Teacher Use of Computers and Calculators in the Mathematics Classroom: Research Results

1
Teacher Use of Computers and Calculators in the
Mathematics Classroom Research Results

• Mike Thomas
• The University of Auckland

2
Overview

• Background
• Method
• Results
• Computers
• Calculators
• Implications

3
School Policy

• 36 of mathematics departments have a technology
  policy
• It is usually very basic

4
Computers in Mathematics Teaching
5
Worldwide Computer Use

• Although computers have been in use in
  mathematics education in this country UK for
  well over twenty-five years, the pattern of usage
  is still very varied and very sparse.
• (Askew Wiliam, 1995, p. 34)

6
UK

• A UK Department of Education report (DFE, 1995)
  noted a low level of computer usage in
  mathematics, with an average of 15.6 minutes of
  lesson time per week spent using the computer
• "Typically then, computer use remains low, and
  its growth slow."
• (Ruthven Hennessey, 2002, p. 48).

7
USA

• In the United States the position has been very
  similar (eg Ely, 1993)
• Manouchehri (1999)
• 181 surveys completed 116 high school
  mathematics teachers
• 51 used computers at least once every 3 weeks
  mainly for drill and practice

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Background - PTK

• Pedagogical Technology Knowledge (PTK)
• teacher attitudes to technology and their
  instrumentalisation of it
• teacher instrumentation of the technology
• epistemic mediation of the technology
• integration of the technology in teaching
• ways of employing technological tools in teaching
  mathematics that focus on the mathematics
• Combines knowledge of self, technology, teaching
  and mathematics
• (Thomas Hong, 2005a Hong Thomas,
  2006)

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Method

• Longitudinal study
• Questionnaire1995 and 2005Posted
• Population all secondary mathematics teachers in
  New Zealand
• Lesson observation and interviews 32 teachers
  in 22 schools

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Some of the questions
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Some of the questions
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Response demographics
2005 HoD mean age of 46.6 years
NZ has 336 secondary schools
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School demographics

• 68.4 co-educational schools
• 57 state and 18.1 integrated schools
• Mean size was 748 students

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Numbers of computers
School with 1800 laptops excluded
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Computers in maths classrooms
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General use statistics

• 31.6 of all secondary mathematics teachers never
  use a computer in their teaching constant over
  10 years

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2005 Area Use
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Curriculum areas used
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Pattern of changes

• Significant increase in use for statistics
  First choice curriculum area (?224.5, plt0.001)
  some use (?29.47, plt0.01)
• Apparent fall in the use of geometry packages
  (not significant, ?22.07)
• Others similar

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Types of software used
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Changing pattern Software

• Decrease in use of specific content-oriented
  programs
• graphical (?25.59, plt0.05)
• mathematical (?238.7, plt0.001)
• statistical packages (?212.3, plt0.001)
• Increase in generic software
• spreadsheet (?228.0, plt0.001)

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Possible reasons

• Budget
• In 2005 only 20/193 mathematics departments had
  a technology budget (range NZ 200-15000, mean
  NZ 2762.50)
• Graphic calculator used for graphing functions?
• Spreadsheet provided with computers

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Gender Differences

• Significantly less use by females in trigonometry
  (?24.44, plt0.05), calculus (?24.89, plt0.05),
  and algebra (?27.68, plt0.01).
• Significantly fewer females mentioned using
  mathematics software (?24.00, plt0.05), or
  statistics packages (?27.85, plt0.01) some
  evidence of less use of the Internet (?23.78,
  n.s.)

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Internet use

• 46.1 of teachers reported some use of it to
  teach mathematics.
• 61.1 of the teachers have access in their
  classroom (and 68.4 in a staff room).
• 26.4 of students have classroom access.
• 95.6 of schools have ICT rooms connected.

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Internet Use Teacher Comments

• That could include going on the web and asking
  questions, looking everywhereTo improve their
  learningis that to do with being self motivated,
  looking for answers to questions themselves?
• With computers there are a lot of web sites and
  programs out there that can actually help them
  students with skills so its just a variety of
  the different ways of doing the skills There
  are also a lot of places they can go and look at
  problems if they are interested in maths.

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Teaching methods
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Changes

• significant decline in the proportion of
• skill development (?24.79, plt0.05)
• free use of the computer (?218.0, plt0.001)
• significant increase in the proportion of
• demonstrations (?219.5, plt0.001)
• due to lack of computers?

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However

• Around 60 reporting computer use for skill
  development and demonstrations, as well as
  investigations
• Directed use and demonstration more common in
  2005, but not as often skill-directed
• Significantly more males than females used
  investigations or problem solving (?28.60,
  plt0.05).
• Are teachers using a constructivist approach with
  computers?

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• Proportions wanting to use computers more in
  their mathematics teaching
• 1995 93.5
• 2005 75.1
• Significant decrease (?247.0, plt0.001), but on
  increased rate of use

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Obstacles to increased use
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Issues

• Availability of computers remains the major issue
• A significant increase in those mentioning it
  first (?27.49, plt0.01)
• Agrees with Zamits (1992), Forgasz (2006). In
  both studies, lack of access to computers was the
  highest ranked factor.

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Reasons Teacher comments

• Access to computers at required time (of year
  and within school timetable blocks) was
  difficult
• There is a problem getting into overused
  computer suites and
• Due to the increased demand for IT classes it is
  very difficult to book a computer room for a
  class of 20-30 students

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Changes

• Significant decline in the proportion of those
  mentioning
• lack of training first (?27.39, plt0.01), no
  change overall
• No change in proportion mentioning
• lack confidence in computer use (?22.31, n.s.)
• There is still a need for training (41.2
  mention)
• only 39.6 of the teachers had recently been on
  any kind of professional development with
  technology
• HODs said that 3.1 teachers would not feel
  confident using technology in their teaching out
  of 7.2 full time and 3.1 part time mathematics
  teachers

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Specific uses of computers

• Powerpoint or Excel
• demonstrate an algorithm
• show how to solve problems using technology
• an alternative to writing notes on the
  whiteboard
• a teacher-directed manner.

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Notes
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Other uses Investigation

• Once theyve got a basic understanding, then
  they can investigate a whole lot more and a whole
  lot quicker if they get a computer to do the
  mechanical part of itthey have to be
  interpreting what its giving it back to themyou
  can get a lot more time for the discussion and
  investigating different optionsthe important
  part of what we do in teaching is probably based
  on their conceptual learning.

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Example

• Powerpoint displayed a concave downward parabola
  in the first quadrant, where one of the roots was
  at the origin, to demonstrate the area bounded by
  the parabola and the x-axis, and how a strip from
  it may be revolved around the y-axis.
• Java scripts showed in a dynamic way how the
  volume is formed. This promoted a three
  dimensional view of the process.
• Demonstrated an element of the volume (a shell)
  taken from the parabola, together with the
  equation to demonstrate its volume, and the
  step-by-step process of obtaining the expression
  for the definite integral.

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Interactive White Boards (IAW)

• Students asked to drag tangent lines, already
  created by the teacher, and place them at a point
  on the curve y x2 1.
• Students were then required to match a triangle
  (also prepared in advance by the teacher) with
  each of the tangent lines drawn.
• Using this triangle, the gradient of the tangent
  and hence the gradient of the curve at each point
  was calculated.
• A table of gradients was produced.

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IAWs
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Another conceptual IAW lesson

• Data collected by students in their Year 12
  Mathematics class at Piha beach. Recorded the
  height of the water along the beach at high and
  low tide.
• Students investigated how data could be modelled
  by a sine curve of the form y A sin B(x C)
  D
• Teacher simply dragged the sine curve graph to
  demonstrate the change in both amplitude and
  period - students marvelled!

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Overview

• Constant gt30 of mathematics teachers never use
  computers in teaching
• While there are many more computers in schools
  and an increased frequency of use, access is
  still the major obstacle
• Common use is graphical, statistical or
  spreadsheet for demonstration or skill
  development
• Only 20.7 of schools had a technology policy,
  and its usually very basic

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The emphasis

• There has been little change over 10 years
• Just 8 of teachers believe computers aid
  understanding
• 16.8 claim they impede learning or understanding

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Calculators in Mathematics Teaching
47
The questions
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Maths department calculators

• 1995 -
• average 22.6 calculators in mathematics
  departments
• 52 Casio
• 96 of Year 12 (age 17 years) and 97 of Year 13
  (age 18 years) students owned their own
  calculators
• 2005 -
• average 45.7 calculators in mathematics
  departments
• 68.6 Casio, 14.4 Texas Instruments and 15.4
  Sharp
• Year 12, 86.4 and Year 13, 87.9 owned their own
  calculator

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Calculators may be detrimental to understanding

• 1995 24.8 agreed calculators may be detrimental
• 2005 26.6 thought that they often are
• The number disagreeing dropped significantly from
  60.2 to 47.1 (?213.7, plt0.001)

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However

• Little benefit in mathematics teaching a large
  majority disagreeing 87.3 in 1995 and 75.6 in
  2005
• Implies? It depends how we use them?

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Obstacles to greater use
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Need for more ideas and resources

• 71.1 agree or strongly agree

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Classroom observations 22 teachers

• 2 groups confident and not confident
• strong confidence more likely to have ideas for
  using technology to teach mathematics
  (Meanstrong4.3, Meanweak3.6)
• Both wanted to improve their ability to teach
  with technology (Meanstrong4.4, Meanweak4.5)

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GC use

• Teacher levels of instrumentation of the GC are
  linked to their confidence
• A low level of confidence in GC use in the
  classroom is characterised by
• an emphasis on passing on to students operational
  matters, such as key presses and menu operations,
  
• an emphasis on procedural calculations, to the
  detriment of the mathematical ideas
• little or no freedom given to students to explore
  with the GC
• GC seen as an add-on to the lesson rather than an
  integral part

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Key entry
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Key presses
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Advantage of technology use
59

• A higher level of instrumentation produces a
  higher level of confidence, which in turn frees
  the teacher to focus more on other important
  aspects, such as the linking of representations
  and investigation of concepts
• linking of representations such as graphs,
  tables, and algebra
• encourage students to engage with conceptual
  ideas of mathematics through individual and group
  exploration of the GC
• investigation of mathematical ideas, and the use
  of prediction and test methodology
• GC has been integrated into the lessons

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Conceptual emphasis in GC use
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Conceptual focus
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PTK practice - comments

• They really understood the concepts and answered
  the things in all cases the correct way
• Its the amount of visual information they can
  generalise for themselves they had a much
  better concept
• Technology is really important for multiple
  representations visual is really important
• Understand it a lot better just by being given a
  chance to play and make those connections
• Trying to make it a bit of fun not learning
  necessarily step-by-step processes

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Good practice

• Personal confidence in, and instrumentation of,
  the technology
• Emphasis on mathematical concepts not key presses
  etc
• Knowing when and how to use technology
  appropriately to reflect on mathematics
• Teaching multiple representations of concepts
  while developing skills
• Engaging and supporting the students
• Ability to shift between technologies

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Funding The Equity Issue

• our students are not rich and so cannot afford
  calculators that our more sophisticated than a
  basic scientific. I am concerned that there is a
  growing gap between the experience of rich and
  poor students. State schools are not sufficiently
  funded to rectify this problem
• This is a decile 3. Its not a high decile
  school. A lot of our students will come from even
  lower decile areas and theyll pay fees to
  come here as well. The parents are committed to
  their education and theres a lot of support. But
  when you are asking for another 75, thats the
  cheapest we could buy, 75 for a graphic
  calculator, its just nah, its not gonna happen.
• They are now down, the GC is now under 80 so
  they are quite attainable. They are less than a
  cellphone. I try to encourage the girls to see
  them as their next best accessory and they will
  probably get the thing in vibrant colours soon
  just like the cell phones.

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NCEA

• Teachers in the study were reasonably happy with
  the level of emphasis on calculators in NCEA
• NCEA has too much emphasis on technology
• 11.7 percent either agreed or strongly agreed
• 44.2 disagreed or strongly disagreed
• 36.9 percent giving a neutral response
• mean agreement score 2.59 out of 5

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NCEA assessment

• it has been a positive thing, in terms of
  getting computers and using them because weve
  been able to write our own standards and
  activities using the basis of what we want to do.
  Like we are doing three statistics achievement
  standards that are internal, that are suitable
  for using computers and doing (NCEA) has
  increased our use of technology in terms of
  teaching not that boring monotonous low skill
  stuff.

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Positive

• NCEA has been really positive for technology in
  mathematics because it has enabled us to take the
  documentation from looking at the standards and
  it says, students will use appropriate technology
  and you have a go to the school management, have
  a go to the board and look if theyre gonna do
  NCEA, they must use appropriate technology, and
  schools been really supportive and provided the
  money.

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Another view

• We are getting a mixed message from the NCEA
  examiners. The standard says appropriate
  technology should be used but the Merit and
  Excellence questions are often designed to
  require algebraic manipulation, so we generally
  teach algebraic techniques for solving equations,
  knowing that weak girls will depend more on their
  calculators than strong ones

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A Strong Contrary View

• NCEA encourages us to teach students to get
  answers only (working is not marked) to questions
  they do not understand by learning which buttons
  to press, on a piece of technology that nobody
  outside a classroom uses, and which will be out
  of date within 3 years

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Curriculum

• need to re-look at the curriculum
• Maths must be adapted to utilise the technology
• Need less emphasis on skills and a shift to more
  conceptual teaching
• Gain more time to tackle and think about more
  challenging work instead of learning and
  practicing methods of calculations

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Overview comments

• I feel technology in lessons is over-rated. I
  dont feel learning is significantly enhancedI
  feel claims of computer benefits in education are
  often over-stated.
• Reliance on technology rather than understanding
  content.
• Sometimes some students rely too heavily on
  technology without really understanding basic
  concepts and unable to calculate by hand.

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• I think it is still important to be able to
  manipulate, learn techniques and apply them. I
  would be concerned if we sacrificed too much of
  the calculus curriculum by using advanced
  calculators and would need to be convinced that
  AS/SAM calculators would not do this
• GCs encourage kids to take short cuts,
  especially in algebra. Real algebra skills are
  lacking as a result
• As the technology reduces in cost most students
  will gain access to it and it will become an
  integral part of most maths lessons

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Where to? Teachers

• a great deal of attention needs to be devoted
  to educating teachers to teach in a new paradigm
  and to rethink their practices. The major
  challenge is understanding and helping
  teachers.
• Manouchehri (1999, p. 44)
• In particular we must consider teacher
  confidence, the influence of teacher beliefs and
  attitudes re technology, and the need for
  appropriate PD

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A model for PTK development
PD feeds into a number of these areas
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See the TLRI Report for a detailed summary

• Coming soon to
• http//www.tlri.org.nz/publications/