What mathematics calculations do adults do in their everyday lives? Part 1 of a report on the Everyday Mathematics Project.
Northcote, Maria ; Marshall, Linda
Introduction
The type of mathematics taught in schools is often criticised for
being irrelevant to students' lives and not based in 'real
life'. This article is Part 1 of a three part report that documents
the findings of a research project that investigated the mathematical
calculations completed by adults in their everyday, non-occupational
lives in an Australian context.
Part 1 of the report on the Everyday Mathematics Project, outlines
the findings that emerged from analysing data gathered from 160
participants who were asked to record the mathematics they completed in
their everyday, non-occupational lives. Firstly, they were asked to
describe three of their most typical types of mathematics calculations
and, next, they completed a daily log of their everyday mathematics
calculations. In all, details of over 1200 calculations were collected
during the first stage of the study and these calculations are the focus
of this article. Based on an analysis of 1224 calculations from 160
participants, this article summarises the topics, frequency, amount,
type, difficulty level and methods used in these calculations.
What mathematics did we do in 1999 and before?
Almost sixty years ago, Wandt and Brown (1957) reported on a study
undertaken in California which investigated the way adults performed
non-occupational calculations in their everyday lives. Wandt and Brown
were among the first researchers to investigate social usage of
mathematics in adult life. They were particularly interested in the role
of mental mathematics and in the role of approximate solutions to
problems, or estimation as it is called today. The findings of their
study revealed that mental calculations outnumbered paper and pencil
(written) calculations, and that, while many calculations required an
estimated answer (30%), most calculations required an exact answer
(70%). Lave (1988) provided further insight into the calculations that
were completed by adults and the context in which they took place, such
as shopping and personal weight management. Her work demonstrated that
the way in which mathematics was used in everyday life did not
necessarily reflect the formal calculation processes that were taught in
schools. Although involving children rather than adults, the study by
Saxe (1988) also found that the way mathematical problems were addressed
in everyday contexts (for example, selling candy) was influenced by the
cultural contexts in which they occurred. The problems associated with
de-contextualising mathematics calculations were further explored by
Evans (2000) and Greiffenhagen and Sharrock (2008).
Seventeen years ago a research study was conducted in Australia to
determine the types of mathematics calculations completed by adults in
their everyday, non-occupational lives (Northcote & McIntosh, 1999).
The study became known as the SAUCER (So, Adults Use Calculations
Everyday Research) Project. By building on and replicating aspects of
Wandt and Brown's (1957) much earlier seminal study, the SAUCER
Project aimed to supplement our knowledge of everyday mathematics within
an Australian context. The 1999 study (Northcote & McIntosh)
included 196 participants who reported 596 calculations that they
completed in their everyday, non-occupational lives. Like Wandt and
Brown's earlier study (1957), the SAUCER project required
participants to record their mathematical calculations across a one day
period. The study found that a high proportion of calculations (85%)
completed by adults in their everyday, non-occupational lives involved
some form of mental mathematics. More of their calculations were
estimations (58%) compared to those that required an exact answer (40%).
Addition (46%) and subtraction (42%) dominated the mathematical
operations that featured in their calculations. When the calculations
were analysed to determine their purpose, time-related issues dominated
(25%), followed by calculations associated with shopping and money
(23%).
When asked about the location in which calculations were completed,
almost half (48%) of the calculations reported took place in the
participants' homes--mainly in the kitchen for the purposes of food
preparation and cooking. Of the remaining calculations completed outside
the home, the most frequently reported location was a shop. Over two
thirds of the calculations were deemed to be at a lower primary level of
difficulty with the remaining calculations (35%) at an upper primary
level and very few (under 2%) at a secondary school level. A variety of
objects such as clocks and measuring devices were used in 19% of the
calculations whereas only 12% of calculations involved the use of
calculators. Most calculations took place in the morning and, on
average, the participants in the study completed 3 calculations per day.
Between 1999 and 2015
Since the 1999 (Northcote & McIntosh) study was conducted and
published, a number of changes have occurred in the Australian
Curriculum: Mathematics (Australian Curriculum Assessment and Reporting
Authority, 2013). Also, Australian teaching standards have been defined
at a national level (Australian Curriculum Assessment and Reporting
Authority, 2013). While changes in the curriculum and teaching standards
have influenced what and how mathematics is taught in Australia, changes
in technology have influenced mathematics and the way we teach
mathematics (Attard, 2013; Goldenberg, 2000; Myers, 2009). Our use of
technology has increased, especially our use of online, mobile and
computerised technologies, resulting in a mixture of both positive and
negative impacts (Lentz, Kyeong-Ju Seo, & Gruner, 2014; Price &
Kirkwood, 2014; Rosen et al., 2014). Benefits to children's
mathematical learning have been identified in some contexts as a result
of using technology, especially in association with the use of virtual
manipulatives, mathematical play in virtual contexts and computational
fluency (Lentz et al., 2014; White & Singh, 2005). However, one of
the problems associated with the overuse of technology by children and
teens, not just in school but in their lives in general, has been
"increased obesity, reduced physical activity, and decreased
health" (Rosen et al., 2014, p. 364).
Despite the benefits and disadvantages of using technology in
mathematics contexts, technology has become an incidental aspect of most
people's everyday lives. This development is reflected in the
rationale for the new Australian mathematics curriculum which cites the
use of technology as being integral to mathematics:
Mathematical ideas have evolved across all cultures over thousands
of years, and are constantly developing. Digital technologies are
facilitating this expansion of ideas and providing access to new tools
for continuing mathematical exploration and invention. (Australian
Curriculum Assessment and Reporting Authority, 2013)
The application of learned mathematics to everyday life has also
become more topical; teachers are encouraged to teach mathematics in a
way that is relevant, meaningful and authentic (Carraher &
Schliemann, 2002; Coben, 2003; National Numeracy Review Report Panel,
2008). The National Numeracy Review Report (National Numeracy Review
Report Panel, 2008) describes functional numeracy as "everyday
fluency with arithmetic and measurement and perhaps the capacity to find
one's way around" (p. 5). Much has been written about
students' and teachers' views about everyday mathematics
(Coben, O'Donoghue, & FitzSimons, 2000; Kargar, Tarmizia, &
Bayat, 2010; Thompson, 1993; Vale, 2002; White, Way, Perry, &
Southwell, 2005/2006) and the effect of poor numeracy on the lives of
adults (Parsons & Bynner, 2005).
However, little research has been conducted to validate claims
about the actual everyday mathematics completed by adults, and adult
numeracy continues to be an under-researched area (Coben, 2003). Despite
a plethora of research studies arguing that everyday mathematics should
be taught to children and adults, and a compilation of assessments aimed
to establish adult competency in mathematics and the outcomes of
curriculum modification (Cooper, Cooper, & Dunne, 2000; Evans,
2000), little further research since Wandt and Brown (1957), Lave (1988)
and Northcote and McIntosh (1999) has been conducted to establish the
specific types of mathematics adults engage in on a daily basis.
Furthermore, very few, if any, investigations have been conducted to
determine the type of non-occupational mathematics calculations
completed by adults within Australian contexts. The importance of adult
numeracy in everyday life has long been, and continues to be, a concern
for educators, school administrators and government bodies (Coben, 2003;
Gal, 2000; Johnston, 2002; National Numeracy Review Report Panel, 2008;
Parsons & Bynner, 2005).
The 2011-2014 study: Everyday Mathematics Project
To update the findings from the 1999 study (Northcote &
McIntosh), a cross-institutional research team from Avondale College of
Higher Education in New South Wales and Edith Cowan University in
Western Australia replicated the earlier study to determine the types,
amount and nature of mathematics calculations completed in the everyday,
non-occupational lives of a group of 160 adults in Australia. This study
has become known as the Everyday Mathematics Project, or SAUCER II, and
was conducted between 2011 and 2014. To gather information of both a
qualitative and quantitative nature, a mixed methods (Creswell &
Plano Clark, 2011) research approach was adopted. This methodology
ensured that the number, type and context of the calculations could be
investigated. To select its participants, researchers in the recent
Everyday Mathematics Project utilised a mixture of sampling methods
including selective sampling (Burns, 2000), to ensure a spread of
participants from a range of age groups, and convenience sampling
(Patton, 2015), to extend the sampling within each age group.
To determine the actual calculations completed, as well as the
purpose and context of these calculations, all of the 160 participants
in the study completed a questionnaire and kept a daily log of
calculations. Twenty of the participants were also interviewed. Five
types of data were gathered:
* Data pool 1: Participant information
Demographic information from the 160 participants was collected,
including age group, gender, location of residence, occupation and level
of education reached.
* Data pool 2: Typical calculations
Before they completed a 24-hour log of their mathematics
calculations, participants were asked to identify three of the most
typical types of calculations they completed in their everyday lives. In
all, 450 calculations were described by the 160 participants.
* Data pool 3: Daily log of calculations
Each participant kept a 24-hour log of the non-occupational
mathematics calculations they completed in their everyday lives. A total
of 774 calculations were reported.
* Data pool 4: Situational data
As part of the 24-hour log, additional situational data were
gathered about the context of each of the 774 calculations including
location, methods, topic, purpose, difficulty level and nature of the
calculations.
* Data pool 5: Interviews
Twenty participants were interviewed to gather further calculation
examples and to explore detailed information about the context of their
calculations.
Analysis of the qualitative data gathered from the
participants' responses to the open-ended questionnaire items and
interviews was conducted using content-analysis and comparative-analysis
methods (Patton, 2015). The quantitative data gathered from the
questionnaires were analysed by compiling summaries and descriptive
statistics, and correlation tests were conducted to determine
relationships between the data sets. Each categorisation of data in the
findings presented in this article, has been linked to the specific data
pools from which they were sourced.
This article outlines the findings that emerged from analysing data
pools 1-3. Part 2 of the report (future article) will report on the
findings from data pools 4-5. Finally, Part 3 of the report will
consider pedagogical implications of the study in conjunction with the
current Australian Curriculum: Mathematics (Australian Curriculum
Assessment and Reporting Authority, 2013).
Participants in the Everyday Mathematics Project (2011-2014) (1)
In the recent study, participants from six different age groups
were sought, including 160 participants from the age of 18, through to
people over 70 years of age (see Table 1).
Further demographic information about the participants is outlined
in Table 2, including their gender, primary occupation, highest level of
occupation and residential location.
Findings from the 2011-2014 study: Everyday Mathematics Project
From the 450 typical calculations and the 774 daily calculations
that the 160 participants reported in the current study, the topic,
number, method, difficulty levels and exact or estimated nature of these
calculations were analysed (3). Examples of each calculation type were
also collected and analysed. The outcomes of these analyses are outlined
below.
Table 2: Demographic information about the participants.
No. of Percentage of
participants participants
Gender
Female 103 64
Male 52 33
Not specified 5 3
Primary occupation
Professional 48 30
Retired 43 27
Student 38 24
Home duties 9 6
Trades 7 4
Other or not specified 17 11
Highest level of education
University or college 95 59
High school 41 26
TAFE 15 9
Other or not specified 9 6
Residential location (2)
Western Australia 83 52
New South Wales 75 47
Queensland 1 0.6
Victoria 1 0.6
An analysis of the 1224 calculations reported by the 160
participants in their questionnaires and daily logs provided insight
into how these calculations were related to the mathematics topics
represented by the three strands of the Australian Curriculum:
Mathematics (Australian Curriculum Assessment and Reporting Authority,
2013).
In some cases, calculations reflected one or more strands. Over 80%
of all calculations were related to number and algebra and just over 60%
were related to measurement and geometry. Very few calculations (less
than 1%) related to statistics and probability (4).
When each calculation was categorised according to the topics of
the strands and content descriptions in the Australian Curriculum:
Mathematics the most common topics of calculations were revealed as
being either money and financial (in the number and algebra strand) or
time (in the measurement and geometry strand). For example,
"Figuring out my gross pay for the hours I worked last week, e.g.,
32 x 22.11 = $70.52" and "What time do I need to go to the gym
for a half hour run + 15 minutes drive to work to be there by 3 pm? 30 +
15 + 15 = 60 minutes (1 hour) = 2 pm". The top ten most common
mathematics topics reflected across the 1224 calculations are outlined
in Table 3.
Calculation method used
While reporting the calculations they completed within a 24-hour
period (774 calculations in all), participants were asked to record the
method they used. The methods they reported included: mental, written,
computer, phone, calculator, use of an object, discussion, counting
aloud and drawing. Some calculations were completed using a combination
of these methods. Most of the calculations were completed using one
method only (636 calculations, 82%), 116 calculations (15%) involved the
use of two methods, 16 calculations (2%) involved three methods and 4
calculations (0.5%) involved a combination of more than three methods.
The most common method was mental mathematics being used in 665
(86%) of the 774 daily calculations reported:
* 551 calculations (71%) involved the use of mental mathematics
alone; and
* 114 calculations (15%) involved the use of mental mathematics
with an additional method (such as written, calculator, phone,
discussion, object, computer).
The second most common method, written mathematics, was used in 79
(10%) of the 774 daily calculations reported, including:
* 26 calculations (3%) involved the use of written mathematics
alone; and
* 53 calculations (7%) involved the use of written mathematics with
an additional method (such as mental, calculator, object, computer).
Other calculation methods included:
* the use of an object such as such as measuring scales, measuring
tapes, cups, watches, clocks, playing cards, timetables, receipts and
rulers (72 calculations; 9%);
* the use of a calculator (60 calculations; 8%);
* the use of a computer (25 calculations; 3%);
* discussion (6 calculations; 1%);
* the use of a phone (5 calculations; 1%);
* counting aloud (3 calculations; 0.5%); and
* a drawing (1 calculation; 0.1%).
Most of the calculations that involved the use of objects were
related to measurement, such as using a measuring cup described as
"making spag bol for dinner--needed to measure sauces" or
using a ruler in a quilting class for "measuring and cutting fabric
(to scale)". Surprisingly, the use of mobile phones and
computerised technology in the context of completing mathematical
calculations did not feature as strongly as may have been expected in
this set of results. As very few calculations were completed in
discussion with others (for example, discussing day-care costs with a
spouse or discussing credit card payments with a bank advisor), it is
assumed that most calculations were conducted by individuals working on
their own.
Exact or estimate
All but two of the 774 daily calculations were reported by the
participants as requiring either an estimated answer, an exact answer or
an answer which included a combination of an estimated and an exact
answer. More than half (62%, 476 of 772) of the calculations recorded in
their daily log required an exact answer, such as "How much money
would I have left in my bank account? $300-$120 = $180. On the other
hand, 37% (285 of 772) of answers to their calculations required an
estimated answer such as "I estimated the time I would take to iron
3 handkerchiefs, 2 shirts, and 1 pair of pyjamas to see if I could do it
before visitors arrived". Very few answers (1.5%, 11 of 772)
required a combination of both exact and estimated answers.
Level of difficulty
Of the 762 calculations that were allocated a difficulty level by
the participants when provided with a 1 (easy) to 5 (difficult) scale,
most calculations were categorised as being easy (level 1) or quite easy
(level 2) whereas very few of the calculations were categorised as quite
difficult (level 4) or difficult (level 5). Table 4 outlines these
findings. A proportion of the calculations were categorised by the
participants in the study as neutral in terms of difficulty. The
participants made their own judgements on the levels of difficulty;
therefore, they are subjective assessments based on their perceptions of
their own abilities in mathematics.
Amount and frequency of daily calculations
The number of daily calculations completed by each of the 160
participants each day ranged from 1 to 18 (range = 17). The mode, or the
most typical number of calculations completed each day (by 38 people),
was 3. The mean number of calculations that adults completed on a daily
basis was 4.8. When analysed by age group, the 18-30 year olds completed
the fewest calculations (mean = 4.17) whereas the 61-70 year old age
group completed the most calculations (mean = 6.57) across a period of
one day. Overall, except for the 70+ year olds (mean = 4.62), there was
an increase in the average number of calculations per day as the
participants' age group increased: showing a lower number of
calculations completed by the younger age group and a higher number of
calculations completed by most older age groups (see Figure 1). A
Pearson product-moment correlation coefficient was computed to assess
the relationship between the mean age of participants and the mean
number of calculations reported in a 24-hour period. Between the 18-30
and 61-70 age groups, there was a high positive correlation between the
two variables (r = 0.95, n = 5, p = 0.007) but this reduced when the 71+
age group was included. This finding was quite different from the
findings of Wandt and Brown's (1957) study which stated: "No
correlation with age was apparent in an inspection of the data" (p.
152).
So, what has changed since 1999?
Similar to the claims made by Brinkworth (1998) about
students' preferences for mental mathematics strategies, the adult
participants in this study also preferred to use mental rather than
written strategies. This result was largely similar to the findings of
previous studies about the prevalence of mental strategies above and
beyond written strategies in adults' non-occupational mathematical
calculations (Northcote & McIntosh, 1999; Wandt & Brown, 1957).
Interestingly, less of the calculations in the recent study were
reported as being completed by using objects (9%) compared to the 1999
study in which 19% of calculations were completed using objects.
However, the number of calculations in which calculators were used (8%
in the recent study and 12% in the earlier study) has not changed
substantially, although participants may not have reported extensive use
of calculators in the recent study since their availability is now
incidental in everyday life for many people (for example, on mobile
phones).
[FIGURE 1 OMITTED]
Wandt and Brown (1957) found that almost one third (193 of 634) of
calculations were approximate, which led them to conclude that
"approximations do enter into a sizeable percentage of everyday
applications of mathematics" (p. 153). However, most of the
calculations in the Wandt and Brown (1957) study were exact: 70% (441 of
634) of calculations. By 1999, the trends were somewhat reversed. The
1999 study (Northcote & McIntosh) indicated that most calculations
were estimations (58%), compared to 40% of calculations which required
an exact answer. More recently, the trends have reversed again. This
study's results about estimations and exact answers were more
similar to Wandt and Brown's (1957) earlier findings. These recent
results indicated that most of the reported calculations required an
exact answer (62%), compared to 37% of calculations that required an
estimated answer.
In terms of the numbers of calculations reported during a 24-hour
period, this recent study found that participants completed an average
of five calculations, which was higher than Wandt and Brown's
(1957) results of four calculations per day, whereas the earlier 1999
study found that the participants completed three calculations per day.
This change may be due to the inclusion of wider age groups of
participants in the recent study. These results should be interpreted
conservatively, as Wandt and Brown suggest:
Since there were undoubtedly some applications
that were inadvertently omitted in the
reports of the subjects, this figure should be
considered to be a conservative estimate of
the average number of non-occupational
applications of mathematics made daily
by the subjects in our sample. (p. 152).
Surprisingly, the results that emerged from analysing the
participants' typical calculations and their 24-hour logs of
mathematical calculations in this replicated study did not reveal
evidence that internet-connected devices or mobile technologies featured
strongly in the processes that adults used to complete mathematical
calculations in their everyday, non-occupational lives. There may be
many reasons for this. For example, the use of mobile-phones, hand-held
tablets and laptop computers may be viewed as so common in every-day
life that the participants may simply have forgotten to record how or
when they were used. The incidental use of technology may have reached a
point where it is almost transparent to some of the participants in the
study. However, when interviewed, participants described additional
examples of how they used technology to complete mathematical
calculations. Findings from an analysis of the participants'
interviews will be reported in the second article of this series of
three articles, How, Where And Why Do Adults Do Mathematics Calculations
In Their Everyday Lives?, to be published in a future issue of this
journal.
In terms of the topics of calculations completed, the recent
study's results were very similar to the 1999 study; most
calculations were related to money and financial issues or time, and
more calculations involved the operations of subtraction and addition
than multiplication or division. For example, "I calculated the
change I would receive from $20 after spending $13.51 on fruit and
groceries" and "Calculated the cost of graduation $65 + $65 +
$175 = $305". The dominance of addition and subtraction may be due
to these operations being easy to complete and because these types of
calculations are so common in everyday contexts. Also similar to the
1999 study, the 2011-2014 study found that very few calculations were
considered difficult with most calculations being reported as being easy
or quite easy.
While age has not been a heavily researched factor in the numeracy
and mathematical skills of adults, Coben (2003, p. 10) reported that
"Younger and older adults tend to have slightly poorer
skills". Although our project did not attempt to assess adult
mathematics abilities or numeracy expertise, the results of this study
show that older adults tend to do more mathematics in their everyday
lives than the younger adults who participated in the study.
Alternatively, the older adults in the study may have been more aware of
themselves doing mathematical calculations and, therefore, may have
recorded more calculations than their younger counterparts. Or, younger
people may have had particular reasons for not completing calculations
as regularly as older people.
Lave (1988) found that everyday mathematics was not necessarily
viewed as being related to completing calculations, but as part of an
everyday activity such as grocery shopping. For example, "Paid for
groceries $40 and received $4 change. $40-$36 = $4". This
phenomenon may also be present in the findings of this study, as
participants may have undertaken more mathematics than they reported.
However, while Lave found that social relationships were often integral
to everyday mathematics activities, the results of this study do not
reflect this--most calculations were completed by the participants on
their own.
The lack of calculations that appeared to be related to the
Australian Curriculum: Mathematics strand of statistics and probability
may be due to participants not associating this strand of mathematics
with calculations, such as those involved in sports reports or articles
in the press that include graphs and tables. In 1957, when the Wandt and
Brown study was conducted, statistics and probability was not generally
considered to be a part of mathematics so it is not possible to compare
this aspect of the recent study with their earlier study.
While the results of this recent study into the everyday
mathematics calculations completed by adults can be compared to earlier
studies, one of the most important contributions of this study is that
it was completed within an Australian context and no such studies that
we are aware of, since the earlier 1999 study, have taken place in
Australia. As such, this study provides a unique account of the types of
mathematical calculations reported across a range of contexts and age
groups by 160 adults living in Australia.
Initial implications of the findings for teachers
The findings presented here about the topics, frequency, amount,
type, nature, and methods used in calculations performed by adults in
everyday life represent a collection of authentic examples of how
mathematics is used in the non-occupational lives of 160 adults ranging
from the age of 18 through to over 70 years. The results of the study
itself could be shared with students to demonstrate the relevance of
their primary school mathematics curriculum to application in adult
life. Also, the data collection instruments could be used with students
to encourage them to study their own use, or their family members'
use, of everyday mathematics. Furthermore, the actual examples of the
calculations reported in this study could be incorporated by teachers
into practical activities for children to demonstrate types and topics
of typical mathematics calculations.
Although the purpose of school is not only to prepare students to
be competent in the everyday uses of mathematics, there are some clear
links between the structure and content of the Australian Curriculum:
Mathematics and the types of calculations reported by the participants
in this recent study of non-occupational mathematical calculations. For
example, the heavy emphasis on calculations involving number appears to
justify the large proportion dedicated to number and algebra as a strand
in the Australian Curriculum: Mathematics. Furthermore, the importance
of the topics, money and financial mathematics, and units of
measurement, in the Australian Curriculum: Mathematics becomes more
evident as these were highlighted as some of the most common types of
calculations. Similarly, the high proportion of calculations that relied
upon mental mathematics skills (86%) appears to justify this aspect of
the current curriculum. Since much of the mathematics reported in this
study required exact calculations (62%), compared to 37% which involved
estimations, teachers are recommended to include both types of exact and
estimated calculations in the activities they plan for primary school
aged children.
Since many calculations were categorised as involving more than one
operation or more than one topic or type of calculation, these findings
support the way in which many teachers already set mathematics problems
for children in primary mathematics classrooms; that is, using a
combination of authentically-based methods, topics and operations. The
fact that many calculations were deemed, by the participants, to be
equivalent in difficulty to lower or middle primary school mathematics,
highlights the relevance of primary school mathematics to everyday life.
Further pedagogical implications for how the findings of this study may
be applied to primary mathematics classrooms will be presented in the
two follow-up articles that will be published in the future about this
project, as Part 2 and Part 3 of this research report.
Conclusion
This recent (2011-2014) study has shown that the most common topics
of the everyday, non-occupational mathematics calculations completed by
the sample of 160 adult participants were related to time, money or
financial issues and these calculations were broadly grouped as number
or measurement calculations. On average, the participants completed
about 5 calculations per day but the most common amount of calculations
completed by 38 people was 3. There was a strong correlation between the
participants' age group and the amount of calculations they
completed each day; participants in the 18-30 year old age group
completed the least amount of calculations whereas those in the 61-70
year old age group completed the most calculations.
The most commonly used method of calculation was mental mathematics
and the second most common method that participants used to complete a
calculation included some form of written method, or 'paper and
pencil' as Wandt and Brown (1957) would have described such a
calculation. Participants also reported using calculators and other
objects to complete calculations. Some used computers and phones, while
other participants discussed their calculations with other people,
counted aloud or created drawings. By far, most of the calculations
appeared to be completed by the participant on their own, rather than
with someone else. The majority of the calculations were categorised by
the participants as being at a low level of difficulty, equivalent with
lower or middle primary school mathematics, and very few of the
calculations were categorised as being difficult. More than half of the
calculations required an exact answer whereas just over a third required
an estimated answer. This represented a definite change in the results
of earlier studies (Northcote & McIntosh, 1999; Wandt & Brown,
1957).
This article is the first in a series of three articles that will
report on the Everyday Mathematics Project (2011-2014) in the Australian
Primary Mathematics Teacher journal. The second article in this series,
How, Where And Why Do Adults Do Mathematics Calculations In Their
Everyday Lives?, will focus on the context of the mathematics
calculations completed by the participants in this study and the third
article, Adults' Everyday Mathematics Calculations: What Does It
Mean For Our Teaching?, will further consider the pedagogical
implications of this project for primary school teachers of mathematics.
Note regarding percentages quoted in this article
For ease of reading, the percentages presented in this article have
been rounded down or up to the nearest whole number, except where the
percentage result was less than 1.0.
Acknowledgements
The authors would like to express their gratitude to:
* the 160 participants who contributed their time and energy to
this project;
* the research assistants who assisted the authors in the
collection of data during the study;
* Avondale College of Higher Education and Edith Cowan University
for funding this project; and
* Alistair McIntosh for his original inspiration to initiate the
SAUCER (So, Adults Use Calculations Everyday Research) Project in
1998-1999.
References
Attard, C. (2013). Teaching with technology: iPads and primary
mathematics. Australian Primary Mathematics Classroom, 18(4), 38-40.
Australian Curriculum Assessment and Reporting Authority. (2013).
Australian Curriculum. Retrieved 1 April, 2014, from
http://www.australiancurriculum.edu.au/
Brinkworth, P. (1998). How do you subtract? Australian Primary
Mathematics Classroom, 3(3), 8-10.
Burns, R. B. (2000). Introduction to research methods (4th ed.).
Sydney: Pearson Education Australia.
Carraher, D. W., & Schliemann, A. D. (2002). Is everyday
mathematics truly relevant to mathematics education? In J. Moshkovich
& M. Brenner (Eds.), Everyday and Academic Mathematics in the
Classroom. Monographs of the Journal for Research in Mathematics
Education, 11, 238-283.
Coben, D. (2003). Adult numeracy: Review of research and related
literature. Nottingham, UK: University of Nottingham.
Coben, D., O'Donoghue, J., & FitzSimons, G. E. (Eds.).
(2000). Perspectives on adults learning mathematics: Research and
practice, 21. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Cooper, B., Cooper, J., & Dunne, M. (2000). Assessing
children's mathematical knowledge: Social class, sex and problem
solving. Buckingham, UK: Oxford University Press.
Creswell, J. W., & Plano Clark, V. L. (2011). Designing and
conducting mixed methods research (2nd ed.). Thousand Oaks, CA: Sage.
Evans, J. (2000). Adults' mathematical thinking and emotions:
A study of numerate practices. London: Routledge/Falmer, Taylor &
Francis Group.
Gal, I. (Ed.). (2000). Adult numeracy development: Theory,
research, practice. Cresskill , NJ: Hampton Press.
Goldenberg, E. P. (2000). Thinking (and talking) about technology
in math classrooms. Issues in Mathematics Education, 1-8.
Greiffenhagen, C., & Sharrock, W (2008). School mathematics and
its everyday other? Revisiting Lave's 'Cognition in
Practice'. Educational Studies in Mathematics, 69, 1-12. doi:
10.1007/s10649-008-9115-7
Johnston, B. (2002). Numeracy in the making: Twenty years of
Australian adult numeracy: An investigation by the New South Wales
Centre Adult Literacy and Numeracy Australian Research Consortium
(ALNARC). Sydney: University of Technology.
Kargar, M., Tarmizia, R. A., & Bayat, S. (2010). Relationship
between mathematical thinking, mathematics anxiety and mathematics
attitudes among university students. International Conference on
Mathematics Education Research 2010 (ICMER 2010), 8(2010), 537-542.
Lave, J. (1988). Cognition in practice: Mind, mathematics and
culture in everyday life. Cambridge: Cambridge University Press.
Lentz, C. L., Kyeong-Ju Seo, K., & Gruner, B. (2014).
Revisiting the early use of technology. Dimensions of Early Childhood,
42(1), 15-31.
Myers, R. Y. (2009). The effects of the use of technology in
mathematics instruction on student achievement. (Doctor of Philosophy),
Florida International University, Miami, Florida. Retrieved from
http://digitalcommons.fiu.edu/cgi/viewcontent.cgi?article=1177&context=etd
National Numeracy Review Report Panel. (2008). National Numeracy
Review Report. Barton, ACT: Commonwealth of Australia. Human Capital
Working Group Council of Australian Governments.
Northcote, M., & McIntosh, A. (1999). What mathematics do
adults really do in everyday life? The Australian Primary Mathematics
Classroom, 4(1), 19-21.
Parsons, S., & Bynner, J. (2005). Does numeracy matter more?
London: National Research and Development Centre for Adult Literacy and
Numeracy. University of London.
Patton, M. Q. (2015). Qualitative research and evaluation methods
(4th ed.). Thousand Oaks, California: SAGE Publications, Inc.
Price, L., & Kirkwood, A. (2014). Using technology for teaching
and learning in higher education: A critical review of the role of
evidence in informing practice. Higher Education Research &
Development, 33(3), 549-564.
Rosen, L. D., Lim, A. F., Felt, J., Carrier, N. A., Cheever, J. M.,
Lara-Ruiz, J. S., ... Rokkum, J. (2014). Media and technology use
predicts ill-being among children, preteens and teenagers independent of
the negative health impacts of exercise and eating habits. Computers in
Human Behavior, 35(June), 364-375.
Saxe, G. B. (1988). The mathematics of child street vendors. Child
Development, 59(5), 1415-1425.
Thompson, I. (1993). An investigative approach to the issue of
attitudes to mathematics. Mathematics Education Review, 1(3), 32-38.
Vale, C. (2002). What do education students value in primary
mathematics curriculum? Mathematics Teacher Education and Development,
4, 28-41.
Wandt, E., & Brown, G. W (1957). Non-occupational use of
mathematics: Mental and written, approximate and exact. The Arithmetic
Teacher, 4, 151-154.
White, A. L., & Singh, P (2005). Computation in the primary
mathematics classroom: Going mental Foundations and creativity: The
strengths and weaknesses of mathematics education in East Asia:
Proceedings of the 3rd East Asia Regional Conference on Mathematics
Education (pp. 1-8). Shanghai: ICMI--EARCOME.
White, A. L., Way, J., Perry, B., & Southwell, B. (2005/2006).
Mathematical attitudes, beliefs and achievement in primary pre-service
mathematics teacher education. Mathematics Teacher Education and
Development, 7, 33-52.
Maria Northcote
Avondale College of Higher Education
<maria.northcote@avondale.edu.au>
Linda Marshall
Formerly Edith Cowan University
<Linda.marshall79@gmail.com>
Topic of calculations
(1) Demographic data about the participants was sourced from Data
pool 1: Participant information, described earlier in this article.
(2) Most participants lived in suburban or semi-rural locations.
(3) Findings reported in this article were sourced from Data pool
2: Typical calculations (450 in all) and Data pool 3: Daily log of
calculations (774 in all), described earlier in this article.
(4) Because some calculations were categorized as being related to
more than one mathematics topic, these percentage statistics add up to
more than 100.
(5) Because some calculations were categorized as being related to
more than one mathematics topic, these percentage adds up to more than
100.
Table 1: Number and age of participants in the 2011-2014
Everyday Mathematics Project
Age range No. of Percentage of
participants participants
18-30 42 26
31-40 22 14
41-50 22 14
51-60 23 14
61-70 14 9
71+ 37 23
TOTAL 160 100
Table 3: Top ten most common mathematics topics (5)
Mathematics No. of Percentage
topic calculations of 1224
calculations (1)
Money 388 32
and financial
Time 370 30
Subtraction 195 16
Addition 194 16
Counting 145 12
Mass and height 105 9
Length 104 8
and distance
Volume 87 7
and capacity
Multiplication 48 4
Fractions 27 2
and ratios
Table 4: Difficulty level of calculations in the Everyday
Mathematics Project.
Level of No. of Percentage of
difficulty calculations total (762)
1. Easy 501 66
2. Quite easy 174 23
3. Neutral 66 9
4. Quite difficult 16 2
5. Difficult 5 1
