Math and Psychological Tasks Analysis

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Task Analysis of Adding Two Double-Digit Numbers with Carrying

Learning to add two double-digit numbers is a highly important step in the elementary school curriculum. This new knowledge brings students to the next stage of their acquaintance with the world of numbers. They come to understand the complexity of mathematic operations and learn logical reasoning. In the long run, it is also crucial to make emphasize performing mental calculations without resorting to paper or a calculator.

Even irrelevant to its practical implementations, this skill is one of the best ways to enhance one’s attention and precision. It develops the sense of number interactions, which is essential for further introduction into more complicated calculations. Thus, proper task analysis is required for teaching children how to add two double-digit numbers first on paper and then in the head. First and foremost, it presupposes determining long- and short-term objectives.

Long-term goals of learning how to add double-digit numbers:

school students must acquire more knowledge and comprehension of mathematic operations;
they must come to understand the principles of mathematic reasoning and communication;
children are going to become more confident through applying mathematic knowledge in practice (e.g. adding product prices in a shop);
they will start solving real problems by using the methods of mathematic reasoning;
they should learn to generate ideas themselves with the help of formal logic.

Practical short-term objectives:

to learn how to generate diversified lists of numbers for further analysis;
to understand how to divide these numbers into groups using digit classification principle (differentiating between single and double-digit numbers)
to see the difference in the process of addition of single-digit and double-digit numbers;
to learn how to make up your problems and solve them;
to demonstrate the acquired knowledge by describing the invented problems to their classmates and analyzing the steps required for their solution;
to check comprehension of the topic successfully coping with a home assignment and handing it into the teacher for corrections.

Identifying and eliminating unnecessary or redundant steps (the task depends on the particular abilities of the students):

in case students show a complete understanding of single-digit numbers addition, revision stage can be considerably shortened or skipped to save time for practicing new material;
if students have no problems with understanding the difference between single and double digits, the teacher can skip lining them up on graph paper;
the number of elementary tasks can be reduced if full comprehension is achieved.

Sequence steps for learning (e.g. 27+15=?):

start with adding numbers in one’s column (7+5=12);
check if the resulting number is bigger than ten;
if it is, the tens must be carried to the column of tens;
add the numbers in the column of tens (2+1+1=4);
combine the results to get the total (27+15=42).
repeat all the steps using other examples (app. 5 times)
solve 5 more problems on your own, without the teacher’s assistance;
explain the techniques you implemented;
correct the mistakes if there are any and account for them.

Prerequisite behaviors:

revise the information about how to perform single-digit numbers addition;
explain the difference between a single-digit and double-digit numbers;
ask questions to ensure full understanding;
explain the notion of carrying;
describe the process children are going to perform step by step and make them write down several examples.

Task Analysis of What a Child Should Do When he/she Becomes Frustrated with Work he/she is Doing at his Desk Independently

In case the child easily becomes frustrated with what he/she is doing, behavior modification is required. The behavior should be modified by encouraging the appearance of adequate reactions and eliminating the causes of problem behavior. Otherwise, frustration with self-performance can lead to depression, indifference to the subject, aggression, and refusal to complete the task. Task analysis is the perfect technique that helps encourage independence. The task is broken into small steps that can be mastered one by one.

However, not only academic problems must be dealt with to cope with frustration. Psychological task analysis is also necessary in this case.

Long-term goals of overcoming frustration connected with failures in independent work:

the child should learn to control his/her negative responses to challenges;
he/she will learn to correct his/her own mistakes without anyone’s help;
he/she must understand that failures are inevitable in the learning process;
the child will become more independent and self-confident.

Practical short-term objectives:

to learn how to overcome immediate adverse emotions and continue working;
to identify the mistakes and correct them within the shortest time possible;
to concentrate on the result;
to catch up with the rest of the class in case more time is required for performing the task;
to make conclusions to avoid mistakes in the future.

Identifying and eliminating unnecessary or redundant steps (the task depends on the psychological peculiarities of the students):

if the child neither demonstrates any signs of aggression and denial nor cries because of getting frustrated, soothing and persuading can be avoided, and the teacher can stay neutral;
in case this type of reaction is not typical for the student, who is usually calm and self-balanced, the teacher can wait and observe his/her behavior for a while and avoid alarming the parents.

Sequence steps for helping the student overcome frustration:

use chaining, which consists in mastering one step of the task at a time and adding it to the previous one; the teacher can help the student complete the task;
provide prompts or clues about the following step for the student to avoid getting lost and mixed up;
give as much support and encouragement as possible;
reward the student for his/her success to reinforce his/her motivation;
let the student try to perform the task again without assistance;
in case the result is still unsatisfactory, restructure the environment or modify the task.

Prerequisite behaviors necessary for establishing contact with the child who is having problems:

both the student and the teacher must be willing to solve the problem and enter communication;
both should keep calm; the teacher must not resort to pressing, shouting or threatening the child with poor marks or any other punishment;
the teacher should approach the student individually without exposing him/her to public attention to avoid mockery;
both the adult and the child should start with identifying the underlying causes of the failure (e.g. the student may have problems with the teacher’s explanations or he/she could have distracted from work by his/her classmates).

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Math and Psychological Tasks Analysis

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