Teaching mathematics for understanding: an analysis of lessons submitted by teachers seeking NBPTS certification
Volume 46 Number 2, June 2009; Pages 501–531
Research into maths education for the upper primary and middle years has consistently underlined the need for teachers to promote conceptual understanding rather than rote learning. One way to develop conceptual understanding is through mathematical content that is cognitively demanding. Topics should extend beyond number and operations to include algebra, geometry, measurement and data analysis, and their interconnections. Tasks should promote problem solving and reasoning. Conceptual understanding is also developed by certain teaching practices, which facilitate group work and discussion, call for hands-on activity or the use of ICT, and connect maths to other subjects or to the wider world. The current study examines one strategic point from which to investigate the take-up of teaching for conceptual understanding: portfolio submissions by upper primary and middle years teachers seeking certification as ‘highly accomplished’ by the USA's National Board for Professional Teaching Standards (NBPTS). The researchers examined portfolios by 32 teachers illustrating ways that they taught and assessed mathematical understanding, and including ‘extensive textual portrayals of instructional practice’ and artefacts such as students’ work samples and tests. The lesson materials were found to cover a wide range of topics, including data analysis and geometry, which earlier research literature reported as being often neglected. The entries also indicated strong use of technology, hands-on work, and contextualised tasks. However, only about half the entries called on students to undertake cognitively demanding tasks such as providing explanations or demonstrating mathematical reasoning. The findings suggest that efforts to reform maths teaching in the USA have had only partial success. They also suggest the need to communicate to maths teachers the value of tasks that impose high cognitive demands, as illustrated for example in a 1996 report on the QUASAR reform project and the TIMSS 1999 study. One promising means for doing so is to ask teachers to examine lesson plans that cover pedagogy designed to promote cognitively demanding student work. This process is known as ‘lesson study’ in Japan, and ‘didactical engineering’ in France.
Key Learning AreasMathematics
Subject HeadingsMathematics teaching
United States of America (USA)
Using inclusion, high demands and high expectations to resist the deficit syndrome: a study of eight Grade Three classes overachieving in reading
Volume 43 Number 1, 15 April 2009; Pages 43–49
Unusually high rates of literacy achievement by groups of disadvantaged, ethnically diverse primary students have been examined in a recent study in Sweden. The research was part of a larger study investigating influences on students’ reading development in 1092 Grade 3 classes in Stockholm. The current, follow-up study involved interviews with teachers of eight strongly performing classes in a multicultural area of the city. Several common themes emerged. The teachers stimulated students' interest in text in a range of ways. Some wrote letters to the children and helped with reading them. Others introduced toys or other props, jointly developing stories about them with each student, with the teacher writing down the stories as they developed. Some children were asked to transcribe wording of signs in public places, an activity that tended to draw approval from bystanders. Predictable daily routines helped the students feel secure, generating confidence to experiment. Linkages were made across subjects and grade levels, especially in terms of preschool activities. Given their diverse language levels, students received individualised treatment, including customised tasks and homework. Students were evaluated individually rather than by set norms. To move language learners toward equity with native Swedish-speaking peers, teachers sought deep collaboration with parents: meetings were frequent, although purely informational, with plain, clear messages to avoid cultural misunderstanding. Teachers urged parents to read to children over holiday breaks and ensure that children borrowed and read library books. Parents were taught reading strategies such as repetition, interaction with the learner, and ways to apply the mother tongue when learning Swedish. For the students, teachers combined cultural sensitivity with high demands, using authentic literature rather than basals or schoolbooks. The few classroom rules were enforced, and achieved quiet environments. Teachers, aware that they were often the sole source of standard language usage for the students, were strict in correcting written work, demanding rewrites as required. Students gave book talks to peers, after earlier modelling by the teacher or librarian. Drama stimulated engagement with and reflection about texts. Students were scaffolded through explicit instruction but were gradually prepared for Sweden’s wider, less directive educational culture.
Key Learning AreasEnglish
Volume 25 Number 2&3, April 2009; Pages 205–220
Students’ knowledge of words can be increased by explicitly teaching them a range of strategies for improving vocabulary. These strategies take students beyond the memorisation of dictionary definitions and the incidental knowledge acquired during reading to a deeper concept of what the words mean. They should be applied across grade levels and subject areas, and should occur before, during and after the reading of texts. One strategy is to teach key morphemes, the smallest units of a word that carry meaning, such as alt (high) or micro (small). Students can be asked to brainstorm words containing selected morphemes and compile them into pre-reading lists to be shared with peers. Each content area tends to have its own key morphemes. Common prefixes and suffixes can be taught in a similar way. Another pre-reading strategy is knowledge rating, where students view keywords that will appear in a forthcoming reading, categorise them according to how confident they are about their meanings, and then discuss them with other students. Graphic organisers can be used to relate concepts. They should have routine, predictable structures to assist struggling students. They must also be conceptually clear, and adapted to the needs of particular students and lessons. Semantic feature analysis calls on students to prepare a chart listing related concepts and noting their similarities and differences. Using a vocabulary self-awareness chart, students list keywords and provide their own definitions and examples; students may add to the list of words supplied by the teacher. Students can also create vocabulary cards: one side of the card contains a word, its definition and a picture by the student illustrating the definition; the other side contains an explanation of how the picture captures the definition. Each of these strategies deepens students’ understanding of words by calling upon prior knowledge and relating new terms and concepts. They may be especially valuable in teaching content area vocabulary, which contains words that rarely appear beyond the given subject area, or have different meanings in other contexts.
Subject HeadingsTeaching and learning
Volume 43 Number 1, 2009; Pages 32–49
The teaching of Shakespeare in Britain has been heavily influenced by 'Active Shakespeare' approaches, which use dramatic techniques to engage students in a way that is perceived by some to 'outweigh any negative effects' of SATs tests. However, although teachers attempt to integrate these methods into their teaching of Shakespeare, teaching tends ultimately to remain focused on test outcomes. In order to determine the influence of the tests on ‘Active Shakespeare’ pedagogy, the author observed a Year 9 English class studying Macbeth. In the first lesson, the text was introduced as a drama with which students could engage. Improvised role-play around set themes was encouraged, and students also clapped out the rhythm of the witches’ dialogue. However, these approaches were designed to lead students toward particular, traditional interpretations of the play rather than to generate their own understandings. Midway through this lesson, the students were directed to read and transcribe an exhaustive plot summary of the play, which was explained as being necessary to test preparation: the study of Macbeth was subsequently framed in terms of the examinations. Another lesson comprised setting aside the 'drama' for explicit instruction in appropriate examination writing techniques; students were then required to write lists of quotations and complete a worksheet on key scenes where questions and teacher-provided answers were presented in a way that mimicked the test format. While the teacher did encourage debate and whole-class discussion of some key themes of the play, this more open-ended approach was cut short in order to direct students back to test-relevant tasks. The examinations shaped class content and pedagogy to such an extent that students only read as far as Act 3, scene 4, the last of the examinable scenes; two-thirds of students were unsure how Macbeth concluded. However, they felt they had been sufficiently prepared for the exam, which required only superficial knowledge of the play. Students seemed unaware of the reasons for studying Macbeth: when asked what the examiners wanted from examination responses, students highlighted a particular format rather than evidence of textual understanding and considered arguments. While students enjoyed ‘Active Shakespeare’ elements, its efficacy, and students' engagement, was limited by the intrusion of the examinations into the classroom discourse. (Editor's note: the SATs test for Year 9 is due to be abolished in July 2009.)
Key Learning AreasEnglish
Subject HeadingsSecondary education
Autumn 2009; Pages 14–15
By promoting social inclusion, Australian schools can improve disadvantaged students’ opportunities to succeed in learning. The Australian Government’s new social inclusion policy agenda aims to redress the inequality experienced by marginalised learners. While children’s school readiness is influenced by their home environment and parents’ education levels, some authorities have criticised schools for being ineffective in addressing disadvantage. Current research indicates that schools and teachers can work to reduce the achievement gap, even in contexts where large proportions of learners are from disadvantaged backgrounds. High performing teachers can have considerable positive effects on student achievement; conversely, students placed with low performing teachers over several years are likely to suffer a long-term impact on their academic performance. Educational systems can improve teaching by recruiting high quality teachers, by providing sufficient professional development and resources, and implementing systems and support to improve all students’ learning. Increased remuneration, improved recruitment procedures, and national accreditation systems would improve teacher efficacy. Whole-school reform involving collaborative, collegial relationships among staff and ongoing, purposeful assessment of learning achievement can help identify and support at-risk students. Socially inclusive policies should be adopted with disadvantaged students in mind, and closer ties with parents and community should be promoted. Schools should work with other social agencies to improve families’ access to and integration of services; parents should be encouraged to play an active role in their children’s learning. Social inclusion policies have implications for schools’ accountability, requiring them to address and close the achievement gap.
Subject HeadingsTeaching profession
The Scientists in Schools project
Volume 55 Number 1, March 2009; Pages 35–38
The Scientists in Schools program establishes partnerships between scientists and science teachers to promote scientific literacy in the community. It aims to connect science teachers and students to ‘real world’ science; provide professional development for teachers and mentoring for students; broaden students’ awareness of career options; promote the sharing of ideas and practices; motivate teachers and students; and deepen scientists’ connections to the community. It is funded by the Australian Government Department of Education, Employment and Workplace Relations and has been administered by CSIRO. The program has set up hundreds of partnerships between individual scientists and science teachers, covering a wide range of grade levels, subject areas, regions and types of schools. Almost half involve secondary teachers. The program was piloted in 2007 and was continued following a positive evaluation, which identified as key benefits the opportunities for professional networking, the sharing of resources, and the rejuvenating effect on participants. Challenges confronted by the project have included ‘getting scientists and teachers informed’, obtaining participants, and organising the partnerships. There were a number of challenges in establishing or activating the partnerships, including the need to fit partnership work into teachers' existing programs, which are often planned up to a year ahead. The article reports on three case studies. A long-established partnership in north Queensland, based around biotechnology, saw the participating scientist extend professional development from his teacher partner to other school staff and to staff at nearby schools. More up-to-date biotechnology material was added to the Year 11 and then Year 10 curricula, and resources of the regional university became more accessible to teachers. Students became more aware of options for careers or higher education within their region, reducing the tendency to move to capital cities. The other case studies concerned a long-distance partnership between a Brisbane-based scientist and a principal at a remote school, and a new partnership in South Australia involving a teacher working with the CREST program and a scientist working in the defence industry.
Key Learning AreasScience
Subject HeadingsScience teaching
School and community
Volume 60 Number 2, March 2009; Pages 184–199
While studies on professional development programs and pre-service teacher learning abound, there is far less research available on in-service teachers’ self-directed learning. The introduction of the ‘public understanding of science’ (PUSc) curriculum in the Netherlands meant that secondary science teachers had to adapt to context-based, social constructivist pedagogies; as a result, many undertook self-directed learning to familiarise themselves with new content and teaching styles. Using a narrative approach, the authors examined eight experienced secondary science teachers’ self-initiated learning in response to the syllabus. Teachers described the types of learning undertaken, and their perceived developments in their content knowledge and learning trajectories since the implementation of the PUSc. The combinations of learning activities undertaken to develop teaching competencies tended to differ from those used for developing content knowledge, and teachers’ learning varied in type, frequency and numbers of activities undertaken. From this, teachers’ development could be grouped into styles of learning that were ‘revolutionary’: initially intense, largely solitary learning that gradually dropped off; or ‘evolutionary’: ongoing, collegial and maintained learning. These styles corresponded with learners’ evaluation of their competencies at the beginning of the PUSc implementation: teachers who felt their competencies were insufficient tended to undergo urgent, ‘revolutionary’ learning until they reached good or sufficient competence, whereas teachers whose competences were initially sufficient developed only slightly over time. However, these teachers directed their learning to refining and deepening their teaching methods to suit students of different levels and to help students actively construct knowledge, whereas the ‘revolutionary’ teachers sought to expand their repertoire of instructional methods and tools to make the abstract concrete for students. These learning styles reflect meaning-based and application-based teaching and learning styles respectively, and have implications for teacher professional development. ‘Revolutionary’ style learners could benefit from the provision of individual, electronic tools, whereas ‘evolutionary’ style learners would be better engaged by joining networks or groups. Teachers whose approaches are application-based could, with support, gradually shift to meaning-based approaches that deepen their pedagogical approaches.
Key Learning AreasScience
Subject HeadingsProfessional development
Volume 79 Number 1, Spring 2009; Pages 39–68
The skills involved in scientific observation are more complex than they appear, and young children attempting to conduct such observation require appropriate disciplinary context and support in order to do so successfully. Where professional biologists are expert observers whose knowledge and experience allows them to analyse and categorise items into taxonomies by comparing and contrasting specific, meaningful features, children’s lack of theoretical context and knowledge of scientific practice results in ineffective, ‘everyday’ observations. Biologists know not only to ask appropriate ‘what’ questions, but also to identify causation through ‘how’ and ‘why’ questions, and document their observations and data using formal, discipline-standard inscriptions. Children, although acute observers, have difficulty in noticing complex systems and their component parts, and in making inferences and connecting observation to theory, and they tend not to record their findings in a meaningful fashion. Their ability to observe meaningful differences and relationships is affected by the absence of sophisticated discipline-specific knowledge; their predictive and evaluative skills are also hampered by a tendency to defer to expectation rather than evidence. However, children can be positioned to observe phenomena in a more scientific manner by learning in contexts that reflect standard disciplinary practice and that support them in connecting their observations with theory. Using a science-as-practice model, children can begin to develop as scientific observers by making purposeful observations about specific phenomena, and through support and scaffolding such as a teacher’s guided question-asking, can start to engage in investigation, argument, and explanation, as well as learning to use scientific tools and representations. Children’s positive dispositions toward science can be supported by facilitating their access to those phenomena that interest them, and by providing ‘time to look’ and question. The article includes an observation framework.
Key Learning AreasScience
Subject HeadingsScience teaching
Direct instruction of comprehension: instructional examples from intervention research on listening and reading comprehension
Volume 25 Number 2, April 2009; Pages 221–256
Direct instruction can help learners of diverse ages and abilities to construct meaning from texts. The authors examine two intervention programs that employ direct instruction principles: the Story Read Aloud Project (SRA), designed to improve primary students’ listening, summarising, and intertextual connection skills; and the Embedded Story Structure Routine (ESS), designed to help secondary students develop skills in self-questioning, story structure analysis, and summarising. Five instructional principles are evident in both programs. The first principle is the use of conspicuous strategies. It involves unambiguous, explicit teaching of important comprehension strategies through explanation and modelling strategies. For example, a detailed explanation of the elements of a non-fiction book, such as headings and diagrams, can assist comprehension. The second principle, mediated scaffolding, refers to the support structures provided for students’ learning. For example, ESS students were given graphic organisers to prompt self-questioning and story-structure analysis using story maps and guided questions: the support offered by these materials could be varied according to learners’ skills. The third principle, strategic integration, uses systematic and explicit instruction to teach students to generalise and relate information, concepts and strategies, and promotes the development of complex conceptual and problem-solving skills. SRA students, for example, received explicit instruction in applying information learnt from a non-fiction text to a narrative text on the same topic: previously learnt information was used to position students to predict what might happen in the narrative text, a strategy requiring knowledge transfer. The principle of priming background knowledge involves activating students’ existing knowledge to help them apply new ideas to known concepts, deepening understanding. ESS students, for example, brainstormed story structure components, then were instructed on how to discriminate between main and supporting ideas. Finally, through judicious review, learners are presented with opportunities to apply, reinforce and develop skills and knowledge. Direct instruction programs such as the SRA and ESS can assist with the development of comprehension skills for students of different ages, abilities, and stages of reading development, and promote the systematic development of more sophisticated strategies.
Key Learning AreasEnglish
Subject HeadingsSecondary education
English language teaching
Volume 23 Number 2, 2009; Pages 57–62
Extended schools provide activities and services to meet the needs of students, parents, and the wider community. Their numbers are increasing in Great Britain, but their value has been questioned in terms of their efficacy, purpose, and the possibility that they will reinforce the application of a ‘deficit model’ to disadvantaged communities. A year-long research project used questionnaires, case studies, and interviews to examine how staff and stakeholders perceived the success of two secondary extended schools. Both schools were situated in low socio-economic contexts, and aimed to become a community ‘hub’ for services and activities, and to facilitate agency ties to assist at-risk students and families. Staff in middle and senior leadership positions were able to articulate the purpose and scope of the program and define procedures and staff roles; other teaching staff, who had more limited involvement with external stakeholders, were less certain. Non-teaching staff demonstrated very little awareness of the program’s extent and purpose, indicating that information and practices could be more effectively communicated. However, professionals from agencies such as family services and the police force confidently linked their roles with others’, and spoke positively of developing key relationships with teachers and feeling part of a cohesive, communicative team. Family welfare workers were perceived by other participants as an essential component of the program’s success, and provided a critical liaison point between school and other agency staff and families, as well as facilitating interventions. The schools, with new structural and staffing flexibility, were found to be in an improved position to respond to students’ and families’ difficulties. Their direct contact with family workers helped mediate problems and improved support channels and agencies’ response times. The school could also be used as a neutral ‘hub’ for meetings, which was important to parents concerned about the social stigma of attending social service offices. However, extended schools programs must be well-integrated to ensure that additional services are not simply seen as add-on features; additionally, all school and external agency staff need to be made aware of the programs' aims and procedures.
Subject HeadingsSocial welfare
School and community
Volume 45 Number 2, April 2009; Pages 217–247
While schools as large and complex organisations must employ some aspects of a bureaucratic structure, the over-emphasis of these elements can undermine teachers' professionalism. Top-down ‘machine bureaucracy’ approaches, which comprise centralised control and standardised processes point to implicit distrust of teaching staff, and can result in staff feeling alienated, reducing their loyalty and commitment to their work and the school community. These approaches also hinder the school’s ability to adapt to changing circumstances. An appropriate leadership orientation for a school is that of the professional learning community, where teaching staff work collectively toward students’ education, engage in collaborative teaching practices, and take part in reflective dialogue to facilitate development. Principals with a professional orientation create flexible, enabling structures to allow teachers to work toward their teaching goals. Providing teachers with greater autonomy and the ability to exercise their professional judgement fosters both teacher professionalism and trust. A survey of 2355 teachers from 80 middle schools in the USA indicated that teachers demonstrate greater professionalism in contexts where trust is evident throughout the school, and where school leaders demonstrate a professional rather than bureaucratic orientation. Teachers in administratively flexible schools perceived greater professionalism, respect and commitment among other staff members; conversely, those in rigid, bureaucratically oriented schools perceived lower levels of professionalism and a lower likelihood of other staff performing beyond minimum expectations. Schools’ cultures of trust were related to leaders’ professional orientation: teachers expressed greater trust toward school principals when they were treated as competent professionals within flexible structures. Importantly, high levels of trust in leaders were also associated with increased trust in other faculty members. In order to cultivate professionalism and trust among teaching staff, leaders should adopt professional orientations, aiming to support teachers as professionals, and to develop structures that facilitate teacher autonomy and decision making.
Subject HeadingsSchool principals
The influence of the Creative Learning Assessment (CLA) on children’s learning and teachers’ teaching
Volume 43 Number 1, April 2009; Pages 3–10
Primary students’ creative learning and teachers’ pedagogical approaches can be promoted by the Creative Learning Assessment (CLA), a framework designed to qualitatively assess the impact of creative arts subjects on overall learning and to support the integration of the arts into the wider curriculum. The main elements of the CLA were an observation framework based on a variously themed learning continuum, a student portfolio, and a five-point progress scale. Observations, interviews and meetings were used to draw trends from a one-year pilot study. The framework was perceived as flexible and supportive in helping to monitor students’ learning and to understand individual learning approaches: one teacher reported that her teaching changed to allow a greater variety of outcomes and incorporation of children’s preferred approaches. The learning continuum themes required teachers to monitor students’ confidence and enjoyment, as well as collaboration and communication: one teacher noticed that a quiet, detached student began to display greater sensitivity and empathy toward others as he engaged with creative projects, and in the workshop atmosphere teased out ideas and approaches with other students. Teachers also monitored students’ creativity, which allowed them to identify strengths that might have been overlooked in academic contexts. One student who struggled with reading and writing was able to communicate complex and coherent ideas through dramatic expression. Students’ skills and subject knowledge developed through application and expert modelling: they became confident users of subject-relevant vocabulary and approaches, were able to reflect with increasing sophistication on their work and the work of others, and became more open to constructive criticism. Teachers used student portfolios and the CLA scale to observe progress and determine subsequent approaches to improve learning: one teacher reported that the scale increased her awareness of time allocation and pedagogical direction. Teacher meetings were used to moderate teachers’ assessment of projects, an activity that helped validate their professional judgements. The CLA had positive effects on both pedagogy and learning, promoting collaborative, reflective approaches and recognition of non-academic skills and abilities; teachers found the framework manageable and effective.
Key Learning AreasThe Arts
Subject HeadingsTeaching and learning
Arts in education
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