LSU 2006 1 Nursing Mathematics: What Skills Do Nursing Students Bring to Drug Calculations?
Roslyn Gillies
Learning Skills Unit
Student Support Services
University of Western Sydney

Slide 2:

LSU 2006 2 A bit about where I come from …

Slide 3:

LSU 2006 3

Slide 4:

LSU 2006 4 what I do …

Slide 5:

LSU 2006 5 and where I do it …

UWS – Sydney, NSW, Australia :

LSU 2006 6 UWS – Sydney, NSW, Australia

A bit about UWS … :

LSU 2006 7 A bit about UWS … 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

How does Nursing Mathematicsfit with Ethnomathematics? :

LSU 2006 8 How does Nursing Mathematicsfit with Ethnomathematics? Several definitions of ethnomathematics …
… the study of mathematics which takes into consideration the culture in which mathematics arises
(University of Idaho website)
… the mathematical practices of identifiable cultural groups
(Ubiratan D’Ambrosio – first used in late 1960s)

Human activities which require some form of mathematics :

LSU 2006 9 Human activities which require some form of mathematics 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)
… and Nursing – dosage calculations!

Mathematical skills nurses require :

LSU 2006 10 Mathematical skills nurses require Computational skills
fractions, decimals, percentages, ratio, measurement, conversion between units
Conceptual Skills- ability to:
set up the problem for calculation
apply an appropriate solution method

The culture and tradition ofteaching drug calculation :

LSU 2006 11 The culture and tradition ofteaching drug calculation Early 1980s – Florence Nightingale’s hospital-trained apprentice system was replaced by higher education training
Occurred in countries such as:
UK
Canada
USA
Australia
New Zealand

Impacts of this change :

LSU 2006 12 Impacts of this change ‘Big bang’ curriculum revolution rather than incremental change
Emphasis on intellectual and higher- level thinking skills, problem solving
Mastery of basic principles rather than facts
Less time in clinical practice situation

Other factors affecting drugcalculation instruction :

LSU 2006 13 Other factors affecting drugcalculation instruction 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

Other factors (cont.) :

LSU 2006 14 Other factors (cont.) 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

The tradition of using formulamethods for drug calculation :

LSU 2006 15 The tradition of using formulamethods for drug calculation Widespread use of formula methods
Examples of formulae taught:
Volume required to deliver a given mass: (Gatford & Phillips, 2002, p. 44)

Another formula taught … :

LSU 2006 16 Another formula taught … Drip rate for Intravenous Infusion:
(Hext & Mayner, 2003, p. 80)

Why are formulae taught? :

LSU 2006 17 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)

The dilemma – Advantages offormula methods :

LSU 2006 18 The dilemma – Advantages offormula methods Standardised methods: one-size-fits-all
Easy to apply
Plug in the numbers and turn the handle to get the answer
Don’t need to think too much

Disadvantages of formulamethods :

LSU 2006 19 Disadvantages of formulamethods Little use of students’ existing problem-solving 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

What the literature says … :

LSU 2006 20 What the literature says … Some students find formulae difficult to use correctly
Formulae may be a cause of conceptual errors
Formula methods are frequently ineffective and result in:
poor skill development
poor retention of skills

What the literature says … (cont.) :

LSU 2006 21 What the literature says … (cont.) 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)

The study :

LSU 2006 22 The study Subjects: 35 recently enrolled first year B Nursing students at UTS
Instruments:
Test – 10 calculations (see OHT)
set in everyday contexts
designed to parallel typical drug calculation problems
Questionnaire – demographic data

Problem types simulated in test :

LSU 2006 23 Problem types simulated in test Calculate:
Number of tablets to deliver a given mass
Volume required to administer a given mass, either:
orally
by injection
Intravenous medications:
drip rate (drops per minute)
time to run the infusion

Some of the questions … :

LSU 2006 24 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?

Slide 25:

LSU 2006 25 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?

Slide 26:

LSU 2006 26 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?

Slide 27:

LSU 2006 27 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??

Research questions :

LSU 2006 28 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?

Scoring – two methods :

LSU 2006 29 Scoring – two methods 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

Student profile :

LSU 2006 30 Student profile Female: 94%
Ages: 17-48 mean 25.6 (sd 7.7)
Mathematics backgrounds:
NSW HSC-level mathematics: 78%
Year 10 (junior high) maths or less: 20%
Maths studied after leaving school: 9%
NESB Language background: 12%

LSU 2006 34 Deficits in students’ skills Inability to set up problem for calculation(Blais & Bath, 1992; Rutherford, 1996)
Computational errors(Gillies, 1994; Gillham & Chu, 1995)
Errors in metric conversions(Rodger & Jones, 2000)

Some of the problem-solvingmethods students used :

LSU 2006 35 Some of the problem-solvingmethods students used Division operations
Unitary method and adaptations
Fraction of a quantity
Proportion (formal set up)
Ratio
Proportional reasoning
Rewrite rate in equivalent form

No of items where correctmethod applied :

LSU 2006 36 No of items where correctmethod applied

Ability to apply correctmethod :

LSU 2006 37 Ability to apply correctmethod 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

Items of particular interest :

LSU 2006 38 Items of particular interest Those with greatest difference between % of students obtaining correct answer and % using correct method–Items 4, 5, 7, 10
ie many more students can apply a correct method than can get the correct answer
These include all three IV infusion problems – traditionally most difficult Qs
For these items, high incidence of causes, other than conceptual difficulties, that prevent success viz computational difficulties

Item 5 – Melika’s working :

LSU 2006 39 Item 5 – Melika’s working

Item 5 – Nicola’s working :

LSU 2006 40 Item 5 – Nicola’s working

Item 5 - Summary :

LSU 2006 41 Item 5 - Summary Key to success:
Being able to convert:
ml to drops
hours to minutes
Being able to express stated ‘drip rate’ in appropriate equivalent forms

Item 7 – Cate’s working :

LSU 2006 42 Item 7 – Cate’s working

Item 7 – Alison’s working :

LSU 2006 43 Item 7 – Alison’s working

Item 7 – Melika’s working :

LSU 2006 44 Item 7 – Melika’s working

Item 7 – Karen’s working :

LSU 2006 45 Item 7 – Karen’s working

Item 7 - Summary :

LSU 2006 46 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)

Item 10 – Karen’s working :

LSU 2006 47 Item 10 – Karen’s working

Item 10 – Melika’s working :

LSU 2006 48 Item 10 – Melika’s working

Item 10 - Summary :

LSU 2006 49 Item 10 - Summary Both students used same method
Both had difficulty in arithmetic processes:
Karen gained a zero is division (2-step process)
Melika lost a zero in same division (long division)

What analysis of students’ working suggests :

LSU 2006 50 What analysis of students’ working suggests 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

Conclusions :

LSU 2006 51 Conclusions 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)
When correct method applied, incorrect answers caused by poor arithmetic skills (Gillham & Chu, 1995; Cartwright, 1996)

Recommendations fornursing educators :

LSU 2006 52 Recommendations fornursing educators 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

Recommendations cont. :

LSU 2006 53 Recommendations cont. If formulae taught, ensure development of understanding:
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:
the conceptual skills of nursing students
students’ ‘native’ problem-solving methods and how they might apply them to drug calculation

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