Overview of Research

Year 9 Support Materials

Year 9 Mathematics snapshot: Pythagoras' Theorem

Assessment Principle 1: Assessment should be an integral part of Teaching and Learning

Reflecting on the Assessment Snapshot

The teacher in this assessment snapshot has deliberately planned assessment activities that provide detailed information about students' thinking and possible incomplete understandings or misconceptions.

In many classrooms, the process of eliciting such evidence [of where students are in their learning] is done mainly on the fly-teachers almost always plan the instructional activities in which they will engage their students, but they rarely plan in detail how they are going to find out where the students are in their learning (Wiliam, 2011, p. 71).

Research into effective teaching practices, however, highlights that teachers who obtain the most growth in student learning, continually plan for and from assessment.

Effective teachers administer assessments that reveal how students think rather than what they know, the quantity of work, or the presentation. They are interested in eliciting students' pre-existing, sometimes incomplete understandings, and their misconceptions in order to identify appropriate starting points for personalised teaching and learning (Forster, 2009, p. 6).

In his synthesis of more than 800 meta-analyses of relating to student achievement, John Hattie concludes,

Teachers need to be aware of what each and every student is thinking and knowing, to construct meaning and meaningful experiences in light of this knowledge, and have proficient knowledge and understanding of their content to provide meaningful and appropriate feedback such that each student moves progressively through the curriculum levels (Hattie, 2009, p. 238).

Understanding students' thinking requires teachers to devise and select assessments that provide fine-grained information about student learning. In 2006, Professor David Andrich recommended to the Curriculum Council (now the School Curriculum and Standards Authority) that fine-grained assessment take precedence over broad classifications of student performance. Curriculum documents, like the Australian Curriculum, and standards frameworks, like the achievement standards, inherently provide broad classifications of student performance. The teacher in this snapshot devised assessment activities which allowed her to examine her students' understandings at a more fine-grained level than is specified in the curriculum.

Reflection questions
  • Is assessment an integral part of your lesson planning?
  • What information do you collect during lessons (your observations, student responses to questions, student participation in group activities and so on) and to what extent is this information used to shape subsequent lessons?
  • Do your assessments enable you to say what your students know and understand about specific aspects of learning?

Assessment Principle 2: Assessment should be educative

Assessment snapshot in the context of research

Reflecting on the Assessment Snapshot

Assessment Principle 2 highlights that good assessment practice informs both the student and the teacher. In an interview at the Australian Government Summer School for Teachers of Mathematics, Professor John Hattie discusses his research into effective feedback. In this interview, Hattie states,

Feedback is to the teacher, it's not the other way round. It is how teachers can see that any assessment they do, any lesson they are running is how they can increase the feedback to them [the teachers] about how they are going, where they are going, and where to next. Then you get a massive dividend in terms of the effect on student learning (Australian Government Summer School for teachers of Mathematics, 2008).

Recent research undertaken by the National Centre for Research on Evaluation, Standards and Student Thinking (CRESST) in the US has examined how teachers learn from formative assessment and how they use the information that they collect. In this research middle school mathematics teachers discussed their assessment practices and the researchers categorised the teachers' responses as binary, mildly-nuanced and highly-nuanced. An example of a binary response was,

…The formative tests frequently happen every Friday. So we'll do the instruction Monday/Tuesday and practice it throughout the week and then see whether or not they learned it on Friday (Frobbieter, Greenwald, Stecher, & Schwartz, 2011, p. 14).

A highly nuanced response was,

I'm looking, for this particular thing, where are they getting stuck? Can they do the first step, which for example, on a division of fractions [problem], did they take a mixed number and change it into an improper fraction…? All right, if they can't do that, then that's one problem. Could they take the second fraction in the division problem and know that they had to flip it over to its inverse or reciprocal? And if they didn't do that, that's a different problem, and maybe it could be fixed right away, but there's some kids that for some reason don't know why it's the second fraction, and might do the first fraction, and think, as long as they did one, it should be all right. So did they get that setup? And then for again, fractions, I'm looking if they've gotten that far, did they go ahead and cross reduce first? Or did they multiply and then try and reduce, which is a much harder way to do it, so why didn't they cross reduce? (Frobbieter et al, 2011, p. 18).

The study did not examine whether teachers who made highly nuanced comments about student performance had the greatest impact on student performance. However, in a separate study also conducted by CRESST, a different research team did examine the relationship between teacher knowledge, assessment practice and student learning. They found that,

Students whose teachers spend more time and who more frequently engage in analyzing and providing feedback on student work achieve higher learning than students whose teachers spend less time and who less frequently do so. Teachers' attention to student learning as evidenced in classroom work-whether through observations of students in classroom discussions or analyses of student responses in science notebooks, other written responses, or end-of-investigation assessments-is associated with higher student performance (Herman, Osmundson, Dai, Ringstaff and Timms, 2011, p. 19).

There is a general acknowledgement in the literature that formative assessment makes considerable demands on teachers' content and pedagogical knowledge because it requires eliciting and analysing evidence of student ability and then acting on that evidence. Herman, et al (2011), however hypothesise that

Educators who analyze student learning, consider potential obstacles or misconceptions limiting this learning, and reflect on the effectiveness of prior and subsequent next steps-may well deepen their content and pedagogical knowledge, particularly if such activities occur in the context of professional learning communities (Herman et al, 2011, p. 2).

Reflection questions
  • Do you use assessments to identify the next skill or understanding a student or group of students need to learn?
  • Have you determined what information you need to collect to better understand your students' learning?

Andrich, D. (2006). A report to the Curriculum Council of Western Australia regarding assessment for tertiary selection. Retrieved http://www.scsa.wa.edu.au/internet/Publications/Reports/General_Reports

Australian Government Summer School for Teachers of Mathematics. (2008). John Hattie: What does feedback mean? Retrieved http://www.youtube.com/watch?v=6E6Kz59bkOs

Forster, M. (2009). Informative Assessment: Understanding and guiding learning. Papers presented at the 2009 Australian Council for Educational Research Conference on Assessment and Student Learning: Collecting, interpreting and using data to inform teaching. Retrieved http://research.acer.edu.au/research_conference/RC2009/17august/11/

Frobbieter, G., Greenwald, E., Stecher, B., & Schwartz, H. (2011). Knowing and Doing: What teachers learn from Formative assessment and how they use information. CRESST Report 802. National Centre for Research on Evaluation, Standards and Student Testing (CRESST). University of California, Los Angeles. Retrieved http://www.cse.ucla.edu/products/reports.php?action=search&query=802

Hattie, J. (2009). Visible Learning. A Synthesis of over 800 meta-analyses relating to achievement. Oxon, England: Routledge.

Herman, J., Osmundsen, E., Dai, Y., Ringstaff, C., & Timms, M. (2011). Relationships between teacher knowledge, assessment practice, and Learning – chicken, egg or omelet. CRESST Report 809. National Centre for Research on Evaluation, Standards and Student Testing (CRESST). University of California, Los Angeles. Retrieved http://www.cse.ucla.edu/products/reports.php?action=search&query=809

Wiliam, D. (2011). Embedded Formative Assessment. Bloomington. IN: SolutionTree.