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Nursing Mathematics: What Skills Do Nursing Students Bring to Drug

Calculations?

Roslyn Gillies

Learning Skills UnitStudent 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 …

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 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)

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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!

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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

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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

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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

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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

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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

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The tradition of using formulamethods for drug calculation

Widespread use of formula methods

Examples of formulae taught:

Volume required to deliver a given mass:

Strength required Volume ofVolume =required stock strengthStock strength

(Gatford & Phillips, 2002, p. 44)

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Another formula taught …

Drip rate for Intravenous Infusion:

(Hext & Mayner, 2003, p. 80)

Volume (ml) Drop factor (drops/ml)Drops/Minute

Time (hours) Minutes (60 minutes/hour)

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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 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

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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

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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

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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)

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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

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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

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Some of the questions …

PRT item4. 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 item4. 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 item5. 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 item7. 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 item7. 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 item10. 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 item10. 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

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

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%

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Mean score

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

Method 1:(score ≥ 8/10) Pass: 11% of students Fail: 89%

Method 2:(score ≥ 24/30) Pass: 17% Fail: 83%

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Pass requirement:100% correct

Methods 1 & 2:(Score: 10/10 or 30/30)

Pass: 0% Fail: 100%

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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)

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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

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No of items where correctmethod applied

01234567

0 1 2 3 4 5 6 7 8 9 10Number of items where correct method applied

No.

of s

tude

nts

nts

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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

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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

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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:

Being able to convert: 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

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)

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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

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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)

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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

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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