Pedagogy Of Mathematics Pdf Tnteu

Which of the following can be used as assessment strategy to encourage interdisciplinary in Mathematics?

A. Projects

B. Field trips

C. Anecdotal records

D. Olympiad

A & B
A & C
B & C
C & D

Answer (Detailed Solution Below)

Option 1 : A & B

Inter-disciplinary approachnot just the combination of two or more disciplines, but one discipline, which is facilitated by one or more disciplines.

Since in question it is asked about assessment strategy which would help in encouragement, hence we have to choose those points which can be categorized under formative assessment becauseformative assessment helps to improve performance and encourage to achieve goals.

Important Points

Assessment strategy to encourage interdisciplinary in Mathematics:

Projects: While working on projects students get to know their weaknesses and strengths.
Field trips: It will help the student assess their abilities and behaviors.

because it will enhance critical thinking, communication skill and it will help to analyze things at all the stages of life.

Additional Information

Also, Anecdotal records and Olympiad are important tools in mathematics and that can be used for assessment but not as an encouragement, as they are used for judging.

Anecdotal records: A summary of an event in which a child or a group of children has taken part.
Olympiad: An Examination conducted by various institution based on a different curriculumto compare the performance of the students with their peers.

Hence, we can conclude that projects and field tripscan be used as assessment strategy to encourage interdisciplinary in Mathematics.

Identify the type of the following word problem:
"I have 6 pencils. Manish has two more than me. How many pencils does Manish have?"

Comparison addition
Comparison subtraction
Takeaway addition
Takeaway subtraction

Answer (Detailed Solution Below)

Option 1 : Comparison addition

In the above question, there is comparison addition is performed.

Given that:-

I have 6 pencils but Manish has more than 2 me

It means Manish have total pencil :- 6 + 2 = 8 pencil

Now we can easily understand their addition is performed and also compared with Manish pencils and my pencil.

Comparison Addition: In this method, we find the relation between two amounts by asking or telling how much more (or less) is one compared to the other.

Additional Information

Comparison Subtraction: The difference between the two groups of numbers, namely, how much one is greater than the other, how much more is in one group than in the other. e.g., if Munna has 15 erasers and Munni 5, how many less does Munni have than Munna?
Takeaway: It is used for subtraction which means 'Remove', or 'Reduce' the group of words or numbers. E.g. How much is left if you take away 3 marbles from 5 marbles. In this way, the children learn to understand 'take away', and relate it to 'add'.

Hence, it becomes clear that the given problem is comparison addition.

Which of the following tasks is least likely to develop critical thinking among students?

Evaluate 72 × 73 in three different ways and compare the result
Formulate any two situation to represent the equation 7x + 3 = 24
A students calculated the volume of a right circular cylinder of radius 3.5 cm and height 10 cm as 38.5 cm³. What did she go wrong?
Calculate the volume of a right circular cylinder of radius 3.5 cm and height 10 cm

Answer (Detailed Solution Below)

Option 4 : Calculate the volume of a right circular cylinder of radius 3.5 cm and height 10 cm

Critical Thinking: The ability to apply reasoning and logic to new or unfamiliar situations, ideas, and opinions. It refers to the process of judging or analysing facts, events, etc. It requires proper analysis, evaluation, inference and explanation.

Thinking critically involves seeing and observing things in an open-minded way and examining an idea or concept in a way to form as many angles as possible.
Reasoning tasks promote critical and creative thinking in mathematics.

Open-Ended questions: Open-ended questions are the questions which can't be answered in yes or no, rather requires a detailed answer with proper explanation. These are a useful tool for primary teachers to help students to discover new ideas and develop critical thinking.

For example:- Following questions are open ended:-

Evaluate 72 × 73 in three different ways and compare the result.
Formulate any two situation to represent the equation 7x + 3 = 24.
A students calculated the volume of a right circular cylinder of radius 3.5 cm and height 10 cm as 38.5 cm3. What did she go wrong?

Close Ended Questions: These allow a learner to choose one answer from a limited list of possible answers.

For example:- Calculate the volume of a right circular cylinder of radius 3.5 cm and height 10 cm.

Here calculating the volume of a right circular cylinder will not develop critical thinking among students, as it is just concern with putting up values into already deduced formula.

Ways to Develope Critical Thinking in a Child:

Begin with a question
Create a foundation
Consult the classics
Use information fluency
Utilize peer groups
Try one sentence at a time
Problem-solving
Return to role-playing

Hence, it becomes clear that the tasks like calculating the volume of a right circular cylinder will not develop critical thinking among students.

Which of the following is not a dimension of assessment of mathematical learning?

Communication
Patterns and procedures
Disposition towards mathematics
Mathematical reasoning

Answer (Detailed Solution Below)

Option 2 : Patterns and procedures

Mathematics is the study of numbers, shape, quantity, and patterns. It relies on logic and connects learning with children's day-to-day life. The assessment of mathematical learning refers to know the learning needs and filling the gap by remedial teaching.

Important Points

Dimensions of assessment of mathematical learning: To ensure a comprehensive assessment in mathematical learning following dimensions should be included:

Concepts and procedures: Although a great deal is known from research about the nature and developmental trends of mathematical concepts and procedures. It is expected that every teacher while teaching mathematics in the classroom, should explore the nature of their student's development of the concepts and procedures. This is because every child has his/her own uniqueness in the development of the concepts and procedures in his/her context which is different from those reading in other schools. In such exploration of children's nature of learning mathematical concepts, assessment has crucial importance

At the elementary stage, all the mathematical concepts and procedures can be included in ten broad areas:
■ Number (Real number system)
■ Number operations (Four processes)
■ Fractions (including decimals)
■ Space and spatial thinking
■ Measurement (both standard and non-standard measures)
■ Problem-solving
■ Patterns
■ Data handling
■ Basic algebraic processes (only in the upper primary stage)
■ Simple equations (only in the upper primary stage)

Mathematical reasoning: Mathematics is distinguished by its strong logical order even from the earliest stage of learning. Inductive and Deductive reasoning is dominantly employed in mathematics learning. The emphasis on reasoning in mathematics learning not only influences the ways of solving and presenting the solutions of mathematical problems. Assessing mathematical reasoning shall include several methods including the tests, both oral, written, and performance, observation of learners' activities, etc.
Dispositions towards mathematics:Mathematics learning both influences and is influenced by the learner's perception, interest, attitude, and personality characteristics. When taught and assessed properly in a learner-friendly environment, the learners can enjoy learning mathematics and can get rid of the anxiety and phobia associated with mathematics learning at the early stage of schooling.
Using mathematical knowledge and techniques to solve problems: This does not need much elaboration because of the fact that mathematics learning in schools means; solving the problems in the textbooks or some other problems similar to the textual problems. And in the course of solving the problems, the students acquire skills in using new techniques and methods.
Communication: One of the important outcomes of mathematics learning is the development of a way of communication that is typically precise, logical, relevant, and disciplined. Both in oral and written communications, these characteristics can be observed. In addition, the use of symbols, figures, graphs, and charts makes the written communications more precise, and orderly. These aspects of mathematical communication have to be included in both formal and informal modes of assessment.

Hence, we conclude that Patterns and procedures are not a dimension of the assessment of mathematical learning.

Confusion Points Concepts and procedures are dimensions of assessment of mathematical learning rather than Patterns and procedure.

Which of the following activities is best suited for the development of spatial understanding among children?

Drawing the top view of a bottle
Locating cities on a map
Noting the time of moon rise
Representing numbers on a number line

Answer (Detailed Solution Below)

Option 1 : Drawing the top view of a bottle

Spatial relationships refer to children's understanding of how objects and people move concerning each other, comparison of two objects like big-small, fast-slow, long-short, colour comparison, near-far, etc.

Important Points

The Spatial Ability is the capacity to understand, reason, and remember the spatial relations among objects or space.

For understanding spatial thinking, students should enable them to understand visualization.
It is the ability to mentally manipulate 2-dimensional and 3-dimensional figures.
Hence, drawing the top view of the bottle is an example of a spatial thinking concept.
It is typically measured with simple cognitive tests and is predictive of user performance with some kinds of user interfaces.

Key Points

Representing number on a line show concept of rational, irrational and whole number concepts.

Hence, drawing the top view of a bottleis a best-suited activity for the development of spatial understanding among children.

Which of the following is the major problem of teaching Mathematics?

Teaching methods of Mathematics teacher
Ability to use Mathematical tools.
Class Room operations
Knowledge of teaching methods

Answer (Detailed Solution Below)

Option 3 : Class Room operations

In a math class, a teacher follows a proper sequence in teaching which is usually practically followed in any classroom.This is known as classroom operations. It plays a major role in Mathematics learnings and one of thechallenges that teacher face in a classroom depending on different factors i.e.,nature of the content, the learning style of the students, knowledge of teaching methods and also depends on the ability to use mathematical tools. This is what exactly done in mathematics class -

At the beginning the teacher introduce the concept for drawing the attention of the learners towards the topic;
Then, try to explain that concept through demonstrating different materials, performing activities, or doing such other activities to clarify the concepts making the students to participate;
Lastly, ask some questions for assessing whether the learners have learned the concepts as you desired.

It should be noted that teaching methods, ability to use math tools comes under the vast category called classroom operations. So instead of choosing three different opinions, one single opinion is selected which covers all the three aspects.

Hence, ' Class Room operations' are the major problem of teaching Mathematics.

A student is not able to solve those word problems which involve transposition in algebra. The best remedial strategy is to

give lot of practice questions on transposition of numbers.
give lot of practise questions of word problems in another language.
explain him/her word problem in simple language.
explain concept of equality using alternate method.

Answer (Detailed Solution Below)

Option 4 : explain concept of equality using alternate method.

During the teaching-learning process, a child makes mistakes willingly-unwillingly or due to some alternative conceptions. It is the job of the teacher to help students to correct those mistakes after diagnosing them.

Remedial strategy refers to the method of teaching that helps the teacher to provide learners with the necessary help and guidance to overcome the problems which are determined through diagnosing them.

Key Points

In the above-mentioned phenomenon, the best remedial strategy is toexplain the concept of equality using alternate methods as it will help learners in:

gaining a better and clear understanding of the concept.
developing a basic sense regarding the general idea of the topic.
changing their misconceptions about the topic with the correct knowledge.

Hence, it could be concluded thatexplaining the concept of equality using alternate methods will be the best remedial strategy in the above-mentioned concept.

Which of the following is a desirable practice in the context of teaching and learning of measurement of volume?

Begin by writing the formula of volume of a cube
Encourage precise calculation right from the beginning
Begin by introducing students to the volume of 2-D figures
Encourage students to figure out ways to calculate the volume of different objects

Answer (Detailed Solution Below)

Option 4 : Encourage students to figure out ways to calculate the volume of different objects

In teaching Mathematics active involvement of students is very important, and teachers must provide opportunities to the students where they get hands-on practical experience. Mathematical concepts are abstract and helping learners construct these meaningfully has always been a challenge for teachers.

A teacher must act as a facilitator and encourage students to figure out ways to solve a particular problem, participate in an activity.
Teachers play an interactive role in fostering the potential of young seedlings to grow and bloom.
Teachers'patience and perseverance significantly impact a child's success in the classroom.
A mathematics teacher plays the role ofphilosopher, friend, and counsellor.

For example: In calculating the volume of different objects, the teacher should encourage students to figure out ways.

NOTE: Just writing formulas and doing up calculations is a deductive approach that reduces the creative thinking ability of the child. So, it should never be used in the mathematics class.

Hence, encouraging students to figure out ways to calculate the volume of different objects is a desirable practice in the context of teaching and learning of measurement of volume.

In which method in teaching Mathematics one proceeds from unknown to known?

Inductive
Deductive
Synthesis
Analysis

Answer (Detailed Solution Below)

Option 4 : Analysis

Mathematics is thestudy of numbers, shape, quantity, and patterns. The nature of mathematics islogicaland it relies on logic and connects learning with learners' day-to-day life.

Teaching methods of mathematics include problem-solving, lecture, inductive, deductive,analytic, synthetic, heuristic and discovery methods. Teacher adopts any method according to the needs and interests of students.

Key Points

Analytic method:

In this method, we proceed fromunknown to known.
We break up the unknown problem into simpler parts and then see how it can be recombined to find the solution. Therefore it is the process of unfolding the problem or conducting its operation to know its hidden aspects.
In this process, we start with what is to be found out and then think of further steps or possibilities that may connect the unknown with the known and find out the desired result.

Hence, it could be concluded that one proceeds from unknown to knownin the use of the analytic method in teaching Mathematics.

Additional Information

Inductive Method:

The inductive approach is based on the process of induction. It is a method ofconstructing a formula with the help of a sufficient number of concrete examples.
Induction means to provide a universal truth by showing, that if it is true for a particular case. It starts from examples and reaches towards generalizations.

Synthetic Method:

The word"synthetic' is derived from the word 'synthesis which means to combine.
In this method, we combine several facts, perform certain mathematical operations, and arrive at the solution.

Deductive method:

In this method, we proceed from general to particular. It does not give any new knowledge.
It encourages dependence on other sources. A child gets ready-made information and makes use of it.

Geometry theorems are taught by experimental method at upper primary classes. In which direction the learning experiences proceed during teaching?

from simple to complex
from complex to simple
from general to specific
from specific to general

Answer (Detailed Solution Below)

Option 3 : from general to specific

Experimental method:- Experiment method is the method in which we use various experiments to reach a conclusion. The experimental method is usually taken to be the most scientific of all methods, the 'method of choice' The experimental method is a means of trying to overcome the problem.

Key Points

Importance of experiment method:-

This method improves student hand skills.
It makes them more productive and increases their active involvement in learning.
Students can create a relationship between theory and practice by experiment method.

Important Points

Geometry is a vital branch of the mathematics curriculum. In upper classes, students study geometry with informal knowledge about points, lines, a variety of two and three-dimensional shapes, etc with geometric relationships. Teachers taught geometry theorems through the experimental method.

It starts with the assertion of a general rule and proceeds from there to a specific conclusion.
Teachers taught them the geometry rules first then they reach the theorem.
It establishes linkage with real-life observations and knowledge already gained.
It starts with a rule and provides for practice and applications.

Hence, we can conclude thatGeometry theorems are taught by experimental method at upper primary classes which follows from general to specific direction the learning experiences proceed during teaching.

The concept of 'zero' can be introduced best through which one of the following operations?

Multiplication
Division
Addition
Subtraction

Answer (Detailed Solution Below)

Option 4 : Subtraction

Mathematics is a man-made, well-disciplined subject, which deals with abstract concepts and things. It has its own language, its own tools and mode of operation to help people in a proper understanding of nature's work and complicated problems of life.

Important Points

Zero (0) is a numerical digit used to represent that number in numerals. It can be used as the additive identity of the integers, real numbers, and many other algebraic structures.

The concept of 'zero' in the classroom can be introduced by the Subtraction process.
We first associate the number 0 with empty and nothing and slowly help them understand the relation of 0 with other numbers.
After that, a teacher can use various activities and tools to explain the concept of zero. some of these are-
- Bowls and Number Cards
- Paper Cups and Branches of Leaves
- Trees with Apples Pictures
- Counters

Hence, we can conclude that the concept of 'zero' can be introduced best through the Subtraction operation by subtracting the same number from the same number. For Example Subtracting 8 from 8 gives Zero. (8-8=0). A teacher can use this activity with balls, a pencil, a pen, or other dummy objects.

Out of the following, which one does not express the view of pure mathematicians regarding mathematics-

It is based on objective facts
It is a study of logic
It is a system of rigour, purity and beauty
It is a tool for solving problems

Answer (Detailed Solution Below)

Option 4 : It is a tool for solving problems

Pure Mathematics:

Pure mathematics is the study of the basic concepts and structures that underlie mathematics.
Its purpose is to search for a deeper understanding and an expanded knowledge of mathematics itself.
Traditionally, pure mathematics has been classified into three general fields: analysis, which deals with continuous aspects of mathematics; algebra, which deals with discrete aspects; and geometry.
The undergraduate program is designed so that students become familiar with each of these areas.

Key Points

The basic characteristic of pure mathematics are:

Applicability and Effectiveness,
Abstraction and Generality,
Objectivity,
Simplicity,
Logical Derivation, Axiomatic Arrangement,
Precision, Correctness, Evolution through Dialectic.
Rigour, Purity, and Beauty.

Note: Pure Mathematics solve mathematical problems and not all the problems.

Therefore, It is a tool for solving problems does not express the view of pure mathematicians regarding mathematics.

"Things which are equal to the same thing are equal to one another." This axiom which is basis to arithmetic and algebra is given by

Euclid
Pythagoras
Descartes
Euler

Answer (Detailed Solution Below)

Option 1 : Euclid

Euclid around 300 B.C. collected all known work in the field of mathematics and arranged it in his famous treatise called Elements.

Euclid assumed certain properties, which were not to be proved. These assumptions are actually "obvious universal truths".
He divided them into two types: Axioms and Postulates.

Axioms:

The things which are equal to the same thing are equal to one another.
If equals are added to the equals, the wholes are equal.
If equals are subtracted from equals, the remainders are equals.
Things which coincide with one another are equal to one another.
The whole is greater than the part.
Things which are double of the same thing are equal to one another.
Things which are halves of the same thing are equal to one another

NOTE :

Pythagoras Theorem: It states that " In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides ". The sides of this triangle have been named as Perpendicular, Base, and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
Euler's theorem is a generalization of Fermat's little theorem dealing with powers of integers modulo positive integers. It arises in applications of elementary number theory.
René Descartes has been dubbed the "Father of Modern Philosophy", but he was also one of the key figures in theScientific Revolution of the 17th Century, and is also considered behind the making of the first modern school of mathematics.

Hence, it becomes clear that Euclid gave the Axiom "Things which are equal to the same thing are equal to one another."

"The sum of any two whole numbers is a whole number."

This property of whole numbers is referred to as

commutative property
associative property
distributive property
closure property

Answer (Detailed Solution Below)

Option 4 : closure property

Multiplication represents the repeated addition of a number with itself. For example: 3 + 3 is represented as 3 × 2.

Important Points

Addition:When two collections of similar objects are put together, the total of them is called addition.

Properties of addition in natural and whole numbers:

Closure property: The sum of two natural/whole numbers is also a natural/ whole number.
Commutative Property: p + q = q + p where p and q are any two natural/ whole numbers.
Associative property: (p + q) + r = p + (q + r) = p + q + r . This property provides the process for adding 3 (or more) natural/whole numbers.
Additive Identity in Whole Numbers: In the set of whole numbers, 4 + 0 = 0 + 4 = 4. Similarly, p + 0 = 0 + p = p (where p is any whole number). Hence, 0 is called the additive identity of the whole numbers.

Key Points

Properties of Multiplication:

Commutative Property:a × b = b × a. Example, 9 × 4 = 4 × 9 = 36
Closure property: If p and q are natural or whole numbers then p × q is also a natural or whole number. Like in the above example, 4 and 9 are natural numbers, so is their multiple (36).
Associative property: (p × q) × r = p × (q × r) (where p, q, and r are any three natural/whole numbers)
Identity of multiplication: The number '1' has the following special property in respect of multiplication. p × 1= 1 × p = p (where p is a natural number)
Distributive property of multiplication over addition: p × (q + r) = (p × q) + (p × r).

Note: There is no distributive property for addition. One should not be confused (p + q) + r = p + (q + r) asdistributive, the given property isassociative property for addition.

Which of the following method provides the proof of the problem?

Project method
Analytic method
Inductive method
Synthetic method

Answer (Detailed Solution Below)

Option 4 : Synthetic method

Synthetic Method:The word "synthetic" is derived from the word 'synthesis'which means to combine. In this method,we combine several facts, perform certain mathematical operations, and arrive at the solution. In this method, we start with theknown data and connect it with the unknown part.

It is the process of putting together known bits of information to reach the point where unknown information becomes obvious and true. Thus in this method, we proceed from hypothesis to conclusion.

It is lead from:

Known to Unknown
Hypothesis to Conclusion (Therefore, it provides the proof of the problem)
Concrete to Abstract
Simple to Complex

Hence, we conclude that the above statement is about synthesis method.

The role of proportional reasoning in understanding the concept related to ratio and proportion was highlighted by

Van Hiele
Zoltan Dienes
Jean Piaget
Lev Vygotsky

Answer (Detailed Solution Below)

Option 3 : Jean Piaget

Proportional Reasoning: It involves understanding the multiplicative relationships between rational quantities (a/b = c/d), and is a form of reasoning that characterizes important structural relationships in mathematics and science.

Proportional reasoning is the ability to compare ratios or the ability to make statements of equality between ratios.
Proportional reasoning is foundational to understanding fractions.
Proportional reasoning involves, detecting, expressing, analyzing, explaining, and providing evidence in support of assertions about, proportional relationships.
It involves thinking about the relations among relations.

Jean Piaget's Views:

Proportional reasoning represents a cornerstone in the development of children's mathematical thinking.
Piaget considers the ability to reason proportionally to be a primary indicator of formal operational thought, and this stage is viewed as the highest level of cognitive development.
Proportional reasoning helps in understanding the concept related to ratio and proportion.
Ratio and proportion are critical ideas for students to understand.

Piaget's Concept of Formal Operational Thought:

It is associated with one's ability to reason proportionally.
The attainment of proportional reasoning is considered a milestone in students' cognitive development.
Piaget described the development of proportional reasoning in three stages:-

Students are not aware of ratio dependence and seek solutions by guessing.
Students are aware of objective dependence.
Proportionality is discovered and applied to obtain correct solutions.

NOTE:

Van Hiele describes how people learn geometry. According to his theory, there are five levels of thinking in geometry.
Zoltan Dienes stands with those of Jean Piaget and Jerome Bruner as a legendary figure whose theories of learning have left a lasting impression on the field of mathematics education.
Lev Vygotsky propounded the 'Socio-Cultural Theory'.

Hence, it becomes clear that the role of proportional reasoning in understanding the concept related to ratio and proportion was highlighted by Jean Piaget.

Which one of the following is an important aspect of measurement of length?

Using non-standard measures
Iteration
Conservation of length
Ability to use scale

Answer (Detailed Solution Below)

Option 4 : Ability to use scale

Measurementof an object is done to quantify its shape, size, perimeter, area, etc. to get an exact idea about its attributes.

The teacher should first introduce thenon-standardized measures at the primary level as children to some extent are familiar with them and can relate to them easily.

Key Points

Non-standard measures may include the use of a hand span to measure the length of any object, comparison between two objects to decide which one is smaller or bigger, use of foot-steps to measure the distance between two things, objects, or places, and so on.
Then the conservation of length must be taught to them i.e., by comparing the two objects or things to introduce the measurement in primary classes.
- Such as compare the height of two children, comparing the length of pencils, and comparing the hand-spans of learners by measuring the length of their desks.
After that, the teacher should introduce the standard units of measurement by mentioning some of the problems of using non-standard measures to give meaning to the use of rulers, scales, and measuring cups.
- Such as measurement of the length of the desk by using hand-spans of learners and show them why the length is different as the size of their hand-spans varies. So, to measure accurately and irrespective of the size of hand-spans, we use a scale or ruler to measure the length of an object.
- There, the main important aspect of measurement of length is the ability the use scale i.e., to measure the length between two points one must know how to use the scale with precision otherwise the measurement will not be valid.
Without having the proper ability to use any measuring scale, one can not do measurement correctly.
And after learning the ability to use scales, the children should be encouraged for Iteration so that they can attain mastery in the ability to use scales properly.

Hence, it could be concluded that the ability to use scale is an important aspect of the measurement of length.

The situation presented by the teacher in the classroom to find the attention of students towards a new topic is known as

Previous knowledge
Introduction
Statement of aim
Ideal question

Answer (Detailed Solution Below)

Option 2 : Introduction

Introduction is the situation presented by a teacher in the classroom to find the attention of students towards a new topic. Introduction to a new topic in the classroom is the most important part of teaching and learning.

Previous knowledge is the test of old topics, discussed or known topics to get the idea of the level of the students in terms of knowledge and thus the teaching strategies/methods/practices can be followed based on students' performance.
Statement of aim is provided when a theoretical or practical is taken by the teacher after a discussion on the topic.
An ideal question is a question based on a well-known topic or the taught topic or based on previous knowledge, asked by the teacher to test the critical thinking of the students.

Which one is not related to the nature of Mathematics?

Exactness
Specific sequence
Expanded expression
Pattern

Answer (Detailed Solution Below)

Option 3 : Expanded expression

Mathematics: Mathematics is a systematized, organized, and exact branch of Science. It plays an important role in accelerating the social, economical, and technological growth of a nation. It helps in solving problems of life that need enumeration and calculation.

Important Points

The nature of Mathematics can be made explicit by understanding the chief characteristics of Mathematics:

Mathematics is a science of discovery.
Mathematics is an intellectual game.
It deals with the art of drawing conclusions.
It is a tool subject.
It involves an intuitive method.
It is the science of exactness, precision, and accuracy.
It is the subject of a logical and specific sequence.
It requires the application of rules and concepts to new situations.
It is a logical study structure and patterns.

Thus, it is concluded that expanded expression is not related to the nature of Mathematics.

Which of the following is NOT true with respect to the learning of Mathematics?

Ability to perform and excel in Mathematics is innate.
Teachers' beliefs about learners have powerful impact on learning outcomes.
Students' socio-economic background impacts their performance in Mathematics.
School's language of instruction can impact a child's performance in Mathematics.

Answer (Detailed Solution Below)

Option 1 : Ability to perform and excel in Mathematics is innate.

Mathematics is a branch of science which deals with counting, calculating, and studying numbers, shapes, and structures. It is the study ofnumbers, shape, quantity, and patterns. It relies on logic and connects learning with children's day to day life.

Important Points

In a rather technical, but uninteresting, sense, mathematical ability is not innate; we cannot recognize the meaning of the symbols 2 + 2 = 4 at birth.

We must, of course, learn the symbols of mathematics before we can express mathematical relationships, i.e., before we can "do math" as is commonly understood.
Mathematics requires rigorous practice, hence, theability to perform and excel in Mathematics is not innate.
Practice makes a man perfect can be rightly used in terms of mathematics.
For the learning of mathematics children's social background and school, the environment plays an important role.

Hence, the statement that the ability to perform and excel in Mathematics is not innate.