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.

Self-reflection

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.

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.

    http://www.jjfbbennett.com/2016/04/visible-learning-quotes.html

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.