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.

Surface learning – setting the foundation

The instructional goals of any lesson need to be a combination or balance of the three phases of learning – surface, deep and transfer. An expert teacher knows when and how to help students move from surface to deep and transfer learning. Despite whatever phase of learning the two key reminders are:

  • Learning intentions and success criteria need to be clearly signalled.
  • The instructional strategy with the highest importance is student learning.

Surface learning is the focus of Chapter 4 of Hattie, Fisher and Frey’s text Visible learning for mathematics. When students are at the the surface phase of learning, high-impact approaches that foster initial conceptual understanding are followed by linked procedural skills. The tasks are efficient, often more engaging and designed to raise student motivation. When considering the fluency quadrant, many tasks will be of low difficulty and low to moderate complexity. There should be discussion and opportunities to connect the tasks to students’ learning and understanding.

…observing someone doing something uses many of the same neural pathways as when you perform the action yourself.  (Hattie, Fisher and Frey, 2017, p107).

One of my favourite references. Number talks helping children build mental math and computation strategies by Sherry Parrish

Making number talks matter by Cathy Humphreys and Ruth Parker

This is why number talks, guiding questions, worked examples and direct instruction are so powerful. I am not going to go in-depth into these as the text does it beautifully. What I will say it that I was first introduced to number talks a couple of years ago when I was doing some work around the development of mental calculation. I became an immediate advocate and have bought a number of texts that illustrate how number talks are conducted.

I will also mention that direct instruction is especially useful in developing students’ surface-level learning but it has the following caveats. It should not:

  • be used as the sole means of teaching mathematics.
  • consume a significant part of the instructional time available for learning.
  • always have to be used at the beginning of a lesson.

All four activities enable teachers to demonstrate the kinds of questioning and listening strategies that exemplify excellent mathematical practice as well as give their students opportunities to begin building these habits of mind (Hattie, Fisher and Frey, 2017, p119). Self-verbalisation and self-questioning, skills that help students think critically, have an effect size of 0.64. The text also provides some simple sentence frames that can be used to facilitate student metacognitive thinking (which has an effect size of 0.69).

In the last part of the chapter, the authors consider how to use vocabulary, manipulatives, spaced practice with feedback, and mnemonics strategically.

Vocabulary instruction is important in all the phases of learning but it is often in the surface phase that students begin to build academic language. Researchers such as Beck that as teachers, we need to support students in the appropriate terminology but not give away the mathematical challenge. A focus on vocabulary has always been a focus in the work my colleagues and I have done in mathematics and numeracy. There are many vocabulary games that can be used in warm-up or transition times and we have always promoted the use of word walls and graphic organisers, the latter two being addressed in this chapter.

The CSA model used for problem solving strategies

Using manipulatives in all the learning phases helps build the links between the object, the symbol and the mathematical idea. It has an effect size of 0.5. Once again, my colleagues and I have promoted the use of manipulates and have commonly referred to the Concrete Semi-abstract Abstract (CSA) model.

Using the dual approach of spaced practice and feedback teaches students about the task and about their thinking. Spaced practice, giving multiple exposures to an idea over several days to attain learning and then spacing the practice of skills over a long period of time, has an effect size of 0.71. Feedback about the process (and not just the task) moves students into deeper learning and has the added advantage of giving a student agency so that they rely lesson on outside judgments and have a more positive mindset.

The use of mnemonics has an effect size of 0.45 and assist students to recall a substantial amount of information.

The authors give readers an insight into research based tasks that have a high effect size in the surface phase of learning. This strong start sets the stage for meaningful learning. Too often, however, the learning ends at the surface level. Teaching for deep and transfer learning must occur. My next blog will look at making learning visible in the deep learning phase.

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.