Test: Error Analysis- 1 - Civil Engineering (CE) MCQ

Concept
let us observe some static characteristics of the device
Accuracy

• it is the closeness of an instrument reading to the true value

True value

• It is equal to the average of infinite reading of measurement performed by a non-standard instrument

Static error = (Measured Value - True Value)

% error= Relative error × 100%
Calculation
Calibrated range 150°C to 200°C
reading of maximum value =200°C
reading of minimum value =150°C
Span =(Maximum value - Minimum value)
Span= 200^∘ C - 150^∘ C = 50^∘C
Static error =± 0.25% of Span
= ± 0.25% of 50^∘C
=± 0.125^∘C
Hence the static error = ± 0.125^∘C
Therefore the correct answer is option 1

Mathematics is a science that deals with logical reasoning, quantitative calculation, practices of counting describing shapes, abstractions of subject matter, etc. Mathematics plays a vital role in daily life.
Important Points
Errors are the difference between the true value and an estimated value of a particular question.

Role of error in mathematics:

• Errors are not always bad. Error plays a crucial role in the teaching-learning process.
• It helps the teacher to understand the thought process of the learner and how well the learner has gained the particular topic.
• Errors allow the learner to experiment. Learners learn from their mistakes.
• Errors reflect the thinking process of the learner.

Thus, Errors play an important role in mathematics they help teachers understand how children construct mathematical concepts.

Additional Information
Teachers should not punish the students for doing an error. The error should be corrected without any criticism.

Mathematics includes complex calculations, the study of patterns, shapes, and various geometrical figures. To develop a liking towards mathematics, the teacher should need to use innovative ideas to teach abstractions of mathematics.

• The manipulative tools are used in the teaching of mathematics to clear the complex and abstract mathematical concepts and to arouse the interest of students while learning mathematics.

Key Points

• Children often start learning numbers and counting even before entering school.
• They are made familiar with rhymes that teach the numbers while playing. The children imitate them and try to speak the numbers verbally.
• At the primary level, the children usually get confused in recognizing the face value and place value of the digits.
• For them, there is no difference between 004 and 400, as they do not understand that the position of a digit determines its place value. They may think that the ‘4’ in 46 represents 4, not 40.
• Instead of teaching the concept of place value using questions given in the textbook only, the teacher should involve the students in play activities that are relatable to real-world and are focused on the concept of place value i.e., use of money in daily life (10 represents 10 rupees whereas 1 represents only 1 rupee coin and 100 on a banknote denotes 100 rupees). 
• This will compel students to think that a specific position of a number says a lot about its position that is its place value.
• The teacher can also use manipulative tools such as base ten blocks to teach the concept of place value to clear their ambivalent thoughts about place value.
• Base ten blocks are also known as the multi-base arithmetic blocks (MAB).
  • These are basically used to teach basic mathematical concepts such as addition, subtraction, numbers, counting, and place value.
  • They are made up of wood or plastic and comes in different sizes to show place value.
  • The single wooden unit used to show the digits at ones place, the tens (having one rod divided into 10 parts) used to show digits at the tens place, and the flat surface of wood which is divided into 10× 10 used to show the digit at hundreds places.
    
• In the above image, there are 4 single wooden units shown in the ones box, so here we have 4 ones. And 6 rods at tens, so 6 tens 6×10 means 60 and 3 flats of 100 i.e., 3×100 =300. By adding all these, 300+60+4 we will get 364. 
• Such kind of manipulative tools can be very helpful in teaching effectively at the primary level and also keep the students engaged in the learning process.

Hence, could be concluded The reason for the error in reading is that the student is not able to understand the concept of place value and feels comfortable using two-digit numbers only because the student is reading only on the basis of face value, so the student needs the concept of place value.

Mathematics deals with data analysis, integration of various fields of knowledge, involves proofs, deductive and inductive reasoning, and generalizations.
Key Points
Error analysis in mathematics
Error analysis is a method commonly used to identify the cause of student errors when they make consistent mistakes. It is a process of reviewing a student’s work and then looking for patterns of misunderstanding. Errors in mathematics can be factual, procedural, or conceptual, and may occur for several reasons. 
Here in this question, the analysis of error is being done-

• To know the nature and characteristics of error that took place by students while solving the problems of Mathematics. 
• It is important to examine the error because this analyses the problem and root of the occurrence of the error.

Hint
Let us understand the other keywords used in the option:

Hence, from the above-mentioned points, it becomes clear that to know the nature and characteristics of error that took place by students while solving the problems of Mathematics is known as Error analysis in Mathematics.

Geometrical instruments are the instruments which are used to construct different types of geometric shapes and figures. The set of geometrical instruments include a scale, ruler, divider, compass and two set-squares. Note that:

• Set squares are the triangle-shaped device used for constructing a straight line and angle.
• Out of these set squares, one is a (90°= 45°+ 45°) set-square and the other is a (90°= 60°+ 30°) set square used to construct object's isometric and orthographic view respectively.

Hence, we conclude that one is a 45° - 45° set-square and the other is a 60° - 30° set- square.

In order to identify the students' problems and areas of weakness, a math teacher uses diagnostic tests. Students' weaknesses and problems with the teaching content, which include one or more types of mathematics, are identified through this test.
The essential steps in educational diagnosis are:

• Identifying the students who are having trouble or need help.
• Locating the errors or learning difficulties.
• Discovering the causal factors of slow learning.

Key Points
Diagnostic mathematical skill test:  The purpose of this test is to diagnose the following types of mistakes made by the student when doing the mathematical operations of addition, subtraction, multiplication, and division.

• Carry over in addition
• Borrowing in addition
• Placement of decimal error
• Borrowing and reducing one from next
• Nothing wrong number
• Tables are not remembered in divisions
• Tables are not remembered in multiplication

Hence, we can conclude that the diagnostic mathematical skill test is used to find errors committed by students during mathematical operations.

Mathematics includes all branches of knowledge and all walks of life as it occupies an important place in all civilizations, past, and present, throughout the world.

• The teaching of mathematics should be done to promote the practical usability of mathematics and to minimize the error performed by children while using mathematical operations.
• Assessment refers to all those activities undertaken by teachers and by their students in assessing themselves that provide information to be used as feedback to modify teaching and learning activities.

Key Points
Misconception is based on the view that it is incorrect due to faulty thinking or judgment. They tend to be consistent and arise from a student's understanding of the concept.

• Place value: It is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.
• Face value:  It is the digit itself within a number.

Here, the teacher has assessed that the majority of students are having difficulty in place value and face value. This misconception could be due to the following reasons:

• Many young children have difficulty with place value because it is abstract. Young children are concrete learners, meaning they need sensory experiences to develop their learning. Using different blocks can help students to connect abstractly with concrete representation.
• It is important to help children to connect the concept of place value to the real world. Often, children do not see how mathematical concepts apply to their individual lives. This can be done by giving real-world examples.
• Teachers may have difficulty teaching place value if they do not personally understand those concepts hence leading misconceptions in students. Teachers must have a thorough understanding of the concepts before teaching to the students.

Thus, it is concluded that the carelessness and short attention span of students in class when Ms. Avni was teaching the concept of place value and face value could not be the possible reason for this misconception.
Hint

• Errors are mistakes that are made due to a short attention span, and carelessness so it is not a misconception. When a student can’t master a topic, he/she is vulnerable to make errors. Errors are nothing but incorrectness made by a student during learning. 

Arithmetic refers to the mathematics of all sorts of numbers like rational, irrational, real, or complex which includes operations such as addition subtraction, multiplication, and division.

Important Points

• In the scenario given in the question, we notice that the student has subtracted the smaller digit from the larger digit one by one which means his concept regarding mathematics and arithmetic is clear but he has misconceptions regarding subtraction which carry 1 in hand.
• The child has misconceptions about place value in the process of subtraction.

Hence, we can conclude that the child has misconceptions about place value in the process of subtraction.

The 5 E's learning model, developed by 'Rodger Bybee' is an instructional model based on five stages which are engaging, exploration, explanation, elaboration, and evaluation.

• This constructivist model of learning ensures the active involvement of learners in the teaching-learning process.

Key Points
The 5 E's learning model is briefly explained below:

Hence, we can conclude that the above scenario relates to the Engagement Phase of 5 E's model of learning.

An inclusive school is a platform where all students irrespective of any differences sit and learn together.
Here, the needs of visually challenged students can be catered by a number of ways.
Teachers can use alternate teaching-learning methods like:

• Asking students to clap or raise hand.
• Proper seating arrangements
• Avoiding gestures, always verbalize whatever is written in blackboard
• Helping students to visualize/imagine the theme taught.

Note:

• Inclusive education doesn’t allow sending students with disabilities to special class or to special educator or making any kind of distinguish among students.
• Providing them extra time may distract other students without visual disabilities and it is not considered.
• Making them sit with high achievers may lower their confidence.

Hence, we conclude that using alternate teaching-learning methods and resources can be an effective strategy in the above situation.