Using smart tests in teaching: how and why

The purpose of smart tests

Good achievement in mathematics and numeracy is essential in all modern economies. It provides the foundation for life-long learning, employment satisfaction and for each country's economic competitiveness. Local and international studies show that even in countries such as Australia which achieves well in mathematics and has much to be proud of in the education system, there is substantial room for improvement.

One of the major challenges in teaching mathematics is to provide personalised learning opportunities that meet the needs of individual students. Many students have misconceptions or gaps in their knowledge which are a barrier for further learning but often go unaddressed. The smart tests aim to give teachers readily useable information about each student's understandings to help the teachers select instruction that will bring about specific conceptual changes.

Smart tests are for formative assessment: they are designed to inform teaching, and so they are used as part of planning and teaching a topic. A few smart tests test skills, but more often they identify how students are thinking about each topic. Smart test diagnoses will enable you to target remedial teaching where it is needed. They can identify students whose understanding is already good, who can move on to something else. They can show the range of different item types that teaching should include. In most aspects of learning maths, there are central ideas which have to be applied in increasingly complex ways, which all need to be taught and assessed.

Smart tests are especially useful for mathematics coaches, schools intending to improve mathematics achievement and to personalise students' learning as well as for teachers teaching mathematics 'out-of-field'.
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How smart tests diagnose student thinking

Smart tests use very carefully designed sets of questions to diagnose student thinking about specific topics. Many of the questions have been used in research projects from around the world. The extensive programming behind the smart tests looks for patterns in students' answers. These patterns are sometimes just patterns in the accuracy of answers: which questions a student gets right and which a student gets wrong. However, in many tests, it is not just the accuracy of the answer that is considered in the pattern, but the actual answers given. frequently, the actual answer that a student gives indicates their underlying thinking, especially when the same thinking is evident in mutliple responses. Information from the set of questions in the smart test is put together to diagnose each student's thinking.

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What smart tests do not do

Because smart tests target very specific learning, they do not give an overall picture of where a student is "up to in maths" but instead they tell the teacher what needs to be taught.

We hope that smart tests are useful and that they help improve student learning. But there is much more to a comprehensive mathematics assessment program. Smart tests are accessed on a screen and computer-marked. For this reason, the questions are short. There are few questions requiring multiple steps. Smart tests use a wide variety of item types, but all have to be machine codable. The only constructed responses are short, mainly single numbers. There are no substantial written answers required, either written as sentences or as multiple lines of mathematical argument. It is not possible to test most aspects of working mathematically in this format. Students need other test items that encourage them to write mathematics logically and explain their reasoning. These limitations need addressing elsewhere in a comprehensive maths program. The smart tests aim to do one job well, so that the teacher has time to undertake the parts of mathematics assessment that need human intervention. Smart tests do not replace normal end-of-topic or end-of-term tests, but they complement them.

Smart tests do not provide direct feedback to students. Most teachers whom we have consulted do not want this. It is a good idea to explain this to students and also explain how the teacher will be using the results to target teaching better.

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How teachers have used smart tests

Typical use of smart tests proceeds as follows. Before a unit of work, a teacher looks at the index of smart tests and selects one or two tests that are relevant to the new unit. Students do the smart tests online, maybe at school or at home. They might only take 5-10 minutes to complete. When the students have completed the test, the teacher automatically receives a report of the levels and types of understandings shown by each student in the class. The teacher uses this information to provide targeted teaching assisted by links to appropriate on-line resources. A parallel smart test might be assigned for students at the end of the unit, so that progress can be tracked and further targeted instruction can be provided if needed.


An important aspect of smart tests is that they can show teachers the range of different item types that your teaching should include. In most aspects of learning maths, there are central ideas which have to be applied in increasingly complex ways, which all need to be taught and assessed. The stages of the smart tests and the items and the topic overviews which are provided with some smart tests can help teachers to appreciate the variation of task within a topic.


Survey data from teachers show that they use the results of smart tests to modify the level of instruction so that it is more or less advanced. It is common for the tests to reveal aspects of the topic that need revision and review before proceeding onto a new topic. However, many teachers report that the test results show that they can begin at a more advanced place than they had expected.


Addressing the needs identified by smart tests can be done with individuals, taken aside for a short time, with groups who are given activities with different goals in mind, or with whole classes by a change in teaching plan.

Here are some of the ways teachers have reported using the results of the smart tests.

I used the smart test “Understanding angle” with my year 7 class. In my teaching I adopted an approach that best addressed the needs of the students based upon the diagnostic test. I was able to avoid certain areas that were well understood and concentrate on areas that were not.

The other end of the spectrum is that I’ve been more confident in moving kids, not making them go over things. I can see “alright, this child has a really good understanding of fractions”. I’m not going to sit and make him (or her) repeat all of those skills so I feel more confident in moving them to something else.

Very useful as a pre-test on reading scales. I found out exactly where each student was at and that enabled me to target my teaching into the areas where it was most needed, while giving extension work to the students who had already gained a good understanding of the topic. Now I am going to retest them using another form of the test to see how effective my teaching has been.

When our Year 7 students did the fractions smart tests, we were surprised to find many students were at Stage 0. All these years we’ve always presumed that they were at a particular level but obviously that’s not happening, and so that’s changed our curriculum, the way we think about teaching fractions.

Excellent formative assessment tool which allowed me as a coach to discuss the various misconceptions and student thinking within a year 8 class. It provided teachers with real data that allowed them to address the misconceptions through their teaching.

I didn't adjust my teaching plan as such, because the results supported what I expected, but confirmation was valuable.

I adapted the simpler task that we were going to approach in class with something that reflected the students' greater level of understanding.

I have put the students into groups and will give them activities to focus on and correct their misconceptions. I will be looking carefully at the [suggested resources] for ideas.

Focussed teaching groups using the Stages as a starting point.

I had assumed that at year 10 my students would have a basic understanding of the idea of percentages - many of them didn't! Instead of going straight into calculating percentages of quantities and calculating whole quantities given a percentage, and then on to financial arithmetic (simple interest), I went back to basics with the students who needed it, and others who could cope with this were assigned the original tasks I had planned.


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