An Informal Inventory is a teacher-made test that is administered to gain an understanding of the student’s mathematics skills. Once the general area of difficulty is determined, a more in-depth analysis is conducted to diagnose the problem.
Informal Inventory should assess the following areas:
· Counting
· Times-table facts
· Place-value tasks
· The four operations (addition, subtraction, multiplication, division)
· Word problems
· Money
· You might also add area and fractions
Clinical Interview
A student is asked to solve a math problem. He is told to “think out loud”’ or to say all the thoughts that he is using to solve the problem.
• The student explains the steps (logical reasoning) he is following to address the question.
• It is important that the student respond freely so his problem processing can be tracked. This can be accomplished in two ways.
1. Introspection -The child speaks about the process that he adopts to solve the problem.
2. Retrospection - The child comments on his thoughts after he has finished a mathematical task.
It is best to combine both introspection and retrospection.
Error Analysis
This refers to the analysis of the kinds of mistakes that a student is making. The four most common types of errors of calculation are:
· Place value
· Computation facts
· Using the wrong process
· Working from right to left
Counting
The teacher should assess the student to determine if he can count in a meaningful manner. The student can be given objects (say 40 matchsticks) and asked to count them. The teacher should note one-to-one interactions, speed of counting, and accuracy. The assessment also should determine whether the student can count the number of dots on a paper spaced in a regular line or spaced randomly, because this would indicate whether the student could apply the knowledge of counting to abstract objects.
Times-table facts
Times-table facts should be assessed to determine if the student can recall times tables and up to what number. Ask the student which tables she can recite. If she says that she knows the three times table, then ask her, "What is three times two” or “What is three times seven?" By asking her to respond to questions in the three times table in a random order, it ensures that the student knows the times table facts and is not relying on rote memory alone. For example, if she were just to recite the tables in sequence it simply could have been memorized in that exact order with no real knowledge of each individual math fact. It is also important for us as teachers to observe whether the student recalls the answer instantly, or whether she needs to count up or use another strategy to get the answer. If the student uses another strategy, then we (the teacher) may wish to question her further to understand the strategy that she uses to recall the times table fact.
Place value
Place value is an important concept to learn in order to perform a number of math tasks correctly. The teacher can examine the place value concept by doing the following:
· Show flashcards with two, three, and four digits on them, and ask the student, "What number is this?"
· Find out whether the student can read numbers in tens (e.g. 65), hundreds (e.g. 573), and thousands (e.g. 7684) correctly.
· Ask the student to write the number eight thousand five hundred and ninety-one or something similar.
· Ask the student to write the number twelve thousand and ten or something similar.
· Ask the student, "What is the value of each digit in this number (e.g. 8549)?"
The four basic operations (addition, subtraction, multiplication, division)
Find out whether the student can perform the four basic math operations. This can be examined by asking students to solve the following equations/operations:
Addition
Insert your own problem samples for this assessment by typing/developing a group of problems that will test addition skills that are being taught/reviewed in your classroom.
Subtraction
Insert your own problem samples for this assessment by typing/developing a group of problems that will test subtraction skills that are being taught/reviewed in your classroom.
Multiplication
Insert your own problem samples for this assessment by typing/developing a group of problems that will test multiplication skills that are being taught/reviewed in your classroom.
Division
Insert your own problem samples for this assessment by typing/developing a group of problems that will test division skills that are being taught/reviewed in your classroom.
Careful selection of computation items (four arithmetic operations) provides useful information to us (the teacher) to make meaningful instructional decisions for each student. Please note that even though some of the examples given above may seem easy, they will provide us with information about the way the student solves the computation problems and his error patterns. The analysis of error patterns is dealt with more comprehensively in a forthcoming section. The teacher should not only observe whether the student has answered the problem correctly; we should also observe the method adopted to solve the problem.
Word Problems
The teacher should examine whether the student can do word problems. A student who has difficulty in reading may find it difficult to know what she has to do. If this is so, then it should be noted and perhaps the problems should be read to the student. The child can be asked to read and solve the following types of problems:
· What is 8 plus 4?
· What is 25 minus 8?
· If 7 boxes contain 3 pens each, how many pens are there altogether?
· John goes to the supermarket to buy 5 chocolates at 40 cents each and 2 drinks at 80 cents each. How much does he pay?
· Cathy and Mary have 18 hair clips to share equally between them. How many should each get?
Take care to note the strong link between reading comprehension and mathematics and the need to teach students how to analyze a math problem. We may try one of these as a strategy:
· Write out the problem as an arithmetic question.
· Now write out a number of questions.
· Ensure that you employ at least the following types of questions:
1. Literal
2. Inferential
3. Vocabulary (specific to the problem concerned and general)
Money
It is important to examine whether students can generalize their knowledge of mathematics to money problems. This can be determined by asking the student the following types of questions:
· How many cents are in one dollar?
· How much is half a dollar?
· Show the child one dollar and ask him, "How much change would I get from one dollar if I bought a chocolate that cost 60 cents?"
· Show the child two cards with $100 written on one and $9 written on the other and ask, "If you have $100, how many books can you buy if each costs $9? How much change would you have left?"
· Say, “You have $10 and you want to buy five items; they cost, respectively, $4.50, $3.50, $1.50, $1.25, and 75 cents. Do you have you enough money to buy all five items? How much more would you need to purchase all five items?"