Considered Student Feedback Informs Practice

1
Considered Student Feedback Informs Practice

• Gaye Williams
• Deakin University, Burwood
• gaye.williams_at_deakin.edu.au

2
Session Overview

• Context
• Unit Goals, Implementation
• The Issue
• SETU evidence
• Solution process
• Theoretical lens framing teaching practice.
• Problems evident from student feedback.
• Reflections through theoretical lens.
• Constructive student feedback to help solve
  problem in future years.
• Linking feedback to theoretical frame to
  identify way forward.
• Other student feedback evidencing success.
• Conclusions

3
Context (General)

• Preparing effective secondary maths teachers is
  not easy.
• Teaching rules and procedures without meaning is
  ineffective (Skemp, 1976).
• We need to provide opportunities for school
  students to learn maths in meaningful ways.
• We need to overcome tendencies for
  student-teachers to revert to how they were
  taught, and/or succumb to ineffective maths
  teaching practices still prevalent in many
  schools.

4
Issues With Traditional Maths Teaching

• School maths experience often negative
• Negative maths experiences shared with next
  generation
• Ill-prepared for unfamiliar problems
• Low mathematical literacy

5
Inhibitors to Change

• Teachers who want to keep teaching how rules
  work without why (Skemp, 1976)
• Educators, parents, and students who perceive
  exploring as play not maths (Williams, 2006)
• Students who pressure to know rules without why
  they work (Anthony, 1996)
• Student awareness of disagreement between school
  and parents on how to learn maths (Whitmore,
  1980)

6
What We Know

• Exploring develops understandings (Schoenfeld,
  1985)
• Interacting supports exploring (Cobb, Wood,
  Yackel, Mc Neal, 1992)
• Accessible tasks (with twists) needing
  thinking just beyond present understandings
  engage students in exploring (Williams, 2002)

7
Challenges for Teacher Education

• Develop realisation that maths teaching must
  change
• Build understandings of why rule works
• Raise awareness of difficulties students
  encounter

8
We Need to Build Know-How

• In
• Task selection / design
• Promoting collaborative interactions
• Encouraging risk taking
• Monitoring student thinking
• Questioning to elicit deep thinking

9
Implementation to Achieve this

• Student teachers work collaboratively with tasks
  found to work for students in schools. They
• Consider student pathways
• Experience frustration when cant recall rules
• Realise more about why rules work
• Identify maths concepts students may build
• Brainstorm questions to extend student thinking
• Feel pleasure on attaining insight and want
  their students to experience this too

10
Research Informing Teaching Practice Flow

• Flow Situations Working just above present
  conceptual level on a self-set challenge almost
  out of reach (Csikszentmihalyi, 1992)
• Spontaneous Intellectual Challenge
• 
  A
  B Concepts and Skills

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Context (Specific)

• At Deakin, secondary maths education units
  include two different in-class cohorts
• a) Undergraduate students 2nd or 3rd year of
  4-year course,
• b) Postgraduates undertaking teacher training
  post-initial-degree
• c) Off Campus teachers converting to maths
  teachers.
• The students undertake the Junior Secondary Unit
  ESM424 in S1, and the Senior Secondary Unit
  ESM425 in S2.

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Identified Issue

• Senior Secondary ESM425, Semester 2 2005 marked
  differences between the proportion of students in
  each cohort with SETU showing very high levels of
  unit satisfaction.
• Junior Secondary Mathematics Curriculum Unit,
  Semester 1 2005 SETU differences not nearly as
  marked

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2005 SETU Alerting Me to Issue

• 2005 (Majority Non-Post-Grad)
• SETU Non-Post-Grad 1 above 4
• SETU Post-Grad 56 above 4
• Previous Observations Fitting With This
• Some 2nd Year students
• Concerned assessed same way as Post Grads
• Perceived workload too great
• Considered unable to consider ways students
  think

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Initial Thoughts About Problem

• My Reflections
• Was the mathematical background of the
  undergraduate cohort much lower in general?
• Did this make the mathematical challenge too
  great?
• Would it be worth while trying to have this unit
  covered in Year 3 when they had covered more
  university maths?

15
Student Feedback Helped Solve the Problem

• Amongst the many comments students made
  identifying what worked and what might need
  revising, two student comments helped me find the
  way forward.
• These were Peter (pseudonym), and Liz (real
  name), two 2005 Post Grad students.

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Peter 2005 Identifies Need For More Pressure to
Read

• I hate to say it but with unit readings I know I
  won't do it unless I'm forced. Perhaps lessons
  where you have to do a presentation on readings,
  I don't know, might work well.
• They do it really well in a subject Curriculum
  assessment an reporting.

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My Initial Reflections

• I do not want to make readings lockstep.
• I want students to select their own foci and read
  the readings that relate to their focus at a
  particular time.
• Clearly, my explicit comments that assignments
  were better for those who had done readings did
  not have sufficient effect.

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Lizs (2005) Insights

• Assignment 1 hard to start
• Possibly use your group work for this
• I think it is because there are two lots of
  challenges (teaching and mathematical)

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My Insight

• Of course, that is why they find the challenge
  too great
• With pedagogical and mathematical challenges just
  out of reach, combined the challenge is too great
• By reducing both the pedagogical and mathematical
  challenges a little, the overall challenge could
  be brought within reach

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Research Informing Teaching Practice Flow

• Flow Situations Working just above present
  conceptual level on a self-set challenge almost
  out of reach (Csikszentmihalyi, 1992)
• Spontaneous Intellectual Challenge
• Intellectual pedagogical and
• Mathematical challenges
• 
  A
  B Concepts and Skills
• 
  
  (mathematical and pedagogical)

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Reducing The Challenges

• Pedagogical
• Increasing student literature reading would
  increase pedagogical knowledge.
• Mathematical
• Increase mathematical knowledge with a greater
  focus on multiple choice questions and the
  reasons for the particular distractors

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Increased Literature Reading

• Add Literature Discussion Space to DSO.
• Require postings of 200 words on three papers
  read, and two postings responding to the postings
  of others.
• 200 word report to focus on what was meaningful
  to the student and their reflections on how it
  will inform their future teaching.
• The pressure was that these were hurdle tasks
  required to complete the unit.

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DSO Literature Discussion

• This initiative was highly successful. Postings
  were detailed and insightful. Research was
  brought into classroom discussions more often.

24
Group Work on Multiple Choice Problems and
Distractors

• There were students who were distracted by some
  distracters provided.
• Groups sometimes found correct answers and
  justified fully. This convinced other groups.
• Students volunteered to present the
  misunderstandings they had had and these were
  often connected to literature associated with
  student difficulties.
• Mathematical and pedagogical learning resulted.

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SETU Evidence Suggesting Successful Initiative

• 2005 (Majority Non-Post-Grad)
• SETU Non-Post-Grad 1 above 4
• SETU Post-Grad 56
  above 4
• 2006 (Majority Non-Post-Grad)
• Combined SETU Reported 83 above 4
• 
  42 of these gt 4.5

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Qualitative Feedback Elaborated SETU Responses

• Changed approach
• Successful engaging of students
• Intensity
• Enjoyment
• Mathematical Learning
• Pedagogical Learning
• Preparation for Future Teaching

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Indicators of Goals Achieved

• The following student feedback came from
  spontaneous comments
• In class
• On DSO
• Through email
• In some cases requests were made for follow up
  elaboration by email.

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Spontaneous Comments Because They Know I Want to
Know

• Gaye,
• Just had some thoughts on my way home tonight
  that I wanted to share before I forgot.
• Discussion of how they would probably only use
  small parts of collaborative learning for a start
  while they worked out what worked
• As I said a lot of things fell into place for me
  today, so perhaps it wasn't just this discussion
  but I just wanted to let you know that it was
  very powerful, and you might be able to
  consciously use it to advantage next year. (2007
  student)

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Finding It Works (Yvonne, 2006)

• I always wanted to find new ways to develop
  students enjoyment of mathematics as it is of
  great concern to me that so many students say
  they hate maths.
• Gayes philosophy is that learning of mathematics
  doesnt just have to be for the smart kids,
  its about creating learning environments that
  encourage and promote shared participation and
  learning for the whole class. Sharing the
  learning can give all students the experience of
  success and understanding.
• Ive seen it work, the look of excitement when
  students discover the maths rules for themselves.

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Evidence of Effective Classroom Practice of
Deakin Students, Sarah Day (2004)

• I have had many opportunities over the past 2
  years to use her research and resources in my
  senior classrooms to enhance relational
  understanding for my students, many of whom had
  previously felt anxious about studying advanced
  mathematics .
• As a student in her classes, I was constantly
  challenged through her innovative teaching
  method, which modelled for us some of the
  practices and theories advocated as best practice
  by current research

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Enhanced Conceptual DevelopmentMichael W (2006)

• I participated in Gaye Williamss class and
  was very unsure of her strange teaching
  techniques. I started to notice that she would
  allow us to talk about mathematics and our
  knowledge on teaching the subject area Near the
  end of my classes with Gaye I started to notice
  that she would plan every lesson and that she was
  guiding our discussions without us realizing. I
  also noticed near the end of the year I was
  feeling confident enough to lead in discussions
  and believed that my personal knowledge of maths
  increased due to our class discussions

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Workload High But Outcomes Worth It (Off Campus
Male Student, 2006)

• I thoroughly enjoyed the unit - I felt there was
  an above average work load, but then I probably
  took more away than average.

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Autonomous Learning (Off Campus Female Student,
2006)

• I felt you positioned yourself as a collaborator
  and not an arbiter of knowledge.
• Even asking for this feedback indicates to me
  that you are genuinely interested in the learning
  process and are open to new ideas.
• This style of teaching had a positive effect for
  my learning. I felt I was being supported to
  investigate issues for myself and that my
  findings would be accepted and valued. The open
  ended nature of the assignments also fostered
  this.

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Learning for the Future (Off Campus, Female
Student, 2006)

• For me, and I assume others, the learning isn't
  necessarily so much in what we read and even in
  what we write in our assignments, but in our
  reflection of what we have written combined with
  the feedback that you provide. In most units we
  go away not knowing which part of our
  planning/thinking let us down.
• Your comments enable us to reflect on our
  learning and truly learn something. Which makes
  our assignments actually useful when we head out
  into the real world, rather than have merely been
  a stepping stone along the way to getting the
  degree.

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Self-Recognised Student-Teacher ChangeHayley
(2006)

• I have learnt not to narrow a students way of
  thinking based on the ways in which I think.
• Im not sure how she did it, but Gaye taught me
  not to block student thinking something that has
  made an incredible difference to the way I
  approach teaching.

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Conclusions

• Careful listening to considered student feedback,
  and reflecting upon it using a theoretical lens
  connecting research and practice can lead to
  productive refinements to unit implementation.
• Considered feedback tends to occur when students
  know their ideas are valued and that they are
  used to inform future practice.

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If you want to know more please feel free to
email.If you would like the powerpoint, please
ask.

• gaye.williams_at_deakin.edu.au

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References

• Anthony, G. (1996). Classroom instructional
  factors affecting mathematics students strategic
  learning behaviours. In P. Clarkson (Ed.),
  Technology in mathematics education (pp. 38-48).
  Melbourne, Victoria Mathematics Education
  Research Group of Australasia.
• Cobb, P., Wood, T., Yackel, E., McNeal, B.
  (1992). Characteristics of classroom mathematics
  traditions An interaction analysis. American
  Educational Research Journal, 29(3), 573-604.
• Csikszentmihalyi, M., Csikszentmihalyi, I.
  (Eds.). (1992). Optimal Experience Psychological
  Studies of Flow in Consciousness. New York
  Cambridge University Press.
• Schoenfeld, A. (1985). Mathematical problem
  solving. New York Academic Press.
• Skemp, R. (1976). Relational understanding and
  instrumental understanding. Mathematics Teaching,
  77, 20-26.
• Whitmore, J. (1980). Giftedness, conflict, and
  under achievement. Boston Allyn and Bacon.
• Williams, G. (2002). Identifying tasks that
  promote creative thinking in Mathematics a tool.
  In B. Barton, K. Irwin, M. Pfannkuch, M. Thomas
  (Eds.), Mathematics education in the South
  Pacific (Vol. 2, pp. 698-705). Auckland, New
  Zealand Mathematical Education Research Group of
  Australasia.
• Williams (2006). Building problem solving
  capacity. Session presented at the Mathematical
  Association of Victoria Annual Conference,
  Latrobe University, December, 2006.
• Gayes PhD Thesis Focused on Such Learning
• Williams, G. (2005). Improving intellectual and
  affective quality in mathematics lessons How
  autonomy and spontaneity enable creative and
  insightful thinking. Unpublished doctoral
  dissertation, University of Melbourne, Melbourne,
  Australia. Accessed at http//eprints.infodiv.unim
  elb.edu.au/archive/00002533/

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Types of Tasks

• Experiment use skills over and over (to gain
  all, most, or fastest game)
• Links to contexts that engage in ways that
  students keep modelling maths against reality
• Exploring in groups and sharing often so class
  build maths concepts from collaborative activity

40
Fours Task

• Make each of the whole numbers 1, 2, 3 4, 20.
• For each, you must use the digit 4 four times and
  as many of these operations as needed
• - - x / v () 2 .
• Make each of the whole numbers from 1-20.
• Think about how to do this really fast.

41

Making Cuboids, Part 1

• Make boxes with 24 of these cubes. How many can
  you make? How do you know that you have got them
  all?
• Can you make a mathematical argument for how you
  know you have got them all?

42
A Fishy Tale
Mathematicians like to find patterns and then
think about why those patterns are found. Find
all of the maths you can about such fish