Friday, April 5, 2013

Criteria-Based Marking In Mathematics

by Richard D Boyce

Traditionally, assessment in Mathematics at high school and beyond has been the timed, formal, pen on paper examination.

Often, talented Maths students have failed to show their expertise in these formal examinations due to exam nerves. Other students who learn in a non-maths/logic way found that the formal situation did not fit into their learning styles.

What has further pointed Mathematics teachers to use a variety of pedagogue and then non-traditional assessment techniques has been the recognition of the existence of Multiple Intelligences. This suggests strongly that students learn in different ways.

Additionally, more students are staying at school longer and studying Mathematics in the hope of gaining entry to more prestigious university courses.

These factors have lead in some educational areas to new Mathematics syllabuses that require assessment tasks to reflect a wide variety of pedagogue as well as the use of computer and calculator technology.

The traditional formal examination remains but has become one of many assessment techniques that may be used. This has led to criterion based marking in the non-traditional assessment tasks.

This article looks at one alternative assessment item that uses criterion based marking. It is summarised and the criteria are included and some further explanation added.

Year 12 Maths B Assignment


Select one of the following projects and use Critical Path Analysis techniques to complete the questions below:
A Compiling School Magazine
B Organising School Musical OR Rock Eisteddfod
C Organising School Senior Formal

What is above was the basis of the assignment. What followed this was the general description of what was expected in this assignment. Then the questions to be answered with regard to the Critical Path Analysis were specified.

They included questions which tested their basic understanding (Techniques) of Critical Path Analysis plus four questions of a problem solving variety. Here is an example of one of each of these.

A techniques question/requirement was:

Construct a network for these activities.

An applications question (problem solving) was:

Select a completion date for your project and show justification mathematically for the latest date on which you could begin the project.

The assignment was marked using three criteria. They were:
  1. Communication (this criterion looks at how the student communicates his/her Mathematics);
  2. Techniques (this criterion assess the student's knowledge of the core ideas/learning work of the topic); and
  3. Applications (this criterion assesses how the student applies his/her knowledge of Mathematics to a problem solving situation, often in an unfamiliar context).

These criteria were the ones used when I wrote Alternative Assessment items late in my career. Obviously, the syllabus documents will specify and define the assessment criteria applicable in each system and how they are applied. I simply use these as an example.

Below are the assessment criteria I used for this assignment.



Sentence construction
Use of Mathematical symbols

Allocation of Standard
H Mostly Very Good S Mostly Satisfactory U Mostly Unsatisfactory



(a) Recorded activities
(b) Recorded time required to complete each activity
(c) Ordered the activities - stated in writing which it precedes
(d) Drawn a Network/s as appropriate
(e) Drawn Precedence Boxes
(f) Completed a forward Scan
(g) Completed a backward Scan
(h) Drawn in the Critical path
(i) Drawn a Gantt Chart
(j) Significant use of the Internet including listing of URLs

Allocation of Standard

A Completed all the above activities correctly
B Completed (a) - (h) correctly
C Completed (a) - (h) maybe some minor errors
D Some attempt
E No attempt



No attempt
Little progress
Substantial progress but no solution
Incorrect solution caused by a major conceptual error
Correct solution and calculations shown (minor errors allowed)
Correct solution and justification of techniques used.


  1. In Techniques and Communication, you will notice all the basic skills are listed. This enables the student to know the least requirements to gain a satisfactory grading.

  2. In Applications, the criteria are generic so as to not lead the student towards a solution. This makes it a real test of how the student uses his/her Mathematics knowledge. Specific marking criteria are developed for the marker to use and these are published for the students after the assessment task is returned to them.

  3. In Applications, you will notice the words 'simple and complex' to describe the problems. The syllabus required a variety of unfamiliar problems from simple to complex in Applications to help delineate between students at the top end of the scale.

  4. One of the important advantages of this type of criteria based marking is that you can use the same criteria over and over once you have revised them. All you do is to change the question.

  5. Lastly, it is important to note that in discussing the assignment initially, the teacher should remind students to address the criteria at all times. This will ensure that they get the maximum grading for each criterion that they are capable of getting.

Our author, as a Head of Mathematics, led his staff in introducing criteria based assessment when syllabus revisions mandated the use of a variety of different pedagogue and assessment techniques. His school became known as an innovative school in the teaching of Mathematics.

He became a presenter of professional development on this issue and many schools borrowed examples of their assessment items to use as the basis of their early trials of these assessment techniques.

For a more detailed look at Alternate Assessment, go to and seek out the eBook, "The Examination and Assessment Book".

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