consequence, teacher preparation programmes have come under increasing scrutiny by scholars and policy-makers. There are renewed efforts to rank institutions that prepare K-12 teachers according to objective metrics, and even tentative efforts to extend the accountability system to pre-service programmes. However, there are doubts about whether teacher preparation programmes ultimately matter very much. As with the validity of metrics conventionally used to identify high-quality teachers such as experience, licensure or the possession of advanced degrees, the effect of teacher preparation programmes on student outcomes has been the subject of debate (Boyd, Lankford, Loeb, Rockoff, & Wyckoff, [<reflink idref="bib6" id="ref2">6</reflink>]; Chingos & Peterson, [<reflink idref="bib9" id="ref3">9</reflink>]; Clotfelter, Ladd, & Vigdor, [<reflink idref="bib10" id="ref4">10</reflink>]; Hill, Rowan, & Ball, [<reflink idref="bib16" id="ref5">16</reflink>]; Kane & Staiger, [<reflink idref="bib18" id="ref6">18</reflink>]).</p> <p>A number of studies have concluded that teacher education does not influence value-added measures in mathematics (Chingos & Peterson, [<reflink idref="bib9" id="ref7">9</reflink>]; Goldhaber, Liddle, & Theobald, [<reflink idref="bib14" id="ref8">14</reflink>]), nor does certification status (Kane & Staiger, [<reflink idref="bib18" id="ref9">18</reflink>]), or mathematics credits (Harris & Sass, [<reflink idref="bib15" id="ref10">15</reflink>]). The questionable effect of teacher preparation programmes may be in part due to the lack of variation among those programmes despite differences that have been reported in surveys with recent graduates (Darling-Hammond, Chung, & Frelow, [<reflink idref="bib11" id="ref11">11</reflink>]). Observational studies indicated that most of the variation actually occurs within programmes (Koedel, Parsons, Podgursky, & Ehlert, [<reflink idref="bib20" id="ref12">20</reflink>]), which may account for the limited differences in apparent effectiveness across different types of programmes (Goldhaber et al., [<reflink idref="bib14" id="ref13">14</reflink>]). Mihaly, McCaffrey, Sass, and Lockwood ([<reflink idref="bib22" id="ref14">22</reflink>]), however, note that these results should be treated with caution because of methodological issues.</p> <p>Despite the paucity of evidence for a direct effect on student outcomes, teacher preparation can influence important mediating factors. For example, teachers who reported greater instructional preparedness had higher levels of efficacy and retention (Darling-Hammond et al., [<reflink idref="bib11" id="ref15">11</reflink>]; Raudenbush, Rowan, & Cheong, [<reflink idref="bib25" id="ref16">25</reflink>]). The specific characteristics of teacher preparation programmes suggested that programme features both vary and are of substantial importance. Ronfeldt, Reininger, and Kwok ([<reflink idref="bib26" id="ref17">26</reflink>]) found that clinical work can improve instructional quality—although like Darling-Hammond et al. ([<reflink idref="bib11" id="ref18">11</reflink>]) and Raudenbush et al. ([<reflink idref="bib25" id="ref19">25</reflink>]), Ronfeldt et al. ([<reflink idref="bib26" id="ref20">26</reflink>]) employed a rather general measure of preparation quality.</p> <p>Preparation programmes can also have an indirect effect by increasing teachers' content knowledge. Teacher knowledge of mathematics has a significant relationship to student learning (Hill et al., [<reflink idref="bib16" id="ref21">16</reflink>]). Also, coursework for pre-service teachers has been shown to have a relationship to student outcomes beginning in their second year of teaching but no relationship was found in the first year likely because new teachers are grappling with the fundamentals of managing the classroom (Boyd, Grossman, Lankford, Loeb, & Wyckoff, [<reflink idref="bib5" id="ref22">5</reflink>]). The capacity of teacher preparation programmes to influence mathematical content knowledge (MCK) is not restricted to the United States; international work also shows that greater instructional content offered to future teachers improves teachers' long-term understanding of mathematics (Baumert et al., [<reflink idref="bib3" id="ref23">3</reflink>]; Kleickman et al., [<reflink idref="bib19" id="ref24">19</reflink>]).</p> <p>That the exposure to instructional content could have an important impact on teachers' mathematical knowledge should be no surprise, given the relationship between content exposure and mathematics learning for K-12 students (Schmidt et al., [<reflink idref="bib33" id="ref25">33</reflink>]; Schmidt & Maier, [<reflink idref="bib31" id="ref26">31</reflink>]). The theoretical basis for this work is the simple yet powerful OTL concept: that the organization of exposure to content (what is covered and for how long) is a key factor in the acquisition of knowledge (Carroll, [<reflink idref="bib7" id="ref27">7</reflink>]). Wiley and Harnischfeger ([<reflink idref="bib37" id="ref28">37</reflink>]) and Berliner ([<reflink idref="bib4" id="ref29">4</reflink>]) further developed Carroll's model and some version of OTL has become a hallmark of the international studies sponsored by The International Association for the Evaluation of Educational Achievement (IEA) such as the studies of mathematics and science commonly referred to as the Third International Mathematics and Science Study (TIMSS) (see Husén, [<reflink idref="bib17" id="ref30">17</reflink>]; Schmidt et al., [<reflink idref="bib33" id="ref31">33</reflink>]; Travers & Westbury, [<reflink idref="bib36" id="ref32">36</reflink>]). Examination of OTL in those countries that did best on the 1995 eighth grade TIMSS assessment yielded a set of mathematics topics commonly included in the educational standards of the highest achieving countries (Schmidt, Wang, & McKnight, [<reflink idref="bib34" id="ref33">34</reflink>]). These topics were used to develop an international benchmark for K-8 students that further study has associated with student learning (Schmidt et al., [<reflink idref="bib33" id="ref34">33</reflink>]; Schmidt & Houang, [<reflink idref="bib29" id="ref35">29</reflink>]).</p> <p>A recent study based on the international TEDS-M data demonstrated that the course-taking patterns of <emph>future lower secondary teachers</emph> in the highest performing <emph>teacher preparation</emph><emph>programmes</emph> had a consistent emphasis despite the fact that these 39 programmes came from four different countries, Poland, the Russian Federation, Taiwan and the US (Schmidt & Cogan, [<reflink idref="bib27" id="ref36">27</reflink>]). Here, we extend the consideration of course-taking patterns to future primary teachers and examine the relationship of the empirically derived international benchmarks for mathematics-, mathematics pedagogy- and general pedagogy-related course-taking (OTL) to the knowledge of future primary and secondary teachers as measured in TEDS-M. The follow-up study, conducted only with the US TEDS-M sample, provides a window on the possible longer term relationship of OTL to teacher self-efficacy. The US teachers had been teaching for 2 years, when we obtained information about their school placement from which we were also able to study whether inequalities among and within teacher preparation programmes are related to inequalities in US schooling. Several US studies have indicated that better prepared teachers are less likely to work at low-income schools, an issue that's also explored internationally in the recent TALIS study (Boyd et al., [<reflink idref="bib5" id="ref37">5</reflink>]; Clotfelter et al., [<reflink idref="bib10" id="ref38">10</reflink>]; Engel, Jacob, & Curran, [<reflink idref="bib13" id="ref39">13</reflink>]; Lankford, Loeb, & Wyckoff, [<reflink idref="bib21" id="ref40">21</reflink>]; OECD, [<reflink idref="bib24" id="ref41">24</reflink>]).</p> <p>In summary, in this paper, we address four questions around the relationship of primary and lower secondary future mathematics teachers' OTL and their knowledge as measured in TEDS-M:</p> <p></p> <ulist> <item> (<reflink idref="bib1" id="ref42">1</reflink>) What is the relationship of an empirically derived international benchmark for OTL to future teachers' mathematics content knowledge and mathematics-related pedagogy knowledge as measured in TEDS-M?</item> <p></p> <item> (<reflink idref="bib2" id="ref43">2</reflink>) What is the distribution of these international OTL benchmarks both within the US and between countries?</item> <p></p> <item> (<reflink idref="bib3" id="ref44">3</reflink>) What is the relationship of US future teachers' OTL and their mathematics and mathematics pedagogy knowledge to their teaching self-efficacy during their first 2 years of teaching?</item> <p></p> <item> (<reflink idref="bib4" id="ref45">4</reflink>) Is the distribution of new teachers to US schools equitable with respect to knowledge and OTL?</item> </ulist> <hd id="AN0121905065-3">Methodology</hd> <p></p> <hd id="AN0121905065-4">The teacher education study</hd> <p>TEDS-M surveyed future teachers in their final year of teacher preparation about their teacher preparation programme and assessed their MCK and their pedagogical content knowledge (PCK). The PCK measure sought to capture the instructionally embedded mathematical knowledge thought to be critical for the professional work of teachers (Ball & Bass, [<reflink idref="bib1" id="ref46">1</reflink>]; Ball, Hill, & Bass, [<reflink idref="bib2" id="ref47">2</reflink>]). The MCK, on the other hand, measured the mathematics content knowledge necessary to teach the relevant mathematics associated with the grade levels for which the teachers were being prepared. TEDS-M focused on the teacher preparation of those who taught mathematics to students in the two grades most often assessed in the TIMSS surveys, grades four and eight. Consequently, TEDS-M focused on two different future teacher populations: (<reflink idref="bib1" id="ref48">1</reflink>) those prepared to teach mathematics in the primary grades, typically grades 1–5; and (<reflink idref="bib2" id="ref49">2</reflink>) those prepared to teach mathematics at the lower secondary level, usually grades 6–8 (see Tatto et al., [<reflink idref="bib35" id="ref50">35</reflink>]). Close to 23,000 potential future teachers of mathematics from nearly 900 programmes found in over 500 colleges and universities participated in the study conducted in 16 different countries.[<reflink idref="bib1" id="ref51">1</reflink>] TEDS-M had two different MCK and PCK assessments: one for future primary teachers and another for future lower secondary teachers. The background and OTL measures were the same for both groups of future teachers.</p> <p>Teacher preparation typically occurs in colleges and universities but government entities play a role in setting academic qualifications for teachers and determine which set of academic preparation experiences is required to teach specific content to students in specific grades. In most TEDS-M countries, mathematics teachers for TIMSS grade four students are prepared as generalists, i.e. they teach mathematics as well as all the other main subjects, and are certified for most if not all the primary grades, K-5. Most eighth-grade mathematics teachers specialize in teaching mathematics and perhaps one other subject and are certified to teach students in the secondary grades, typically grades 6–12 depending on the system.</p> <p>In a few TEDS-M countries such as Chile, Germany, Norway and the US, teachers may be prepared and certified by their government to teach students in both of the TIMSS focal grades. These teachers also tend to be specialists yet not have the same mathematics preparation as those who will teach upper secondary. Teacher preparation institutions in most countries have at least two types of programmes: one designed to prepare primary teachers of mathematics and one designed to prepare mathematics teachers for students in the secondary grades. Institutions in the few countries mentioned above may have a third programme that prepares mathematics teachers for students in a set of grades that include both fourth and eighth. TEDS-M randomly assigned half of the future teachers enrolled in programmes preparing them to teach mathematics to both primary and lower secondary students to the primary assessment and the other half to the lower secondary assessment. Consequently, the curriculum summaries analysed here were created at the programme level (type) for each academic institution in each country.</p> <hd id="AN0121905065-5">US TEDS-M sample and follow-up study</hd> <p>US data were collected in two consecutive years: in 2008 at 51 randomly selected public colleges and universities and in 2009 at 30 randomly selected private colleges and universities (Center for Research in Mathematics and Science Education, [<reflink idref="bib8" id="ref52">8</reflink>]). In all, nearly 3300 future teachers participated: 1501 future primary teachers in public institutions and 895 future primary teachers in private institutions; 607 future lower secondary teachers in public institutions and 293 future lower secondary teachers in private institutions. Primary future teachers were enrolled in 101 different programmes and lower secondary future teachers were enrolled in 96 different programmes across the 81 institutions. Twenty-five programmes prepared teachers to teach both the primary and lower secondary grades.</p> <p>In the US, we conducted a follow-up survey of the TEDS-M teacher preparation programme graduates. These surveys asked teachers about their experiences after 2 years of teaching, incorporating questions covering a broad range of topics, including how well prepared they felt they were to teach a list of specific mathematics topics appropriate to the grade level at which they were teaching. Linking this information to the results of the original TEDS-M enabled an exploration of the long-term impact of teacher preparation programmes and the differences among these programmes. Having gathered information about the schools in which these teachers were teaching, we also examined how school characteristics were related to teachers' preparation.</p> <p>Approximately, 1700 of the US future teacher sample participated in the follow-up survey, about a 52% response rate, conducted about 2 years after the original TEDS-M. Analyses of varying demographics suggested that respondents were roughly similar to the original TEDS-M sample, although participants in the follow-up had slightly higher TEDS-M test scores. In addition, the balance among primary, secondary and mixed-preparation teachers in the follow-up sample was virtually identical to that in the original TEDS-M sample.</p> <hd id="AN0121905065-6">The creation of an international benchmark</hd> <p>Using the results of the TEDS-M survey, Schmidt, Houang, and Cogan ([<reflink idref="bib30" id="ref53">30</reflink>]) and Schmidt, Cogan, and Houang ([<reflink idref="bib28" id="ref54">28</reflink>]) identified a statistical relationship between relative OTL exposure and the performance of future teachers on the two assessments (MCK and PCK) at both the primary and secondary level, with a greater proportion of mathematics course-taking resulting in higher MCK and PCK scores. However, Schmidt et al. ([<reflink idref="bib28" id="ref55">28</reflink>]) also found most of the variation in OTL resided within (at the individual future teacher level) rather than between programmes. Only 19% of the variation in mathematics content knowledge (MCK) could be attributed to institutional effects (for both primary- and secondary-prepared teachers).</p> <p>Previously, Schmidt et al. ([<reflink idref="bib34" id="ref56">34</reflink>]) used the OTL of K-12 students in the top-achieving nations on the original 1995 TIMSS to develop an international benchmark for high-quality mathematics standards. Following a similar logic, Schmidt and Cogan ([<reflink idref="bib27" id="ref57">27</reflink>]) identified the 39 lower secondary teacher preparation programmes[<reflink idref="bib2" id="ref58">2</reflink>] out of all 392 programmes in the 15 TEDS-M countries with the highest means on the mathematics content knowledge test in order to identify the coursework (content) typically taken by students in those programmes. This was done as a guide to help develop a potential list of essential topics for future lower secondary mathematics teachers. In this paper, we focus on the implications for US future teachers as well as to apply the international benchmark to the other 353 lower secondary programmes to study how broadly applicable the benchmark is. Additionally, we extend the approach to create an OTL benchmark for future primary-school teachers.</p> <p>Specifically, in order to create the empirically derived international benchmark for lower secondary mathematics teachers, Schmidt and Cogan identified the top 10% of programmes across all 16 countries based on the mean MCK score for future teachers in each programme. They then identified the courses (topics)[<reflink idref="bib3" id="ref59">3</reflink>] that the vast majority of these future teachers reported having taken. The programmes making up the top 10% were essentially the same whether based on the MCK or the PCK score. This may be explained in part by the relatively high correlation between these two scores (0.93) at the programme level (there is a much weaker relationship at the individual level). The top 10% of lower secondary programmes included 39 programmes from four countries: Poland (<reflink idref="bib1" id="ref60">1</reflink>), the Russian Federation (<reflink idref="bib15" id="ref61">15</reflink>), Taiwan (<reflink idref="bib17" id="ref62">17</reflink>) and the US (<reflink idref="bib6" id="ref63">6</reflink>).</p> <p>To qualify as part of the lower secondary benchmark of essential courses for teacher preparation programmes (what was called the A+ benchmark), courses had to be taken by at least 80% of future teachers within at least 90% of the top-performing programmes. This procedure identified nine courses. The 90% of programmes criterion ensured that the benchmark reflected a consensus and was not unduly influenced by any one programme, especially those with large numbers of future teachers (see Schmidt & Cogan, [<reflink idref="bib27" id="ref64">27</reflink>] for more detail). As a part of the benchmark, Schmidt and Cogan also identified a set of electives which were taken by most of the future teachers but were not as widespread across the programmes as the core requirements. Electives were identified as having been taken by at least 80% of future teachers within 80% of the top-performing programmes. The resulting course benchmarks for lower secondary are displayed in table 1.</p> <p>Table 1. Requirements and electives identified from the top-performing international lower secondary programmes—the A+ international benchmark.</p> <p> <ephtml> <table><thead><tr valign="top"><td> </td><td>Requirements</td><td>Electives</td></tr></thead><tbody><tr valign="top"><td>University mathematics</td><td>Beginning calculus</td><td>Abstract algebra</td></tr><tr valign="top"><td>Calculus</td><td>Analytic geometry</td></tr><tr valign="top"><td>Multivariate calculus</td><td>Axiomatic geometry</td></tr><tr valign="top"><td>Differential equations</td><td>Number theory</td></tr><tr valign="top"><td>Linear algebra</td><td>Set theory</td></tr><tr valign="top"><td>Probability</td><td> </td></tr><tr valign="top"><td>Math education</td><td>Math instruction</td><td>Math standards</td></tr><tr valign="top"><td>Observing/analysing math teaching</td></tr><tr valign="top"><td>School mathematics</td><td>Functions/equations</td><td>Geometry</td></tr><tr valign="top"><td>Numbers</td></tr><tr valign="top"><td>Statistics</td></tr></tbody></table> </ephtml> </p> <p>1 Source: Adapted from Schmidt and Cogan</p> <p>It is notable to find so many common courses as part of the lower secondary benchmark given that it was derived from programmes in four different countries on three continents. The set of nine core courses included six university mathematics courses (beginning calculus, calculus, multivariate calculus, linear algebra, probability and differential equations); two mathematics education courses (mathematics instruction including methods for teaching math such as problem posing strategies—a basic methods course; and observation, analysis and reflection on mathematics teaching); and one school-level mathematics course covering algebra, trigonometry and analytic geometry. The mathematics education course (observation, analysis and reflection of mathematics teaching) was experienced by the smallest share of future teachers across the 39 top-performing programmes, 92%. By contrast, each of the three university mathematics courses (beginning calculus, calculus and linear algebra) were taken by 99% or more of the future teachers. Among this set of nine courses, there is a strong emphasis on the content of mathematics with only two focusing directly on mathematics instruction. A similar emphasis was found among the electives, which included five additional mathematics courses (such as abstract algebra, number theory and axiomatic geometry), three school mathematics topics and a pedagogy course focusing on the country's mathematics standards.</p> <hd id="AN0121905065-7">Findings</hd> <p></p> <hd id="AN0121905065-8">Lower secondary teacher preparation: who took what</hd> <p>The preparation A+ benchmarks provide an empirical basis for defining high expectation OTL in lower secondary preparation programmes. We now, in this paper, look at the results of applying the benchmark to the 15 TEDS-M countries. Table 2 shows what percentage of US future teachers attained the benchmark (defined in one of two ways: any eight or more of the nine courses taken; or all nine courses taken) during their preparation programmes. These future teachers also took a number of popular elective courses. By way of comparison, US results are compared with the other nations that participated in the TEDS-M. In the US, we also divided the sampled programmes into subgroups: the top 25% and the bottom 25% of programmes as defined by mean mathematics content performance.</p> <p>Table 2. Per cent of future lower secondary teachers reporting they had experienced eight or more (8/9) of the nine or all nine of the core international benchmark courses.</p> <p> <ephtml> <table><thead><tr valign="top"><td>Country</td><td>(8/9)</td><td>(9)</td></tr></thead><tbody><tr valign="top"><td>Botswana</td><td>73</td><td>25</td></tr><tr valign="top"><td>Chile</td><td>5</td><td>1</td></tr><tr valign="top"><td>Georgia</td><td>78</td><td>43</td></tr><tr valign="top"><td>Germany</td><td>35</td><td>14</td></tr><tr valign="top"><td>Malaysia</td><td>88</td><td>71</td></tr><tr valign="top"><td>Norway</td><td>16</td><td>5</td></tr><tr valign="top"><td>Oman</td><td>97</td><td>82</td></tr><tr valign="top"><td>Philippines</td><td>68</td><td>33</td></tr><tr valign="top"><td>Poland</td><td>92</td><td>66</td></tr><tr valign="top"><td>Russian Federation</td><td>97</td><td>87</td></tr><tr valign="top"><td>Singapore</td><td>68</td><td>46</td></tr><tr valign="top"><td>Switzerland</td><td>54</td><td>16</td></tr><tr valign="top"><td>Taiwan</td><td>95</td><td>75</td></tr><tr valign="top"><td>Thailand</td><td>84</td><td>66</td></tr><tr valign="top"><td>United States</td><td>32</td><td>14</td></tr><tr valign="top"><td>US top 25%</td><td>77</td><td>46</td></tr><tr valign="top"><td>US bottom 25%</td><td>11</td><td>4</td></tr></tbody></table> </ephtml> </p> <p>Across all US lower secondary teacher preparation programmes, only around one-third (32%) of future teachers reached the eight or more benchmark (8/9). In both Taiwan and the Russian Federation, 95% or more reached the 8/9 benchmark. Additionally, while over 75% of all future teachers in Taiwan and the Russian Federation took all nine benchmark courses, less than 15% of US teachers did so. There were substantial differences among subgroups of US lower secondary programmes. In the top quarter of programmes <emph>in the United States</emph>, the percentage taking eight or more increased to nearly 77%. By contrast, only 11% of the future teachers trained in programmes with lower average scores (in the bottom 25% of the US distribution) reached the 8/9 benchmark criterion.</p> <p>Not only is the overall percentage of US future teachers meeting the international benchmark quite low (less than a third), especially in comparison with the Russian Federation and Taiwan, but course-taking by US future teachers is uniformly low among the various components of the benchmark. US future teachers ranked near the bottom in taking all nine courses, between 11th and 14th. Similarly, the averages for the top quarter of US programmes were in the middle of the international distribution.</p> <p>Table 3 provides greater detail on US future lower secondary teachers course-taking, related to the international benchmark. The least likely benchmark course to be taken by these US future teachers was differential equations. Among future teachers in the top 25% of US programmes, only 70% reported having had this course. At the bottom quarter of US programmes, 30% of future teachers reported having taken differential equations. An even more striking difference between the top and bottom quarter of US programmes, however, is seen for multivariate calculus: nearly 95% of future teachers took multivariate calculus in the US higher performing programmes as compared with only 11% in the bottom quarter of programmes. Most future teachers in the bottom quarter of US programmes reported taking a university mathematics probability course (80%). However, relatively few of these teachers reported having taken most of the other benchmark courses likely implying this to be an elementary probability course, i.e. one that was not calculus based. Enrolment data from the lowest quarter of programmes suggests they produce approximately three-fifths of all future lower secondary mathematics teachers in the US.</p> <p>Table 3. Per cent of future lower secondary teachers reporting they had experienced each lower secondary international benchmark course.</p> <p> <ephtml> <table><thead><tr valign="top"><td>Country</td><td>Linear algebra</td><td>Beginning calculus</td><td>Calculus</td><td>Multivariate calculus</td><td>Differential equations</td><td>Probability</td><td>Functions</td><td>Math instruction</td><td>Math teaching</td></tr></thead><tbody><tr valign="top"><td>Botswana</td><td>88</td><td>98</td><td>100</td><td>65</td><td>96</td><td>72</td><td>93</td><td>98</td><td>79</td></tr><tr valign="top"><td>Chile</td><td>37</td><td>39</td><td>24</td><td>9</td><td>39</td><td>66</td><td>58</td><td>90</td><td>69</td></tr><tr valign="top"><td>Georgia</td><td>97</td><td>95</td><td>95</td><td>92</td><td>95</td><td>88</td><td>96</td><td>71</td><td>72</td></tr><tr valign="top"><td>Germany</td><td>76</td><td>78</td><td>68</td><td>43</td><td>48</td><td>69</td><td>71</td><td>82</td><td>65</td></tr><tr valign="top"><td>Malaysia</td><td>98</td><td>98</td><td>99</td><td>84</td><td>98</td><td>98</td><td>98</td><td>91</td><td>84</td></tr><tr valign="top"><td>Norway</td><td>57</td><td>53</td><td>58</td><td>12</td><td>23</td><td>90</td><td>97</td><td>86</td><td>82</td></tr><tr valign="top"><td>Oman</td><td>100</td><td>100</td><td>99</td><td>98</td><td>98</td><td>99</td><td>97</td><td>97</td><td>90</td></tr><tr valign="top"><td>Philippines</td><td>92</td><td>90</td><td>94</td><td>52</td><td>87</td><td>93</td><td>96</td><td>89</td><td>77</td></tr><tr valign="top"><td>Poland</td><td>99</td><td>100</td><td>98</td><td>95</td><td>86</td><td>100</td><td>96</td><td>92</td><td>89</td></tr><tr valign="top"><td>Russian Federation</td><td>99</td><td>99</td><td>100</td><td>96</td><td>99</td><td>99</td><td>99</td><td>97</td><td>93</td></tr><tr valign="top"><td>Singapore</td><td>82</td><td>87</td><td>89</td><td>70</td><td>78</td><td>75</td><td>93</td><td>98</td><td>89</td></tr><tr valign="top"><td>Switzerland</td><td>92</td><td>96</td><td>76</td><td>26</td><td>65</td><td>93</td><td>95</td><td>84</td><td>86</td></tr><tr valign="top"><td>Taiwan</td><td>100</td><td>100</td><td>100</td><td>94</td><td>93</td><td>99</td><td>98</td><td>85</td><td>88</td></tr><tr valign="top"><td>Thailand</td><td>96</td><td>100</td><td>100</td><td>88</td><td>86</td><td>96</td><td>96</td><td>84</td><td>89</td></tr><tr valign="top"><td>United States</td><td>68</td><td>69</td><td>58</td><td>44</td><td>44</td><td>85</td><td>81</td><td>76</td><td>76</td></tr><tr valign="top"><td>US top 25%</td><td>98</td><td>98</td><td>96</td><td>95</td><td>70</td><td>91</td><td>85</td><td>86</td><td>84</td></tr><tr valign="top"><td>US bottom 25%</td><td>52</td><td>52</td><td>34</td><td>11</td><td>30</td><td>80</td><td>78</td><td>75</td><td>75</td></tr></tbody></table> </ephtml> </p> <p>Finally, we found the average percentage of future teachers who took a given benchmarked course for each quartile of the mathematics content knowledge distribution. The course-taking patterns of future secondary teachers were quite similar among the three highest quartiles. Together these programmes represent approximately two-fifths of US future teachers. By contrast, future teachers at the lower MCK institutions are much less likely to have taken the A+ courses, especially with respect to linear algebra, differential equations and the calculus topics. It is the bottom quartile of programmes that is quite distinct in terms of course-taking related to mathematics and it is from that quartile of programmes that 60% of America's teachers emerge.</p> <hd id="AN0121905065-9">Highest performing programmes: course-taking or student academic background</hd> <p>The question arises as to whether the analytic approach taken in the previous section simply reflects a selection bias, i.e. the better programmes attract the most talented future teachers and it is that which accounts for the programmes' performance rather than future teachers' course-taking (OTL). Before turning to the issue of whether higher average performance at the programme level on the mathematics content test is more reflective of selection or preparation, we first estimated the variance components to determine the degree to which differences in adherence to the international benchmark was associated more with future teacher choices or with programme differences. The results clearly demonstrated that most of the variation in course-taking was attributable to individual future teacher-level decision-making, <emph>not</emph><emph>programme</emph><emph>types.</emph> Among future lower secondary teachers, between 7 and 15% of the variance in the scale indicating the number of the nine international benchmark courses taken by a future teacher (benchmark OTL) was due to programme differences (5 and 11% of variation in benchmark OTL for future primary teachers—see next section). For future teachers from mixed programmes who received specific mathematical training but were more oriented towards primary school, there was a great deal more variation attributable to programme differences (35–37%). This finding is unsurprising, as the mixed programme type included a wide variety of types of programmes, in part due to differences in state accreditation policies. Despite these differences by programme type, in every instance far more of the variation occurred within programmes at the individual teacher level thus supporting the conclusions of Koedel et al. ([<reflink idref="bib20" id="ref65">20</reflink>]).</p> <p>One potential concern with the methodology used to identify the benchmark is that it was derived from the identification of the coursework (OTL) typically taken by the future teacher at the top-performing programmes assuming this to provide an empirically derived definition of high-quality teacher preparation in mathematics. If those programmes identified as high-performing recruit disproportionately from the best secondary students in that country, the reason for the high performance might have little to do with course-taking, and as a result, the benchmark could simply be a reflection of selection bias. This would especially be possible for the lower secondary benchmark OTL scale as the variation in course-taking across countries, programmes and individuals was substantially greater than was the case for primary teacher preparation (see next section). As a result, we focus our attention in this section on lower secondary programmes.</p> <p>The list of nine courses defining the benchmark was developed by examining the commonalities in course-taking of the vast majority of students in at least 90% of the 39 programmes identified as having the highest mean performance on the mathematics content test. Those 39 programmes were from four countries but 32 of them came from the Russian Federation and Taiwan. In those countries, the course requirements for secondary students entering the university would typically be quite consistent as almost all students entering the university are required to have 4 years of mathematics. Even if the universities are stratified in their selectivity, most students would come with a similar background in mathematics and as a result would likely take similar university-level coursework.</p> <p>With this hypothesis in mind, we found that at least 95% of the future lower secondary teachers in the Russian Federation and Taiwan took at least eight of the benchmark courses. Additionally, 75% of the Taiwanese future teachers and 87% of the Russian future teachers took all nine courses. The number of courses taken on average over all the programmes in the Russian Federation and Taiwan was 8.96 and 8.63, respectively. Hence, the selection of the nine courses in the benchmark OTL is not likely the result of selection bias since most of the students in the remaining 35 programmes in these two countries also took the same courses.</p> <p>Poland, which had one programme included in the set of 'A+' programmes, had 92% of its future teachers taking eight or nine of the benchmark OTL courses and two-thirds taking all nine. The only exception to this general pattern was the US which contributed six programmes to the development of the benchmark. Here, less than a third of future lower secondary teachers took at least eight of the courses. Given the course-taking structure of the K-12 curriculum in the US at the time when these future teachers would have been in high school and the highly selective nature of US universities, selection bias would be much more likely to occur. First of all, the six US programmes played a smaller role in the definition of the A+ benchmark (6/39), but fortunately in the US, additional data were available to explore the issue of selectivity more thoroughly.</p> <p>For the US sample, we were able to obtain the college entrance (SAT/ACT) scores for the future teachers. The two tests were equated[<reflink idref="bib4" id="ref66">4</reflink>] and included in a programme-level analysis relating the benchmark OTL scale (0–9) to the mathematics content knowledge test (MCK). Both were statistically significantly related to average performance. The <emph>R</emph>-square indicated that 48% of the variance was accounted for and the overall model was statistically significant (<emph>p</emph> < 0.0001). (The analysis for primary teachers yielded similar results but the benchmark had a smaller relationship with MCK as is discussed in the next section.) The results suggested that selection was significantly related to performance, <emph>but so was OTL as defined by the benchmark OTL scale</emph>.[<reflink idref="bib5" id="ref67">5</reflink>]</p> <p>It would be ideal to run a similar analysis across all 392 lower secondary teacher preparation programmes in all 15 countries but international data similar to US college entrance scores were not available. However, the number of years of high-school mathematics taken was available in all countries. Although a poorer alternative to a test (it was related to the SAT/ACT measure in the US with a correlation coefficient of 0.35), we fitted a parallel model using it with the benchmark OTL scale to predict MCK performance at the programme level.</p> <p>Both were again statistically significant at the model level (<emph>p</emph> < 0.0001) but the high-school measure was only marginally significant (<emph>p</emph> < 0.048), while the benchmark OTL scale was strongly related to MCK, accounting for 43% of the variance. The benchmark OTL scale had an estimated effect size of slightly more than one-third of a standard deviation. The fact that the size of the relationship of benchmark OTL to performance at the programme level was so large across all 392 programmes together with the US results controlling for college entrance scores adds credence to the hypothesis that the international benchmark derived from the 39 A+ programmes represents a substantively meaningful definition of high-quality teacher preparation in mathematics for lower secondary teachers rather than a spurious selection bias artefact.</p> <hd id="AN0121905065-10">Primary teacher preparation: who takes what</hd> <p>Despite its attention from policy-makers, lower and upper secondary teachers do not constitute the majority of teachers overall. According to the National Center for Education Statistics Common Core of data, 55% of US teachers during the 2010–2011 school year were primary-school teachers. Due to mathematics' hierarchical structure, it is commonplace that the foundations for later learning are established in a student's early grades. As mentioned earlier, the preparation of primary school teachers is profoundly different from lower secondary teachers. Whereas future lower secondary teachers focus their education on mathematics and mathematics teaching to support their professional focus, future primary school teachers are expected to be conversant in every subject. Although the importance of mathematics has grown in the wake of accountability-based policies, mathematics must compete with science, social studies and (most of all) reading. Given the young ages of their students, future primary teachers (especially in the early grades) must also take account of basic questions of children's psychological and social development. All of these issues suggest that although a thorough understanding of basic mathematics in the early grades is essential, that education is provided by teachers who may have a very limited background (or interest) in mathematics.</p> <p>In this section, we replicated the analyses of lower secondary teachers (described above) for future primary teachers in order to identify an international benchmark for teachers prepared to teach mathematics in the primary grades 1–5. For primary programmes, the number of countries and the specific programmes in those countries varied more when based on content or pedagogical content test performance. The top 10% of content knowledge-based programmes came from seven countries: Norway (<reflink idref="bib1" id="ref68">1</reflink>), Poland (<reflink idref="bib17" id="ref69">17</reflink>), the Russian Federation (<reflink idref="bib11" id="ref70">11</reflink>), Switzerland (<reflink idref="bib1" id="ref71">1</reflink>), Taiwan (<reflink idref="bib10" id="ref72">10</reflink>), Thailand (<reflink idref="bib5" id="ref73">5</reflink>) and the US (<reflink idref="bib4" id="ref74">4</reflink>). Based on PCK performance, the top 10% of programmes came from eight countries: Norway (<reflink idref="bib4" id="ref75">4</reflink>), Poland (<reflink idref="bib11" id="ref76">11</reflink>), the Russian Federation (<reflink idref="bib3" id="ref77">3</reflink>), Singapore (<reflink idref="bib1" id="ref78">1</reflink>), Switzerland (<reflink idref="bib2" id="ref79">2</reflink>), Taiwan (<reflink idref="bib10" id="ref80">10</reflink>), Thailand (<reflink idref="bib1" id="ref81">1</reflink>) and the US (<reflink idref="bib17" id="ref82">17</reflink>). A core of 29 programmes was in the top 10% for both tests. These came from six countries: Norway (<reflink idref="bib1" id="ref83">1</reflink>), Poland (<reflink idref="bib10" id="ref84">10</reflink>), the Russian Federation (<reflink idref="bib3" id="ref85">3</reflink>), Taiwan (<reflink idref="bib10" id="ref86">10</reflink>), Thailand (<reflink idref="bib1" id="ref87">1</reflink>) and the US (<reflink idref="bib4" id="ref88">4</reflink>). The content-based test requirements were a subset of those based on the PCK test. Consequently, the primary benchmark discussed represents the union of the two test-based requirements (unlike the secondary benchmark, which was based only on mathematics content knowledge performance). The courses identified are presented in table 4.</p> <p>Table 4. Requirements and electives identified from the international top-performing primary programmes—the A+ international benchmark.</p> <p> <ephtml> <table><thead><tr valign="top"><td> </td><td>Requirements</td><td>Electives</td></tr></thead><tbody><tr valign="top"><td>University mathematics</td><td>Number theory<xref ref-type="table-fn" rid="TFN0002">*</xref></td><td>Analytic geometry</td></tr><tr valign="top"><td>Probability<xref ref-type="table-fn" rid="TFN0002">*</xref></td><td>Axiomatic geometry</td></tr><tr valign="top"><td>Math education</td><td>Math instruction</td><td>Math standards</td></tr><tr valign="top"><td>Observing/analysing math teaching</td></tr><tr valign="top"><td>School mathematics</td><td>Measurement</td><td>Geometry</td></tr><tr valign="top"><td>Numbers</td><td>Functions</td></tr></tbody></table> </ephtml> </p> <p>2 Courses such as these can exist at different levels of mathematical sophistication. It is our assumption that for the most part these two represent very elementary courses perhaps even designed explicitly for future teachers.</p> <p>The emphasis in the set of courses comprising the international primary benchmark suggests a different focus for primary teacher mathematics preparation. Although the vast majority of the required courses were mathematics oriented—four out of five (80%)—for the two university mathematics courses, number theory and probability, we assume them to be very elementary courses (based on the absence of other university-level coursework such as linear algebra and calculus). The two school mathematics courses, measurement and numbers, also suggest a less advanced mathematics emphasis than that for lower secondary teachers. This finding is not particularly surprising, given that mathematics is not the principal emphasis of primary teacher preparation.</p> <p>As with Table 3, Table 5 compares the proportion of US future primary teachers meeting the international primary benchmark compared with other countries participating in the TEDS-M. For US primary future teachers, the per cent reaching the international benchmark was rather consistent whether the subgroup of programmes came from those in the top or the bottom 25% of US programmes, or represented the entire US primary programme sample as a whole. Although this percentage was rather high, about 85%, it was not as high as the corresponding percentages in Taiwan and the Russian Federation. A majority (56%) of US future teachers took all five benchmark courses. More future primary teachers met the relevant international benchmark than was the case for the lower secondary teachers. On the other hand, like lower secondary teachers, US future primary teachers ranked relatively low on the benchmark OTL scale—between 9th and 12th of 15 countries. Although US future teachers did a bit better in two categories (Numbers and Measurement), their overall ranking was still in the lower half of countries.</p> <p>Table 5. Per cent of future primary teachers reporting they had experienced four or more (4/5) of the five or all five of the core international benchmark courses.</p> <p> <ephtml> <table><thead><tr valign="top"><td>Country</td><td>(4/5)</td><td>(5)</td></tr></thead><tbody><tr valign="top"><td>Botswana</td><td>92</td><td>76</td></tr><tr valign="top"><td>Chile</td><td>94</td><td>60</td></tr><tr valign="top"><td>Georgia</td><td>84</td><td>50</td></tr><tr valign="top"><td>Germany</td><td>54</td><td>33</td></tr><tr valign="top"><td>Malaysia</td><td>92</td><td>68</td></tr><tr valign="top"><td>Norway</td><td>91</td><td>70</td></tr><tr valign="top"><td>Philippines</td><td>97</td><td>80</td></tr><tr valign="top"><td>Poland</td><td>85</td><td>60</td></tr><tr valign="top"><td>Russian Federation</td><td>96</td><td>64</td></tr><tr valign="top"><td>Singapore</td><td>81</td><td>55</td></tr><tr valign="top"><td>Spain</td><td>92</td><td>64</td></tr><tr valign="top"><td>Switzerland</td><td>92</td><td>72</td></tr><tr valign="top"><td>Taiwan</td><td>91</td><td>74</td></tr><tr valign="top"><td>Thailand</td><td>96</td><td>79</td></tr><tr valign="top"><td>United States</td><td>85</td><td>56</td></tr><tr valign="top"><td>US top 25%</td><td>89</td><td>59</td></tr><tr valign="top"><td>US bottom 25%</td><td>86</td><td>57</td></tr></tbody></table> </ephtml> </p> <p>The international primary benchmark had much lower variability than the secondary benchmark. With the exception of Germany, every nation participating in the TEDS-M had averages of above 80% receiving instruction in four or more of the five basic benchmark courses. Generally speaking, there is a strong international consensus in the type of preparation necessary for future primary-school teachers.</p> <hd id="AN0121905065-11">Teacher course-taking and self-reported preparedness to teach mathematics</hd> <p>In the previous section, we examined the short-term relationship between mathematics OTL and mathematics knowledge for future primary and secondary teachers. In this and the next section, we explore the long-term effects mathematics coursework has on graduates of teacher preparation programmes. We explore both the impact of OTL on <emph>individual</emph>-level efficacy once teachers have entered the workforce, as well as the <emph>aggregate</emph> relationship of differences in teacher preparation to equity at the K-8 level. Our essential question is, having derived benchmarks for the mathematics preparation of future teachers, does the application of these benchmarks have a relationship to K-8 schooling in the United States?</p> <p>First, we explored the relationship between teacher course-taking in their teacher preparation programmes as defined by the two benchmark OTL scales and how well prepared they felt they were to teach the mathematics topics <emph>after they had begun teaching</emph>. As mentioned above, research suggests that the features of teacher preparation programmes may not be felt until after the first transitional year in the classroom (Boyd et al., [<reflink idref="bib5" id="ref89">5</reflink>]). Teachers 2 years into their teaching were asked to evaluate their academic preparation to teach each of a set of mathematics topics on a four-point scale (1–4). Responses were averaged across topics, with higher scores representing more confidence to teach the mathematics topics appropriate to their grade level. This approach has been used successfully in other studies but has been shown to be somewhat of an overestimate (Schmidt & McKnight, [<reflink idref="bib32" id="ref90">32</reflink>]). As a general metric of how well prepared a teacher feels, it also taps into a teacher's broader notion of how well equipped he or she is to teach mathematics, above and beyond the formal mathematical knowledge they have acquired.</p> <p>Using standard regression techniques, we ran two separate analyses for US teachers who were currently teaching primary school and for those currently teaching lower secondary (see table 6). Only 4% of those teaching lower secondary had been prepared as strictly secondary teachers, with the remainder divided evenly between those trained as lower secondary and those trained as primary-school teachers. The control variables in the model included the two TEDS-M tests, SAT equivalent (college entrance) scores and an indicator of whether their preparation was in a public or private institution, as well as an indicator for the particular test taken, e.g. primary or lower secondary.</p> <p>Table 6. Estimated regression coefficients relating teacher course-taking and self-reported academic preparation to teach mathematics topics.</p> <p> <ephtml> <table><thead><tr valign="top"><td> </td><td>Current lower secondary teachers</td><td>Current primary school teachers</td></tr></thead><tbody><tr valign="top"><td>Benchmark OTL</td><td>0.121<xref ref-type="table-fn" rid="TFN0003">*</xref></td><td> </td></tr><tr valign="top"><td>Benchmark OTL</td><td> </td><td>0.132<xref ref-type="table-fn" rid="TFN0003">*</xref></td></tr><tr valign="top"><td>SAT/ACT</td><td>0.001<xref ref-type="table-fn" rid="TFN0003">*</xref></td><td>0.001</td></tr><tr valign="top"><td>MCK</td><td>0.001<xref ref-type="table-fn" rid="TFN0003">*</xref></td><td>0.002<xref ref-type="table-fn" rid="TFN0003">*</xref></td></tr><tr valign="top"><td>PCK</td><td>0.001</td><td>−0.001</td></tr><tr valign="top"><td>Public</td><td>0.114</td><td>0.023</td></tr><tr valign="top"><td>Test form control</td><td>−0.419</td><td>−0.136</td></tr><tr valign="top"><td>Constant</td><td>0.567</td><td>1.726</td></tr><tr valign="top"><td>Adjusted <italic>R</italic>-square</td><td>0.269</td><td>0.058</td></tr><tr valign="top"><td><italic>N</italic></td><td>430</td><td>660</td></tr></tbody></table> </ephtml> </p> <p>3 Statistically significant at the 0.05 level.</p> <p>The pre-service benchmark OTL scale had a statistically significant relationship to how well prepared to teach mathematics lower secondary teachers believed they were even after controlling for their SAT score, their MCK and PCK scores, and whether they went to a public or private university (see table 6).</p> <p>The fit of the model as indicated by the <emph>R</emph><sups>2</sups> was better for lower secondary than primary-school teachers, which might be expected given the greater variation in preparation of those teaching the lower secondary grades. For primary teachers, course-taking was statistically significant (<emph>p</emph> < 0.05) with a similar estimated effect size, but the model as a whole was not statistically significant. As a result, the following analyses focus on the lower secondary mathematics teachers.</p> <p>The results presented in table 6 were robust with respect to alternative specifications of the model. Multi-level modelling yielded essentially identical results, as might be expected given the small amount of variation due to teacher preparation programmes as illustrated in the variance component estimates described previously. Separating the sample into those who took the primary and secondary mathematics content test does not change the statistically significant positive association of benchmark OTL with instructional preparedness. Specifically focusing on lower secondary, additional robustness checks confirmed the main findings. In one iteration, the individual mathematics topics used to generate the dependent variable were divided into four topical categories,[<reflink idref="bib6" id="ref91">6</reflink>] and the analyses were run for each category separately. For each of the four different mathematics topic groupings, teachers who had a higher rating on the benchmark OTL scale felt more prepared to teach mathematics (with algebra having the strongest relationship). Dividing the benchmark OTL scale components into three substantive categories (mathematics, math education and school mathematics), also generated substantively similar results, with mathematics having the strongest relationship to feelings of instructional preparedness. Finally, decomposing the benchmark into individual course-taking suggests that calculus carried the most weight in predicting preparedness. These results are consistent with those found in the TALIS study.</p> <p>For the lower secondary teachers, course-taking as measured by the benchmark OTL scale also had a modest correlation with the content knowledge test (for both the secondary and primary version of the test). This suggests the hypothesis that the course-taking of future teachers has both a direct relationship to teacher confidence to teach mathematics topics as well as an indirect relationship through its association with MCK. To explore this, we did a maximum likelihood path analysis in which we specified a model, with the benchmark OTL scale identified as having a direct relationship to self-reported teacher preparation as well as an indirect relationship through content knowledge performance.[<reflink idref="bib7" id="ref92">7</reflink>] The college entrance exam scores (SAT/ACT) were also specified as having paths to both of these variables. Since the measure of mathematics content knowledge was closest in time to the follow-up data, there is no direct path from SAT/ACT to instructional preparedness included in figure 1. If included, this path does not achieve statistical significance and does not alter the other coefficients in the model.</p> <p>Graph: Figure 1. Estimated path model relating US teacher course-taking and mathematics content knowledge performance to preparedness to teach lower secondary mathematics.[<reflink idref="bib10" id="ref93">10</reflink>]</p> <p>This analysis was done for the 93 lower secondary mathematics teachers who were prepared in lower secondary or mixed preparation programmes and who as a consequence took the secondary version of the MCK test. The results of the analysis are presented in figure 1. All paths except the one specifying a relationship between SAT/ACT and the benchmark OTL scale[<reflink idref="bib8" id="ref94">8</reflink>] were statistically significant, with benchmark OTL having a strong direct relationship to instructional preparedness to teach mathematics, and also a modest indirect relationship (0.08), for a total effect of 0.59.[<reflink idref="bib9" id="ref95">9</reflink>]</p> <hd id="AN0121905065-12">Who goes where: teacher preparation and teacher placement</hd> <p>Next, we examined whether new teachers who were better prepared in mathematics as reflected by their scores on the two TEDS-M tests were more likely to be hired by the wealthiest schools. The two international benchmark scales could also be viewed as a measure of better teacher preparation. The question addressed in this section is whether teachers who have been better prepared to teach mathematics (according to the primary and lower secondary benchmark OTL scales) are disproportionately hired by more advantaged schools—thus exacerbating educational inequality. To test this, we again focused on the follow-up survey.</p> <p>TEDS-M follow-up responses about which school respondents were employed by were merged with National Center of Education Statistics (NCES) school demographic data. Schools were classified according to the NCES division of schools into 0–25%, 25–50%, 50–75% and 75–100% low-income students (defined by eligibility for free and reduced meals). TEDS-M respondents were also divided into four quartiles, based on their mathematics content knowledge test performance (split further into those who took the primary or lower secondary test). They were also divided into quartiles based on the two benchmark OTL scales. For analyses related to the primary benchmark OTL scale, teachers were divided into terciles rather than quartiles.</p> <p>The results for lower secondary teachers supported the conclusion that better prepared teachers are less likely to take jobs at high-poverty schools (see table 7). Only 8% of the better prepared teachers (teachers highest on the lower secondary benchmark OTL scale) were teaching in high-poverty schools, compared with 31% of the lowest benchmark OTL teachers. Additionally, more than half of the better prepared teachers were teaching at the two categories of middle-income schools, compared to only a quarter of the teachers who took the fewest of the benchmark courses. These patterns were statistically significant (<emph>p</emph> < 0.001). The relationship was less clear for primary-prepared teachers, failing to reach statistical significance (<emph>p</emph> < 0.12). However, it should be noticed that the primary benchmark OTL scale had much less variance, with 60% having the maximum rating of 5. The lower variation and right skew could blunt the strength of the relationship.</p> <p>Table 7. Percentage of teacher employment by preparation and school poverty.</p> <p> <ephtml> <table><thead><tr valign="top"><td /><td>Lower secondary teachers</td><td /></tr><tr valign="top"><td>School poverty</td><td> Lowest benchmark OTL</td><td>Highest benchmark OTL</td><td>Total</td></tr><tr valign="top"><td /><td>1</td><td>2</td><td>3</td><td>4</td><td /></tr></thead><tbody><tr valign="top"><td>0–25%</td><td>44</td><td>45</td><td>34</td><td>40</td><td>40%</td></tr><tr valign="top"><td>25–50%</td><td>9</td><td>36</td><td>29</td><td>31</td><td>29%</td></tr><tr valign="top"><td>50–75%</td><td>16</td><td>11</td><td>22</td><td>22</td><td>18%</td></tr><tr valign="top"><td>75–100%</td><td>31</td><td>9</td><td>15</td><td>8</td><td>13%</td></tr><tr valign="top"><td><italic>N</italic></td><td>45</td><td>105</td><td>94</td><td>118</td><td>362</td></tr></tbody></table> </ephtml> </p> <p>We found somewhat different results if 'better prepared' was defined by performance on the mathematics content knowledge test, especially for the primary teachers (see table 8). There the dominant pattern was not that better prepared teachers were less likely to have taken jobs in high-poverty schools (although there was a small difference in that direction—18% versus 24%) but that the higher performing teachers on the test were more than twice as likely as the lowest performing primary teachers to have taken jobs in the wealthiest schools (<emph>p</emph> < 0.001). The pattern for the lower secondary teachers was in general the same as found in table 7 (10% versus 23%) but was not statistically significant (<emph>p</emph> < 0.09).</p> <p>Table 8. Percentage of teacher employment by MCK performance and school poverty.</p> <p> <ephtml> <table><thead><tr valign="top"><td /><td>Primary teachers</td><td /></tr><tr valign="top"><td>School poverty</td><td>Lowest MCK </td><td>Highest MCK</td><td>Total</td></tr><tr valign="top"><td /><td>1</td><td>2</td><td>3</td><td>4</td><td /></tr></thead><tbody><tr valign="top"><td>0–25%</td><td>21</td><td>32</td><td>30</td><td>45</td><td>32%</td></tr><tr valign="top"><td>25–50%</td><td>29</td><td>29</td><td>31</td><td>20</td><td>27%</td></tr><tr valign="top"><td>50–75%</td><td>25</td><td>31</td><td>23</td><td>18</td><td>24%</td></tr><tr valign="top"><td>75–100%</td><td>24</td><td>8</td><td>17</td><td>18</td><td>17%</td></tr><tr valign="top"><td><italic>N</italic></td><td>179 </td><td>170 </td><td>175 </td><td>171 </td><td>695</td></tr></tbody></table> </ephtml> </p> <p>One salient feature of the data is that a disproportionate share of the TEDS-M future teachers who were working as teachers had been hired by higher income schools. Only 13% of primary-prepared teachers and 17% of secondary-prepared teachers were working at low-income schools, compared with 32% of primary teachers and 40% of secondary teachers at high-income schools.</p> <hd id="AN0121905065-13">Discussion</hd> <p>There are three principal conclusions to be drawn from our analysis of the TEDS-M and follow-up data. First, there is a significant relationship between what teachers study in their teacher preparation programmes and self-reported preparation to teach mathematics. Previous research has provided strong evidence that OTL—content coverage—has a strong relationship to K-12 educational outcomes (examined in <emph>Why Schools Matter</emph>, Schmidt et al., [<reflink idref="bib33" id="ref96">33</reflink>]). The research presented here suggests that course-taking is also a key factor in teacher preparation. Analysis of the course-taking patterns of the top-performing teacher preparation programmes across 16 countries revealed a reasonable consensus about what courses or content topics are appropriate for preparing future teachers. For example, at the lower secondary level, more rigorous mathematics content, such as university-level mathematics around the key areas of functions (e.g. calculus which serves as a foundation for more advanced mathematics) and probability, characterized the highest performing programmes. Nonetheless, results from international studies must always be interpreted carefully when applied to any individual country. Thus, these benchmarks simply provide a way for a country to examine, to reflect and to learn.</p> <p>Results from the TEDS-M follow-up studies indicated that these international benchmarks are related to how well prepared teachers say they are after teaching mathematics for 2 years. Teachers whose course-taking more closely reflected the international benchmarks indicated much greater confidence in teaching mathematics topics. The association between teachers' self-reported ability to teach mathematics and their previous course-taking is quite robust, even after accounting for the teacher's background and mathematics knowledge.</p> <p>Second, although a small number of US teacher preparation programmes have among the highest mean mathematics content knowledge scores internationally, the reality is that many teachers do not receive internationally competitive mathematics training before they enter the classroom. This is a particular problem in lower secondary, as roughly three-fifths of such future math teachers graduate from the bottom quarter of teacher preparation programmes in the US. In addition, our analysis reveals that the least prepared teachers, where only about 1 in 10 have had their teacher preparation include the coursework defined by the top programmes in the world, are more likely to be hired by the poorest, most disadvantaged schools, contributing to educational inequality. Further, despite the fact that the international primary benchmark only constitutes five courses, only a little over half of future US primary teachers reported taking all of them.</p> <p>Finally, the TEDS-M studies underscore the critical difference between primary and lower secondary teacher preparation in mathematics, a distinction that should be kept clearly in the forefront of researchers and policy-makers. Although the basic relationship between teacher course-taking and confidence to teach mathematics is quite similar for primary and lower secondary teachers, the overall relationship is more muted in the case of primary teachers. Likewise, while the proportion of teachers reaching the benchmark varies wildly across different lower secondary programmes (and countries), there is much less variation at the primary level.</p> <p>The differences between primary and lower secondary preparation should be no surprise. Because they are math specialists, mathematics preparation is a dominant focus of future lower secondary mathematics teachers. Primary school teachers, on the other hand, are expected to be proficient in teaching many subjects, and to do so at a more basic level. The fundamental difference in the content and grade-level focus of primary and lower secondary mathematics teachers means that the expectations of teachers and the thrust of policy must be just as different.</p> <p>For example, we have argued previously that because the US population generally does less well on international K-12 mathematics assessments, American teacher preparation programmes are drawing from a weaker pool of future mathematics teachers. To recruit future teachers with the same mathematics knowledge as the average person from Taiwan, the US would have to recruit from the top quarter of US eighth graders (see figure 2). This is a particular issue in primary teacher preparation, as selection effects appear to have a stronger relationship to a primary teacher's ability to teach mathematics. This may be due in part to the fact that mathematics makes up only a portion of the content for which teachers are expected to prepare. As a consequence, improving the mathematics preparation of primary teachers represents a considerable challenge, one that requires a great deal of careful study.</p> <p>Graph: Figure 2. TIMSS 2003 eighth grade mathematics achievement distributions. Adapted from 'TIMSS 2003 International Mathematics Report: Findings From IEA's Trends in International Mathematics and Science Study at the Fourth and Eighth Grade,' by Mullis, Martin, Gonzalez, and Chrostowski ([<reflink idref="bib23" id="ref97">23</reflink>], p. 465). Copyright 2004 by TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College. Figure reproduced from CRMSE 2010.</p> <p>Lower secondary teacher preparation is a different story, in that course-taking patterns within teacher preparation programmes account for a greater proportion of the variation in preparation to teach mathematics. The fact that the majority of future US lower secondary teachers graduate from the weakest US programmes suggests the hypothesis that this may contribute to the modest performance of US students on international assessments. However, the results also point to a possible remedy: the international benchmark for secondary teacher course-taking suggests the hypothesis that improvements in the course requirements of teacher preparation programmes might improve the performance of US lower secondary mathematics teachers, and ultimately that of their students as well.</p> <hd id="AN0121905065-14">Notes on contributors</hd> <p>William H. Schmidt is a University Distinguished professor of statistics and education at Michigan State University. He serves as director of the Education Policy Center and holds faculty appointments in Statistics and Education. Previously, he served as National Research Coordinator and Executive Director of the US National Center which oversaw participation of the United States in the IEA-sponsored Third International Mathematics and Science Study (TIMSS). He has published in numerous journals including the <emph>Journal of the American Statistical Association</emph>, <emph>Journal of Educational Statistics</emph>, <emph>EEPA</emph>, <emph>Science, Educational Researcher</emph> and the <emph>Journal of Educational Measurement</emph>. He has co-authored 10 books including <emph>Why Schools Matter, Teacher Education Matters, and Inequality for All</emph>. His current writing and research concerns issues of academic content in K-12 schooling including the Common Core State Standards for Mathematics, assessment theory and the effects of curriculum on academic achievement. He is also concerned with educational policy related to mathematics, science and testing in general. He received the 1998 Willard Jacobson Lectureship from The New York Academy of Sciences and is a member of the National Academy of Education. In 2009, he was elected in the first group of Fellows in the American Educational Research Association. He served on the Steering Committee for Review of the Evaluation Data on the Effectiveness of NSF-Supported Mathematics Curriculum Materials. He received his A.B. in mathematics from Concordia College in River Forrest, IL and his PhD from the University of Chicago in psychometrics and applied statistics. He was also awarded an honorary doctorate degree from Concordia University in 1997.</p> <p> <emph>Nathan A. Burroughs</emph> is a Senior Research Associate at the Center for the Study of Curriculum Policy at Michigan State University, where his research focuses on educational inequality and teacher preparation in math and science using large scale assessments and survey data. He has also published work on normative issues related to education and citizenship. Previously, Burroughs served as a Research Associate at the Center for Evaluation and Education Policy at Indiana University, where he conducted research on a range of topics, including achievement gaps among high-ability students and college persistence, as well as providing evaluation and technical assistance services to state and federally funded agencies. He received his PhD in Political Science from the University of Georgia.</p> <p> <emph>Leland S. Cogan</emph> is a Senior Researcher with the Center for the Study of Curriculum Policy at Michigan State University and was the U.S. Assistant Director for the Teacher Education Study in Mathematics (U.S. TEDS-M). He has taught courses in educational psychology, educational research methods and coordinated data collection and analyses for the Survey of Mathematics and Science Opportunities, the multinational project that researched and developed the TIMSS' questionnaires. He has collaborated in observational and quantitative studies of educational practices and policy and co-authored technical reports, articles, and books on TIMSS. His research interests focus on mathematics and science curricula and the preparation of teachers to teach these subjects in schools. He has undergraduate degrees in microbiology and psychology and a doctorate in educational psychology from MSU.</p> <p> <emph>Richard T. Houang</emph> is the Director of Research for the Center for the Study of Curriculum Policy and a member the Michigan State University College of Education faculty. He earned his PhD in Psychometrics and Research Methods from the University of California at Santa Barbara. His substantive interests include curriculum assessment, the study of the relationship between mathematics and science curriculum and student achievement, evaluation research methodology, causal modeling, domain-referenced and classroom assessment. He has taught advanced graduate level courses in Psychometrics Theory, Quantitative Research Methods, and Multivariate Analysis Methods. He has co-authored numerous books on curriculum analysis and international comparative education and has published in journals including American Educational Research Journal, Science, Educational Researcher, Educational Studies in Mathematics, ZDM, and Perceptual and Motor Skills.</p> <hd id="AN0121905065-15">Acknowledgement</hd> <p>This work was supported by the Bill & Melinda Gates Foundation and the GE Foundation.</p> <hd id="AN0121905065-16">Appendix 1</hd> <p>Table 1A. Covariance matrix for path analysis related to figure 1.</p> <p></p> <p> <ephtml> <table><thead><tr valign="top"><td /><td>SAT</td><td>MCK</td><td>Benchmark scale</td><td>Competence</td></tr></thead><tbody><tr valign="top"><td>SAT</td><td>6012.3</td><td /><td /><td /></tr><tr valign="top"><td>MCK</td><td>1337.8</td><td>2078.1</td><td /><td /></tr><tr valign="top"><td>Benchmark scale</td><td>5.7</td><td>22.8</td><td>3.2</td><td /></tr><tr valign="top"><td>Competence</td><td>7.9</td><td>13.4</td><td>0.7</td><td>0.5</td></tr></tbody></table> </ephtml> </p> <ref id="AN0121905065-17"> <title> Notes </title> <blist> <bibl id="bib1" idref="ref42" type="bt">1</bibl> <bibtext> Oman did not study their primary teacher preparation programmes and Spain did not study their lower secondary programmes. Consequently, although 16 countries participated, only 15 countries are represented in either the primary or lower secondary programme analyses. In TEDS-M, a programme is a formally defined unit within each teacher preparation institution sampled according to the TEDS-M sampling frame.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref43" type="bt">2</bibl> <bibtext> In this section, 'programme' refers to an aggregate of all teacher preparation units with the same level (primary, lower secondary or mixed) at the same institution. This simplification was necessary in order to make valid international comparisons, given the great diversity in organizing teacher preparation across the 16 countries.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref23" type="bt">3</bibl> <bibtext> The use of the work 'Course' requires an inference for some countries given the variation in instructional organizations to make international comparisons feasible. The scope of the mathematics content topics listed in the questionnaire would typically define courses in most countries. See Schmidt, Cogan, et al. ([28]) and Schmidt and Cogan ([27]) for more details.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref29" type="bt">4</bibl> <bibtext> SAT and ACT scores were equated based on a concordance study by Dorans (1999).</bibtext> </blist> <blist> <bibl id="bib5" idref="ref22" type="bt">5</bibl> <bibtext> We found similar results using multilevel analysis: accounting for college entrance exam scores reduces the benchmark OTL coefficient, but its association with MCK remains statistically significant.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref2" type="bt">6</bibl> <bibtext> Category 1: whole number, fraction & decimals, percentages; Category 2: negative, rational, and real #s, proportionality/ratios, Category 3: geometry; Category 4: slope, functions, linear & non-linear equations.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref27" type="bt">7</bibl> <bibtext> The covariance matrix for this analysis is found in the Appendix 1.</bibtext> </blist> <blist> <bibl id="bib8" idref="ref52" type="bt">8</bibl> <bibtext> The absence of the relationship between SAT/ACT and course-taking provides further evidence that the relationship of OTL to test performance is not due to selection effects.</bibtext> </blist> <blist> <bibl id="bib9" idref="ref3" type="bt">9</bibl> <bibtext> Model fit passed threshold tests such as: chi-square, NFI, GFI and CI (<emph>χ</emph><sups>2</sups> = 0.2; <emph>p</emph> < 0.64). 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Houang</p> <p>Reported by Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib24" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib10" firstref="ref4"></nolink> <nolink nlid="nl3" bibid="bib16" firstref="ref5"></nolink> <nolink nlid="nl4" bibid="bib18" firstref="ref6"></nolink> <nolink nlid="nl5" bibid="bib14" firstref="ref8"></nolink> <nolink nlid="nl6" bibid="bib15" firstref="ref10"></nolink> <nolink nlid="nl7" bibid="bib11" firstref="ref11"></nolink> <nolink nlid="nl8" bibid="bib20" firstref="ref12"></nolink> <nolink nlid="nl9" bibid="bib22" firstref="ref14"></nolink> <nolink nlid="nl10" bibid="bib25" firstref="ref16"></nolink> <nolink nlid="nl11" bibid="bib26" firstref="ref17"></nolink> <nolink nlid="nl12" bibid="bib19" firstref="ref24"></nolink> <nolink nlid="nl13" bibid="bib33" firstref="ref25"></nolink> <nolink nlid="nl14" bibid="bib31" firstref="ref26"></nolink> <nolink nlid="nl15" bibid="bib37" firstref="ref28"></nolink> <nolink nlid="nl16" bibid="bib17" firstref="ref30"></nolink> <nolink nlid="nl17" bibid="bib36" firstref="ref32"></nolink> <nolink nlid="nl18" bibid="bib34" firstref="ref33"></nolink> <nolink nlid="nl19" bibid="bib29" firstref="ref35"></nolink> <nolink nlid="nl20" bibid="bib27" firstref="ref36"></nolink> <nolink nlid="nl21" bibid="bib13" firstref="ref39"></nolink> <nolink nlid="nl22" bibid="bib21" firstref="ref40"></nolink> <nolink nlid="nl23" bibid="bib35" firstref="ref50"></nolink> <nolink nlid="nl24" bibid="bib30" firstref="ref53"></nolink> <nolink nlid="nl25" bibid="bib28" firstref="ref54"></nolink> <nolink nlid="nl26" bibid="bib32" firstref="ref90"></nolink> <nolink nlid="nl27" bibid="bib23" firstref="ref97"></nolink>
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  Group: Ti
  Data: The Role of Subject-Matter Content in Teacher Preparation: An International Perspective for Mathematics
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– Name: Author
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  Data: <searchLink fieldCode="AR" term="%22Schmidt%2C+William+H%2E%22">Schmidt, William H.</searchLink><br /><searchLink fieldCode="AR" term="%22Burroughs%2C+Nathan+A%2E%22">Burroughs, Nathan A.</searchLink><br /><searchLink fieldCode="AR" term="%22Cogan%2C+Leland+S%2E%22">Cogan, Leland S.</searchLink><br /><searchLink fieldCode="AR" term="%22Houang%2C+Richard+T%2E%22">Houang, Richard T.</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22Journal+of+Curriculum+Studies%22"><i>Journal of Curriculum Studies</i></searchLink>. 2017 49(2):111-131.
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  Data: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
– Name: PeerReviewed
  Label: Peer Reviewed
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  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 21
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2017
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Elementary+Secondary+Education%22">Elementary Secondary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Higher+Education%22">Higher Education</searchLink><br /><searchLink fieldCode="EL" term="%22Postsecondary+Education%22">Postsecondary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Teacher+Education%22">Teacher Education</searchLink><br /><searchLink fieldCode="DE" term="%22International+Education%22">International Education</searchLink><br /><searchLink fieldCode="DE" term="%22Educational+Policy%22">Educational Policy</searchLink><br /><searchLink fieldCode="DE" term="%22Comparative+Analysis%22">Comparative Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Teacher+Education+Programs%22">Teacher Education Programs</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Teacher+Surveys%22">Teacher Surveys</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+Secondary+Education%22">Elementary Secondary Education</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Teachers%22">Mathematics Teachers</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+School+Teachers%22">Elementary School Teachers</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+School+Teachers%22">Secondary School Teachers</searchLink><br /><searchLink fieldCode="DE" term="%22Achievement+Tests%22">Achievement Tests</searchLink><br /><searchLink fieldCode="DE" term="%22International+Assessment%22">International Assessment</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Tests%22">Mathematics Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Achievement%22">Mathematics Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Science+Tests%22">Science Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Science+Achievement%22">Science Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Preservice+Teachers%22">Preservice Teachers</searchLink>
– Name: SubjectThesaurus
  Label: Assessment and Survey Identifiers
  Group: Su
  Data: <searchLink fieldCode="SU" term="%22Trends+in+International+Mathematics+and+Science+Study%22">Trends in International Mathematics and Science Study</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1080/00220272.2016.1153153
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0022-0272
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: International comparative studies in education provide a fresh perspective on K-12 education policy by enabling countries to learn from each other's approaches. The recently conducted Teacher Education and Development Study--Mathematics provides a worldwide lens by which to examine the role of subject-matter in the preparation of US teachers of mathematics for primary and lower secondary students. More specifically, a previous study looking at the international top-performing teacher preparation programmes identified a common set of learning experiences (topics/content) related to mathematics. This empirically derived international benchmark is used in this paper to examine the quality of the mathematics preparation of future US teachers in various university and college programmes.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: Ref
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  Data: 37
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  Data: 2017
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  Label: Accession Number
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  Data: EJ1132575
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        Value: 10.1080/00220272.2016.1153153
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      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 21
        StartPage: 111
    Subjects:
      – SubjectFull: Teacher Education
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      – SubjectFull: Educational Policy
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