**Approach**

*Conceptual framework*

The conceptual framework is adapted from that used in the international Teacher Education and Development Study in Mathematics (TEDS-M) (Tatto, Schwille, Senk, Ingvarson, Peck & Rowley, 2008). Although Australia contributed to the development of the instruments and the conceptual framework, Australian teacher education institutions did not participate in the study itself.

The report of the MT21 study (Schmidt et al, 2007), which was the precursor to the TEDS-M study indicated that teacher preparation courses appeared to have a significant impact on pre-service teachers, but further study was needed to establish the importance of the relative balance in courses between opportunities to learn mathematics content, mathematics education and general pedagogy. If change is to be achieved at the teacher education level, a sound evidence base is needed against which new courses and units in mathematics education can be planned.

CEMENT will establish for Australia the appropriate balance among mathematics content, mathematics pedagogy and general approaches to teaching. CEMENT will do this in a way that accommodates local differences within a nationally coherent approach, and addresses draft National Professional Standards for Teachers, hence providing an evidence-based approach to course development.

The conceptual framework for TEDS-M includes three domains: Characteristics of Future Teachers, Characteristics of Teacher Educators, and Characteristics of Teacher Education Programs (Tatto et al., 2008). These domains are interrelated yet act independently on outcomes of teacher education programs against a background of policy and practice unique to the place of education. The same domains are relevant in Australia. The broad policy framework in which Australian mathematics educators operate, however, is similar across the nation (i.e., National Standards for Teaching and the Australian National Curriculum) hence this aspect is not included in the model used. The conceptual model that will form the basis of this project is shown in Figure 1. The sections following the figure explain each aspect of the framework for this project.

*Figure 1*: Conceptual framework for improving the effectiveness of teacher preparation for mathematics teaching (adapted from Tatto et al., 2008, p. 15).

__1. Characteristics of future teachers__

*.*Background information such as previous professional experience, age, gender, location, qualifications, study experiences, attitudes to and beliefs about mathematics and mathematics learning (including about themselves as mathematics learners) are likely to impact on pre-service teachers in a variety of ways. Many primary pre-service teachers enter their university courses with very negative and even fearful attitudes to mathematics (Beswick, 2006; Brown, 2009), and with weak mathematical knowledge (Mays, 2005; Brown, 2009). Although these background characteristics cannot be changed, collecting these kinds of data will provide valuable information about the relative importance of student characteristics compared with lecturer and institution characteristics and enable institutions to tailor courses to the particular needs of their entering cohorts.

__2. Characteristics of teacher educators__

*.*Teachers in classrooms influence school students’ outcomes (e.g., Hill, Rowe, Holmes-Smith, & Russell, 1996), and the same is true of the influence of tertiary educators on tertiary students’ outcomes (Biggs, 2003). Hence considerations such as the backgrounds of teacher educators, recency of classroom experience, tenure of position, qualifications and so on should be considered in any model addressing pre-service teacher outcomes. Also relevant are lecturers’ beliefs about such things as mathematics, mathematics teaching and learning, and the needs and capacities of the pre-service teachers with whom they work.

__3. Characteristics of teacher education programmes__

*.*In addition to the nature of the mode of delivery and level (e.g., undergraduate or post-graduate entry) there are less easily identified organisational constraints which could also impact on outcomes such as: whether mathematics education units are stand-alone or combined with other learning areas; the number of mathematics education units experienced, who delivers these (Education or Mathematics lecturers), and when they are located in the course; the organisational arrangements within the institution such as the nature of the faculty or school and multi-campus arrangements as well as the growing emphasis on distance and online learning. Teachers tend to teach as they were taught (Ball, 1990), and they attach great importance to their experiences in schools (Beswick, 2006; Richardson, 1996). Hence, the place of the practicum in relation to mathematics education units, and the manner and extent to which these experiences are integrated into the university-based elements of programs will be a crucial element of this aspect of the conceptual framework.

__4. Pre-service teacher outcomes__

*.*Mays (2005) found that

*a surprising proportion of Australian pre-service primary teachers had difficulty with mathematical content at about grade 8 curriculum level.*At the secondary level, mathematical knowledge is generally assumed from the academic backgrounds of pre-service teachers. It is known, however, that an increasing number of “out-of-area” teachers are teaching in secondary mathematics classrooms with limited pre-service education in mathematics (Brown, 2009; Australian Council of Deans of Science, 2006; Human Capital Working Group, Council of Australian Governments, 2008). This project will provide tools to establish the mathematics content knowledge of pre-service teachers in courses from which many of the “out of area” teachers are recruited, such as science and physical education.

"… the subject is taught reasonably well at technical level but not at the excitement level, and it's probably because many of the teachers are being asked to teach outside their own areas of expertise."… the subject is taught reasonably well at technical level but not at the excitement level, and it's probably because many of the teachers are being asked to teach outside their own areas of expertise.

Gavin Brown, quoted in The Australian, 11 March 2010

It is recognised that teachers of mathematics require more than just content knowledge. Shulman’s (1987) seminal work identified seven knowledge-types considered important for teachers: (i) content knowledge; (ii) general pedagogical knowledge; (iii) curriculum knowledge; (iv) pedagogical content knowledge (PCK); (v) knowledge of learners and their characteristics; (vi) knowledge of education contexts; and (vii) knowledge of education ends, purposes, and values (p.8). In the intervening years, there has been considerable progress in identifying the nature of the knowledge that teachers of mathematics need. Ma (1999), for example, described “Profound Understanding of Fundamental Mathematics” (p. 22). Even and Tirosh (2002) emphasised the importance of teachers’ knowledge of their students’ mathematical learning. Hill, Rowan and Ball (2005) described Mathematical Knowledge for Teaching which they described as that “… mathematical knowledge used to carry out the

There are a number of existing tools for measuring pre-service teachers’ proficiencies with these complex knowledge types as well as their beliefs and confidence that are also known to impact on teaching. These include multiple choice questions (e.g., Hill, Rowan and Ball, 2005), short answer survey questions (e.g., Watson, Callingham and Donne, 2008); Likert scale items (e.g., Beswick, 2008) and combinations of these to create a “profile” (e.g., Beswick, Watson & Brown, 2006; Watson, Beswick & Brown, 2006; Watson, Beswick, Brown & Callingham, 2007; Watson, Beswick, Caney & Skalicky, 2006). These tools will provide the basis in CEMENT for the development of web-based surveys administered to pre-service teachers in their final years of training.

*work of teaching mathematics*” (p. 373, italics in the original) including providing examples, explaining concepts, correcting work and using a range of representations of mathematical ideas.There are a number of existing tools for measuring pre-service teachers’ proficiencies with these complex knowledge types as well as their beliefs and confidence that are also known to impact on teaching. These include multiple choice questions (e.g., Hill, Rowan and Ball, 2005), short answer survey questions (e.g., Watson, Callingham and Donne, 2008); Likert scale items (e.g., Beswick, 2008) and combinations of these to create a “profile” (e.g., Beswick, Watson & Brown, 2006; Watson, Beswick & Brown, 2006; Watson, Beswick, Brown & Callingham, 2007; Watson, Beswick, Caney & Skalicky, 2006). These tools will provide the basis in CEMENT for the development of web-based surveys administered to pre-service teachers in their final years of training.

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