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.

Putting students in the driver’s seat of their learning

The true purpose of getting an education is to apprentice students into becoming their own teachers. We want them to be self-directed, lifelong learners , and to have curiosity about the world. We want them to have the tools they need to formulate their own questions, pursue meaningful answers, and through metacognition, be aware of their own learning in the process.                   (Hattie, Fisher and Frey, 2017, p176)

Hattie, Fisher and Frey mention three phases of learning – surface, deep and transfer. My previous two blogs explored the first two phases of learning: surface and deep. The final phase is that of transfer. In mathematics, this phase occurs when students are able to make connections among mathematical understandings and then use those understandings to solve problems in unfamiliar situations, while being very aware of what they are doing. Because learning is cyclical, transfer occurs all the time.

The authors use the example of Linda who understood the mechanics of mathematics (surface learning mixed with a little bit of deep learning) but had no idea how to apply that knowledge to real world contexts.

Why do I need this?

Linda reminds me very much of myself when I attended secondary school and continually battled with the subject of maths. I loved it, particularly the challenge of the discipline but was extremely frustrated in that I did not know how to apply what I had learned to different situations or real world contexts. I also constantly questioned why I had to learn certain things, such as sine, cos and tan. I was never shown how trigonometry is used in contexts outside of school.  Relevancy is a major condition of transfer which is basically answering the questions, “Why do I need to learn this and when will I ever use it?”

Learning becomes more meaningful when learners see what they’re learning as being more meaningful in their own lives.

Hattie, Fisher and Frey state that it is also extremely important that teacher knows the learner developmentally and experientially in order to promote transfer of learning.  The authors recommend two stages of transfer: near and far. Near transfer occurs when a new situation is paired to a context that a student has already experienced. A great way for students to develop transfer learning is to consider similarities and differences between the new and a recently completed idea.

Venn diagram

Using graphic organisers such as the Venn diagram can help students consider the similarities and differences.Hattie writes that comparing and contrasting new with old problems has an effect size of 1.23.

The leap is bigger for far transfer as the student has to make connections to more removed situations.

Hattie, Fisher and Frey mention a few things to consider when planning tasks for transfer. Tasks:

  • should be selected to encourage connections
  • should be of higher complexity with higher difficulty
  • may not have clear entry points
  • may have multiple steps
  • may not have one correct solution – students have to make judgments about the best solution and justify their thinking with evidence
  • incorporate maths ideas that can be applied in other learning areas
  • may take more than one lesson to solve
  • should have relevancy
  • should be developmentally appropriate.

Metacognition, the ability to think about our thinking, promotes transfer learning. Palinscar (2013) described metacognitive awareness as having three parts:

  • knowledge about our learning selves
  • an understanding of the task demands and necessary strategies to complete it
  • the means to monitor learning and self-regulate

To develop metacognitive skills, students need to learn the art of self-questioning. Self-verbalisation and self-questioning have an effect size of 0.64. Self-questioning enables students to track their understanding and re-align when off target. Hattie recommends using pre-lesson questions (What are today’s goals?) and post-lesson questions (What was today’s goals?) to encourage metacognition.

Self-reflection is a follow-up technique after the lesson that encourages students to understand where they were and where they are now.


Rich class discussion promotes transfer learning. In mathematical discussions, students should be able to represent their thinking to others, pose questions, and engage in disagreements respectfully. The caveat is that it is not unrelated storytelling, random opinion sharing or teachers doing most of the talking. The teacher’s role is to use questioning to lift student thinking, press for evidence and have students make links amongst concepts.

For students to take the driver’s seat of their own learning, they need a sense of how the mathematics that they know is organised. Creating an organisational structure for mathematical knowledge is a powerful tool.

Peer tutoring requires the tutor to connect what the tutee needs to learn to what the tutee already knows and understands. Peer tutoring has an effect size of 0.55 and works best when programs are structured, the tutor receive training and the tutor and tutee are of different ages. It allows the tutor to solidify his/her understanding and the tutee to improve their learning.

Giving students opportunities to explore their own ways of using what they have learned is critical for transfer learning and should be woven into classroom life. Students should be continually challenged to develop projects and investigations across the school day.

This makes me think of a recent initiative being used in Queensland: Age Appropriate Pedagogies which encourages the use of a range and balance of pedagogical approaches in the classroom.

Age appropriate pedagogies conceptual framework

The conceptual framework includes six approaches to teaching and learning: event-based, project, explicit instruction, inquiry learning, play-based learning, direct teaching/instruction and a blended approach (Department of education and training, Qld Government). Only ever using one approach such as direct instruction will limit a student’s ability to transfer learning.

Problem-solving teaching also encourages the transfer of mathematics learning and is different to a problem-solving process.

Problem-solving teaching in mathematics

It is similar to the design thinking necessary for the new Australian Curriculum learning area of Technologies.

Design thinking in AC Technologies – thanks to Grant Smith (one of my regional colleagues)

Problem-solving teaching helps students engage in the process of determining the cause of a problem; using multiple perspectives to uncover issues; identifying, prioritising, and selecting alternatives for a solution; designing an intervention plan; and evaluating the outcomes. (Hattie, Fisher and Frey, 2017, p193)

Design challenges for any age group can be identified by listening to students’ wonderings about the world around them. An example may be designing a school garden to grow vegetables for cooking.

How to design a school garden?

Reciprocal teaching also assists students to transform their mathematical thinking and is a literacy strategy that develops comprehension of the mathematical problem. Students work collaboratively to build their understanding of texts. There are four stages and students are encouraged to keep a record of their thinking and work. :

  1. predicting – students use knowledge of mathematics and the information provided to predict what is happening and to decide what mathematics may be needed to solve the problem.
  2. clarifying – students make lists of information that they might need to solve the problem – unfamiliar vocabulary, known facts and necessary information to solve the problem.
  3. solving – students use their problem-solving strategies to find one or more solutions to the problem and are encouraged to use multiple representations.
  4. summarising – this is a time for individual self-reflection  that includes justifying the solution, reflecting on the effectiveness of the selected strategies and evaluating their participation.

Students need the opportunity to apply what they have learned in mathematics to unfamiliar situations but it would be nearly impossible to transfer without surface and deep learning. Transfer learning should not be left to chance and requires caring teachers to deliberately design opportunities by knowing their students and using effective strategies.

Stay tuned. My blogs have slowed down as I am back at work but I have one more blog for this text. It will look at the last chapter – Assessment, feedback and meeting the needs of all learners and will be posted within the next couple of weeks.

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.

Going beyond surface learning in mathematics

Too often, learning ends at the surface level. (Hattie, Fisher and Frey, 2017, p131) How do we go beyond surface learning and into deeper learning?

As mentioned in my previous blog, surface learning is the beginning of conceptual understanding. The challenge for teachers is not to over rely on it and to know when and how to move students from surface to deep learning. Deep learning (the focus of Hattie, Fisher and Frey’s fifth chapter in their text Visible learning form mathematics) provides students with opportunities to consolidate mathematical understandings and to make deeper connections among ideas.
One of the reasons I write this blog is to take my own reading to a deeper level and to make connections with other research and focuses in my work.

With appropriate instruction, surface learning transforms into deep learning. (Hattie, Fisher and Frey, 2017, p35)

In deep learning, mathematical tasks will be cognitively more demanding, more open-ended and have multiple ways of solving them or multiple solutions. As teachers, we have to make judgments about how much surface learning is required in preparation for this deep learning.

Who is doing the talking?

To promote deep learning, students need opportunities for mathematical talk. Accountable talk is promoted by Lyn Sharratt in her work in the Metropolitan region. Hattie, Fisher and Frey state that students should be drenched in accountable talk and this chapter provides a number of language frames that scaffold the use of language to support a mathematic topic.  A number of other supports for accountable talk are also mentioned.


Who is doing the thinking?

When it comes to mathematical thinking in whole class or group discussion, the authors mention three sociomathematical norms, norms that promote true mathematical discourse. Reading the text gives an insight into how a skilled mathematics teacher can promote the following:

  1. Explanations that are mathematical arguments and include justifications.
  2. Errors as opportunities to reconsider problems from a different point of view.
  3. Intellectual autonomy that recognises participation.

Are students being encouraged to collaborate?

Collaboration is another important dimension of deep learning. Humans learn better when they interact with other humans and the authors recommend that 50% of class time over a week be devoted to student discourse and interaction with their peers. Effective collaboration and cooperative learning tasks must:

  • be complex enough that students need to work together.
  • allow for argumentation.
  • include sufficient language support.
  • provide individual and group accountability.

How are students being grouped?

Students should be grouped strategically. The authors point out that fixed ability grouping does not help students to understand the math they are learning. It can affect motivation and make students dislike maths. The most effective grouping strategy is one that is flexible and balanced and allows for a moderate range of skills.

Are you using manipulatives and encouraging multiple representations?

Just as in the surface learning chapter, this one wraps up with a look at the importance of multiple representations and the strategic use of manipulatives to promote deep learning. Students demonstrate stronger problem-solving abilities and deeper mathematical understanding when are encouraged to represent mathematics in a variety of ways. Representations can be physical, visual, symbolic, verbal and contextual.

In the Metropolitan region of Queensland, my colleagues and I have always promoted the think board (an idea we found in First Steps in Mathematics), It can be used in a variety of ways as a graphic organiser for different representations and a way of showing the connections.

The thinkboard can be used as pre-assessment, formative assessment or collaborative learning

An example of an annotated think board

Using the CSA model to develop use of the Multiplication and Division Triangle (a strategy for problem solving)







Manipulatives shouldn’t be limited to surface learning and can be used to make concepts concrete and visible. They assist students to see patterns, make connections and form generalisations. Again the Concrete Semi abstract Abstract (CSA) model (also promoted by my Metropolitan colleagues) is a useful frame to assist teachers with choices around  the instructional sequence from physical to visual to symbolic representations.

All of the above have high effect sizes and assist in making deep learning visible. My next blog will look at transfer learning, the application of surface and deep learning.


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.

Mathematical tasks and talks

What were your mathematics lessons like as a student? What would students say about your current mathematics lessons?

In primary school, I can remember the blackboard (yes, I am that old) being covered in numerous columns of mathematical operations, all very similar but with increasing difficulty. I don’t remember receiving too many problems to solve and I certainly wasn’t allowed to discuss my solutions or ways of working. In fact, there really was only one way to do it – the traditional algorithm as modelled by the teacher – on my own and in silence.

In the beginning of my teaching career, I emulated some of what I experienced in my own education – lots of operations for students to solve. I made it harder by setting them out horizontally or increasing the size of the numbers. Problem solving was on a Friday. If students finished quickly, I gave them more.  Thankfully, my understanding of higher order thinking, collaboration, discussion, and the importance of problem solving and reasoning increased as my experience as a classroom teacher increased.

Imagine my concern last year, when during another heated discussion over homework, my son in year 10 argued, ‘Why do I have to do twenty of these, Mum, when I have already got the first three right? They are all the same?” I had no answer as he was absolutely right. Completing extensive, repeated, context-free exercises is not going to develop the transferable and flexible understanding of mathematical processes (Hattie, Fisher and Frey, 2017).

Procedural fluency cannot be developed without true and meaningful comprehension and ‘drill-and-kill’ exercises without understanding can harm students’ mathematical understandings, their motivation level, and the way they view mathematics. (Hattie, Fisher and Frey, 2017, p75)

Mathematical tasks and talk that guide learning is the title for Chapter 3 in the text, Visible learning for mathematics.

When it comes to planning and implementing maths lessons, Hattie, Fisher and Frey (2017) mention three important ideas to take into consideration.

1.  Spaced practice is more effective than mass practice with an effect size of 0.71.

2.  Math is not a speed race and speed is not a part of fluency. Speed can damage students’ self-perception of their maths ability.

3. Tasks should not focus solely on procedures as conceptual understanding can be sacrificed.

Good mathematical instruction involves reasoning, exploration, flexible thinking and making connections. Students should know that learning isn’t easy and that there is an enjoyment in meeting the challenges of learning demands.

There are typically two types of tasks – exercises and problems. Exercises make up most of traditional text book practice, are without context and are provided to allow students to practise a particular skill.  Problems are generally written in words and apply or provide a context for a mathematical concept. There are those that focus on using a particular concept and those that are non-routine or open ended.

Problems should be used to introduce an idea so that students can model a situation and begin to develop conceptual understanding. Non-routine or open ended problems involve more that applying a mathematical procedure for solutions. Students  need a toolkit of strategies and some ‘out-of-the-box’ thinking to solve these.

Hattie, Fisher and Frey, 2017, p77

Hattie, Fisher and Frey advise teachers to consider the level and type of challenge a given task provides and have developed a fluency quadrant to assist with this consideration:

Low Difficulty Low Complexity

  • When students need to build automaticity
  • After mastering conceptual understanding and learned thinking strategies and procedures
  • If limited to this quadrant – learning isn’t going to be robust

High Difficulty Low Complexity

  • Builds perseverance
  • Problems or exercises that extend current knowledge to a more difficult situation
  • Students work independently before consulting with a peer, then returning to problem individually a second time

Low Difficulty High Complexity

  • Extends understanding to more complex situations
  • Supported by students working collaboratively and justifying their thinking

High Difficulty High Complexity

  • Pushes students to stretch and extend their learning


Hattie, Fisher and Frey (2017) mention a number of characteristics that assist students to build understanding and confidence in mathematics. These include:

  1. Teachers using questioning and prompts to build understanding.
  2. Mistakes being valued and seen as opportunities.
  3. Students considering different approaches and noting their similarities and differences.
  4. Lessons having an element of productive struggle which is accompanied by perseverance.
  5. Rich discourse.

The chapter finishes with a focus on posing purposeful questions and the use of prompts and cues. Purposeful questions help teachers check for understanding and the use of prompts and cues encourages students to do the cognitive work, moving them on in their learning.

Identifying the right approach at the right time is critical.  Misalignment between tasks and types of learning (surface, deep and transfer) puts students at risk.

Giving students appropriate tasks at the right time in their learning cycle is crucial to move students from surface to deep and transfer learning (Hattie, Fisher and Frey, 2017, p73).

My next blog will explore what tasks the authors have found to work at each stage of the 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.

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.

Making learning visible in mathematics

Graduation – Masters of Education 2005


How does one become a lifelong learner? How do we develop a love of learning? Hattie, Fisher and Frey (2017) argue that making learning visible assists teachers and students to become lifelong learners with a love of learning. I am proud to say that I am a lifelong learner (as signified in the name of my blog).

After reading the first chapter of  Visible Learning for Mathematics, I spent some time considering how my passion for learning came about. I came to the conclusion that I was lucky enough to enter a profession that I love: one that involves constant re-invigoration and one with which I have a natural affinity. I was also lucky to have two brilliant mentors in my education: my English teacher in year 11 and 12 (Mrs Kay Gardiner) and my Children’s Literature lecturer when I completed my Bachelor of Education (Professor Kerry Mallan).

The above-mentioned ladies were instrumental in my love for English and literature and yet I ended up spending four years of my career specialising in numeracy and mathematics.  As mentioned in my previous blog, I have always loved the challenge of mathematics but was never very successful in my P-12 grades. My experiences were very much ‘chalk and talk’ and the learning of procedures and formulas. I then struggled when it came to applying those procedures and formulas in a test.

Hattie, Fisher and Frey stress the importance of teachers erasing many of the ways they were taught mathematics and replacing this with intentional instruction, collaborative learning opportunities, rich discussions about mathematical concepts, excitement and persistence when solving complex problems, and applying ideas to situations and problems that matter. I can certainly concur with that – my understandings, application (and marks) would have improved considerably in a classroom such as this.

The first chapter of  Hattie, Fisher and Frey’s book looks at making learning visible for both students and teachers; the debate between direct instruction and dialogic approaches; and the balance of surface, deep and transfer learning.

Hattie, Fisher and Frey write that visible learning:

  • helps teachers identify the attributes and influences that work.
  • helps teachers better understand their impact on the learning of their students.
  • helps students become their own teachers.

When it comes to the two approaches of direct instruction and dialogic, both focus on students’ conceptual understanding and procedural fluency and neither advocates memorising formulas and procedures. Both models suggest:

  • designing mathematical instruction around rigorous mathematical tasks.
  • monitoring student reasoning.
  • providing many opportunities for skill- and application-based experiences.

Differences include types of tasks, role of classroom discussion, collaborative learning and role of feedback. Hattie, Fisher and Frey (2017) have put together an explicit table that explores the similarities and differences of both approaches and how ‘knowing what strategies to implement when for maximum impact‘ is precision teaching (p26).The authors state that it is not a choice of one approach over the other. Both have a role to play throughout the learning process but in different ways.

Finally, Hattie, Fisher and Frey address the balance of surface, deep and transfer learning. Surface learning provides the toolbox of conceptual understandings, procedural skills and vocabulary and labels of a new topic. It helps students develop metacognitive skills and can be used to address student misconceptions and errors.  Students need this toolbox but there is often an over reliance on surface learning and the goal is much more.

Deep learning is where students begin to consolidate understanding of mathematical concepts and procedures and begin to make connections among ideas. This is often accomplished when students work collaboratively, use academic language and interact in deeper ways with ideas and information.

Transfer learning is the ultimate goal. Students have the ability to take the lead in their own learning and apply thinking to new contexts and situations. They are self-directed with the disposition to formulate their own questions and the tools to pursue the answers.

As a classroom teacher, I was eclectic. I believe I used different pedagogical practices and had a balance of direct and dialogic approaches but it was more instinctive rather than intentional and precise. I believe I spent too long in the surface learning. Deep and transfer learning would have happened to some degree but I don’t believe it was always intentional.

As teachers, we have choices. Understanding these phases of learning assists us to make instructional choices that will impact student learning in a positive way.  Hattie, Fisher and Frey’s text helps with precision teaching and my next blog will look at the second chapter that focuses on teacher clarity. Until then…

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.

Oral rehearsal

I am about to put together a presentation on oral language so my next few blogs will explore the research that supports this area. There are many aspects to oral language and I have already explored  Konza’s work on oral language as part of the Big 6.

This blog will consider the importance of oral rehearsal, something that Lyn Sharratt (author of Putting faces on the data) paid a lot of attention to in her recent work with Metropolitan schools in Brisbane, Queensland.

It is interesting when you google ‘oral rehearsal’ – there isn’t much about it. Yet, oral rehearsal in writing is a necessary prerequisite for thoughtful writing pieces (Sharratt & Fullan, 2012).

Not only is it necessary for writing, but any speaker should be given opportunity to rehearse before sharing their thoughts in a public forum. This includes teachers in staff meetings and professional development and of course, students before they have to share orally in the classroom.

This makes sense – how many of us ‘rehearse’ what we are going to say prior to a formalised presentation. One of the reasons I sometimes avoid contributing in a public forum, is because I haven’t had the opportunity to rehearse what I would like to say. If I feel like this, how do some of my students feel?scared

Calkins (2001) stated that, ‘In schools, talk is sometimes valued and sometimes avoided….and this is surprising – talk is rarely taught…Yet talk, like reading and writing, is a major motor – I could even say the major motor – of intellectual development’ (p.226).

A search in the United Kingdom of the term, Oral Rehearsal, undertaken by the Department for Children, Schools and Families found ten references:

  • Using writing partners and oral rehearsal, 
  • After oral rehearsal, write explanatory texts independently from a flowchart or other diagrammatic plan, using the conventions modelled in shared writing. 
  • Rehearse sentences orally before writing and cumulatively reread while writing
  • The trainer repeatedly models rehearsal of sentences in speech before committing them to paper…
  • The importance of oral rehearsal and cumulative re-reading
  • Oral rehearsal before writing 
  • Rehearse sentences orally before writing and cumulatively reread while writing 
  • A range of drama and speaking and listening activities that support appropriate oral rehearsal prior to the written outcomes. 
  • Oral rehearsal prior to writing…. In pairs, children rehearse phrases and sentences, using some of the ideas suggested. 
  • Scribe the sentence, modelling its oral rehearsal before you write it. 
  • Oral rehearsal: in particular, those children who have poor literacy skills; for children with poor language skills.

All of these refer to rehearsing orally prior to writing. I would go further and promote oral rehearsal before speaking informally and formally.

A study by Myhill and Jones noted that a teacher employing oral rehearsal practice in her classroom observed improvement in the use of imaginative written text and in low-attaining writers. She attributed improvement in her student’s writing to the fact that oral rehearsal allowed the children ‘to think about before writing it down’ and that oral rehearsal made it ‘easier to change it [writing] in talk than when it had been written down.

oral rehearsalGive students the opportunity to talk things out prior to speaking publicly or to written responses!


Teaching reading to the older student

Teaching reading doesn’t have an end date. As students enter into later primary and secondary education, it is important that all teachers in any subject area are assisting them to navigate and understand these increasingly more complex and sophisticate texts. This is even more important for readers who are struggling. Sometimes as teachers of upper primary and secondary students, it is hard to find something that supports the teaching of reading.

Tactical Teaching Reading

At the end of 2014, I was introduced to Tactical Teaching Reading. The sole licensed distributor is Tactical  Steps Education who have taken over STEPS professional development. Their motto for Tactical Teaching Reading says it all – Not a reading teacher but a teacher of reading. Reading is in every learning area and the strategies taught in this course are applicable to any learning area. Tactical Steps Education offers both teacher and facilitator courses.


The course involves three workshops:

Workshop 1 – How to help students use reading processes. This workshop looks at research on adolescent literacy and a number of processes that can be used before, during and after reading. Processes that are incorporated include activating background knowledge, clarifying vocabulary, monitoring understanding and processing what has been read.

Workshop 2 – How to make reading strategies visible. Good readers use a number of strategies when reading. These include adjusting reading rate, predicting, connecting and self-questioning. Struggling readers need these strategies to be explicitly taught. This workshop looks at the explicit teaching of reading strategies to help students understand texts. It considers 18 universal strategies used by good readers. Again the strategies are aligned to before, during and after reading.

Workshop 3 – How to build text form knowledge. Text complexity and sophistication increases as students progress in their schooling. All students need to be taught how to navigate these more sophisticate texts in their various contexts. This workshop helps teachers to build students’ ability to pinpoint purpose, organisation, language features and text structures of subject area texts.

Participants in this course are provided with three course books and each contains 14 practical activities that can be used repeatedly in lesson with texts already in use. I found that some of these strategies were ones that I was familiar with or had used once upon a time and forgotten.  What I really like is a quick reference to some before, during and after reading activities that can be applied to any learning area.

At the end of 2014, I spent time relating some of these strategies to reading in secondary mathematics.  Since then, not only have I used these strategies in the classroom, but I have also used them for adult learning.

Pinpointing purposes


Pearson Mathematics textbook year 8

I applied the strategy Pinpointing purposes to this mathematical text. This strategy required students to preview the text and set a purpose.  Students self-questioned to clarify the purpose of reading and to consider how they would achieve that purpose. Pinpointing purpose

This was a great strategy in that it helped students comprehend the text, enabled them to skim and scan and to determine the importance of what they were reading. I was then able to have students apply the reading to a context.

Clarifying questions:

How does the title prepare us to read the text?

What are the important terms in this text?

How do they relate to percentages?

Students worked in pairs and did a think pair share where they shared their purpose for reading. They then decided on a joint purpose. Student then reflected on the steps they undertook to achieve the purpose.

By applying this information to something contextual, it made the reading so much more meaningful. In this case, students related the content of applying percentages to financial transactions to selling soft drink at the market stall.

Benchmarking percentages

Application of the information to a ‘real-life’ context.

Fostering independent reading

The last two stages of the Gradual release of responsibility are You do it together and You do it alone. Coincidentally, these stages align nicely with the last two reading procedures recommended by the authors of First Steps in Reading Resource Book : Book discussion groups and Independent reading. With each stage, more responsibility for learning and reading is being given to the student.

content area conversationsFostering student talk is vital for learning, particularly when they employ the use of academic language. From their book, Content-Area Conversations, Fisher, Frey and Rothenberg state that students need more time to talk and that the key to learning is for students to talk with one another in purposeful ways, using academic language (2008).

Book discussion groups (You do it together) promote student talk. Small groups of students meet to discuss, respond to and reflect on a common text that they have chosen. Key features include students selecting their texts from a range of available texts and each student having their own copy. A pre-determined amount of time is allocated for each text and groups meet on a regular basis. Different groups can be reading different texts and several groups can be meeting simultaneously.

It is the students’ responsibility to be prepared for each meeting and to contribute to the discussion of the text.  Keeping a journal or response journal is great way for students to respond and reflect personally on the text. Another idea is to use an online forum such as an edStudio to respond to the text. There are many online discussion groups set up by authors and public libraries but it would be important to ensure these are legitimate sites.

An example of a book discussion group is a Literature circle, which I have found to be very effective and also appealing to students. I gradually introduced and modelled the roles by using one text with the whole class, before encouraging the students to run their own literature circles. My role as a teacher was then visiting each group and just listening, providing support when needed.  It is important to offer a variety of texts for students to choose from. I have offered photocopied articles or the introduction to a chapter book. It is really exciting to hear students discussing a text in a deep and meaningful way. There is a lot of information on the internet, but here is a link to Sheena Cameron’s resources on literature circles – a great start if this is something that interests you.

IMG_1138The last procedure is independent reading and of course it fits the last stage of the gradual release process (You do it alone). This is our goal – students independently reading and applying the reading strategies that they have been exposed to during the other procedures. Students choose their own texts but are encouraged to select from a wide variety of literary and informational texts (I have collected hundreds of books and refuse to part with any of them as they form a vital part of my classroom). Texts could include those previously read in the other reading procedures, other texts written by the same author and texts that match the students’ interests.  It is all about reading for enjoyment.

silent reading

When I began teaching, I knew independent reading  as Uninterrupted Silent Sustained Reading (USSR). When I first used USSR in the classroom, I also read silently but as I became more experienced I saw this as a fantastic opportunity to listen to and question students individually about what they were reading.

pgcummings via Compfight cc

Each day during independent reading, I would sit beside students and ask what the text was about, what they were enjoying, how they were applying the focused reading strategy for the week and take a short, informal running record. By the end of the week, I would have sat with each student at least once and collected absolutely invaluable data about his/her reading.

Allington (2002) wrote that dedicated reading and writing should be planned for as much as half of each day with at least 90 minutes of ‘eyes-on and minds-on’ texts. This could certainly be achieved using the variety of reading procedures recommended by the authors of First steps in reading across all the curriculum learning areas.

I will leave this blog with a couple of things to ponder. In your classroom:

  • Is your reading approach over the course of a week balanced?
  • As the week (or unit) progresses, do you use a gradual release of responsibility?
  • How much time each day is dedicated to planned reading (and writing)?
  • Are you using texts from all the different curriculum learning areas as a part of that balanced reading approach?
  • What is the ratio of teacher talk to student talk?


Reading together

The goal for any teacher is to gradually give responsibility more and more to students and this needs to be a scaffolded approach.  The next stage in the Gradual release of responsibility is where teachers and students work together (We do it). Three reading procedures promoted in the First Steps in Reading (FSiR) Resource book can be used to assist in the teaching of reading: Language experience, Shared reading and Guided reading.

Connecting reading and writing is essential and the reading procedure of Language experience is perfect for combining the two. Field knowledge is built when students are involved in a shared experience such as an excursion or cooking. shared_writingThis is an opportunity to take photos and have students orally rehearse what they have been doing.  This experience then forms the  basis for a jointly constructed text.

The text is created by the whole class using their oral language and scribed by the teacher. Once revised and edited, the published text can then be used for future reading sessions and as a springboard for other reading activities, such a sequencing, sentence matching and cloze exercises.

Shared reading is exciting and interactive. All students can see the enlarged text, are able to observe a good reader in action (usually the teacher modelling strong reading behaviours) and have the opportunity to read along. Texts can be re-used several times but need to maintain the students’ interest and attention.

shared readingShared reading image

This whole class sharing can then lead to smaller groups which are differentiated according to extension, consolidation or knowledge. To add interest, I love using choral reading and readers theatre. There are so many texts that are already prepared and ready for these variations.

IMG_1134 The True Story of the 3 Little Pigs

The final reading procedure for the We do It stage is Guided reading. Guided reading enables teachers to support small groups of students who are using similar reading strategies and are reading texts of a similar level. Students should have individual copies of the text which is pitched at their instructional level. The text should provide a challenge but without being so difficult that students become disheartened, allowing practice of reading behaviours that have already been introduced. guided reading

The teacher’s role is to guide or direct students to a section of a text whereby a focus question is set. Students make a prediction and then read the section silently. They are then encouraged to share and discuss their responses, ensuring they can substantiate their viewpoints using the text.  This is also an opportunity to discuss reading strategies they may have employed to find the required information.This process is continued until the text or session is completed.

At the end of the guided reading session, time should be allocated for reflection. The text can then be made available for independent or home reading and practice activities can be developed that relate to the selected focus.

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