Test: Error Analysis- 2 - Civil Engineering (CE) MCQ

Mathematics is a branch of science which deals with counting, calculating, and studying numbers, shapes, and structures.

• It is the study of numbers, shape, quantity, and patterns.
• It relies on logic and connects learning with children's day-to-day life.

Key Points
Problems in Teaching and Learning of Mathematics:

• Lack of practice - If the students will not do enough practice and revision then they tend to forget what they already learned and also they can face difficulty in learning new mathematical concepts which require higher reasoning skills.
• Crude assessment - It is one of the barriers of teaching-learning in mathematics as it tends to emphasize only the computational skills of students instead of focusing on conceptual understanding.
• Lack of teaching aids - If the teacher is unable to use or desirably doesn't use good teaching aids in the teaching-learning process then he is not making the learning process interesting and unique for students which may affect their performance.
• Sense of fear and failure - A good mathematics teacher is the one who removes the sense of fear and failure among students while learning mathematics so that they can learn without being hesitant. The students need to be interested, curious, and active while learning otherwise learning will not effectively take place.
• Lack of interest - The students need to be interested, curious, and active while learning otherwise learning will not effectively take place. 
• Inadequate teacher preparation - The teacher should prepare well his lesson plan, the teaching aids to be used, and the goals and objectives to be achieved throughout the whole process of the teaching-learning process.
• Lack of pedagogical knowledge of teachers - Also, a teacher needs to be well aware of the needs, desires, and interests of the students so that the learning process can be made interesting for them.

Hence, it can be concluded that from the above-mentioned options, Crude Assessment, Lack of Interest, and Inadequate Teacher Preparation are the major problems in teaching and learning mathematics.

Concrete reasoning involves the ability to analyze information and solve problems on a literal ("concrete") level. We use concrete materials when we think through and solve hands-on problems. Explaining concepts through concrete materials helps in:

• Understanding of basic cause and effect relationships.
• Basic knowledge of names of objects, places, and people.
• To give the knowledge of the grouping concepts i.e. dividing  44 children into 2 equal groups and then demonstrating the children into diving the students of the class into 2 groups of 22 each. This is how we use concrete material which is helpful in determining the difference between 44 and 404 for children.
• Solving problems that do not involve theory, metaphor, or complex analogy.

Therefore, when students write 44 as 404 as a teacher, we will address this by explaining the principle of exchange using concrete materials.

Mathematics is a branch of science which deals with counting, calculating, and studying numbers, shapes, and structures. Among all the school subjects, maximum emphasis is attached to learning mathematics. You must have experienced, during your student days and also being a teacher, the extent of pressure exerted on children to perform at a higher level in mathematics in comparison with other subjects. Sue Atkinson in her book "Mathematics with Reason" has provided an introduction to her book:

• Mathematics starts from the secure 'home learning' which is established in the child before he comes to school.
• Mathematics is based on understanding.
• Math's emphasizes on child's method of calculation and problem solving and discards the previous practices that used to emphasize on standard written algorithms.
• Mathematics is regarded as a powerful tool for interpreting the world and therefore should be rooted in real experience across the whole curriculum.
• It is brought out of the child's everyday situations.
• Mathematics with reason is rooted in action, that is, learning by doing.
• Mathematics with reason puts emphasizes little on representing numbers on paper as 'sum' but emphasizes more on developing mental images in the child.
• To master mathematics, the main tool for child and teacher is the mastery of language, not pencil and paper exercises from textbooks.
• The child is motivated to talk about what he is doing.
• Errors are part of the learning process. The child, when free from criticism, will experiment more rapidly.
• Mathematics with reason puts emphasis the process of thinking, and these are made explicit in the conversations between adult and child.

Hence, we conclude that Errors are accepted as an essential part of the mathematics learning process.

To explain students any concept, a teacher needs to follow a specific sequence. For this to materialize, he may even require some teaching materials.
Note that:

• To explain the concept of Quarter in class-III, a teacher should first make students aware of fractions by showing activity or practically cutting a whole into half and quarters so that the concept of students are cleared before they study via books or blackboard.
• Teacher should then show the picture or the pictorial diagram as examples of the practical/activity done. This would clear the doubts and queries regarding quarter running through the mind of students.
• Finally, the teacher should write the Symbol (regarding last activity) on the blackboard because the students are all aware of it and can understand it better.

Hence, we conclude that the correct sequence is BCA.

Explanation:

• Bead strings are ideal for helping to maintain student interaction in the classroom.
• If a student reads 203 as twenty-three then a teacher can use beads and strings activity.
• This activity is great for emergent learners during maths lessons.
• They are perfect for both group as well as individual led work, encouraging problem-solving, number exploration, and familiarity with multiples of ten.

Important Points
Beads and Strings activity:

• Bead strings are used for visualizing numbers with a moveable object.
• A teacher can hide or cover certain parts of a bead string so the students find it easier to count each bead by counting it one by one. 
• We can Use bag tags to label the beginning and end of the string as 0 and 100.
• A 10 bead string contains five white and five red beads.

Key Points
Recognizing the number 203:

• Split the beads to represent the numbers 20 & 23, then ask the pupil what number it represents.
• From the beads below, you could prompt students to count all the green beads, and write down the number it represents.
• Then by doing this activity a pupil comes to know that there is a difference between 23 & 203. So 

So Misconception of Recognising a Number can be cleared by Beads and Strings activity.  So Option 3 is the correct answer.
Additional Information
Other Uses of beads and strings activity:

• Recognizing numbers
• Place value
• Estimation skills
• Large numbers
• Addition and subtraction