A tale of two tests

Leanne Rylands and Don Shearman, Western Sydney University

l.rylands@westernsydney.edu.au

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics in Gramado, Brazil, November 2017, “Brazil Delta 2017’

In Australia, students can come to university to study subjects requiring maths without having done maths in their last 2 years of high school! Some degrees have mathematics prerequisites but many Science degree do not have high school mathematics as a prerequisite. In 2016 at Western Sydney University, 50.5% of Australian students registered for first year mathematics and statistics did no mathematics in their last 2 years of school and 15% only studied the lowest level of mathematics at school in their last 2 years.

Conjecture: Diagnostic mathematics tests can be useful

Diagnostic tests

• Let teachers know the level of their students
• Let students know where they need to improve skills
• Predict performance
• Inform non-mathematicians and decision makers about the level of maths knowledge of students with hard data to counter accusations that you can’t teach.

Test for design students: 10 minute test with 14 questions. Fail if less than 11/14. Six attempts to achieve, last attempt at end of semester. Counts 10% of course mark but is a requirement for passing course. 61 students still enrolled at end of semester, all attempted the test at least once. 11 (18%) did not reach 11/14 by end of semester.

Engineering test: 50 minutes, 50 multiple choice questions, need 70% or must do a preliminary course. Placement test.

For design students,

• over 50% could not get 11/14 on 1^st attempt
• almost a quarter can’t change m into cm, or divide by 100, add 2 simple fractions
• almost a third could not simplify -6 + 4 x – 5 – 3
• 5 (10%) could not mark 2/5 on a number line showing 0 to 2.
• 11 (18%) did not reach 11/14 by the end of semester
• The test lifted the skills of students
• Those who didn’t reach the threshold of 11/14 would have failed the course anyway based on their other marks.

For engineering,

• Reduction of failure rate for maths 1 from 50% to 30%. [Perhaps threshold for placement test needs to be raised from 70%, some suggest]
• 40% of those who failed the preparatory course also failed another course. Are they doing the right courses?

When students had the freedom to choose whether or not to do the preliminary test, most did not choose to take the strong advice given to them. Now it is forced, they must do the preliminary course if they score below 70%.

Where do the design students go when they score below 11/14 and need to prepare for a re-take? There is a support centre that arranges 1-1 meetings, consultations in libraries, online tutors. CogBooks (an adaptive learning programme similar to ALEKS) is under investigation.