Transcript Slide 1

Nursing Mathematics: What Skills Do
Nursing Students Bring to Drug
Calculations?
Roslyn Gillies
Learning Skills Unit
Student Support Services
University of Western Sydney
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A bit about where I come from …
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what I do …
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and where I do it …
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UWS – Sydney, NSW, Australia
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A bit about UWS …
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Six campuses covering entire west of
Sydney
36 000 students – 32 000 undergrads
Larger campuses: Parramatta & Penrith
Smaller: Hawkesbury & Blacktown
Motto: ‘Bringing knowledge to life’
Emphasis on practical courses, providing
educational opportunities for students in
the region
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How does Nursing Mathematics
fit with Ethnomathematics?
Several definitions of
ethnomathematics …
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… the study of mathematics which
takes into consideration the culture in
which mathematics arises
(University of Idaho website)
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… the mathematical practices of
identifiable cultural groups
(Ubiratan D’Ambrosio – first used in late 1960s)
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Human activities which
require some form of mathematics
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Architecture - construction
Weaving – textiles and baskets
Sewing – turning cloth/skins into clothing or
shoes that fit
Agriculture – calendars to mark seasons, planning
for quantity and storage, layout of gardens and
fields
Kinship relations
Ornamentation – tilings and beadwork
Spiritual and religious practices
(uidaho.edu website)
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… and Nursing – dosage calculations!
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Mathematical skills nurses require
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Computational skills
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fractions, decimals, percentages, ratio,
measurement, conversion between units
Conceptual Skills- ability to:
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set up the problem for calculation
apply an appropriate solution method
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The culture and tradition of
teaching drug calculation
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Early 1980s – Florence Nightingale’s
hospital-trained apprentice system was
replaced by higher education training
Occurred in countries such as:
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UK
Canada
USA
Australia
New Zealand
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Impacts of this change
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‘Big bang’ curriculum revolution
rather than incremental change
Emphasis on intellectual and higherlevel thinking skills, problem solving
Mastery of basic principles rather
than facts
Less time in clinical practice
situation
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Other factors affecting drug
calculation instruction
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Increasing student diversity
Multidisciplinary nature of nursing maths
(maths applied in a nursing context)
Medication calculation frequently a
stressful task performed on the ward
No clear policy on whose responsibility it
is to develop and maintain nurses’ drug
calculation competence
Little agreement on teaching methods
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Other factors (cont.)
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Assumption that maths skills taught in
the abstract will be successfully
transferred to nursing context
Some nursing educators admit to poor
maths skills and difficulty in teaching drug
calculations
Limited opportunities for students to
practice drug calculation skills
Reliance on formula methods that do not
always result in students retaining skills
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The tradition of using formula
methods for drug calculation
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Widespread use of formula methods
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Examples of formulae taught:
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Volume required to deliver a given
mass:
(Gatford & Phillips, 2002, p. 44)
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Another formula taught …
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Drip rate for Intravenous Infusion:
(Hext & Mayner, 2003, p. 80)
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Why are formulae taught?
“… to bypass the need to appropriate
or understand any mathematical
structure and to impose consistency
on what were seen to be dangerous
variations in strategy”
(Hoyles et al., 2001, p. 13)
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The dilemma – Advantages of
formula methods
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Standardised methods: one-sizefits-all
Easy to apply
Plug in the numbers and turn the
handle to get the answer
Don’t need to think too much
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Disadvantages of formula
methods
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Little use of students’ existing problemsolving skills
Encourage belief that drug calculation is a
separate branch of mathematics
Do little to encourage students to think
through the problem and understand the
calculation method
Do little to encourage estimation and
checking strategies to ensure calculated
dosage is reasonable
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What the literature says …
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Some students find formulae
difficult to use correctly
Formulae may be a cause of
conceptual errors
Formula methods are frequently
ineffective and result in:
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poor skill development
poor retention of skills
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What the literature says … (cont.)
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In workplace situations nurses
make little use of formulae learnt
Instead, nurses use a variety of
correct proportional reasoning
methods that preserve the meaning
of the problem situation
(Hoyles et al., 2001)
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The study
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Subjects: 35 recently enrolled first
year B Nursing students at UTS
Instruments:
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Test – 10 calculations (see OHT)
set in everyday contexts
 designed to parallel typical drug
calculation problems
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Questionnaire – demographic data
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Problem types simulated in test
Calculate:
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Number of tablets to deliver a given
mass
Volume required to administer a given
mass, either:
 orally
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by injection
Intravenous medications:
drip rate (drops per minute)
 time to run the infusion
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Some of the questions …
PRT item
4. A 12.5 kilogram bag of flour lasts a
cook 5 days. How many days will 45
kilograms of flour last the cook?
Parallel DCT item
4. On hand is Benadryl 12.5 mg per 5
mL. How many millilitres will you
give if Benadryl 45 mg is ordered?
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PRT item
5. An automatic drip feeder installed in an
aviary is to deliver 600 millilitres of water
to the birds every 10 hours. If the feeder
delivers 60 drops per millilitre, how many
drops are delivered each minute?
Parallel DCT item
5. An intravenous drip is to deliver 600 mL
of normal saline over 10 hours. If the
giving set delivers 60 drops per mL, what
is the drip rate in drops per minute?
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PRT item
7. A dripping kitchen tap loses 1 litre of water over 8
hours. It is established that 15 drops of water is
equivalent to
1 millilitre. Calculate in drops per minute the rate
at which the tap is losing water.
Parallel DCT item
7. A patient is ordered 1 litre of normal saline over 8
hours. The intravenous giving set delivers 15
drops per mL. Calculate the drip rate in drops per
minute?
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PRT item
10. A car travelling on a country road is losing water
from the radiator at the rate of 25 drops per
minute. The driver uses his last 600 millilitres of
water to top up the radiator. How long will it take
for this amount to leak out if 20 drops of water is
equivalent to 1 millilitre?
Parallel DCT item
10. An intravenous giving set is delivering an
infusion at the rate of 25 drops per minute. The
patient is to have 600 mL of Hartmann’s. How
long will the infusion take if the giving set delivers
20 drops per mL??
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Research questions
Before being exposed to drug calculation
instruction of special formulae:
 How well do students perform on tasks
similar to drug calculations?
 How successful are students in applying
appropriate problem-solving methods to
set up the problem for calculation?
 What are the ‘native’ methods used by
students to solve such problems?
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Scoring – two methods
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Method 1 – right/wrong – test mark
out of 10
Method 2 – score/3 for each item –
test mark out of 30
1 mark: some progress
 2 marks: correct method used
 3 marks correct method and correct
answer
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Student profile
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Female: 94%
Ages: 17-48 mean 25.6 (sd 7.7)
Mathematics backgrounds:
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NSW HSC-level mathematics: 78%
Year 10 (junior high) maths or less:
20%
Maths studied after leaving school: 9%
NESB Language background: 12%
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Mean score
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Method 1 (score/10)
Mean score: 3.65 (sd: 2.25)
Method 2 (score/30)
Mean score: 15.17 (sd: 7.57)
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Pass requirement:
80% correct
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Method 1:
(score ≥ 8/10)
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Pass: 11% of students
Fail: 89%
Method 2:
(score ≥ 24/30)
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Pass:
17%
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Fail:
83%
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Pass requirement:
100% correct
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Methods 1 & 2:
(Score: 10/10 or 30/30)
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Pass: 0%
Fail: 100%
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Deficits in students’ skills
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Inability to set up problem for
calculation
(Blais & Bath, 1992; Rutherford, 1996)
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Computational errors
(Gillies, 1994; Gillham & Chu, 1995)
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Errors in metric conversions
(Rodger & Jones, 2000)
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Some of the problem-solving
methods students used
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Division operations
Unitary method and adaptations
Fraction of a quantity
Proportion (formal set up)
Ratio
Proportional reasoning
Rewrite rate in equivalent form
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No. of students nts
No of items where correct
method applied
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
Number of items where correct method applied
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Ability to apply correct
method
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On average, another 1.4 Qs per
student where correct method used
For 26% of students, a further 3-4
Qs where correct method used
For 40% of students, at least 2
additional Qs where correct method
used
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Items of particular interest
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Those with greatest difference between %
of students obtaining correct answer and %
using correct method–Items 4, 5, 7, 10
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ie many more students can apply a correct
method than can get the correct answer
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These include all three IV infusion problems
– traditionally most difficult Qs
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For these items, high incidence of causes,
other than conceptual difficulties, that
prevent success viz computational
difficulties
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Item 5 – Melika’s working
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Item 5 – Nicola’s working
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Item 5 - Summary
Key to success:
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Being able to convert:
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ml to drops
hours to minutes
Being able to express stated ‘drip
rate’ in appropriate equivalent
forms
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Item 7 – Cate’s working
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Item 7 – Alison’s working
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Item 7 – Melika’s working
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Item 7 – Karen’s working
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Item 7 - Summary
Simplest process:
 Change ml to drops early
 Leave conversion of hours to mins
until the end (otherwise large
numbers result)
 Also valuable was the ability to
express division in fraction form and
cancel down (avoids long division)
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Item 10 – Karen’s working
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Item 10 – Melika’s working
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Item 10 - Summary
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Both students used same method
Both had difficulty in arithmetic
processes:
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Karen gained a zero is division
(2-step process)
Melika lost a zero in same division
(long division)
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What analysis of students’ working
suggests
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Difficulties with IV problems are not
always because of conceptual
difficulties
Many students able to set up
problem and apply appropriate
method
Having applied an appropriate
method, poor conceptual skills may
prevent progress to correct answer
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Conclusions
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On average, students able to apply correct
method to half of the 10 items – even
before any drug calculation instruction
Many students fairly well equipped to deal
with even the most difficult drug calculation
problems (IV problems)
Methods students use involve multiple
steps that preserve meaning of problem
(Hoyles et al., 2001)
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When correct method applied, incorrect
answers caused by poor arithmetic skills
(Gillham & Chu, 1995; Cartwright, 1996)
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Recommendations for
nursing educators
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Need to reassess the appropriateness of
focus on teacher-taught formulae for drug
calculations
Avoid ‘killing off’ students’ existing
problem-solving skills
Avoid fostering the belief that drug
calculation is a separate and unrelated
branch of maths
Encourage students who prefer to use
‘native’ methods and assist them in
refining those methods
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Recommendations cont.
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If formulae taught, ensure development of
understanding:
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Unravel the multiple steps embodied in the formula
Stress these steps may be performed separately
Encourage students to think flexibly and apply a
range of problem-solving methods – leads to
mathematically powerful students (Schoenfeld, 1992)
Further research needed in areas such as:
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the conceptual skills of nursing students
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students’ ‘native’ problem-solving methods and how
they might apply them to drug calculation
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