Acquiring The Principles Of Mathematics And Science - IELTS Reading Answers & Explanations
From IELTS Practice Test Plus 3 Academic Reading Test 5 · Part 2 · Questions 14–26
Reading Passage
You should spend about 20 minutes on Questions 14–26, which are based on Reading Passage 2 on pages 105–106.
Acquiring the principles of mathematics and science
A It has been pointed out that learning mathematics and science is not so much learning facts as learning ways of thinking. It has also been emphasised that in order to learn science, people often have to change the way they think in ordinary situations. For example, in order to understand even simple concepts such as heat and temperature, ways of thinking of temperature as a measure of heat must be abandoned and a distinction between ‘temperature' and ‘heat' must be learned. These changes in ways of thinking are often referred to as conceptual changes. But how do conceptual changes happen? How do young people change their ways of thinking as they develop and as they learn in school?
B Traditional instruction based on telling students how modern scientists think does not seem to be very successful. Students may learn the definitions, the formulae, the terminology, and yet still maintain their previous conceptions. This difficulty has been illustrated many times, for example, when instructed students are interviewed about heat and temperature. It is often identified by teachers as a difficulty in applying the concepts learned in the classroom; students may be able to repeat a formula but fail to use the concept represented by the formula when they explain observed events.
C The psychologist Piaget suggested an interesting hypothesis relating to the process of cognitive change in children. Cognitive change was expected to result from the pupils' own intellectual activity. When confronted with a result that challenges their thinking – that is, when faced with conflict - pupils realise that they need to think again about their own ways of solving problems, regardless of whether the problem is one in mathematics or in science. He hypothesised that conflict brings about disequilibrium, and then triggers equilibration processes that ultimately produce cognitive change. For this reason, according to Piaget and his colleagues, in order for pupils to progress in their thinking they need to be actively engaged in solving problems that will challenge their current mode of reasoning. However, Piaget also pointed out that young children do not always discard their ideas in the face of contradictory evidence. They may actually discard the evidence and keep their theory.
D Piaget’s hypothesis about how cognitive change occurs was later translated into an educational approach which is now termed 'discovery learning'. Discovery learning initially took what is now considered the 'lone learner' route. The role of the teacher was to select situations that challenged the pupils’ reasoning; and the pupils’ peers had no real role in this process. However, it was subsequently proposed that interpersonal conflict, especially with peers, might play an important role in promoting cognitive change. This hypothesis, originally advanced by Perret-Clermont (1980) and Doise and Mugny (1984), has been investigated in many recent studies of science teaching and learning.
E Christine Howe and her colleagues, for example, have compared children’s progress in understanding several types of science concepts when they are given the opportunity to observe relevant events. In one study, Howe compared the progress of 8 to 12-year-old children in understanding what influences motion down a slope. In order to ascertain the role of conflict in group work, they created two kinds of groups according to a pre-test: one in which the children had dissimilar views, and a second in which the children had similar views. They found support for the idea that children in the groups with dissimilar views progressed more after their training sessions than those who had been placed in groups with similar views. However, they found no evidence to support the idea that the children worked out their new conceptions during their group discussions, because progress was not actually observed in a post-test immediately after the sessions of group work, but rather in a second test given around four weeks after the group work.
F In another study, Howe set out to investigate whether the progress obtained through pair work could be a function of the exchange of ideas. They investigated the progress made by 12-15-year-old pupils in understanding the path of falling objects, a topic that usually involves conceptual difficulties. In order to create pairs of pupils with varying levels of dissimilarity in their initial conceptions, the pupils' predictions and explanations of the path of falling objects were assessed before they were engaged in pair work. The work sessions involved solving computer-presented problems, again about predicting and explaining the paths of falling objects. A post-test, given to individuals, assessed the progress made by pupils in their conceptions of what influenced the path of falling objects.
Questions
Questions 14–19 Matching Headings
Reading Passage 2 has SIX paragraphs, A–F.
Choose the correct heading for paragraphs A–F from the list of headings below.
Write the correct number, i–ix.
i. A suggested modification to a theory about learning.
ii. The problem of superficial understanding.
iii. The relationship between scientific understanding and age.
iv. The rejection of a widely held theory.
v. The need to develop new concepts in daily life.
vi. The claim that a perceived contradiction can assist mental development.
vii. Implications for the training of science teachers.
viii. An experiment to assess the benefits of exchanging views with a partner.
ix. Evidence for the delayed benefits of disagreement between pupils.
Questions 20–21 Multiple Choice (Two Answers)
Choose TWO letters, A–E.
The list below contains some possible statements about learning.
Which TWO of these statements are attributed to Piaget by the writer of the passage?
Questions 22–23 Multiple Choice (Two Answers)
Choose TWO letters, A–E.
Which TWO of these statements describe Howe’s experiment with 8–12-year-olds?
Questions 24–26 Summary Completion
Complete the summary below.
Choose NO MORE THAN TWO WORDS from the passage for each answer.
How children learn
Piaget proposed that learning takes place when children encounter ideas
that do not correspond to their current beliefs. The application of this theory
gave rise to a teaching method known as 24 . At first this
approach only focused on the relationship between individual pupils and
their 25 . Later, researchers such as Perret-Clermont became
interested in the role that interaction with 26 might also play
in a pupil’s development.
Answers & Explanations Summary
| # | Answer | Evidence | Explanation |
|---|---|---|---|
| Q14 | v | It has also been emphasised that in order to learn science, people often have to change the way they think in ordinary situations | Excerpt/Passage Explanation: The passage states that students must change how they view and understand the common world around them if they want to learn science properly. Answer Explanation: The answer means that in order to study science, people must learn to think differently about things they see in their everyday lives. Reason For Correctness: The correct answer is 'v' because Paragraph A explains that learning science requires changing one's mindset in 'ordinary' or daily situations. It provides the example of 'heat' and 'temperature' to show how people must move away from common, simple ideas to more specific, scientific ones. This process of creating a new scientific understanding is called 'conceptual change,' which matches the heading's mention of developing 'new concepts' for 'daily life.' |
| Q15 | ii | Students may learn the definitions, the formulae, the terminology, and yet still maintain their previous conceptions | Excerpt/Passage Explanation: The passage explains that students might memorize specific words and math rules, but they still keep their old, incorrect ideas in their minds instead of learning the new concepts correctly. Answer Explanation: The answer identifies the main idea of the paragraph as the issue where students only understand things on a surface level. Reason For Correctness: The correct answer is 'ii' because Paragraph B describes a 'difficulty' where students memorize names, words, and math rules but do not truly change their way of thinking. This is known as 'superficial understanding'—where a person knows the facts but does not understand the deep meaning. The paragraph mentions that students can 'repeat a formula' (surface knowledge) but 'fail to use the concept' (lack of deep understanding) when looking at real things happening in the world. |
| Q16 | vi | He hypothesised that conflict brings about disequilibrium, and then triggers equilibration processes that ultimately produce cognitive change | Excerpt/Passage Explanation: The passage explains that when someone faces a disagreement with their own ideas (conflict), it causes a temporary state of confusion (disequilibrium). This then starts a process to fix the confusion, which finally results in a change in how the person understands things (cognitive change). Answer Explanation: The answer "vi" means that Paragraph C explains how seeing something that goes against what you believe can help your mind grow and improve. Reason For Correctness: The correct answer is "vi" because Paragraph C describes a theory by the psychologist Piaget. He believed that when students see something that challenges their current thoughts—referred to as "conflict" or a "perceived contradiction"—it forces them to rethink and change their ideas. This process of "cognitive change" or mental development happens because the student must solve the problem to find a new balance in their thinking. Keywords like "conflict" and "challenge" in the text match the word "contradiction" in the heading, while "cognitive change" and "progress" match "mental development." |
| Q17 | i | Discovery learning initially took what is now considered the 'lone learner' route. The role of the teacher was to select situations that challenged the pupils’ reasoning; and the pupils’ peers had no real role in this process. However, it was subsequently proposed that interpersonal conflict, especially with peers, might play an important role in promoting cognitive change | Excerpt/Passage Explanation: The passage describes how the theory of learning first focused on a single student. Then, it explains a new idea: that talking and having different opinions with other students ('peers') is actually very important for changing how a person thinks. Answer Explanation: The answer means that an update or a small change was made to an existing idea about how people learn. Reason For Correctness: The correct answer is 'i' because Paragraph D discusses how the 'discovery learning' theory changed over time. At the start, the theory focused on a student working alone (the 'lone learner'). Later, researchers added a new idea: that disagreement or 'conflict' between students is actually a good way to help them learn. This addition is a 'modification' (change) to the original theory about how learning happens. Key words like 'initially' (at the start) and 'subsequently' (later) show this progression. |
| Q18 | ix | They found support for the idea that children in the groups with dissimilar views progressed more after their training sessions than those who had been placed in groups with similar views. However, they found no evidence to support the idea that the children worked out their new conceptions during their group discussions, because progress was not actually observed in a post-test immediately after the sessions of group work, but rather in a second test given around four weeks after the group work | Excerpt/Passage Explanation: The passage explains that students with different opinions did better than students who thought the same. However, they did not show what they learned right after the lesson. They only showed improvement in a test taken four weeks later. Answer Explanation: The answer means that this paragraph talks about research showing that when students have different ideas (disagree), it helps them learn, but this learning takes some time to show up. Reason For Correctness: The correct answer is supported by Paragraph E, which explains a study where children with 'dissimilar views' (which represents disagreement) were compared to those with similar views. The study found that those with different ideas improved more. Most importantly, it notes that this 'progress' or benefit was not seen 'immediately' but was found four weeks later, which matches the idea of 'delayed benefits.' |
| Q19 | viii | In another study, Howe set out to investigate whether the progress obtained through pair work could be a function of the exchange of ideas | Excerpt/Passage Explanation: The passage says that Howe did a new research project to see if students learned better when they worked in groups of two and shared their thoughts with each other. Answer Explanation: The answer means that Paragraph F is best described by the heading: "An experiment to assess the benefits of exchanging views with a partner." Reason For Correctness: The correct answer is viii because Paragraph F describes a specific study focused on how students learn when working in pairs. The text explains that the researcher (Howe) wanted to see if "pair work" (working with a partner) and the "exchange of ideas" (sharing and discussing different views) helped the students understand science better. The paragraph details how they set up these pairs and tested their progress, which directly matches the idea of an experiment to assess the benefits of exchanging views with a partner. |
| Q20 | — | — | |
| Q21 | B / D | in order for pupils to progress in their thinking they need to be actively engaged in solving problems that will challenge their current mode of reasoning. However, Piaget also pointed out that young children do not always discard their ideas in the face of contradictory evidence. They may actually discard the evidence and keep their theory | Excerpt/Passage Explanation: The passage states that for students to grow mentally, they must work on problems that test their logic. It also explains that children might choose to keep their original ideas and throw away any proof that shows their ideas are incorrect. Answer Explanation: The answer B means that when students face hard problems that make them question the way they think, it helps them learn better. The answer D means that children sometimes ignore new facts because they want to keep believing what they already believe. Reason For Correctness: The correct answer identifies two ideas from Piaget found in paragraph C. First, he believed that for students to keep learning, they must solve problems that challenge their current way of thinking (the 'mental challenge' mentioned in B). Second, he noted that children do not always change their minds; instead, they might ignore evidence that proves them wrong so they can keep their old ideas (as stated in D). |
| Q22 | — | — | |
| Q23 | A / E | In one study, Howe compared the progress of 8 to 12-year-old children in understanding what influences motion down a slope. In order to ascertain the role of conflict in group work, they created two kinds of groups according to a pre-test: one in which the children had dissimilar views, and a second in which the children had similar views. They found support for the idea that children in the groups with dissimilar views progressed more after their training sessions than those who had been placed in groups with similar views. However, they found no evidence to support the idea that the children worked out their new conceptions during their group discussions, because progress was not actually observed in a post-test immediately after the sessions of group work, but rather in a second test given around four weeks after the group work | Excerpt/Passage Explanation: The passage describes how the researcher, Howe, checked how well children understood a science topic (moving down a slope). It shows they were tested three times: first with a 'pre-test,' then a 'post-test' right after the study, and finally another test four weeks later. Answer Explanation: The answer identifies two correct descriptions of the study: first, that children had their knowledge of a scientific problem checked (A), and second, that they were given three separate tests at different times (E). Reason For Correctness: The correct answer is supported by the details in Paragraph E. First, it mentions that the experiment looked at children’s 'understanding what influences motion down a slope,' which is a scientific problem. Second, it describes three specific testing events: it mentions a 'pre-test' used to divide the children into groups, a 'post-test' given immediately after the study, and a 'second test' (meaning second after-test, or the third total test) given four weeks later. This confirms that there were three tests given over a period of time. |
| Q24 | discovery learning | Piaget’s hypothesis about how cognitive change occurs was later translated into an educational approach which is now termed 'discovery learning' | Excerpt/Passage Explanation: The passage states that Piaget's theory about how children learn was turned into a way of teaching that is called 'discovery learning'. Answer Explanation: The answer 'discovery learning' is the name of a specific teaching method that came from Piaget's ideas about how children's thinking changes. Reason For Correctness: The correct answer is 'discovery learning' because the passage explicitly links Piaget’s hypothesis to this specific educational approach. In paragraph D, it states that Piaget’s ideas were 'translated into an educational approach,' which is a synonym for 'teaching method.' The text then uses the phrase 'now termed,' which means 'known as,' immediately followed by the name 'discovery learning.' |
| Q25 | teacher | The role of the teacher was to select situations that challenged the pupils’ reasoning; and the pupils’ peers had no real role in this process | Excerpt/Passage Explanation: The passage says that in the early version of this teaching method, the teacher's job was to give students difficult tasks, and other students (peers) did not help at all. Answer Explanation: The answer is the person who runs the classroom and provides the student with problems to solve. Reason For Correctness: The correct answer is found in paragraph D. It explains that when 'discovery learning' first began, it was for the 'lone learner,' meaning the student worked alone. In this setup, only the teacher was involved because they chose the lessons, while 'peers' (other students) were not involved yet. This confirms that the initial focus was on the relationship between the student and the teacher. |
| Q26 | peers / friends | However, it was subsequently proposed that interpersonal conflict, especially with peers, might play an important role in promoting cognitive change. This hypothesis, originally advanced by Perret-Clermont (1980) and Doise and Mugny (1984), has been investigated in many recent studies of science teaching and learning | Excerpt/Passage Explanation: The passage states that researchers including Perret-Clermont believed that disagreeing or working with other students of the same age (peers) helps a child improve their way of thinking. Answer Explanation: The answer means other students who are around the same age or in the same class as the child. Reason For Correctness: The correct answer is derived from Paragraph D, which discusses how researchers like Perret-Clermont expanded on the idea of learning. While earlier theories focused on a child learning alone, these researchers suggested that 'interpersonal conflict' (interacting with others and having different opinions) with 'peers' (other children) is actually very important for a student's development and learning. |