About the series

The new books by Mohan Dhall have been carefully created as part of a comprehensive series that develops Critical Thinking and Mathematical Reasoning skills. Mohan, an expert in gifted education and critical thinking, has designed the series in a manner that builds the capacity for students to think critically as they progress through the series. Many questions will challenge even the brightest of students. The stimulus created is unmatched in any series produced in Australia or elsewhere. This should help students to prepare for unexpected test items, where an application of critical thinking skills is assessed – rather than rote memory that does not assess fluid intelligence. Each question utilises psychometric principles and has been created with a view to assisting students develop their analytical and logical reasoning faculties.

Critical Thinking Skills

Each Critical Thinking book assesses visual acuity, working memory, the capacity to argue, apply reasoning rules, the capacity to understand independent and interdependent events, estimation skills, apply inductive and deductive reasoning, hypothesis test, detect fallacy in argument and logically reason throughout. 

Book 1

Book 1 is the first book of the series and accordingly introduces students to the format of questions evident in the Critical Thinking test in the new NSW Selective Schools Exam. However, though the format of questions may look similar, there is a nuance to the questions, and many will test students. 

It is important in this first book for students to build confidence through recognising question types and building familiarity. However, do not underestimate what is on offer. The challenge here is for students to attempt the questions without guidance. They need to be focused on correct processes, rather than ‘right answers.’ Parents and educators can assist the development of their child’s critical thinking through reading the fully worked solutions and by following the lines of reasoning. These can then be used to guide student practice.

Books 2 and 3

Books 2 and 3 of the series introduce students to a very wide range of logical reasoning questions, many of which will excite and challenge through their novelty and creativity. The use of visual stimulus is important here as it tests interpretation skills as well as the application of rules to situations. The capacity to apply thinking in iterative ways is also tested in this book as there are several different questions for many single-stimulus items. This has been purposefully incorporated in order to extend and build critical thinking skills as a demonstration of fluid intelligence.

Book 4 (coming soon)

This is an ‘exam readiness’ book and focuses on the two things:

• The ability to recognise different question types and the type of approach(es) to solving them
• The capacity to work under time pressure, as each question has a suggested time of completion

As with each other book, every question is new and all of the stimulus used has been generated for a purpose: exposing students to novel test items that assess their ability to reason from data given, and to demonstrate a wide variety of critical thinking skills including data interpretation.

Mathematical Reasoning

Each Mathematical Reasoning book assesses visual acuity, working memory, perceptual reasoning, pattern recognition, deductive logic, probability and estimation, symbolism and coding. Students are required to analyse data, apply numerical relationships, understand the role of distractors and discern between relevant and non-relevant data.

Book 1

Book 1 is the first book of the series and accordingly introduces students to the format of questions evident in the Critical Thinking test in the new Selective Schools Exam. However, though the question format may look similar, there is a nuance to the questions, and many will test students.

It is important in this first book for students to build confidence through recognising question types and building familiarity. However, do not underestimate what is on offer. The challenge here is for students to attempt the questions without guidance. They need to be focused on correct processes, rather than ‘right answers.’ Parents and educators can assist the development of their child’s critical thinking through reading the fully worked solutions and following the lines of reasoning. These can then be used to guide student practice.

Books 2 and 3

These books build on and extend essential mathematical reasoning skills for critical thinking students. There is a huge range of novel stimulus, 2D and 3D shapes, graphical interpretation, numerical reasoning, deductive and inductive reasoning, number relationships and pattern recognition. The questions will assess the students’ capacity to evaluate, understand cause and effect relationships and also apply inductive reasoning through generalisation.

Book 4 (coming soon)

This is an ‘exam readiness’ book and focuses on the two things:

• The ability to recognise different question types and the type of approach(es) to solving them
• The capacity to work under time pressure as each question has a suggested time of completion

As with each other book, every question is new and all of the stimulus used has been generated for a purpose: exposing students to novel test items that assess their ability to reason from data given, and to demonstrate a wide variety of critical thinking skills including data interpretation.

Fully worked solutions in ALL books

The purpose of fully worked solutions is to assist educators, parents and students to understand logical thinking methodology as it applies to critical thinking and mathematical reasoning. Through fully worked solutions students can be guided as to how the logical application of rules can be applied. Note, that for many question types there are different approaches. Hence the step-by-step act as a guide as to the various questions and question types can be approached. However, they are not intended to limit students or educators/parents as there are often several different but equally valid means by which to answer critical thinking problems. Indeed, that this is the case points to the strength of critical thinking as a necessary cognitive development for all people.

Do these books apply to other tests?

The Critical Thinking Series and the Mathematical Reasoning Series are designed based on psychometric principles. Any valid test will assess thinking and fluid intelligence, rather than crystallised intelligence. Hence these books are extremely useful for OC tests, Scholarships Tests and the regular classroom when teachers seek to build critical thinking as an essential feature of their practice.

Timing and Time Management

It is important that parents and educators understand the importance of teaching time management as a last skill NOT a first skill to learn. This is because time can create pressure on students when they are first learning ‘how to do’ and this can hamper their thinking. Nothing lowers student self-esteem more than being pressured by unnecessary extraneous factors when they are confronted with new learning.

Working memory and auditory working memory (AWM)

An essential factor in critical thinking is the capacity to retain information and rules in short term or working memory. Working memory is necessary if students are to be able to recall the essential facts and rules that are needed to successfully solve the problem posed. Data may need to be intellectually manipulated or it may be subject to rules that must be applied.

Sometimes students will have no idea what is required in a question. This is absolutely to be expected. There can be several reasons for this:

• Rules may be complicated
• Data may be detailed
• There might be irrelevant information included as a distractor. The skill here is for students to learn to distinguish between what is relevant and what is not relevant
• The language requirements may imply a certain level of background knowledge. The use of words such as ‘successive’, ‘consecutive’, ‘corroborate’, ‘hypothesis’ and so forth will test many students who are unfamiliar with these terms. The use of these terms is purposeful – students need to understand what the language in questions means and hence know what to do
• There can be a mix of visual and written information, and these data sets may cohere or not

Auditory working Memory (AWM)

It can be extremely helpful for students who do not understand a question to read it out loud. In the process of hearing themselves, students tend to read more closely, including aligning what they hear with what they see. This alone is a very useful strategy and will help them to better understand what is needed for mastery of the question.

AWM also helps students retain information for longer. This means that they will be able to utilise the information and find it easier to mentally manipulate as required.

A further strategy to assist students is for educators and parents can ask students to tell them what is required in a question. The requirement to request students to articulate can help those guiding them to determine any issues with understanding. It can also help students to clarify exactly what they need to do