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.