Verbal Ability ...

Directions: Read the passage and answer the question that follows.

It's harder than you might think to make a dinosaur. In Jurassic Park they do it by extracting a full set of dinosaur DNA from a mosquito preserved in amber, and then cloning it. But DNA degrades over time, and to date none has been found in a prehistoric mosquito or a dinosaur fossil. The more realistic prospect is to take a live dinosaur you have lying around already: a bird. Modern birds are considered a surviving line of theropod dinosaurs, closely related to the T. rex. and velociraptor. By tinkering with how a bird embryo develops, you can silence some of its modern adaptations and let the older genetic instructions take over. This obviously adds to the general merriment of the world, and will eventually kickstart a roaring trade in exotic quasi-Jurassic pets. But there are a surprising number of other projects that aim to bring back more recently vanished wild animals, from the woolly mammoth to the Pyrenean ibex.

Advances in gene-editing technology promise to make "de extinction" a potentially viable enterprise, but what exactly is the point? To answer this question, the Swedish science journalist Torill Kornfeldt has travelled to meet the researchers involved for his excellent book The Re-Origin of Species that raises a number of deep questions and paradoxes about our relationship with nature.

Part of the motivation is simply aesthetic, and part derives from a kind of species guilt. Scientists disagree over whether it was in fact humans, rather than early climate change, that killed off mammoths, giant sloths and other megafauna, but reviving them, to some minds, would be a kind of symbolic expiation for all our other environmental depredations, returning us to a prelapsarian innocence in our relationships with other animals.

A more pragmatic criticism of de-extinction is that it diverts resources from the attempt to save species that have not yet become extinct. Kornfeldt visits the splendidly named Frozen Zoo in San Diego, which since the 1970s has accumulated a collection of cells from nearly 1,000 species frozen in liquid nitrogen. By cloning cells from a dozen rhinos, the zoo's director Oliver Ryder hopes to re-establish a sustainable population; or, as Kornfeldt nicely puts it: "Twelve test tubes could enable new baby rhinos to rumble about once more like miniature armoured vehicles."

There are no right or wrong answers in this area, but as Kornfeldt implies, the rhetoric of such debates still revolves around a few presumptive virtues that are rarely interrogated deeply. The aim of greater "biodiversity", for instance, often cited by the de-extinction researchers she interviews, is never, in truth, an absolute goal. We could save millions of people a year if we eradicated the malaria-carrying mosquito – perhaps, as researchers are now trying to do, by replacing them with genetically sterile individuals – but that would be a decrease in biodiversity. The fungi threatening to kill off some of our best-loved tree species, also covered in this book, are themselves organisms, as much as the trees they attack. Inevitably, those discussing such ideas are always choosing one species over another, and judging one ecosystem as somehow more authentic than another – not that nature itself cares much either way, being the most brutal engine of extinction on the planet.

Directions: Read the passage and answer the question that follows.

It's harder than you might think to make a dinosaur. In Jurassic Park they do it by extracting a full set of dinosaur DNA from a mosquito preserved in amber, and then cloning it. But DNA degrades over time, and to date none has been found in a prehistoric mosquito or a dinosaur fossil. The more realistic prospect is to take a live dinosaur you have lying around already: a bird. Modern birds are considered a surviving line of theropod dinosaurs, closely related to the T. rex. and velociraptor. By tinkering with how a bird embryo develops, you can silence some of its modern adaptations and let the older genetic instructions take over. This obviously adds to the general merriment of the world, and will eventually kickstart a roaring trade in exotic quasi-Jurassic pets. But there are a surprising number of other projects that aim to bring back more recently vanished wild animals, from the woolly mammoth to the Pyrenean ibex.

Advances in gene-editing technology promise to make "de extinction" a potentially viable enterprise, but what exactly is the point? To answer this question, the Swedish science journalist Torill Kornfeldt has travelled to meet the researchers involved for his excellent book The Re-Origin of Species that raises a number of deep questions and paradoxes about our relationship with nature.

Part of the motivation is simply aesthetic, and part derives from a kind of species guilt. Scientists disagree over whether it was in fact humans, rather than early climate change, that killed off mammoths, giant sloths and other megafauna, but reviving them, to some minds, would be a kind of symbolic expiation for all our other environmental depredations, returning us to a prelapsarian innocence in our relationships with other animals.

A more pragmatic criticism of de-extinction is that it diverts resources from the attempt to save species that have not yet become extinct. Kornfeldt visits the splendidly named Frozen Zoo in San Diego, which since the 1970s has accumulated a collection of cells from nearly 1,000 species frozen in liquid nitrogen. By cloning cells from a dozen rhinos, the zoo's director Oliver Ryder hopes to re-establish a sustainable population; or, as Kornfeldt nicely puts it: "Twelve test tubes could enable new baby rhinos to rumble about once more like miniature armoured vehicles."

There are no right or wrong answers in this area, but as Kornfeldt implies, the rhetoric of such debates still revolves around a few presumptive virtues that are rarely interrogated deeply. The aim of greater "biodiversity", for instance, often cited by the de-extinction researchers she interviews, is never, in truth, an absolute goal. We could save millions of people a year if we eradicated the malaria-carrying mosquito – perhaps, as researchers are now trying to do, by replacing them with genetically sterile individuals – but that would be a decrease in biodiversity. The fungi threatening to kill off some of our best-loved tree species, also covered in this book, are themselves organisms, as much as the trees they attack. Inevitably, those discussing such ideas are always choosing one species over another, and judging one ecosystem as somehow more authentic than another – not that nature itself cares much either way, being the most brutal engine of extinction on the planet.

Directions: Read the passage and answer the question that follows.

It's harder than you might think to make a dinosaur. In Jurassic Park they do it by extracting a full set of dinosaur DNA from a mosquito preserved in amber, and then cloning it. But DNA degrades over time, and to date none has been found in a prehistoric mosquito or a dinosaur fossil. The more realistic prospect is to take a live dinosaur you have lying around already: a bird. Modern birds are considered a surviving line of theropod dinosaurs, closely related to the T. rex. and velociraptor. By tinkering with how a bird embryo develops, you can silence some of its modern adaptations and let the older genetic instructions take over. This obviously adds to the general merriment of the world, and will eventually kickstart a roaring trade in exotic quasi-Jurassic pets. But there are a surprising number of other projects that aim to bring back more recently vanished wild animals, from the woolly mammoth to the Pyrenean ibex.

Advances in gene-editing technology promise to make "de extinction" a potentially viable enterprise, but what exactly is the point? To answer this question, the Swedish science journalist Torill Kornfeldt has travelled to meet the researchers involved for his excellent book The Re-Origin of Species that raises a number of deep questions and paradoxes about our relationship with nature.

Part of the motivation is simply aesthetic, and part derives from a kind of species guilt. Scientists disagree over whether it was in fact humans, rather than early climate change, that killed off mammoths, giant sloths and other megafauna, but reviving them, to some minds, would be a kind of symbolic expiation for all our other environmental depredations, returning us to a prelapsarian innocence in our relationships with other animals.

A more pragmatic criticism of de-extinction is that it diverts resources from the attempt to save species that have not yet become extinct. Kornfeldt visits the splendidly named Frozen Zoo in San Diego, which since the 1970s has accumulated a collection of cells from nearly 1,000 species frozen in liquid nitrogen. By cloning cells from a dozen rhinos, the zoo's director Oliver Ryder hopes to re-establish a sustainable population; or, as Kornfeldt nicely puts it: "Twelve test tubes could enable new baby rhinos to rumble about once more like miniature armoured vehicles."

There are no right or wrong answers in this area, but as Kornfeldt implies, the rhetoric of such debates still revolves around a few presumptive virtues that are rarely interrogated deeply. The aim of greater "biodiversity", for instance, often cited by the de-extinction researchers she interviews, is never, in truth, an absolute goal. We could save millions of people a year if we eradicated the malaria-carrying mosquito – perhaps, as researchers are now trying to do, by replacing them with genetically sterile individuals – but that would be a decrease in biodiversity. The fungi threatening to kill off some of our best-loved tree species, also covered in this book, are themselves organisms, as much as the trees they attack. Inevitably, those discussing such ideas are always choosing one species over another, and judging one ecosystem as somehow more authentic than another – not that nature itself cares much either way, being the most brutal engine of extinction on the planet.

Directions: Read the passage and answer the question that follows.

It's harder than you might think to make a dinosaur. In Jurassic Park they do it by extracting a full set of dinosaur DNA from a mosquito preserved in amber, and then cloning it. But DNA degrades over time, and to date none has been found in a prehistoric mosquito or a dinosaur fossil. The more realistic prospect is to take a live dinosaur you have lying around already: a bird. Modern birds are considered a surviving line of theropod dinosaurs, closely related to the T. rex. and velociraptor. By tinkering with how a bird embryo develops, you can silence some of its modern adaptations and let the older genetic instructions take over. This obviously adds to the general merriment of the world, and will eventually kickstart a roaring trade in exotic quasi-Jurassic pets. But there are a surprising number of other projects that aim to bring back more recently vanished wild animals, from the woolly mammoth to the Pyrenean ibex.

Advances in gene-editing technology promise to make "de extinction" a potentially viable enterprise, but what exactly is the point? To answer this question, the Swedish science journalist Torill Kornfeldt has travelled to meet the researchers involved for his excellent book The Re-Origin of Species that raises a number of deep questions and paradoxes about our relationship with nature.

Part of the motivation is simply aesthetic, and part derives from a kind of species guilt. Scientists disagree over whether it was in fact humans, rather than early climate change, that killed off mammoths, giant sloths and other megafauna, but reviving them, to some minds, would be a kind of symbolic expiation for all our other environmental depredations, returning us to a prelapsarian innocence in our relationships with other animals.

A more pragmatic criticism of de-extinction is that it diverts resources from the attempt to save species that have not yet become extinct. Kornfeldt visits the splendidly named Frozen Zoo in San Diego, which since the 1970s has accumulated a collection of cells from nearly 1,000 species frozen in liquid nitrogen. By cloning cells from a dozen rhinos, the zoo's director Oliver Ryder hopes to re-establish a sustainable population; or, as Kornfeldt nicely puts it: "Twelve test tubes could enable new baby rhinos to rumble about once more like miniature armoured vehicles."

There are no right or wrong answers in this area, but as Kornfeldt implies, the rhetoric of such debates still revolves around a few presumptive virtues that are rarely interrogated deeply. The aim of greater "biodiversity", for instance, often cited by the de-extinction researchers she interviews, is never, in truth, an absolute goal. We could save millions of people a year if we eradicated the malaria-carrying mosquito – perhaps, as researchers are now trying to do, by replacing them with genetically sterile individuals – but that would be a decrease in biodiversity. The fungi threatening to kill off some of our best-loved tree species, also covered in this book, are themselves organisms, as much as the trees they attack. Inevitably, those discussing such ideas are always choosing one species over another, and judging one ecosystem as somehow more authentic than another – not that nature itself cares much either way, being the most brutal engine of extinction on the planet.

Directions: Read the passage carefully and choose the best answer for the following question.

Theodor Adorno's 1967 essay on Arnold Schoenberg makes an excellent case for the great composer as a spiritual successor to J.S. Bach, the 18th century classical composer generally acclaimed as the father of modern tonality.

Adorno's case is built on the composers' treatment of melodic subjects, which he views as 'pure' in an intellectual and philosophical sense. He contrasts this to the work of the classical and romantic composers, specifically Beethoven, whose work he views as overcommitted to the formal façade unintentionally constructed by Bach: essentially he claims that Beethoven et al rejected Bach's challenging, philosophically constructive methodology in favor of "a category existing prior to the subject-matter and oriented on external consensus", a category Adorno broadly defines as style.

However, Adorno makes numerous problematic assumptions that denigrate the works of Beethoven, Brahms, Wagner, etc., and also Bach himself. Adorno accuses composers of bowing to an audience's expectation for 'pleasurable sensations' at the expense of meaning. This view is contingent upon an anachronistic view of music's public acceptance, as well as an unjustifiable set of aesthetic standards; moreover, it ignores social and economic factors of artistic production. Adorno declares that Beethoven's use of form and treatment of the subject constitutes a mistake corrected in the composer's later career. Adorno claims that Schoenberg avoided pre-conceived forms, but Adorno's analysis of the two predecessors is misleading and provides inadequate context for a comparison of the three.

And while Adorno acknowledges the aesthetic preferences that bias his claims, and provides adequate explanation for them through analysis of Schoenberg's music, he fails to acknowledge his implicit claim that the treatment of the subject in Bach and his successors is less intellectually, philosophically, or aesthetically valid when it focuses more on the cause by which the work arises rather than the purpose it serves. Adorno therefore in his praise of Schoenberg willfully ignores Schoenberg's massive ideological departure from the western tradition. Through his misleading arguments that favor a specific style, Adorno validates his own philosophical methodology at the expense of many composers' works.

Adorno's essay is marked by indignation at Schoenberg's reputation for inaccessibility. According to Adorno, this is a result of anti-intellectualism: "if one does not understand something, it is customary to project one's own inadequacy on to the object, declaring it to be incomprehensible". Adorno then criticises the compositional mainstream of betraying its artistic standards, noting that "schools such as Debussy's, despite the aesthetic atmosphere of art for art's sake, have met this expectation" of providing pleasure to the listener. On aesthetic grounds, he can no more justify the value of Schoenberg's dissonant modernism than Debussy's 'affability,' other than to say that Schoenberg challenges certain consumer assumptions that Adorno views as problematic.
Modern aesthetic standards cannot be retroactively applied: Debussy's compositions, while successful, were wildly experimental: when criticised for avoiding the very same facades that Adorno decries, Debussy responded that his music was governed only by his pleasure—a remark that, while possibly hedonistic, reflects the same logic that led Schoenberg to abandon classical tonality. To bring Adorno back to his main example, Beethoven was one of the most controversial, avant-garde composers of his day. Reviews of his work constantly criticise the random chord and key changes, and absurd instrumentation—criticisms matched in character by only a few composers in history, Schoenberg probably foremost.

Directions: Read the passage carefully and choose the best answer for the following question.

Theodor Adorno's 1967 essay on Arnold Schoenberg makes an excellent case for the great composer as a spiritual successor to J.S. Bach, the 18th century classical composer generally acclaimed as the father of modern tonality.

Adorno's case is built on the composers' treatment of melodic subjects, which he views as 'pure' in an intellectual and philosophical sense. He contrasts this to the work of the classical and romantic composers, specifically Beethoven, whose work he views as overcommitted to the formal façade unintentionally constructed by Bach: essentially he claims that Beethoven et al rejected Bach's challenging, philosophically constructive methodology in favor of "a category existing prior to the subject-matter and oriented on external consensus", a category Adorno broadly defines as style.

However, Adorno makes numerous problematic assumptions that denigrate the works of Beethoven, Brahms, Wagner, etc., and also Bach himself. Adorno accuses composers of bowing to an audience's expectation for 'pleasurable sensations' at the expense of meaning. This view is contingent upon an anachronistic view of music's public acceptance, as well as an unjustifiable set of aesthetic standards; moreover, it ignores social and economic factors of artistic production. Adorno declares that Beethoven's use of form and treatment of the subject constitutes a mistake corrected in the composer's later career. Adorno claims that Schoenberg avoided pre-conceived forms, but Adorno's analysis of the two predecessors is misleading and provides inadequate context for a comparison of the three.

And while Adorno acknowledges the aesthetic preferences that bias his claims, and provides adequate explanation for them through analysis of Schoenberg's music, he fails to acknowledge his implicit claim that the treatment of the subject in Bach and his successors is less intellectually, philosophically, or aesthetically valid when it focuses more on the cause by which the work arises rather than the purpose it serves. Adorno therefore in his praise of Schoenberg willfully ignores Schoenberg's massive ideological departure from the western tradition. Through his misleading arguments that favor a specific style, Adorno validates his own philosophical methodology at the expense of many composers' works.

Adorno's essay is marked by indignation at Schoenberg's reputation for inaccessibility. According to Adorno, this is a result of anti-intellectualism: "if one does not understand something, it is customary to project one's own inadequacy on to the object, declaring it to be incomprehensible". Adorno then criticises the compositional mainstream of betraying its artistic standards, noting that "schools such as Debussy's, despite the aesthetic atmosphere of art for art's sake, have met this expectation" of providing pleasure to the listener. On aesthetic grounds, he can no more justify the value of Schoenberg's dissonant modernism than Debussy's 'affability,' other than to say that Schoenberg challenges certain consumer assumptions that Adorno views as problematic.
Modern aesthetic standards cannot be retroactively applied: Debussy's compositions, while successful, were wildly experimental: when criticised for avoiding the very same facades that Adorno decries, Debussy responded that his music was governed only by his pleasure—a remark that, while possibly hedonistic, reflects the same logic that led Schoenberg to abandon classical tonality. To bring Adorno back to his main example, Beethoven was one of the most controversial, avant-garde composers of his day. Reviews of his work constantly criticise the random chord and key changes, and absurd instrumentation—criticisms matched in character by only a few composers in history, Schoenberg probably foremost.

Directions: Read the passage carefully and choose the best answer for the following question.

Theodor Adorno's 1967 essay on Arnold Schoenberg makes an excellent case for the great composer as a spiritual successor to J.S. Bach, the 18th century classical composer generally acclaimed as the father of modern tonality.
Adorno's case is built on the composers' treatment of melodic subjects, which he views as 'pure' in an intellectual and philosophical sense. He contrasts this to the work of the classical and romantic composers, specifically Beethoven, whose work he views as overcommitted to the formal façade unintentionally constructed by Bach: essentially he claims that Beethoven et al rejected Bach's challenging, philosophically constructive methodology in favor of "a category existing prior to the subject-matter and oriented on external consensus", a category Adorno broadly defines as style.

However, Adorno makes numerous problematic assumptions that denigrate the works of Beethoven, Brahms, Wagner, etc., and also Bach himself. Adorno accuses composers of bowing to an audience's expectation for 'pleasurable sensations' at the expense of meaning. This view is contingent upon an anachronistic view of music's public acceptance, as well as an unjustifiable set of aesthetic standards; moreover, it ignores social and economic factors of artistic production. Adorno declares that Beethoven's use of form and treatment of the subject constitutes a mistake corrected in the composer's later career. Adorno claims that Schoenberg avoided pre-conceived forms, but Adorno's analysis of the two predecessors is misleading and provides inadequate context for a comparison of the three.

And while Adorno acknowledges the aesthetic preferences that bias his claims, and provides adequate explanation for them through analysis of Schoenberg's music, he fails to acknowledge his implicit claim that the treatment of the subject in Bach and his successors is less intellectually, philosophically, or aesthetically valid when it focuses more on the cause by which the work arises rather than the purpose it serves. Adorno therefore in his praise of Schoenberg willfully ignores Schoenberg's massive ideological departure from the western tradition. Through his misleading arguments that favor a specific style, Adorno validates his own philosophical methodology at the expense of many composers' works.

Adorno's essay is marked by indignation at Schoenberg's reputation for inaccessibility. According to Adorno, this is a result of anti-intellectualism: "if one does not understand something, it is customary to project one's own inadequacy on to the object, declaring it to be incomprehensible". Adorno then criticises the compositional mainstream of betraying its artistic standards, noting that "schools such as Debussy's, despite the aesthetic atmosphere of art for art's sake, have met this expectation" of providing pleasure to the listener. On aesthetic grounds, he can no more justify the value of Schoenberg's dissonant modernism than Debussy's 'affability,' other than to say that Schoenberg challenges certain consumer assumptions that Adorno views as problematic.
Modern aesthetic standards cannot be retroactively applied: Debussy's compositions, while successful, were wildly experimental: when criticised for avoiding the very same facades that Adorno decries, Debussy responded that his music was governed only by his pleasure—a remark that, while possibly hedonistic, reflects the same logic that led Schoenberg to abandon classical tonality. To bring Adorno back to his main example, Beethoven was one of the most controversial, avant-garde composers of his day. Reviews of his work constantly criticise the random chord and key changes, and absurd instrumentation—criticisms matched in character by only a few composers in history, Schoenberg probably foremost.

Directions: Read the passage carefully and choose the best answer for the following question.

Theodor Adorno's 1967 essay on Arnold Schoenberg makes an excellent case for the great composer as a spiritual successor to J.S. Bach, the 18th century classical composer generally acclaimed as the father of modern tonality.

Adorno's case is built on the composers' treatment of melodic subjects, which he views as 'pure' in an intellectual and philosophical sense. He contrasts this to the work of the classical and romantic composers, specifically Beethoven, whose work he views as overcommitted to the formal façade unintentionally constructed by Bach: essentially he claims that Beethoven et al rejected Bach's challenging, philosophically constructive methodology in favor of "a category existing prior to the subject-matter and oriented on external consensus", a category Adorno broadly defines as style.

However, Adorno makes numerous problematic assumptions that denigrate the works of Beethoven, Brahms, Wagner, etc., and also Bach himself. Adorno accuses composers of bowing to an audience's expectation for 'pleasurable sensations' at the expense of meaning. This view is contingent upon an anachronistic view of music's public acceptance, as well as an unjustifiable set of aesthetic standards; moreover, it ignores social and economic factors of artistic production. Adorno declares that Beethoven's use of form and treatment of the subject constitutes a mistake corrected in the composer's later career. Adorno claims that Schoenberg avoided pre-conceived forms, but Adorno's analysis of the two predecessors is misleading and provides inadequate context for a comparison of the three.

And while Adorno acknowledges the aesthetic preferences that bias his claims, and provides adequate explanation for them through analysis of Schoenberg's music, he fails to acknowledge his implicit claim that the treatment of the subject in Bach and his successors is less intellectually, philosophically, or aesthetically valid when it focuses more on the cause by which the work arises rather than the purpose it serves. Adorno therefore in his praise of Schoenberg willfully ignores Schoenberg's massive ideological departure from the western tradition. Through his misleading arguments that favor a specific style, Adorno validates his own philosophical methodology at the expense of many composers' works.

Adorno's essay is marked by indignation at Schoenberg's reputation for inaccessibility. According to Adorno, this is a result of anti-intellectualism: "if one does not understand something, it is customary to project one's own inadequacy on to the object, declaring it to be incomprehensible". Adorno then criticises the compositional mainstream of betraying its artistic standards, noting that "schools such as Debussy's, despite the aesthetic atmosphere of art for art's sake, have met this expectation" of providing pleasure to the listener. On aesthetic grounds, he can no more justify the value of Schoenberg's dissonant modernism than Debussy's 'affability,' other than to say that Schoenberg challenges certain consumer assumptions that Adorno views as problematic.

Modern aesthetic standards cannot be retroactively applied: Debussy's compositions, while successful, were wildly experimental: when criticised for avoiding the very same facades that Adorno decries, Debussy responded that his music was governed only by his pleasure—a remark that, while possibly hedonistic, reflects the same logic that led Schoenberg to abandon classical tonality. To bring Adorno back to his main example, Beethoven was one of the most controversial, avant-garde composers of his day. Reviews of his work constantly criticise the random chord and key changes, and absurd instrumentation—criticisms matched in character by only a few composers in history, Schoenberg probably foremost.

Direction: Read the following passage and answer the question that follows:

There are several key difficulties surrounding the topic of percentages. Research has shown that there has been one difficulty which is more common than others; the meaning of the terms ‘of’ and ‘out of’. Hansen (2011) states that both terms represent an operator which needs explaining. Teachers need to address these before the topic is introduced to stop any confusion. ‘Of’ represents the multiplication operator, for example: 60% of 70 means 0.6 multiplied by 70; ‘out of’ represents the division operator, for example 30 out of 50 means 30 divided by 50. The teaching of these terms needs to be clear prior to teaching, so that children are confident in what these terms represent.

Killen and Hindhaugh (2018) believe that once children understand that 1/10 is equal to 10% they will be able to use their knowledge of fractions, to determine other multiples of 10. For example; Find 40% of 200. If children are aware that 10% is 20, then it will become obvious to them that 40% must be 80. This method enlightens many other practical ways to find other percentages of a quantity. Once children know 10%, they may also start finding half percent’s, such as; 5% or 25%. However, Killen and Hindhaugh (2018) state that a difficulty could occur when they are asking for a percentage of a quantity. If children  are being asked to find the percentage, they may believe that the answer is always in percent. For example; find 60% of £480. Children may be capable of calculating the answer of 288 but instead of writing down £288, they may write down 288%. Teachers will need to explain this issue and address to children that once calculating the answer, it must be in the same units as the given quantity.

Hansen also comments that the key to succession in the understanding of percentages is the relationship and understanding the children have with fractions and decimals. For example: they should be aware that 50% is equivalent to ½ and 0.5, and 25% is equivalent to ¼ and 0.25. Teaching these topics in isolation of each other should be strictly avoided as this may destroy a child’s deep mathematical understanding. Killen and Hindhaugh agrees with this as they noted that children need to continually link decimals, fractions and percentages to their knowledge of the number system and operations that they are familiar with. Reys, et al (2010) believes however that percentages are more closely linked with ratios and proportions in mathematics and how important it is for teachers to teach these other topics to a high level. This is to later reduce the amount of errors a child has over percentages. However, these theorists also agree that understanding percentages requires no more new skills or concepts beyond those used in identifying fractions, decimals, ratios and proportions. Reys, et al states that an effective way of starting these topics is to explore children’s basic knowledge of what percentage means to them.

Barmby et al noted that a misconception occurs whenever a learner’s outlook of a task does not connect to the accepted meaning of the overall concept. Ryan and Williams state that it is more damaging for children to have misconceptions of mathematical concepts than difficulties calculating them. Killen and Hindhaugh begin to talk how the use of rules and recipes are commonly used more so by teachers that are not fully confident with percentages. The main point of the argument is that if children are taught these rules linked to percentages, misconceptions can occur. This could be caused if the child forgets or misapplies the rule to their working out. This method is not the most reliable to children but can be a quick alternative for teachers to teach their class, if they are not fully confident in the topic themselves. This links to one of the most common misconceptions in the primary classroom. Killen and Hindhaugh state that it is the teacher’s responsibility for their children’s successes in that subject area. If the teaching is effective, then the child will become more confident and develop more links revolving the topic of percentages. This will result in the child having a high level of understanding. However, if the teaching is not up to standard the child may lose confidence in themselves and end up being confused with the simplest of questions.

Direction: Read the following passage and answer the question that follows:

There are several key difficulties surrounding the topic of percentages. Research has shown that there has been one difficulty which is more common than others; the meaning of the terms ‘of’ and ‘out of’. Hansen (2011) states that both terms represent an operator which needs explaining. Teachers need to address these before the topic is introduced to stop any confusion. ‘Of’ represents the multiplication operator, for example: 60% of 70 means 0.6 multiplied by 70; ‘out of’ represents the division operator, for example 30 out of 50 means 30 divided by 50. The teaching of these terms needs to be clear prior to teaching, so that children are confident in what these terms represent.

Killen and Hindhaugh (2018) believe that once children understand that 1/10 is equal to 10% they will be able to use their knowledge of fractions, to determine other multiples of 10. For example; Find 40% of 200. If children are aware that 10% is 20, then it will become obvious to them that 40% must be 80. This method enlightens many other practical ways to find other percentages of a quantity. Once children know 10%, they may also start finding half percent’s, such as; 5% or 25%. However, Killen and Hindhaugh (2018) state that a difficulty could occur when they are asking for a percentage of a quantity. If children  are being asked to find the percentage, they may believe that the answer is always in percent. For example; find 60% of £480. Children may be capable of calculating the answer of 288 but instead of writing down £288, they may write down 288%. Teachers will need to explain this issue and address to children that once calculating the answer, it must be in the same units as the given quantity.
Hansen also comments that the key to succession in the understanding of percentages is the relationship and understanding the children have with fractions and decimals. For example: they should be aware that 50% is equivalent to ½ and 0.5, and 25% is equivalent to ¼ and 0.25. Teaching these topics in isolation of each other should be strictly avoided as this may destroy a child’s deep mathematical understanding. Killen and Hindhaugh agrees with this as they noted that children need to continually link decimals, fractions and percentages to their knowledge of the number system and operations that they are familiar with. Reys, et al (2010) believes however that percentages are more closely linked with ratios and proportions in mathematics and how important it is for teachers to teach these other topics to a high level. This is to later reduce the amount of errors a child has over percentages. However, these theorists also agree that understanding percentages requires no more new skills or concepts beyond those used in identifying fractions, decimals, ratios and proportions. Reys, et al states that an effective way of starting these topics is to explore children’s basic knowledge of what percentage means to them.

Barmby et al noted that a misconception occurs whenever a learner’s outlook of a task does not connect to the accepted meaning of the overall concept. Ryan and Williams state that it is more damaging for children to have misconceptions of mathematical concepts than difficulties calculating them. Killen and Hindhaugh begin to talk how the use of rules and recipes are commonly used more so by teachers that are not fully confident with percentages. The main point of the argument is that if children are taught these rules linked to percentages, misconceptions can occur. This could be caused if the child forgets or misapplies the rule to their working out. This method is not the most reliable to children but can be a quick alternative for teachers to teach their class, if they are not fully confident in the topic themselves. This links to one of the most common misconceptions in the primary classroom. Killen and Hindhaugh state that it is the teacher’s responsibility for their children’s successes in that subject area. If the teaching is effective, then the child will become more confident and develop more links revolving the topic of percentages. This will result in the child having a high level of understanding. However, if the teaching is not up to standard the child may lose confidence in themselves and end up being confused with the simplest of questions.