It’s what you do with assessment that counts!


 Embedding assessment into pedagogical practice

One of the reasons, I have enjoyed this text so much is the parallels of thought with my own eclectic beliefs around teaching and learning.  Hattie, Fisher and Frey’s final chapter in their book, Visible learning for mathematics explores the importance of assessment, feedback and meeting the needs of all learners.

Rather than using the terminology of formative and summative assessment, the authors use formative and summative evaluation. Their argument for this choice is that as the evaluator, it is the teacher’s role to interpret where a student is during and after a lesson and how to improve his or her teaching in response to this evaluation.

Hattie, Fisher and Frey state that it is daily formative evaluation that allows to teachers to make instructional decisions about what will occur next. Carol-Anne Tomilson, the guru of differentiation states that formative assessment is the heart of differentiation as it provides the evidence as to what students know, don’t know and when done correctly, formative assessment provides both the teacher and student with information as to what to do next.  The authors suggest a process for formative evaluation with the following key elements:

Taken from Hattie, Fisher and Frey Visible learning for mathematics

Hattie has several internal questions for learners to self-regulate and for teachers to ask about their instruction:

  • Where am I going? What are my goals?
  • How am I going there? What progress have I made towards the goal?
  • Where to next? What activities can I do to make better progress?

Some examples of strategies to check for student understanding include: asking questions; numbered heads together; response cards; purposeful sampling; exit tickets; and lots of opportunities to self-assess.

Feedback ( a slide from a maths presentation I conducted)

Hattie, Fisher and Frey discuss feedback for the teacher (adjusting teaching) and feedback for the student (adjusting learning). Hattie considers the four levels of  feedback (task, process, self-regulatory and self) and considers each type’s impact. Not surprisingly the most common types of feedback are on task and process. However, for students to work towards self-regulation, self-regulatory feedback is crucial. It plays a prominent role during deep and transfer learning. The final type of feedback, self (Excellent job! You are so smart!) appears to have a zero to negative impact on learning. The effect size of feedback that fosters learning and perseverance has an effect size of 0.75.

The authors discuss the importance of differentiation in order to meet the needs of all the learners. They quote Tomilson and write that differentiated instruction is the use of a variety of instructional approaches to modify content, process, and/or products in response to the learning readiness and interest of academically diverse students (1995, p.80).

They conclude the chapter with some evidence-based provocations.

  1. Grade-level retention has an effect size of -0.13, yet a Response to Intervention (RTI) where students receive supplemental and intensive interventions throughout the year delivered by knowledgeable adults has an effect size of 1.07.
  2. Ability grouping – within-class and between-class ability group that is rigid, long-term and can make assumptions about student learning needs should be avoided (effect size of ability grouping is 0.12). Needs-based instruction with flexible grouping however can be very effective as it is student-centred, based on students’ understandings and engages students in small group learning (effect size of small group learning is 0.49).
  3. Test prep, including teaching test-taking skills, has insufficient evidence to justify continued use and has an effect size of 0.27. It wastes a lot of time and the gains are short-term. What does need to be taught is the content and how to learn the content (effect size for study skills is 0.63) and how to best prioritise time doing a task within the context of regular lessons. The best test prep is ongoing, high-quality instruction (p230).
  4. Homework generally has little impact on students’ learning and has an effect size of 0.29. This does alter as students move through their schooling years – early years – 0.10, middle school level – 0.30 and high school level – 0.55. This can be related to the type of homework given as students get older. Homework that provides another chance to rehearse something already taught and that the student has already begun to master can be effective. Homework that involves new materials, projects or work students cannot do independently is the least effective.

My own connections

This year, the Metro region of Qld State Schools has done a lot of work around what makes a standards based curriculum (such as the Australian Curriculum) work well. One of those aspects is teacher expertise that embeds assessment into pedagogical practice. When I begin planning a unit of work or the teaching of a concept, I backward map from the summative assessment task. It is important to have the end goal in mind. The best way I can really understand the demands of the task is to actually do the assessment myself and to unpack the marking guide, so I can provide opportunities for students to have unlimited growth and personal learning.

I then consider what I already know about the students in relation to the demands of the assessment and the important concepts of the unit and design a quick pre-assessment for things I don’t know. Finding out what students know and don’t know allows precision of teaching.

As the unit progresses, I then have quick formative assessments in mind, those I will do daily and those that I use as more formal check ins with my fellow year level teachers. These allow me to give students ‘just-in-time, just-for-me’ information when and where it can do the most good.


Check out ticket – mental strategies for multiplication and division

One quick formative assessment that I use consistently is the exit ticket.  Not only am I able to give ‘just-in-time’ feedback to individual students, but I am able to see trends and patterns and adjust my teaching and groupings to cater for these. This particular image of one I used in a year 4/5 class gave me so much information. I could see what mental strategies students were applying, what stage of multiplicative thinking they were at, whether they could justify their thinking and a self-reflection on where they felt they were in their application of mental strategies.

This embedding of assessment (and feedback) within pedagogical practice means no surprises when the summative assessment is given. The students and I know how they are going and what their next steps for learning is. I am also able to adjust my teaching in response to real-time data and make good decisions about instruction.  The brilliant thing is that the data gathered in the summative assessment can then be used to inform the next unit.

Embedding assessment in pedagogical practice

Where are you when it comes to assessment, feedback and meeting the needs of your learners particularly in the learning area of mathematics? This final chapter explores these ideas in detail. Hattie, Fisher and Frey have produced a fabulous book that is easy to read, easy to apply, makes learning visible and puts the student at the centre of teaching and learning. Well worth a read.

NB The main reason I blog is to give teachers (who are time poor) access to current research texts. The blog is constructed from my notes which are only snippets of the chapters and are my impressions. I recommend purchasing and reading the book for the in-depth information and resource support.
Hattie, J., Fisher, D., & Frey, N. (2017). Visible learning for mathematics What works best to optimize student learning Grades K-12. Thousand Oaks, CA: Corwin.

Teacher clarity

Visible learning for Mathematics

Think about when you set yourself a goal.  It might be a health goal, a work goal, a personal goal… How did you go about achieving it?

My goal this Easter holidays was to revisit my blog and publish at least one post about a current research text.  To achieve this goal, I had to begin by clarifying exactly what I wanted to achieve by defining the end point.

I then had to evaluate my starting point in relation to that end point. I recognised that I hadn’t made a post since Easter last year and that I needed to select a text and to re-familarise myself with my blog.

I then had to consider all the things I needed to do to be successful to reach that end point. Creating an interesting and appealing post; taking notes from the text; considering how to frame the post; writing a personalised summary; considering what images would enhance the post; imposing a time frame; considering copyright. For each of these I had to seek the resources to help achieve my end point.

Prior to publishing and as I constructed my draft post, I had to check in on what was needed to be successful and to seek or give myself feedback.

What I was doing is something that ultimately we want students to be able to do. Student goal setting or having students determine their own criteria has been shown to boost achievement (Hattie, Fisher and Frey, 2017). As teachers, having a clear path does not leave learning to chance.

Learning intentions, success criteria, preassessments and checking for understanding all contribute to teacher clarity.

Teacher clarity, which according to Hattie has an effect size of 0.75, is the focus of the second chapter in Hattie, Fisher and Frey’s text, Visible learning for mathematics.  It begins with careful consideration when planning a unit or lesson and the composing of learning intentions that make the unit or lesson very clear to both the teacher and students. This is extended to consistent evaluation of where students are in the learning process and describing success criteria so that students can assess their own progress and teachers can monitor how students are progressing with a mathematical idea or concept.

Learning intentions describe what teachers want students to learn – when students know the target, it is more likely that the target will be achieved. The following are some of my take-aways about learning intentions. They:

  • are critical for students of mathematics.
  • should be shared with students.
  • should be referred to throughout the lesson.
  • do not always have to be shared at the outset of a lesson as they can be withheld until a learning experience has occurred.
  • can be used to compare with what they have learned from the lesson.

Hattie, Fisher and Frey also mention the importance of establishing language and social learning intentions. Language learning intentions focus on the vocabulary and academic language needed to master the content. We all know the language demands of mathematics are immense, particularly for English as an Additional Language or Dialect (EALD) students. In addition, a focus on language goals will enhance student reasoning, something that many students fall down on in the marking guide. High quality maths lessons also require collaboration and establishing social learning intentions will foster collaboration and communication.

Success criteria describe what success looks like when the learning goal is achieved. They are specific, concrete and measurable statements. Lyn Sharratt promotes co-construction of success criteria and Hattie, Fisher and Frey’s research supports this. Student goal setting or having students determine their own criteria boosts achievement and has an effect size of 0.56. Allowing students to draft success criteria in relation to the marking guide promotes maximum acceptance and effectiveness. An important note: the more complex the summative assessment, the more time that is needed to understand and deconstruct success criteria.

Hattie, Fisher and Frey describe learning intentions as the bookend for learning and success criteria as the bookend used for measuring success. Strategic use of learning intentions and success criteria promote student self-reflection and metacognition  which has an effect size of 0.69. One of the most important things a student can learn is internal motivation and Hattie, Fisher and Frey state that learning intentions and success criteria increase student motivation.

Preassessment helps determine the gap between a student’s current level of understanding and the expected level of achievement. It allows  teacher to be precise in determining learning intentions and establishing success criteria. Teachers are also able to effectively differentiate and meet the instructional needs of their students.

Formative assessment allows that checking for understanding. What do my students need to learn today and how will I know that they have learned it? What feedback can be given to students to help their learning progress. A great example is the use of exit tickets which allow teachers to gauge progress. 

As far as my goal of revisiting my blog and publishing at least one post about a current research text over the Easter break goes, I achieved it (in fact, exceeded it as I am up to blog #3). It was through making my goal very clear (learning intention), establishing what was necessary to be successful (success criteria), evaluating my starting point (preassessment) and evaluating how I was going with what I had deemed to be successful (checking for understanding).

Tune in to my next blog, which will have a brief look  at chapter three of this text: Mathematical tasks and talk that guide learning.

Hattie, J., Fisher, D., & Frey, N. (2017). Visible learning for mathematics What works best to optimize student learning Grades K-12. Thousand Oaks, CA: Corwin.