IPM module 3 Week 2 – Critical thinking in the form of a critique

IPM module 3

Week 2 – Critical thinking in the form of a critique:

Notes, examples and language

In order to be able to critique a text you have to be sufficiently familiar with the topic. Since

the only topic I am familiar with in sufficient depth is mathematics I will show two examples

texts, one based on mathematics and one based on statistics.

Example 1: Solving a quadratic equation

Question: Find the roots of �� − 2� + 3 = 0.

Solution: Using the quadratic formula we have

� = 2 ± �−2�� − 4�1��3�2 .

Hence � = −3 or � = +1. (providing we have real roots)

Critical thinking (in the form of a critique):

1st half: comparing benefits of using the quadratic formula against factorisation (a general

comment)

Although this formula always works to give the real roots of a quadratic its use can be quite

laborious. A more efficient way in this particular case could have been to factorise by sight.

This would then be taking advantage of the factor theorem of algebra.

2nd half: detail - describes specific problems when using factorisation

Note that, although factorisation always works in theory, in practice we usually want the

coefficients of the quadratic to be simple enough for us to perform the mental arithmetic

required.

Example 2: On mathematics: Finding the max and min of a function using calculus

Question: Find and classify all the turning points of the function f(x) = (x – 1)(x + 1)(x + 2).

Solution

Summary and critique

Identify in the commentary below all places where I am summarising and where I am

critiquing.

In this solution we start by expanding the factored form of f(x). The next step

then finds the first derivative of this function. However, there is an inconsistent

use of notation since the symbol ‘y’ has been used instead of f(x). In terms of

mathematical presentation it is important to be consistent in one’s use of

notation. Therefore, it would be more appropriate to continue with the same

notation for the function as has been originally stated in the question, and write

df/dx.

Also, the derivative is equated to zero at the same step as the derivative has

been found. In general, when solving optimisation problems, these two aspects

are presented as two different steps. In other words it is more appropriate to

first find the derivative to be

���� = 3�� + 4� − 1

and then, since we wish to find stationary points, we equate this derivate to

zero:

3�� + 4� − 1 = 0

The next step involves simply solving this quadratic, from which we get the x

ordinate of the stationary points.

After this comes the usual test for classifying stationary points. In this case the

first derivative test has been used, but equally the second derivative test could

have been used. Both tests have their advantages and disadvantages, namely

that the second derivative test can sometimes be quicker, but may fail to give a

valid answer in certain cases. The first derivative test will always work, but can

take longer to apply, particularly if there are many turning point to have to test.

The last two steps of the solution classify the stationary points as well as giving

their coordinates.

There is, however, a missing part to the solution. The question asked for all turning points of

the function, and this solution has only presented three of the turning points (specifically the

three that are called stationary points). It does not present the solution to the other two

turning points which exists on this function, namely the point of inflection which exists

between the maximum point and the minimum point. This is a serious omission in the

presentation of a mathematical solution, and would need to be corrected before it could be

considered a complete solution to the problem.

Example 3: A text on logarithms

The following text is taken from “Making Sense of Logarithms as Counting Divisions”, Christof

Weber, The Mathematics Teacher, Vol. 112, No. 5 (March 2019), pp. 374-380.

“Students’ difficulties understanding the meaning of logarithms could stem in part

from differences between teachers’ and students’ views of them. Effective teaching

does not mean providing only the explanations that make sense for experts, but

also introducing conceptualizations that make sense from the point of view of

learners. This requires not only common mathematical knowledge but also a kind

of mathematical knowledge that is specific to the task of teaching (or specialized

content knowledge; Ball, Hill, and Bass 2005). For the teaching of logarithms, this

means that it is not enough for teachers to know the exponential definition

“log� � = � if and only if �� = �.

[…] The purpose of this article is to unpack some specialized content knowledge

for teaching logarithms. […] On the basis of my own teaching experience, teachers

can make logarithms meaningful for students by beginning with [the]

conceptualization, as it refers not to exponents, but to a more accessible concept—

division.

(a lot of comparison here)

[…] But what does logarithm mean? This word and its literal translation, which is

“number of ratios” or “ratio number,” are not self-explanatory at all (possible

problem identified). But (possible solution to problem) if we interpret ratio

number as the “number that counts ratios” or as “number of divisions,” its meaning

becomes apparent. For instance (example), the logarithm (base 2) of 8 is 3 because

8 must be divided by 2 three times to yield 1. This “number of divisions”

interpretation of logarithms is, for learners, quite different from the “logarithms as

exponents” interpretation. However, from a mathematical point of view, asking for

the number of divisions, b ÷ a? = 1, is the same as asking for the exponent, b = a?.

This means that the division-counting property (as I call it) is mathematically

equivalent to the exponential property (critical thinking - synthesis), although

historically these two interpretations are separated by more than a century.”

Identifying the critique in the text above

See lesson.

Example 4: A text on statistics

The following text is taken from Linda L. Cooper & Felice S. Shore (2008), “Students'

Misconceptions in Interpreting Center and Variability of Data Represented via Histograms and

Stem-and-Leaf Plots”, Journal of Statistics Education.

"Perhaps, the presumption for some undergraduate statistics courses is that the groundwork

has been laid. However, research on primary and secondary students has already documented

difficulties in reasoning about quantitative data when it is provided in the aggregate, as in

histograms, line plots or other frequency graphs (Friel & Bright, 1995; McClain, 1999; Watson,

et al., 2003). Results from the Sixth Mathematics Assessment of the National Assessment of

Educational Progress (NAEP) indicate that more than three-fourths of 8th graders and more

than two-thirds of 12th graders were unable to correctly identify the median value for one of

the variables shown in a scatter plot (Zawojewski & Heckman, 1997), though the authors

were unable to conclude whether the difficulty stemmed from the graphical representation or

a misunderstanding of median.

[...] Taken together, the existing body of research indicates that students entering college may

have only a superficial understanding of center and variability, and are likely to have

particular difficulty extracting information about those features when data are presented in

graphical form. Our concern is that as students in introductory college courses move beyond

descriptive statistics, collectively little attention from precollege and college courses has been

focused upon making connections between measures of center and variability and graphical

representations."

Identifying the critique in the text above

See lesson.

The language/discourse of critical thinking (/critique)

The examples above on presenting critical thinking (as critiques of the topics) involved

certain types of vocabulary, phrasing and sentence building. The way in which this vocabulary

and phrasing can be built is iluustrated in the table on the next page.

The aim of this table is to show you examples on an underlying principle of what constitutes

critique language and description. This underlying principle is what you should aim to learn

and understand. Then you will know how to write in a critical manner, and you will only need

to learn individual vocabulary, terminology, and phrasing in order to express your own

criticality.

For example, given the following from example 1

• Effective teaching does not mean providing only the explanations that make sense for

experts, but also introducing conceptualizations that make sense from the point of

view of learners.

We can rewrite this as illustrated below whilst retaining the features and essence of a critique

• Beyond using teaching simply to impart the standard meaning of logarithm, it is

important to support learners in developing their own understanding of the concept of

logarithms,

or

• An important element in learning about logarithms is the way in which learners make

sense of this in their own way. This is something which is not considered in the

standard way of teaching logarithms whereby only the expert definition is given.

Similarly, given the following from example 2

• However, research on primary and secondary students has already documented

difficulties in reasoning about quantitative data when it is provided in the aggregate, as

in histograms, line plots or other frequency graphs (Friel & Bright, 1995; McClain,

1999; Watson, et al., 2003). Taken together, the existing body of research indicates that

students entering college may have only a superficial understanding of center and

variability, and are likely to have particular difficulty extracting information about

those features when data are presented in graphical form.

We can rewrite this as illustrated below whilst retaining the features and essence of a critique

• Previous assumptions about college students’ understanding of measures of center and

variability have proved incorrect. It has been shown that such students seem to have

little understanding of these statistics. As a result, they have difficulty identifying such

measures when data are presented in graphical form. Specific research by Friel &

Bright, 1995; McClain, 1999; and Watson, et al., 2003 has found that primary and

secondary students have difficulties in reasoning about quantitative data when such

data is presented in aggregate form, as in histograms, line plots or other frequency

graphs.

or

• The ability to understand measures of center and variability can be seen in the way

students recognise, or not, such features in data presented in aggregate form, as in

histograms, line plots or other frequency graphs. However, the assumption that

students enter college with an adequate understanding of these features has been

shown not to be the case. For example, research by Friel & Bright, 1995; McClain, 1999;

and Watson, et al., 2003 has found that primary and secondary students have

difficulties in reasoning about measures of center and variability.

Below is a random critique using key vocabulary and phrasing in order to illustrate the

critique-ness of the critique below. Bear in mind that the example below is extreme, but it is

designed to highlight the nature of critique-ness:

This method is sufficiently inaccurate as to be flawed and unsuccessful because of

its limited use in the relatively narrow domain, and its irrelevant use of an

unscientific model.

⎩⎪⎨⎪⎧

person

method

process… ⎭⎪⎬⎪⎫

X is a

⎩⎪⎨⎪⎧

important

fundamental

crucialdecisive

… ⎭⎪⎬⎪⎫

⎩⎪⎨⎪⎧

aspect

element

issue

… ⎭⎪⎬⎪⎫

of/in/about …

because …

due to …

by reason of …

in that …

The {1, 2, 3…}

⎩⎪⎨⎪⎧

important

fundamental

crucialdecisive

… ⎭⎪⎬⎪⎫

⎩⎪⎨⎪⎧

aspects

elements

issues

… ⎭⎪⎬⎪⎫

of/in/about …

are …

because …

due to …

by reason of …

in that …

Table: Examples of critiques type sentences using certain types of vocabulary and phrasing.

Other examples of language which can be used when writing in a critique manner is shown below

might have / could have / would

have

In other words

the analysis could be …

An alternative approach

might/would be to …

Not only has/have … but

also …

Particularly important

/relevant/useful waswere … Of less significance was/were It may be that … this could be explained by …

certain changes/

additions/elaboration might be

needed …

An explanation/description

/example of … would be

appropriate

The author then does … but

without doing …

However, if this approach

were used/adopted … then …

There are many resources for helping you learn to write academic and technical English.

Some of these can be found at

• http://www.opentextbooks.org.hk/zh-hant/ditatopic/4220

• http://www.phrasebank.manchester.ac.uk/

• https://www.ref-n-write.com/trial/academic-phrasebank/

• www.springer.com › document › Free+Download+-+Useful+Phrases

• nnkt.ueh.edu.vn › uploads › 2019/06 › Academiv-Phrase-Bank

but be careful about how you use these in order not to end up plagiarising.

Some criteria for developing a critical thinking (/critique)

Apart from the aspects of critique used in example 1 and example 2 above, other aspects

include:

• Comparing and contrasting: Look for similarities and differences between what

different authors have said or done.

Examples

1) Between the logarithm function and the exponential function, the most common

approach is to define the logarithm first (as an integral) and then define the

expoential as the inverse of the logarithm. However, such an approach requires

the student to first learn calculus before they can use these two functions, thus

leaving the use of these function quite late in the student’s learning.

On the other hand the exponential function can be introduced after the binomial

theorem, which is part of algebra, and comes much earlier in the student’s

learning.

2) Although both the mean and the median are both aimed at finding the average

vakue of the data, a major difference can be observed between the two

measures, namely that the former is sensitive to outliers whereas the latter is

not.”

There are two points to note here:

i) firstly, note the language of “similarity and difference”.

ii) secondly, look for synonyms and antonyms of such language (see the sources

you have been told about in other classes, as well as a thesaurus, as well as

online phrasebanks)

• Commenting on the methodology used: How has the author collected the data? How

have they analysed the data? What methods are they using to analyse the data?

Examples

1) Descriptive statistics can only be used to categorise and summarise the data collected.

It cannot be used to infer or generalise anything about the larger set of data from

which your data comes from. However, descriptive statistics does allows us to see an

overall pattern or trend (such as by the use of graphs).

2) Inferential statistics allows us to make generalisations and inference. In this way we

can take a sample, study it and reasonably extrapolate or infer the behaviour of the

population from which the sample came. There is, however, a disadvantage to

inferential statistics in that the analyses and results are never accurate. There will

always be errors in the final results, and the conclusions based on these results will

only be approximate.

• Identifying flaws or weaknesses and strengths and positive: Look for problems,

limitations, assumptions, etc in theories, arguments, methods, practice, etc.

Examples

1) “In his use of the mean Smith (1990) has failed to take into account the aspect of

outliers in his data. As a result of this his calculation for the mean is not as

representative of the middle as it could be. One way of overcoming this flaw

could be to …”

2) “However, Jones (1995) does not assess the effect of ignoring the outliers in his

data when calculating the line of best fit.”

3) “The use of the z-test on this data has the limitation that it can only be applied

to data which is (approximately) normally distributed.”

• Offer constructive suggestions: Offer suggestion for correction, improvements, etc.

Examples

1) “A much more accurate trend curve could have been developed if the author

had used an exponential fit instead of the linear fit to his data.”

2) “It would have been useful for the author to calculate two lines of best fit: one

containing the outlying data, and one ignoring the outlying data. In this way a

comparison could have been made between the two best-fit lines in order to …”

3) “Given that the data used is skewed, a more appropriate test would have been

the chi-squared test. This would then have allowed ...”

These are only four aspects of what can be considered for a critique. By reading widely you

will come to see other aspect which can be considered.

So how can critical thinking (/critique) be defined?

At its simplest level, a critique is an opinion about the author’s work. But it is not just any

opinion. It is a form of opinion which is a reflective and detailed evaluation or assessment of

the significance, assumptions, flaws, etc. of the author’s work. A critique therefore requires a

particular way of thinking. By looking at as many examples as possible we can come to see a

critique as:

• asking about links between ideas,

• asking about the importance and relevance of arguments and ideas,

• asking whether or not things could have been improved, changed, done differently,

etc…,

• asking whether or not any limitations or assumptions or hypotheses or inferences

were made,

• asking about any consequences, side effects or unseen reactions as a result of the work

done by the auhor,

• asking about errors, inconsistencies, conflicting evidence, gaps, etc. in the research,

• asking about the strengths and/or weaknesses in the research,

• … in other words, asking questions of the work (literature review, data collection and

analysis, results, discussion, conclusions) done by the author;

Finally, a critique (as a form of critical thinking) is seen to be a critique by the use of a

particular type of vocabulary (nouns, adjectives, synonyms, etc.), constructed via phrasing and

sentences and paragraphs in a particular way.

So we might say that

Critique = critique language (vocabulary and phrasing)

+ a close, reflective reading of the text

in order to identify what could be done differently

based on what was already done, how it was done, why it was done.

What can we critique?

Anything can be critiqued:

• The literature;

• Someone’s interpretation of the literature;

• The design of the experiment;

• The data collection methods;

• The analysis of the data;

• The theoretical framework/model/methodology used;

• Any assumptions made;

Linguistic features of a critique

(1) 3rd conditional or past unreal conditionals, e.g.:

• “The analysis might have been stronger if …”

• “The writer could have focused more on …”

• “The study would have achieved greater accuracy if …”

(Note - In a critique the if clause is often placed second in the sentence, after the main

clause1. Why do you think this is?)

(2) Inversions when a negative or an adjectival phrase begins a sentence, e.g.:

• “Not only has this study challenged previous findings, it has also…”

• “In no part of the methods section do the authors specify precisely what …”

• “Particularly salient were the observations on …”

• “Of less significance were the findings …”

(Note – Inversions foreground or give special emphasis to the information/idea located at

the beginning of the sentence. Why might a writer choose to do this?)

(3) Hedging/Boosters to make clear precisely how weak/strong a claim is, e.g.:

• “This arguably goes further than …”

• “It may be that this factor …”

• “… and it could be explained on the basis that …”

• “and this is certainly a major advance …”

• “ … the authors have clearly established …”

(4) Attitude markers revealing the atttitude of the writer of the critique to its subject-matter,

e.g.:

• “Surpisingly the author did not consider …”

• “It is difficult to understand why …”

• “… is particularly interesting.”

(5) Self-mentions, e.g.:

• “… but, as it seems to me, this …”

• “I was not persuaded by this argument.”

• “I believe …”

• “Nevertheless, I would argue that this approach …”

(Note - The use of self-mentions varies considerably from discipline to discipline and

likewise opinions about the stylistic appropriacy of self-mentions can vary (sometimes

considerably) from tutor to tutor within a particular faculty or department. Therefore you

should check with your tutor or department whether it is considered acceptable to use

self-mentions when writing a critique before you start to write.)

(6) Choice of lexis

The table on the next page contains a list of vocabulary items which are commonly used

when writing a critique2.

1 Swales, J. and Feak, C. (2012). Academic Writing for Graduate Students. 3rd ed., Ann Arbor, MI: University of Michigan at 260

Verbs Adverbs Adjectives Nouns

account for

aid

analyse

answer

appear

assert

collect

combine

complete

describe

employ

exhibit

fail

predict

raise

represent

review

seem

succeed

suffer from

suggest

wonder

accurately

completely

correctly

currently

enough

exactly

fully

inaccurately

incorrectly

insufficiently

later

necessarily

really

relatively

successfully

sufficiently

unfairly

unsuccessfully

accurate

ambitious

apparent

beneficial

careful

competent

complete

complex

correct

detailed

difficult

effective

extra

fair

flawed

good

important

impressive

inaccurate

incorrect

ineffective

innovative

insignificant

insufficient

interesting

likely

limited

little

modest

obvious

potential

preliminary

reasonable

reliable

remarkable

restricted

scientific

serious

significant

similar

accuracy

analysis

aspect

assumption

collection

consideration

difference

difficulty

effect

element

factor

flaw

growth

impact

implication

importance

inaccuracy

increase

information

insight

model

reduction

significance

source

site

tool

2 Adapted from Swales & Feak (2012) (op. cit.); Nesi & Gardner (2012) (op. cit.)

Verbs Adverbs Adjectives Nouns

simple

small

successful

sufficient

suitable

unfair

unimportant

unlikely

unreasonable

unreliable

unsatisfactory

unscientific

unsuccessful

unusual

useful

==================================================

Other texts to use

Example 1

1) “Many workshops and meetings with the US high school mathematics teachers

revealed a lack of familiarity with the use of transformations in solving equations and

problems related to the roots of polynomials. When asked to find a quadratic equation

whose solutions are reciprocals of ax2 + bx + c = 0, the teachers uniformly tried to

answer the question using the quadratic formula and could not generalize the problem

and the answer to nth degree equations. The substitution x = 1/y was new to them.

Following a demonstration of the solution to this problem, they were able to find an

equation whose solutions are twice (or n times) as large as the solutions of a given

equation, or increased by a constant.

The workshop participants were also introduced to the two approaches for

deriving the quadratic formula described in this article. They believed that their

students will benefit from the transformational approach.”

Libeskind, Shlomo (2010) “The use of transformations in solving equations”,

International Journal of Mathematical Education in Science and Technology, 41:3, 432 - 434

2) “Parametric integrals are often proposed as exercises where induction formulas

and/or closed formulas are established (see [1] and [2]); proofs of various properties

of the given sequence of integrals can be built on these formulas. In this paper we

derive combinatorial identities from sequences of definite integrals, the proof being

generally based on the computation of definite integrals of parametric polynomials and

using telescopic methods.

In section 2, a sequence of definite integrals of a simple polynomial is studied;

the computations lead to a combinatorial identity.

In section 3, a sequence of definite integrals is studied following three different

pathways. This study provides connections between definite integrals of polynomials,

trigonometric integrals and combinatorics.

In section 4, parametric integrals depending on two parameters are studied.

Finally, in section 5, a modification of the telescopic method leads to a new

computation of the sum of the alternating harmonic series.”

Dana-Picard, T.(2007) “Sequences of definite integrals”,

International Journal of Mathematical Education in Science and Technology, 38:3, 393 - 401

3) “In this note we present a method in which we develop an analytic solution for certain

classes of second-order differential equations with variable coefficients. By the use of

transformations and by repeated iterated integration, we obtain a desired solution.

This represents an alternative way to obtain a solution to such methods as classic

power series techniques and other approaches (see, for example, Ince [1], where the

author uses successive approximations). It is, at times, more involved than traditional

methods.”

Wilmer III, A. and Costa, G. B.(2008)

“Solving second-order differential equations with variable coefficients”,

International Journal of Mathematical Education in Science and Technology, 39:2, 238 - 243,

1) Original text

“Many workshops and meetings with the US high school mathematics teachers

revealed a lack of familiarity with the use of transformations in solving equations and

problems related to the roots of polynomials. When asked to find a quadratic equation

whose solutions are reciprocals of ax2 + bx + c = 0, the teachers uniformly tried to

answer the question using the quadratic formula and could not generalize the problem

and the answer to nth degree equations. The substitution x = 1/y was new to them.

Following a demonstration of the solution to this problem, they were able to find an

equation whose solutions are twice (or n times) as large as the solutions of a given

equation, or increased by a constant.[…]”

version 1

“Many meetings with high school mathematics teachers revealed a lack of familiarity

with the use of transformations and problems related to polynomials. When asked to

find a equation whose solutions are reciprocals of ax2 + bx + c = 0, the teachers

uniformly tried to answer the question using the formula and could not generalize the

problem and the answer. Using x = 1/y was new to them. Following a demonstration,

they were able to find an equation whose solutions are twice as large as the solutions

of a given equation, or increased by a constant.[…]”

version 2

“Many workshops and meetings with the US high school mathematics teachers showed

that these teachers were not familiar in solving equations with the use of

transformations. Neither were they familiar with using transformations involving

problems where you have to find roots of polynomials. When asked to find a quadratic

equation ax2 + bx + c = 0 whose solutions are reciprocals of this equation, the teachers

uniformly tried to answer the question using the quadratic formula, and the

generalization to nth degree equations was beyond them. The substitution x = 1/y was

new to them. The solution to this problem was demonstrated to them, after which they

were able to find an equation whose solutions are twice (or n times) as large as the

solutions of a given equation, or increased by a constant.[…]”

Version 3

“Many workshops and meetings with the US high school mathematics teachers

revealed a lack of familiarity with the use of a technique which allows them to simplify

difficult equations into simpler ones, specifically when it comes to finding values of x

which makes those equations equal to zero. When asked to find an equation of degree

2 whose solutions are reciprocals of that equation, the teachers uniformly tried to

answer the question using the formula for finding the roots of a quadratic equation,

and could not generalize the problem and the answer to equations of degree n. The

substitution x = 1/y was new to them. Following a demonstration of the solution to this

problem, they were able to find an equation where the roots are twice (or n times) as

large as the roots of a given equation, or increased by a constant.[…]”

==========================================

Appendix

Example 1: On means, medians and modes in statistics

An example of critique

In analysing the data author A has used the mean as his measure of central tendency,

explaining that the advantage of this is that, because all data values are used in finding the

mean, taking the mean for different samples of a population tends to give similar results. This

indicates that the mean is robust, i.e. it resists very well any fluctuations between different

samples.

However, the problem with using the mean is that it is sensitive to outliers. The further the

outliers(s) the more it will affect the mean, resulting in a value of the mean which is not

representative of the “middle” of majority of the data.

For example, the mean salary from £1200, £1000, £900, £1100, and £4000 is £1640. But it is

clear that £1640 is not representative as an average of the majority of the salaries. And the

reason we have such a high average is due to the single value of £4000. So one single value can

significantly skew the value of the mean away from the most representative average.

It may be that the data the author used had no outliers or was not sensitive to outliers.

However, this is not addressed, nor is any other reason for omitting the problems of the use of

the mean as a measure of central tendency.

In terms of measuring central tendency, author B has used the median. In his paper

author B states that this has the advantage of overcoming the problem caused by outliers

when using the mean. He then goes onto to say that the disadvantage of the using the median

as a measure of central tendency is that, because the median is not calculated arithmetically

(and therefore does not use each data value) it is easily affected by the type of sample we take

from the population.

However, author A mentions “Author B does not elaborate on how or why the use of the

median overcomes the problems caused by the use of the mean”. For example, there is no

explanation of the fact that the reason the median is totally immune to the effect of outliers is

because it is based on finding the value which lies exactly in the middle of the data set, once

this has been arranged into ascending order.

According to author A, the simple example of using the salaries would suffice to illustrate this

point, namely we would firstly arrange these in ascending order to be £900, £1000, £1100,

£1200, £4000, and then we would choose the middle value. In this case the middle value is

£1100, which is much more representative of the general average, and is not affected by the

single high value of £4000.

Furthermore, both papers use only one measure of central tendency when analysing their

data. It seems that their research would have benefited from using both measures as well as

an analysis of the difference between these two measures as used on their respective data

sets. This could then have provided answers to which types of data are more suited to using

the mean and which are more suited to using the median.

Exercise 1: A text on big data

Consider the following two chunks of text taken from A literature review on big data analytics,

B. Shdifat, D. Cetindamar, S. Erfani, 2019 proceeding of PICMET ’19: Technology management

in the world of intelligent systems.

Text 1

Text 2

Exercise 2: For next week

Bring a paper/text (ormore than one paper/text if you wish) of your own choice.

The exercise for next week will be for you to

• find passages in the paper/text where the author is critiquing something;

• identify what type of language is used to write the critique as a critique;

• critique the author’s paper/text. In other words, try to find suggestions, improvements,

corrections, alternatives, etc. to the author’s ideas.

Summary of linguistic structures used in my critique

• Critique (Hedging): However, if … then certain additions and elaboration

might need to be … in order to …

• Summary: For example, one of the … they assume is …

• Critique (3rd conditional): An explanation of … would be appropriate, along

with …

• Summary: The author then continues by …

• Critique: But without giving …

• Critique (3rd conditional): Again, showing … would greatly help …

• Summary: The author now moves on to …

• Summary: He firstly states … and then …

• Critique (Rhetorical question): But where did the … come from? How did the

author …

• Critique (3rd conditional): In terms of a more … it would be constructive to …

• Solution to critique: In other words, … the author could then …

• Summary: Having proved the theorem the author then goes on to show …

along with …

Note that you can write a summary without doing a critique, but you can’t write a critique

without first summarising certain aspects of the text and are going to critique.