Assessment and Mathematics: Where are we going wrong?

Thousands of children in Australian schools have recently sat the national literacy and numeracy test (NAPLAN), and many teachers have been busy administering a whole range of assessments because it’s report writing season and boxes need to be ticked. My question is, how often do we ask ourselves why we’re assessing? What are we doing with the results apart from using them for reporting purposes? I’ve spent quite a bit of time in schools lately, and after talking to lots teachers and seeing a range of mathematics assessment tasks and work samples, I’ve begun to reflect on some of the things we could do better.

“Effective pedagogy requires effective assessment, assessment that provides the critical links between what is valued as learning, ways of learning, ways of identifying need and improvement, and perhaps most significantly, ways of bridging school and other communities of practice” (Wyatt-Smith, Cumming, Elkins, & Colbert, 2010, p. 320)

It’s through our assessment we communicate most clearly to students those learning outcomes we value, yet it’s often held that no subject is as associated with its form of assessment as is mathematics (Clarke, 2003). Assessment practices in mathematics often consist of formal methods such as tests and examinations (Wiliam, 2007), and it’s believed that such strategies need as much consideration for renewal as does content and classroom pedagogy. Although lots of progress has been made in terms of improving mathematics teaching and learning and curriculum, many such improvements have failed due to a mismatch between assessment practices and pedagogy (Bernstein, 1996; Pegg, 2003). It’s been suggested that in mathematics, there should not be more assessment, but more appropriate assessment strategies implemented to inform learning and teaching as well as report on progress and achievement (Australian Association of Mathematics Teachers, 2008; Clarke, 2003). And this is the point I want to highlight – assessment to inform teaching. Regardless of the type of assessments we use, are we using assessment data in the right way?

What do you do with your assessment work samples? Do you simply use the scores to determine how students are grouped, or what aspects of a topic you need to cover? How often do we, as teachers, take the time to analyse the work samples in order to identify specific misconceptions? Imagine a scenario where students are grouped according to assessment scores. Each of those groups are then exposed to pedagogies intended to address the ‘level’ of the group. What if, within each group, there were a range of misconceptions? And what about the top groups? What if work samples that resulted in accurate answers exposed misconceptions despite being correct?

When students transition from one level of schooling to another, it’s not uncommon to hear teachers complaining about the broad range of abilities, and more specifically, those students who appear not to have achieved the most basic skills. How have these students managed to get to kindergarten/Year 3/Year 6/high school/university without knowing how to……? Mathematics content is hierarchical – when students miss out on learning concepts in the early years, the gaps in knowledge continue to widen as they progress through school. Whether caused by inattention, absence from school, or any other reason, students find it hard to catch up when they’re missing pieces of the mathematical jigsaw puzzle. It’s like building a house on faulty foundations.

So how can we fix this? A teacher recently told me that she didn’t have time to analyse the responses in an assessment task. Isn’t this our job? How can we manage workloads so that teachers have the time to really think about where students are going wrong, and how can teachers access professional learning to assist them in being able to identify and address students’ misconceptions?

I think one way we can address this situation is to think carefully about the design and the quantity of assessment tasks. Administer fewer, better quality tasks that are designed to assess both the content and the processes of mathematics. That is, tasks that require students to show their working, explain their thinking, and produce an answer. The more they show, the more we see. Another strategy to assist teachers is to provide time for teachers to look at assessment samples and analyse them collaboratively, discussing the identified misconceptions and planning strategically to address them.

The knowledge that teachers need to effectively teach mathematics is special. We need to know more about mathematics than the average person – we need to understand where, why and when our students are likely to go wrong, so we can either avoid misconceptions occurring, or address them when they do. This specialist knowledge comes from continued professional learning and collaboration with peers. Don’t just rely on the curriculum documents – we need to look beyond this to ensure we have that specialist knowledge.

This post posed more questions than answers in relation to assessment in the mathematics classroom. Hopefully it will spark some conversation and thinking about what we are doing with the assessment work samples we gather, regardless of why type of assessments they are. If we don’t try and change the way we use assessment, we’ll always have those students who will struggle with mathematics, and while there will always be a range of achievement levels in every group of students, that doesn’t mean we shouldn’t keep trying to close those gaps!

 

References:

Australian Association of Mathematics Teachers. (2008). The practice of assessing mathematics learning. Adelaide, SA: AAMT Inc.

Bernstein, B. (1996). Pedagogy, symbolic control and identity: Theory, research, critique. London: Taylor and Francis.

Clarke, D. (2003, 4-5 December). Challenging and engaging students in worthwhile mathematics in the middle years. Paper presented at the Mathematics Association of Victoria Annual Conference: Making Mathematicians, Melbourne.

Pegg, J. (2003). Assessment in mathematics. In J. M. Royer (Ed.), Mathematical cognition (pp. 227-260). Greenwich, CT: Information Age Publishing.

Wiliam, D. (2007). Keeping learning on track: Classroom assessment and the regulation of learning. In F. K. J. Lester (Ed.), Second handbook of mathematics teaching and learning (pp. 1053-1098). Greenwich, CT: Information Age Publishing.

Wyatt-Smith, C. M., Cumming, J., Elkins, J., & Colbert, P. (2010). Redesigning assessment. In D. Pendergast & N. Bahr (Eds.), Teaching middle years: Rethinking curriculum, pedagogy and assessment (2nd ed., pp. 319-379). Crows Nest, NSW: Allen & Unwin.

 

9 thoughts on “Assessment and Mathematics: Where are we going wrong?”

  1. Oh if only some amazing research was done into where teachers will get the time to do all this. I have always been a great believer in research and believe I have efficient use of time but in year when I am implementing new Science History/ Geography curriculum documents while still trying to perfect multi modal texts for a new grade every year ;cope with my school requirement for pre assessment and post assessment in Maths; integrate technology into all areas; differentiate for a myriad of diagnosis and communicate effective with all parties involved I am seriously just feeling that I am merely in ” survival” mode!

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    1. I agree, Margaret – there has to be a better way! Sadly, you’re not alone in saying that you’re operating in survival mode – each year the demands on teachers seem to continue to build until they reach breaking point. It would be wonderful if we could take the time to stop, re-evaluate, and rethink how things are done and where the priorities are!

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      1. I believe that we have reached the point that every time we implement something new we need to stop doing something else. So, dear teachers, whenever you add something to your teaching practice, please deduct something else. This is the way to maintain sanity.

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  2. Research indicates, and we all seem to agree, that productive struggle results in deep learning, the type that changes our brain structures. As teachers, we also know that if a student isn’t equipped with the appropriate prior learning, a growth mindset and the time and feedback to engage with such meaningful learning, then he or she will often disengage and give up, and soon come to believe that s/he is not a ‘maths person’, s/he does not have the capacity to learn mathematics. It’s so important to ask the questions about how our assessment is informing our teaching and whether it supports our students in their struggle with problem knowledge. I loved this post. It asks all the questions for teachers to reflect and improve.

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    1. Thanks for your comments, Cathy. It’s so important that we continually question our practice to ensure our most important stakeholders, our students, are our priority.

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  3. Maybe teachers could collate a bank of assessment tasks designed to show up misconceptions students have in particular content areas. If teachers across Australia left these tasks in a common place- a bit like maths 300 then perhaps that would make it easier for everyone? What would a good platform for this be?

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    1. Great suggestion Georgie. I’ll give it some thought – this may be a very big job as there would need to be some quality control as well as a high degree of organisation!

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  4. I like to start learning about a concept with a diagnostic assessment and then group kids according to specific needs, shuffling them around as necessary based on formative assessment along the way. At the end, I still like a straightforward pen and paper/digital summative assessment and after I’ve covered a few linked sub-strands, throw in a rich task to see who’s generalising and integrating knowledge successfully.

    Unfortunately I’ve not found many good diagnostic assessments that link well with the new syllabus. I thought the assessment resources from numeracyskills.com.au may have fit the bill, but after having used them, they don’t give me the detail that I’d like.

    I love Georgie’s suggestion of creating a bank of these resources – I’d certainly be up for that!

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