Issues+and+Challenges


 * ==__Issues/Challenges and Responses within the key stages of development__==

__**Exposure to money and prior experiences**__
 * - Issues/Challenges**
 * The proliferation of credit cards, ATMs and electronic funds transfers in modern society could lead to young children having limited exposure to coins and notes. Young children in modern society are likely to have had more experiences observing payments conducted through credit or debit cards than those involving cash. This is problematic for a number of reasons including the fact that it develops misconceptions about money and its value. One major issue that could arise from primary exposure to credit and debit cards is the confusion in young learners about the fact that different things/services have different costs. There is no different card used for different purchases -whether paying for something that is $3 or $300 there is no distinction between them for young learners. Another issue arising from this is that there is no immediate way to see the deduction from the card therefore there is no clear way to see that money does run out.
 * - Response**
 * Learners need to be made aware that "electronic money is a store of monetary value, held in digital form, which is available for immediate exchange in transactions" (Kienzle & Perrig, 1996). In other words, learners need to be made aware that digital money is real money, as it holds the same value as notes and coins. For example, using a credit card to make a $50 purchase has the same result as if you were to pay with cash. Providing as much exposure to electronic transactions as possible, whilst making the connections between electronic payments and funds being debited from a financial account, will help learners to understand that electronic money is real money and is used in the same way as real money when purchasing goods and services.
 * Booker, Bond, Sparrow, & Swan (2010) stress the importance of providing opportunities of children to handle real money, thus activities that allow the manipulation of these concrete materials would be highly beneficial for preparing students for mathematics learning in the 'money and financial mathematics' strand.

- **Issue/Challenges**
 * __Mathematical literacy__**
 * Metalanguage could be confusing including for instance the statement, "he 'made' money''. This statement insinuates that one has actually physically produced/made the money as opposed to conducting a process for which the payment is currency.
 * Financial literacy is increasingly recognised as an important and challenging area for today's learners, and is defined as understanding and applying knowledge of money and finances to financial decision making (Australian Securities and Investment Commission (ASIC, 2011). While some assessments indicate that Australians have "reasonable financial literacy", some groups within the broader population may have difficulties with financial concepts (ASIC, 2011).


 * - Response**
 * It is essential that learners of all ages are exposed to the use of correct language and terms when learning about money and financial mathematics (Anderson, 1995). A class shop would provide a suitable context for using and developing "money" language (Anderson, 1995). Explicit discussion of the evolution of currency may allow learners to understand the concept that money is, as Anderson (1995) explains, " a medium of exchange that people agree to accept for things they sell or work they do". For example, to address the specific issue above, it needs to be clear to learners that money can be 'earnt' by an individual or group as a payment in return for goods or services.
 * Knowing that children are increasingly targeted as consumers, money education needs to equip learners with the abilities to make sound financial decisions (ASIC, 2011). By covering the areas of; understanding money; consumer literacy; personal finance; and money management within the maths curriculum as well as across curriculum areas financial literacy is developed (Australian Association of Mathematics Teachers (AAMT), 2009).

__**Coin recognition and value**__
 * - Issues/Challenges**
 * Learners may attribute a coin's size to its value, i.e. the 50c coins is worth more because the $2 coin because it is bigger (ACARA, 2011; Siemon et al., 2011).
 * Counting coins and notes to make a particular value may be problematic for learners who have not developed the understandings to allow them to recognise that one coin can be '5' cents (Siemon et al., 2011). This occurs because student's knowledge of number and measurement are still linked to counting objects, therefore they will be challenged by the fact that a coin is worth five and not one (Siemon et al, 2011).
 * Booker (2010, p.490) states that "money is the unit used to measure the value or cost placed on objects". This creates a challenge for some learners because what is considered to be of value to people will differ vastly (Siemons et al, 2011).
 * Coins are worth more spread out on a table than when they are stacked up.
 * Learners could attribute the numerical value on the coin with its value. This could cause confusion as 50c could be seen as being more than $5 because fifty is more than five.


 * - Response**
 * Recognising the value of coins as separate from their size is one challenge for learners. Siemon et al (2011) believes that for many students the only way to learn the value of coins is through repeated exposure and hands on manipulation of coins. "For many students the value of coins will be learnt only through repeated exposure to, and practice, in handling various coins" (Siemon et al., 2011, p. 624). Anderson (1995) believes that if possible these opportunities should involve real coins as fake coins can be different in size and appearance.
 * Counting with money may be quite difficult for students to grasp because they are explicitly taught in foundation year that "each object must be counted only once" (ACARA, 2011). Therefore for learners to gain competency with counting coins and their value the development of key number skills must come first (Booker et al., 2010). For instance to be able to recognise that one coin can represent 'five' learners must be able to trust the count (Siemons et al., 2011). Further to this the ability to work with both 1 digit and 2 digit numbers is needed to be able to manipulate money amounts involving dollars and cents (Booker et al.,2010). Use of a class shop provides hands on experiences where students can experiment with value of notes and coins (Booker et al., 2010).
 * Value and worth are different distinctions, as money is used to measure value, the distinction between value and worth needs to be explicitly elaborated (Siemons et al, 2011). Discussion in the classroom environment, where learners think of things they value highly and compare their judgments with other peers could help to teach the idea that worth is relative (Siemons et al, 2011). Using catalogues to rank items in an order of value is one activity where learners can investigate differences in worth, and value (Siemons et al, 2011).
 * Trusting the count refers to the idea that children "may not believe that if they counted the same collection again they would arrive at the same amount" (Siemon et al., 2011). Therefore learners who have difficulty recognising the value in coin collections as the same irregardless of how they are placed may not have yet reached the stage of being able to trust the count (Department of Education and Early Childhood Development (DEECD), 2009). To address this challenge learners may benefit from tasks that develop "rich part-part -whole Knowledge", such as hands on practise with recognising visual representations of numbers (DEECD, 2009).
 * For learners who have difficulties with discerning coin values because of the numerical representation ie. judging $5 as 'less than' 50c, the misconception could be stemming from difficulties understanding place value. For instance, to understand that the 5 in $5 is a countable and composite unit that represents 500c and is therefore the higher value (DEECD, 2009). Bundling sticks and other materials are often used to demonstrate the idea of a composite unit (Siemon, 2011). The big idea that '10 of these is 1 of those' could be seen in money maths as learners work with building equivalent representations of particular amounts for instance 10 x10c coins = $1.

__**Equivalency**__
 * - Issues/Challenges**
 * Equivalency, The idea that a collection of two fifty cent coins is the same value as five twenty cent coins or one dollar coin.

- **Response**
 * Beginning at a foundation level, it is essential for learners to make accurate visual and physical representations of mathematical concepts in order to help them gain a clear understanding of the content they are learning (Thompson, 1994). The basis for equivalence could also be seen to relate to the number skills developing in the substrand of number and place value where students group and partition collections as it involves developing the skills of understanding the inherent value of each coin as a composite countable unit. Similarly the mental strategies needed to group or add small collections of coins to a particular value can be seen to depend upon the developing mental addition strategies in the number and place value substrand (ACARA, 2012)


 * __Rounding Money__**
 * -Issue/Challenge**
 * Students may encounter issues with rounding money because cents are rounded to the nearest 5 cents rather than the nearest 10cents (Siemon et al., 2011).
 * Students may become confused when rounding the total of a number of items/costs because they may believe that this should be done individually (Anderson, 1998).
 * When rounding dollars and cents to the nearest dollar the language used could become confusing for a learner. This is because "the language of ones is followed by the language of tens and ones" (for example $2.89 is read as two dollars and eighty-nine cents).


 * -Response**
 * A clear understanding about the real life connections involved in rounding to the nearest five cents is necessary for learners who are beginning to deal with rounding (Anderson, 1995). Using a shop in classrooms provides opportunity so that learners can practise with items that are not priced only in 5c or 10c increments (Anderson, 1995). This also gives a real life context to explicitly demonstrate that rounding applies to the final purchase price when a number of items are bought (Anderson, 1995).
 * It is important that students have an overall understanding of the purpose for rounding money. Anderson (1995) believes that the explicit teaching of rounding associated with money is necessary. Students need to understand when rounding should occur and that rounding only applies to the total price of a purchase when multiple items are bought (Anderson, 1995). Providing real-life situations could be a way of showing students how this strategy could be useful when it comes to using financial mathematics in everyday life (i.e. rounding the cost of a grocery shop or rounding for the purpose of comparing). When rounding dollars and cents to a whole dollar amount it is likely to help students consider the whole number of cents (Siemon et al, 2011).
 * When approaching rounding amounts of money it can be confusing for learners as the dollar and cent amounts in one unitary price are said as two separate whole number amounts (Siemon et al, 2011). When approaching the rounding of money it may therefore be helpful to make connections to the area of measurement where learners may be familiar with the idea of two distinct units that have a relationship, such as centimetres and metres (Siemon et al, 2011).


 * __Percentages__**
 * -Issues/Challenges**
 * When working with money and financial mathematics students may develop issues and challenges around the numerical understandings needed to work with money calculations such as percentages. Students may confuse tenths with hundredths so that they believe that 0.3 is 3% not 30% (Mathematics Navigator, n.d). This problem is reversed when writing a percentage as a decimal, for example representing 5% as 0.5 instead of 0.05%(Mathematics Navigator, n.d.).
 * Students identifying what the original price of an item was before a discount is given. The problem must be worked out backwards to solve it. e.g. If the problem was that 12% was given, $88 was paid and the original amount was the unknown some learners will try to find original cost by adding 12% of $88. Similar to this challenge could be the understanding that an increase of a percentage followed by a decrease of a percentage will take the total back to the original value...this also applies vice versa (Mathematics navigator, n.d). Similarly, finding the increase or decrease instead of the final amount which requires students to make choices on the appropriate algorithm as well as manipluating the numbers (Mathematics Navigator, n.d.).


 * -Response**
 * Students find identifying the operation to be used when working with percentages to be challenging (Mathematics Navigator, n.d). This could be because percentages are generally introduced as " things in their own right" (Eastaway & Askew, 2010). One way to develop understanding of percentages is to use them as a tool to make comparisons, such as comparing exam results. for instance a comparison between exam marks where a learner got a result of 21/25 on one exam and 16/20 on another may be seen to be comparable results as in both cases 4 questions were missed. However using percentages allows us to measure things that were not on a common scale - so changing how many questions were on the tests, getting 1/9 or 91/100 demonstrates the usefulness in percentages (Eastaway and Askew, 2010). For learners to be able to think in percentages they first must master the numerical understandings of Partitioning so that they have grasped fractional and decimal thinking (DEECD, 2009). Once fractions and decimals are well understood proportional reasoning helps students develop the skills to work with percentages, namely through building understandings of the concepts of seeing units in different representations and this conceptual understanding lessons the chance of students becoming over reliant on rule based algorithms (DEECD, 2009). When specifically discussing the comparison of decimals and percentages there may be a misconception regarding place value of decimals. Using a similar idea of place value as a hundreds, tens and ones board, decimals can be identified as tenths hundredths and thousands with Zeros added to demonstrate the worth of decimals (Eastaway and Askew, 2010). Before this stage though, students need to be introduced to concepts such as the idea that multiplication does not always result in a bigger number, again concepts which may have been missed while working with decimals and fractions, and may need revisiting in hands on ways (DEECD, 2009).
 * Calculations with percentages may not always be straightforward and students may struggle to know what is being required of them when working with percentages. This could be seen to be because of misunderstandings from language used when discussing percentages. Many people think of 100% as being 'everything', yet this causes problems when things have increased by 120% as learners are confused that you can have more than 'everything' (Eastaway and Askew, 2009). Instead it is important to build the understanding that percentages can be any value and that per cent means divided by 100 (Eastaway & Askew, 2010). Another way to think about percentages could be to remember " think percentages, think hundredths" (Seimon et al. 2011). Encouraging learners to think about percentage as a part, or fraction of the whole by asking "percentage of what?" can be useful to help learners understand calculations involving percentages (Seimon et al. 2011)

-**Issues/Challenges**
 * __Decimals and base numerical systems__**
 * Learners could misunderstanding that all numeration systems are base ten Through thinking that in all currency systems 100c = $1.


 * - Response**
 * The Australian curriculum emphasises using other currency systems to deepen the learners understanding of base numerical systems ( ACARA, 2012). Further to this teaching approaches could emphasis times when conversions occur that are not in 10s, for instance in time or imperial measures (Eastaway & Askew, 2010). While there is less use of these older style measurements these days, an understanding of them allows for a deeper understanding of the concepts of how our decimal system works (Eastaway & Askew, 2010).

__**Best Buys**__
 * - Issues/Challenges**
 * Students may automatically assume that the better buy is automatically decided using the ticketed price rather than also comparing the amount of the product on offer (i.e) assuming that a 250ml coca cola at $2 is a better buy than a 600ml coca cola at $4, because $2 is the 'lesser' amount).
 * Critical analysis could lead to the question arising about what constitutes a "best buy". Contributing factors such as quality could come into play.


 * -Response**
 * The inability to calculate "best buys" could be seen to be connected with Piaget's theory of proportional reasoning -a skill developed from the stage of concrete to formal operations that depends on many interconnected ideas and strategies (Snowman et al., 2009; DEECD, 2009). The capacity to identify and describe what is being compared is not always straightforward (for example is the cost being compared based on the whole product or the cost per equal unit) (DEECD, 2009). Breaking down whole items into equal fractions so that it can be compared to a similar item with a price per unit, is the type of skill that students are expected to develop to be able to make 'best buy' judgements. This seems to relate to the mathematical concepts built up in the Number and Algebra strand of The Australian Curriculum such as within the substrand of fractions and decimals as it involves the use of understanding that one 'buy' can be seen as a fractional amount of another (ACARA, 2012). Furthermore, connecting students experience of mathematics to real life situations of relevance such as shopping can provide an engaging context likely to enhance the mathematical learning (AAMT, 2009). So that other number skills such as the ability to use mathematical calculations to establish a 'price per unit' are applied as the idea that smart shoppers need to compare both the price and the size of the containers when looking for the best value needs to be communicated to the learners (Department of Education and Communities (DEC), 2011). This involves being able to make equivalent comparisons, therefore students who have difficulties understanding or working out the idea of a best buy may need to revisit the conceptual ideas of multiplicative thinking as the ability to think about multiplication in a number of different ways supports the mental skills necessary to "solve a wider range of problems involving equal groups, simple proportion, combinations, and rate" (DEECD, 2009).
 * Discussion about value and worth are critical literacy skills.It is therefore worth recognising that individuals will all have their own distinct views in regards to money (AAMT, 2009). It may be assumed therefore, that judgements about quality could be one of the areas that come up when discussing best buys. Knowing that education toward financial literacy requires respecting the idea that "different lenses" may be used by different people will then inform teachers toward explicit teaching of the knowledge needed to make informed decisions (AAMT, 2009). Namely to teach the mathematical concepts underpinning best buys while allowing discussion into the issues of what constitutes a best buy (DEC, 2009).