The story behind the 1,400 meta-analyses, the over 80,000 studies included in those analyses, and the 300 million students represented in the Visible Learning research is this: learning best occurs when teachers see the learning through the eyes of their students and students see themselves as their own teachers. In mathematics, when learners see themselves as their own teachers, becoming Assessment-Capable Visible Mathematics Learners, they embrace certain dispositions, engage in specific learning processes, and assimilate feedback in the learning of mathematics content and processes. Teaching mathematics in the Visible Learning classroom aims to build and support assessment-capable visible learners (Frey, Hattie, & Fisher, 2018). This more than triples the rate of learning in one school year (Effect Size = 1.33).
So, what is an assessment-capable visible learner in mathematics?
The following characteristics are common in assessment-capable visible mathematics learners:
1. They are active in their mathematics learning.
Learners deliberately and intentionally engage in learning mathematics content and processes by asking themselves questions, monitoring their own learning, and taking the reins of their learning. They know their current level of learning: “I am comfortable finding the simultaneous solution for a system of equations using graphing, but need more learning on the elimination and substitution approach. I know there are examples in my interactive notebook that I can use to prepare for tomorrow’s challenge problem.”
2. They are able to plan the next steps in their progression toward mastery in learning mathematics content.
Because of the active role taken by an assessment-capable visible mathematics learner, these students can plan their next steps and select the right tools (e.g., manipulatives, problem-solving approaches, and/or metacognitive strategies) to support working toward given learning intentions and success criteria in mathematics. For example, a student might respond to feedback, saying, “There is a more efficient way to solve this quadratic equation. I am going to use completing the square this time to see if I can find a more precise answer.”
They know what additional tools they need to successfully move forward in a task or topic: “To find the solution to the system of equations, I am going to use substitution. Looking at the graph of this system of equations, the solutions does not appear to be a pair of integers. Substitution will allow me to find a more accurate and precise solution.”
3. They are aware of the purpose of the assessment and feedback provided by peers and the teacher.
Whether the assessment is informal, formal, formative, or summative, assessment-capable visible mathematics learners have a firm understanding of the information behind each assessment and the feedback exchanged in the classroom. “Yesterday’s exit ticket surprised me. Ms. Norris wrote on my paper that I needed to revisit the process for isolating x and then substituting the expression into the second equation. So, today, I am going to work out the entire process in my notebook and not try to skip steps or do parts of the process in my head.” Put differently, these learners not only seek feedback, but they recognize that errors are opportunities for learning, they monitor their progress, and adjust their learning (adapted from Frey et al., 2018).
With an effect size of 1.33, planning and implementing a mathematics learning environment that allows learners to see themselves as their own teacher is essential in today’s classrooms. In Visible Learning schools and classrooms, teachers work deliberately, intentionally, and purposeful with their learners to monitor their learning progress in mathematics.
How do we build assessment-capable visible learners in mathematics?
Rather than checking influences with high-effect sizes off the list and scratching out influences with low-effect sizes in our mathematics classrooms, we should match the best strategy, action, or approach with the learning needs of our math learners. As we emphasize in the upcoming grade-level series, using the right approach at the right time increases our impact on student learning in the mathematics classroom (Almarode, Fisher, Assof, Hattie, & Frey, in press; Almarode, Fisher, Assof, Moore, Hattie, & Frey, in press). For both teachers and students, Visible Learning in the mathematics classroom is a continual evaluation of impact on learning. Let’s look at a specific, and often controversial example in the mathematics department workroom: the use of calculators.
Should I allow my students to use calculators?
The use of calculators is not really the issue and should not be our primary focus. Using calculators has a relatively small effect size of 0.27. Instead, our focus should be on the intended learning outcomes for that day and how calculators support that learning. In other words, is the use of calculators the right strategy or approach for the learners at the right time for this specific content?
This requires that both teachers and students have clarity about the learning intention – what the learning should be for the day, why students are learning about this particular piece of content and process, and how we and our learners will know they have learned the content. Teaching mathematics in the Visible Learning classroom is not about a specific strategy, but a location in the learning process. This requires us, as mathematics teachers, to be clear in our planning and preparation for each learning experience and challenging mathematics tasks. Using guiding questions, we can best blend what works best with what works best when.
| Guiding Questions | What to Consider in Planning Process |
| What do I want my students to learn? | Rather than what I want my students to be doing, this question focuses on the learning. What will we be learning today? |
| What evidence shows that the learners have mastered the learning or are moving toward mastery? | As I gather evidence about my students’ learning progress, I need to establish what they should know, understand, and be able to do that would demonstrate to me that they have learned the content. |
| How will I check learners’ understanding and progress? | Once I have a clear learning intention and evidence of success, I must design checks for understanding to monitor progress in learning. |
| What tasks will get my students to mastery? | Now I need to decide which tasks, activities, or strategies best support my learners. |
| How will I differentiate tasks to meet the needs of all learners? | What adjustments will I make to ensure all learners have access to the learning? |
| What resources do I need? | I need to create and/or gather the materials necessary for the learning experience (e.g., manipulatives, handouts, grouping cards, worked examples, etc.). |
| How will I manage the learning? | Finally, I need to decide how to manage the learning (e.g., groups, transitions, etc…). |
So, it turns that the the question, “Should I allow my learners to use calculators?” is the wrong question.
Our focus as teachers should be to create a classroom environment that focuses on learning and provides the best environment for developing assessment-capable visible mathematics learners who can engage in the mathematical processes as well as mathematics content. Through these specific, intentional, and purposeful decisions in our mathematics instruction, we pave the way for helping learners see themselves as their own teachers, thus making them assessment-capable visible learners in mathematics.
If you’re interested in learning more about making assessment-capable visible mathematics learners, Teaching Mathematics in the Visible Learning Classroom Grade-Level Series (K-2, 3-5, 6-8, and 9-12) will be out in the next several months.
References
Almarode, J., Fisher, D., Assof, J., Moore, S. D., Hattie, J., & Frey, N. (in press). Teaching mathematics in the visible learning classroom, grades 6 – 8. Thousand Oaks, CA: Corwin Press.
Almarode, J., Fisher, D., Assof, J., Hattie, J., & Frey, N. (in press). Teaching mathematics in the visible learning classroom, high school. Thousand Oaks, CA: Corwin Press.
Frey, N., Hattie, J., & Fisher, D. (2018). Developing assessment-capable visible learners. Thousand Oaks, CA: Corwin Press.
Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. New York, NY: Routledge.
