Background of NAPLAN tests
NAPLAN is an acronym for National Assessment Program: Literacy and
Numeracy which came into being nationally in Australia in 2008. Year 3,
5, 7 and 9 students have taken NAPLAN tests every year since 2008. Test
results give information about how students are performing in Literacy
and Numeracy and are used to inform parents/carers of student's
progress and to provide information to schools to help rectify literacy
and numeracy problems in different stages of schooling.
Australian Curriculum Assessment and Reporting Authority (ACARA)
manage the national testing and Queensland Studies Authority (QSA)
administers, marks and reports on the testing in Queensland. Previous
test papers, sample questions, a summary of previous results and other
relevant information can be found at the following website: http://www.
naplan.edu.au/tests/tests_landing_page.html
In this article the language used in Year 7 and 9 NAPLAN numeracy
tests will be investigated. In both Years 7 and 9 students complete two
numeracy papers of 32 questions with a time limit of 40 minutes. In one
paper they may use a calculator and in the other calculator use is not
permitted.
Referring to previous NAPLAN numeracy tests it is evident that
every question demands an understanding of everyday language and
mathematical language which includes specific mathematics terminology
and the concise use of vocabulary as well as symbols, graphs and other
representations of mathematical operations and concepts.
Focusing on the use of language is a crucial strategy in good
mathematics teaching. Issues of language in the Year 7 and 9 NAPLAN
numeracy tests will be discussed with reference to previous research in
the teaching and learning of mathematical language.
Language use in NAPLAN Numeracy Tests
'Language is a medium through which students learn
mathematics' (Leach & Bowling, 2000, p. 24) and a large amount
of the literature has focused on language leading to problems with the
learning of mathematics.
Many authors have discussed the difficulties of words that have
multiple meanings (Pierce & Fontaine, 2009; Saxe, 1988). For
instance, words used in English often have a different meaning in
mathematics. Teachers need to 'recognise and make explicit the
difference between 'mathematical' English and
'natural' English' (Dawe & Mulligan, 1997 cited in
Frigo, 1999, p. 15). Examples of such words from the Year 7 and 9 tests
are mean, grid, rate, volume, balance, scale, key, face, head, tail,
capacity, mode, range, die, positive, product, expression, prime,
regular, right and rule. Even within mathematics words such as scale,
cube and square have more than one meaning. In some cases, the same word
functions as a different part of speech, for instance square can be a
noun, verb or adjective.
Often many different words can be used to describe the same concept
in mathematics (Spanos, Rhodes, Dale & Crandall, 1988). For instance
subtraction, minus, take-away and difference are used for the same
concept but the word difference is most often used in the NAPLAN
testing. It should also be noted that the word chance in lower years
becomes increasingly replaced by the word probability and the word
average becomes mean in later years.
Knowledge of the meanings of prefixes like bi- and di- both meaning
two, tri- meaning three, quad-meaning four are also important. This can
be confusing because often two prefixes indicate the same number for
instance both sex- and hex- represent six (sex- originating from Latin
and hex- from Greek). Examples of words using hex- and sex- are hexagon,
hexagonal and sextant, sextet, sextuplet. Bi- and di- are found in
binary, bisect, binomial, bias, biannual, bilateral, bilingual, bicycle,
bipolar and diagonal, diameter, divide, dialogue. Other important
prefixes are circum- meaning around tetra- meaning four, pent(a)-
meaning five, kilomeaning thousand, mega- meaning million and micro-
meaning a millionth. More prefixes are shown in the table below, many of
which are utilised in the NAPLAN numeracy tests.
The word altogether is used in a number of questions. Altogether is
often taken to imply addition. However, this is not always the case in
these questions. In the same way, the word total does not necessarily
imply addition. This indicates the pitfalls of teaching that a
particular word always implies a specific mathematics operation.
Mathematical text is lexically dense which means that it contains a
minimum of redundant words, that is, contextual clues (NSW Department of
School Education, 1997). Students' attention needs to be drawn to
dense phrases which contain multiple concepts which can pose
difficulties to students for example reflex angle, closest to, possible
outcomes, exactly halfway, number sentence, per person, satisfies
equations, best estimate, number line, equal length, regular hexagon,
percentage decrease, square based pyramid, positive whole number,
satisfy the inequality, average daily saving, stem and leaf plot,
standard six sided die, product of prime factors, right angled isosceles
triangle, four consecutive whole numbers, three quarter turn clockwise,
sum of dots on opposite faces.
Symbols in mathematics can also pose problems for students. In the
NAPLAN numeracy tests for Year 7 and 9 many symbols or words for symbols
or combinations of words and symbols are used. Examples of the included
symbols in one or both Year 7 and 9 are: the four operations (+, -, +,
x), am and pm, symbols for units such as mL, kg, mg, m, km, cm, mm,
[m.sup.2], [cm.sup.2], [degrees]C, symbols such as $, <, [check],
[10.sup.3] and %,--and [degrees] for percentage, negative and degrees,
3D for three dimensional, N, S, E, W for the four directions, x, h for
variables, fractions written as numbers and grid references such as A3.
A combination of words and symbols is seen in 6-sided, 6 metres, 3
times, litres per 100 km and words are used when writing cubic metres,
minutes, metres per minute, cents. Square centimetres, litres, grams,
kilograms, dollars and grams and numbers such as seventy-five are
written as either words or symbols. Large numbers are often written in
prose form.
In addition to words and symbols causing misunderstandings,
mathematics also introduces graphs, diagrams and other representations
which add to the complexity (Lowrie & Diezmann, 2009). Lowrie and
Diezmann (2009) pointed out that students may have problems interpreting
graphics in word questions and they stated, 'Students'
performance may thus be a measure of their ability to comprehend the
graphical (or linguistic) components of a task rather than their
knowledge of the mathematics within the task' (Lowrie &
Diezmann, 2009, p. 146). Students need practice interpreting information
in the many different visuals in NAPLAN tests and they need to examine
these representations carefully for help with meaning. However, in many
cases the words and visual image duplicate each other and it is possible
to answer the question without understanding every aspect of the
question,
Common themes in the NAPLAN tests are shopping involving prices
(costs), sale prices, percentage increases, travelling questions
involving maps, distances, speeds, petrol consumptions and directions,
areas and perimeters of land (paddocks), recipes involving masses,
volumes, capacities and ratios, questions based on sport/game scores
giving rise to scores, means, medians and so on and probability
questions based on marbles or lollies such as jelly beans, questions and
movies, timetables, ticket sales, temperatures, surface areas,
population figures. Teachers need to expose students to word questions,
including reading the questions, especially on the above topics.
The NAPLAN tests allow just over a minute per question which does
not seem long for students who are struggling to understand and complete
the questions in the allocated time. However, special provisions such as
readers, scribes, use of dictionaries and extra time are available for
some students for instance ESL and special needs students if
applications are forwarded to the relevant bodies. Current information
on this can be found in the Test preparation handbook on the NAPLAN
website.
Students should be introduced to resources such as dice, coins
(emphasising the head and the tail), spinners, money, maps, recipes,
games, calendars and clocks as they are referred to in the test
questions.
As expected, more context-based questions appear in the Year 9 than
the Year 7 tests. Examples in the Year 7 and 9 NAPLAN questions refer to
recipes, floodlights, smudges, conveyor belts, satellite dishes,
air-conditioners, paddocks, planks, rockets, aeroplane seating, exchange
rates, films, sticks, watches, alarm clocks, DVD players, leaflets and
the summit of a mountain all of which are probably unfamiliar to some
students especially rural and LBOTE students. Some of the vocabulary and
several contexts may be unfamiliar to certain groups of students,
raising equity questions. This issue has been highlighted by many
researchers such as Zevenbergen, Dole and Wright (2004). Although the
NAPLAN tests have been attractively presented, they have not been
designed to be inclusive of all Australians. Questions which contain
familiar content and are attractive to indigenous peoples should be
included in each paper.
Numeracy is more than straightforward mathematical computation and
includes the interpretation of information presented in printed and
other forms. It is reasonable that NAPLAN numeracy tests present
students with age-appropriate challenges in interpreting information in
print form. However, Abedi argued that
There is a difference between language that is an essential part of
the content of the question and language that makes the question
incomprehensible to many students ... While it is important to
understand and value the richness of language in an assessment system;
it is also important to make sure that ... students ... not be penalised
for their lack of English proficiency in areas where the target of
assessment is not language. Though we understand the views of some
language modification critics in not 'dumbing down' assessment
questions by simplifying the language, we also recognise the distinction
between necessary and unnecessary linguistic complexity. (Abedi, 2009,
p. 173)
Conclusion
NAPLAN tests from 2008, 2009 and 2010 have similar layouts,
questions and use of language. The NAPLAN test papers and some
additional trial questions are freely available on the web making it
possible for students to practice on previous tests.
Teachers need to ensure that students become familiar with the
necessary mathematical language. This article should not be seen as
implying that teachers should aim to teach primarily for test purposes,
but rather that vocabulary is an important part of mathematics teaching
and learning. In terms of the NAPLAN testing, it is important that
students have a sound knowledge of mathematics language in order to feel
well prepared for the testing. This must occur in mathematics
lessons--English teachers cannot be expected to teach the nuances of
mathematical language. This means that mathematics teachers must also
become teachers of language and literacy.
Teachers' guidance can assist students to master the language
of mathematics. And as Murray, 2009 stated, 'The language, and
progressively the more specialist language, is necessary for learning
and even more, understanding mathematics' (Murray, 2009, p. 6).
References
Abedi, J. (2009). Validity of assessments for English language
learning students in a national/ international context. Estudiossobre
Education, 16, 167-183.
Frigo, T. (1999). Resources and teaching strategies to support
Aboriginal children's numeracy learning. A review of the
literature. Retrieved October 18, 2010, from
http://research.acer.edu.au/ indigenous_education/11/
Leach, S. & Bowling, J. (2000). A classroom research project :
ESL students and the language of mathematics. Australian Primary
Mathematics Classroom, 5(1), 24-27.
Lowrie, T. & Diezmann, C.M. (2009). National numeracy tests: A
graphic tells a thousand words. Australian Journal of Education, 53 (2),
141-158.
Ministerial Council for Education Early Childhood Development and
Youth Affairs (MCEECDYA). (2010). National assessment program literacy
and numeracy. Viewed 10 March, 2010, at http://
www.naplan.edu.au/home_page.html
Murray, J. (2009). Two heads are better than one. Retrieved October
18, 2010, from http://nrich. maths.org/public/viewer.php?obj_id=6383
NSW Department of School Education. (1997). Teaching literacy in
mathematics in Tear 7. Sydney: Author.
Pierce, M.E. & Fontaine, L.M. (2009). Designing vocabulary
instruction in mathematics. Reading Teacher, 63(3), 239-243.
Saxe, G.B. (1988). Linking language with mathematics achievement.
In R.R. Cocking & J.P. Mestre (Eds.), Linguistic and cultural
influences on learning mathematics. Hillsdale, NJ: Lawrence Erlbaum
Associates.
Spanos, G., Rhodes, N.C., Dale, T.C. & Crandall, J. (1988).
Linguistic features of mathematical problem solving: Insights and
applications. In R.R. Cocking & J.P. Mestre (Eds.), Linguistic and
cultural influences on learning mathematics (pp. 221-240). Hillsdale NJ:
Lawrence Erlbaum Associates.
Zevenbergen, R., Dole, S. & Wright, R. (2004). Teaching
mathematics in primary schools. Crows Nest, NSW: Allen and Unwin.
Table 1. More examples of prefixes
Prefix and meaning Examples of words which include the
prefix
mon(o)- and uni- meaning one or monolith , monorail , monotony ,
single monocle, monocycle, monologue,
monotreme, unit, uniform,
unification, unicorn, unique
tri- meaning three triangle, trillion, triomino,
trinomial, third, tripod, triplets,
tricycle, tricolour, triple, triad
quadr- or quart- meaning four quadrilateral, quadrillion,
quarter; quartile, quadrant,
quadratic, quartet, quart,
quadbike, quadruplets, quadrangle
oct- meaning eight octagon, octopus, octane, octopod
October
dec(a) or dek(a)- meaning ten decade, decagon, decillion
deci- meaning one tenth decimal system, decimetre,
decilitre
cent- or centi- meaning hundred cents, centimetre, century
or hundredth centenary, centennial, centipede
midcentury, percentage, percent,
milli- meaning thousand or millimetre, millennium
thousandth
de- meaning taking something decrease, deduce, descend, decline
away the opposite decentralisation , deforestation
poly- meaning many polygon(2D), polyhedron (3D) ,
polymer polyomino, polynomial,
polygamous,
Teachers should encourage students to take note of common roots in
words, for example, rectangle and rectangular, cylinder and
cylindrical, parallel and parallelogram, clock and clockwise or
anticlockwise, reflect and reflection, half and halfway and division
and divisible or divisor.