 MODULE 5: Informal Mathematics Assessment

When we work with individual students we need to appraise their skills and deficits in
mathematics. One can use norm-referenced or informal mathematics tests. A norm
referenced test has limited use in planning instruction for such students. The informal
tests provide information that informs what a particular student can and cannot do
and helps us to find out "any incorrect" reasoning that led to the wrong answer.

Informal mathematics assessment can be conducted in different ways. The three most
commonly employed methods are:

o Informal inventory
o Clinical interview
o Analysis of mathematics errors

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.

 An informal inventory should assess the following areas.

o Counting
o The teacher should assess the child to determine if he can count
meaningfully. The child can be given objects (say 40 match sticks) and
asked to count them. The teacher should note one-to-one
correspondence, speed of counting and accuracy. It should also be
assessed to determine if the student can count the number of dots on a
paper spaced in a regular line or randomly because it would indicate to
the teacher if the student can apply his knowledge of counting to
abstract objects
o Times table facts
o Times table facts should be assessed to determine can the student recall
times-tables and up to what number. Ask the student which tables he
can say. If he says that he knows the three times table then ask him to
say 'What are three times two or three times seven? By asking him to
respond to questions in the three times table in a random order we want
to ensure that the student knows the "the times table facts" and is not
relying on rote memory, for example, if he were to recite the tables in
sequence. It is important for the teacher to observe that if the student
recalls the answer instantly or counts up or uses another strategy. If the
student uses another strategy then the teacher may wish to explore the
strategy that he uses to recall the time table facts.
o Place-value tasks
 o The place value is a very important concept to learn in order to perform
a number of mathematics tasks correctly. The teacher can examine the
place value concept by undertaking the following:
 Showing flash cards with two, three and four digits on them and asking the student
"What number is this?"

 Finding out if the student can read numbers in tens (e.g. 65) hundreds (e.g. 573),
and thousands (e.g. 7684) correctly.

Asking the student to write the number eight thousand five hundred and ninety
one or similar.
twelve thousand and ten or similar.

 Asking the student "What is the value of each digit in this number (e.g. 8549) ?

o The four operations

 Find out if the student can perform the four basic arithmetic operations.
This can be examined by asking the student to solve the following sums.

 Addition

 Subtraction
 Multiplication

 Division

Careful selection of computation items (four arithmetic operations) provide useful

information to the teacher to make meaningful instructional decisions for each
student. Note although all the examples given above are 'easy' they provide the
teacher with information about the way the student solves the computation
problems and his error patterns. The analysis of error patterns is dealt more
comprehensively in a forthcoming section. The teacher should not only observe
whether or not the student has answered the problem correctly, he should also
observe the method adopted to solve the problem.
o Word problems

 The teacher should examine if the student can do word problems. A student who
has difficulty in reading may find it difficult to know what he has to do. If this is so
then it should be noted and perhaps the problem 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 seven boxes contain three pens each, how many pens together?
John goes to the supermarket to buy five chocolates at 40 cents each and two
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?

 Note:
 The strong link between reading comprehension and mathematics.
 The need to teach children how to analyse a mathematics problem.
o Money
 It is important to examine if students can generalise their knowledge of
mathematics to solve money problems.
This can be determined by asking the student the following types of questions?
 How many cents in one dollar/peso?
How much is half a dollar/peso?
 Show the child one dollar/peso and ask him,
"How much change would I get from one dollar/peso if I buy a chocolate which
costs 60 cents?"
 Show the child two cards with $/Php 100 and $/Php 9 written on each of them and
ask,
"If you have $/Php 100, how many books can you buy if each costs $/Php 9/10?
Would you have any change left?"
 You have $/Php 10 and you want to buy five things which costs $/Php 4.50, $/Php
3.50, $/Php 1.50, $/Php 1.25 and 75 cents.
"Have you enough money to buy all five things?"

o You might also add : Area and Fractions

 Clinical interview
 A student is asked to solve a mathematics problem. He is told to ‘think out aloud’
or to say out all the thoughts that he or she is using to solve the problem.
 The student explains the steps (logical reasoning) he is following to address the
question.
 To know what the child is thinking, it is important that the child responds freely.
This can be accomplished in two ways.
o Introspection -The child speaks about the process that he adopts to solve
the problem.
o Retrospection- The child comments on his/her thoughts after he has
finished a mathematical task.
o It is best to combine both introspection and retrospection.
o The four operations

 Error analysis
Analysis of kinds of mistakes that a student is making. The four most common
types of errors of calculation are:

o Place value
 Students who make this type of error are confused about the specific significance
given to the position of a digit in a number. They frequently make errors in
regrouping, carrying and borrowing.
 Example:

 What is the error here?

There is no set error pattern. The student has written random numbers as the
answers suggesting that he is not aware of how should the computation be carried
out

o Computation facts
 Students make errors in four basic operations of addition, subtraction,
multiplication and division.
Example:

 Can you work out what the child did wrong?

o Using the wrong process
Students who make this kind of error often do so because they follow wrong
mathematical process. They either confuse the +, -, ×, ÷ signs or are not aware of
what these signs mean.
Example:

o Working from right to left

 While solving a mathematics (four operations) problem students reverse the
direction of calculation. Instead of working from right to left, they work from left
to right.

 Example: