**Case Study**

During my time teaching mathematics at Baden Powell College (my first teaching placement, please see Educational Setting for a description of the College) I observed a wide range of ability levels amongst the students, even though the students had been grouped by ability level using pre-testing for each unit. NAPLAN preparation was a constant pressure in the first two week block, with the first part of each numeracy lesson being devoted to two or three practice questions before the main lesson began. One of these practice questions had been a relatively simple problem involving adding fractions, decimals and percentages, and was met across the classroom with incomprehension or outright horror. Going through the solution on the board with the class did not make the students’ feelings abate in any way, so I decided to modify an upcoming lesson to incorporate a brief review of addition and subtraction of fractions. I had hoped that this would give the students more confidence should they encounter a similar problem on their NAPLAN exams.

I consulted the Victorian Essential Learning Standards (VELS) for mathematics at Level Four and found that by the end of their primary education the students should have extended their existing knowledge of fractions and decimals and be able to add, subtract and multiply fractions and decimals. Given this, I devised a plan to use a portion of a lesson revising worked examples on the board, with problems of increasing difficulty, and then setting the students a variety of questions to answer on their own. I had allocated forty minutes for both the worked examples and time for doing problems, believing it to be a quick revision session and that a wider variety of activities were not warranted.

During the lesson, it was painfully obvious that I had seriously misjudged what would be required. Students were unable to offer any prior knowledge of the process of adding or subtracting fractions, or even what was meant by the lowest common denominator. When I moved on to the worked examples on the board many of the students became more confident, loudly declaring that they’d seen this before and didn’t need revision. I assigned those students the prepared questions to complete, and continued to guide the rest of the class through the examples. It became apparent that many if not most of the students did not have an understanding of the basic concepts of fraction equivalence, let alone the ability to work with fractions. This meant that the time I had allocated to revision was nowhere near sufficient, and I was unable to complete all the activities on my lesson plan as the students spent much more time on the fractions work than anticipated.

I do not consider this to have been a successful lesson, but it was an incredibly useful experience as it taught me to never assume what the students’ prior learning is. In a similar situation I would use a stringent method of pre-testing to gauge skill and understanding levels, and only then plan accordingly. Naturally this is hard to accomplish in a short pre-service teacher placement, but the experience was informative and invaluable.

I consulted the Victorian Essential Learning Standards (VELS) for mathematics at Level Four and found that by the end of their primary education the students should have extended their existing knowledge of fractions and decimals and be able to add, subtract and multiply fractions and decimals. Given this, I devised a plan to use a portion of a lesson revising worked examples on the board, with problems of increasing difficulty, and then setting the students a variety of questions to answer on their own. I had allocated forty minutes for both the worked examples and time for doing problems, believing it to be a quick revision session and that a wider variety of activities were not warranted.

During the lesson, it was painfully obvious that I had seriously misjudged what would be required. Students were unable to offer any prior knowledge of the process of adding or subtracting fractions, or even what was meant by the lowest common denominator. When I moved on to the worked examples on the board many of the students became more confident, loudly declaring that they’d seen this before and didn’t need revision. I assigned those students the prepared questions to complete, and continued to guide the rest of the class through the examples. It became apparent that many if not most of the students did not have an understanding of the basic concepts of fraction equivalence, let alone the ability to work with fractions. This meant that the time I had allocated to revision was nowhere near sufficient, and I was unable to complete all the activities on my lesson plan as the students spent much more time on the fractions work than anticipated.

I do not consider this to have been a successful lesson, but it was an incredibly useful experience as it taught me to never assume what the students’ prior learning is. In a similar situation I would use a stringent method of pre-testing to gauge skill and understanding levels, and only then plan accordingly. Naturally this is hard to accomplish in a short pre-service teacher placement, but the experience was informative and invaluable.