Quality Teaching

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Quality Teaching
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• The aim of this workshop is to describe the key
  characteristics of expert teachers of numeracy.
  Naturally most of these characteristics will be
  transferable to teaching other areas of the
  curriculum.
• During the course of the workshop you will be
  presented with suggestions on how to facilitate
  the ideas with other teachers. This will enable
  you to construct your own workshop or staff
  meeting programme.

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How important is good teaching?

• The first question to consider is, How much
  difference to student achievement do teachers
  actually make?

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• In the next frame there is a pie chart from
  research by Professor John Hattie, from the
  University of Auckland. He quantifies the overall
  effect on student achievement of these factors
• Students (Personal characteristics like
  intelligence, co-operation, effort)
• Home (Expectations for success, intellectual
  support, appropriate physical and emotional care)
• Teachers (Types of actions taken, expectations,
  effort)
• Peers (Expectations, support for each others
  efforts)
• Schools (Organisational structure, quality of
  resources)

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Factors contributing to achievement

• Match the five sectors of the achievement pie
  with the factors below
• Students
• Home
• Teachers
• Peers
• Schools

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How big is the impact of teaching?

• Hatties analysis of thousands of research
  studies show this combined effect

Teachers
Students
Schools
Home
Peers
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• Adrienne Alton-Lee, from the Ministry of
  Education, suggests that the proportion of
  student achievement due to teaching effect varies
  between 15 and 60 depending on the context.
  Hatties is a combined figure.
• Under what circumstances do you think the effect
  due to teaching would be high?

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Is the effect uniform?

• The effect due to teaching is most significant in
  situations where the learning is least supported
  by the students everyday environment. An obvious
  case is learning specialised subjects at senior
  secondary and tertiary level, e.g. calculus or
  Japanese as a second language.
• The teaching effect is also very high for younger
  students whose home environment least supports
  them educationally. Almost uniformly there is a
  connection between socio-economic status of
  caregivers and the achievement of students.

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• To summarise Teachers make a significant
  difference to student learning and they do so
  most in situations where the students are needy.

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Characteristics of quality teachers?

• So what is it that quality teachers do that makes
  the difference?
• A good place to start is to ask your colleagues
  the following question
• You observe a teacher in action. The lesson is
  sensational, the best you have seen in your
  career. There is so much going on that it is hard
  to describe why the lesson is so good. You decide
  to focus on the teachers behaviour.
• What characteristics does this teacher have that
  make her an expert?
• Write down a few characteristics that you think
  an expert teacher has.

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• Good management is a necessary but not sufficient
  condition
• Often responses to the previous question are
  about classroom management. For example, the
  teacher
• Is well organised
• Ensures that students listen to instructions
• Provides appropriate work
• Develops orderly routines

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• These logistical characteristics are important
  but they are not enough. Hattie distinguishes
  experienced teachers, that is those who can
  manage classrooms well, from expert teachers,
  that is those who optimise their students
  learning. To be an expert teacher you must have
  much more!

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Clusters of quality practice

• The characteristics of expert teachers of
  numeracy can be grouped in these clusters
• 1. Relationships with students
• 2. Planning and assessment
• 3. Problem focus
• 4. Connections
• 5. Instructional responsiveness
• 6. Student empowerment
• 7. Equity
• This workshop will discuss each cluster.

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Relationships with students

• Russell Bishop, from The University of Waikato,
  lead a project called Kotahitanga aimed at
  improving the achievement of Maori student. A key
  finding of the project was that students achieved
  best in classrooms where the teacher related well
  to them as individuals and valued their cultural
  identity.

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• Bishops work also focused on teachers
  attribution for the achievement of Maori
  students. Effective teachers had high but
  realistic expectations for all their students and
  conveyed their expectations to students. These
  teachers believed that what they did made a
  difference. Ineffective teachers attributed lack
  of achievement to students background or
  constraints imposed by the school system.

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Planning and assessment

• A critical part of effective teaching is mapping
  out anticipated learning trajectories for
  students to learn a particular idea, and
  providing sufficient appropriate experiences to
  support this learning. Quality teachers choose
  activities for a learning purpose and are
  transparent with their students about this
  purpose.

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• Expert teachers apply a dynamic relationship
  between their assessment of students learning
  and their planning of the next learning step.
  They employ a variety of assessment techniques,
  particularly their own observations, and regard
  any particular assessment as formative, a
  landmark on a journey rather than an endpoint in
  itself. Planning is responsive to assessment and
  vice versa.

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Problem Focus

• Studies into student achievement in mathematics
  across countries have compared the practice of
  teachers in nations that produce high
  achievement. The most astounding result has been
  that lessons in particular countries have
  considerable similarity. Each country appears to
  have a prevalent teaching culture.

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• The teaching cultures of the high performing
  nations are similar only in the high proportion
  of class time thats students are engaged in
  problem solving as opposed to listening to
  teacher explanations or practicing.

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• In these countries, such as Korea, The
  Netherlands, Slovakia, Japan, and Singapore, the
  problems presented are carefully structured and
  sequenced. Students work co-operatively or
  individually on the problems, often encountering
  difficulty, before the processing of solutions
  collectively with the support of the teacher.

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Connections

• Expert teachers have strong pedagogical-content
  knowledge (PCK). PCK is a term used by Lee
  Schulman to describe what a teacher needs to know
  in order to teach a topic effectively. In
  numeracy, this involves knowing the mathematical
  idea, how it connects to other mathematical
  ideas, what contexts and representations could be
  used to present it and the cognitive obstacles
  and misconceptions students commonly encounter in
  learning it.

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• Mike Askew and Margaret Brown, from Kings
  College in London, studied over 700 numeracy
  lessons and concluded that the expert teachers
  were those who were connectivist. These
  teachers used their strong PCK to help their
  students make connections for themselves. Later
  in the workshop there are suggestions for
  developing teachers PCK through a workshop.

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Instructional responsiveness

• Responsiveness implies that teachers are prepared
  to alter the course of a lesson or sequence of
  lessons based on the needs of students. To do so
  expert teachers actively listen to their students
  and mentally process the responses. To do so
  expert teachers create environments where
  students feel confident to take risks, pose
  conjectures and explain their ideas to others.

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• Active listening to the ideas of students and
  acting from these ideas is a critical aspect of
  responsiveness. Paul Cobb described this as the
  creation of socio-mathematical norms. While
  expert teachers value all ideas from their
  students, they also see their role as the
  development of mathematical power. Do not treat
  all ideas as equal because they are not. A
  critical role of teachers is to help students
  evaluate the relative strengths of ideas and
  explanations.

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Student Empowerment

• Students perception of responsibility for their
  own learning links strongly to high achievement.
  Expert teachers develop independence through
  sharing learning outcomes with their students,
  requiring students to make their own
  instructional decisions, providing regular
  personalized feedback and encouraging
  meta-cognition (thinking about thinking).

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• Expert teachers also provoke high order thinking,
  such as analysing, justifying and synthesising
  through the questions they ask.

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Equity

• Success for all students involves catering for
  diverse needs. Quality teaching involves careful
  allocation of resources, particularly time, to
  maximise learning opportunities. Expert teachers
  provide additional resources for students with
  high needs.

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• Students learn best in situations where they
  either ask questions of others or respond to the
  questions of others. Expert teachers employ a
  variety of instructional groupings so students
  can learn from each other.

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Improving classroom teaching

• A growing body of research into change management
  in schools is highlighting the importance of
  de-privatising classrooms. Situations where
  teachers observe colleagues teaching, provide
  feedback, and are observed by others has shown
  considerable potential to enhance classroom
  practice.

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• In Victoria, Australia, Hillary Hollingsworth has
  used the analysis of videoed lesson footage as a
  key strategy for getting teachers to reflect on
  their practice. The dimensions of quality
  teaching discussed above provide an important
  observational framework for such peer
  observation.

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An observational framework

• The first step in the process is for the teacher
  observed to nominate one or two clusters that he
  or she feels are an area of focus. This happens
  before the observation.

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• The observer then notes events that occur during
  a lesson segment against the appropriate habit/s.
  It is important that the notes are factual
  statements about what occurred rather than
  opinions or interpretations.
• Use video to capture the lesson segment so that
  the noted events can be replayed several times.

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Follow-up Discussions

• The post-observation discussion focuses on the
  teacher examining the events, discussing the
  rationale for the instructional decisions made,
  and considering the future implications of the
  observations.

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• Experience has show that observers need practice
  in avoiding judgmental comments and actively
  listening to the explanations of the observed
  teacher. It is vital that clear goals are set
  from the discussion and both parties follow up
  these goals through more observations.

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Workshop Ideas

• A Peer observation
• Video part of a mathematics lesson. Make sure
  that the tape is no longer than 10 minutes.
• Nominate a cluster that you want them to observe.
• Play the video as they record comments.
• Role-play an observer conducting the follow-up
  discussion using the video to recall events.
• Challenge the teachers to nominate a peer with
  whom they will have a mutual observation
  arrangement. Get them to timetable when the
  observations and discussions will occur.
• Schedule a staff or syndicate meeting to review
  the success of the observations.

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Answer these questions together

• B Pedagogical-Content Knowledge for Fractions
• To make teachers aware of the dimensions of
  pedagogical-content knowledge
• What do the parts of a fraction symbol, like ,
  mean?
• The denominator (bottom number) means?
• The numerator (top number) means?
• The vinculum (line) means?
• How might a fraction like relate to other
  mathematical ideas like
• Decimals and percentages, i.e. 0. and 66.
• Ratios, i.e. 21
• Angles (turns), i.e. 120
• Measurements, i.e. metres 666 millimetres
• Division, i.e. 23

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• What contexts from the everyday world of students
  can we use to teach fractions?
• a. What representations (equipment,
  diagrams, words, symbols) can we use in
  teaching fractions?
• b. What advantages/disadvantages do these
  representations have?
• What misconceptions do students develop about
  fractions, usually by over-generalising what
  happens with whole numbers?

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Readings

• The following screens list some readings that you
  may find useful related to the topic of quality
  teaching.

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• Alton-Lee, A. (2003). Quality teaching for
  diverse students in schooling best evidence
  synthesis. Ministry of EducationWellington.
• Hattie, J (2002). What are the attributes of
  excellent teachers? In New Zealand Council for
  Educational Research Annual Conference.
  NZCERWellington
• Bishop, R., Berryman, M., Richardson, C.,
  Tiakiwai, S. (2003). KotahitangaThe experiences
  of year 9 and 10 Maori students in mainstream
  classes. WellingtonMinistry of Education.
• Stigler, J. Hiebert, J. (1997) Understanding
  and Improving Classroom Mathematics Instruction
  An Overview of the TIMSS Video Study, In Raising
  Australian Standards in Mathematics and Science
  Insights from TIMSS, ACERMelbourne
• Clarke, D., Hoon, S.L. (2005) Studying the
  Responsibility for the Generation of Knowledge in
  Mathematics Classrooms in Hong Kong, Melbourne,
  San Diego and Shanghai, In Chick, H. Vincent,
  J. (Eds.), Proceedings of the 29th Conference of
  the International Group for the Psychology of
  Mathematics Education July 10-15, 2005, PME
  Melbourne

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• Askew, M., Brown, M., Rhodes, V., William, D.
  Johnson, D. (1997). Effective Teachers of
  Numeracy, Kings College, University of London
  London.
• Shulman, L. S. (1987). Knowledge and Teaching
  Foundations of the New Reform. Harvard
  Educational Review, 57(1), 1-22.
• Brophy, J., Good, T. (1986). Teacher behaviour
  and student achievement. In M.C. Wittrock (Ed.),
  handbook of research on teaching, 3rd ed. (pp.
  328-375). New York MacMillan.
• Slavin, R.E. (1996). Research on co-operative
  learning and achievement What we know and what
  we need to know. Contemporary Educational
  Psychology, 21, 43-69.