Literature review #2 - Transfer of Learning by R. Haskell

 Haskell, Robert. Transfer of Learning.

One of my hunches regarding the poor PAT results of our students was that we may not necessarily teach what is being tested. I shared my thoughts on the difference between "teaching to the test" versus teaching the specific math areas that students will be assessed on. I searched the web for any relevant research but couldn't find anything particularly useful until I came across "Transfer of Learning" by Robert Haskell.

Dr. Robert E. Haskell was a Professor of psychology at the University of New England (passes away in 2010), whose work in the area of learning transfer spans a range of disciplines, including math, science, education, business, and psychology.

Haskell's insightful book, 'Transfer of Learning: Cognition, Instruction, and Reasoning,' explores the interesting topic of how we can effectively apply our knowledge in diverse contexts. By exploring the historical roots of transfer and underscoring the importance of building a solid knowledge foundation, Haskell convincingly argues for the significance of explicit teaching and practice. emphasizes the importance of understanding key concepts, strategies, and declarative knowledge in facilitating successful knowledge transfer. The book provides valuable insights on fostering critical thinking and problem-solving skills in students, empowering them to apply their learning to real-world situations.

Just in case, I'd like to explain that declarative knowledge in math involves knowing and understanding the key ideas and concepts that form the foundation of mathematical thinking and problem-solving. It is like the building blocks of learning, providing a solid foundation for further learning, deeper understanding and the ability to apply what you know.

In conclusion, Haskell's work aligns with my belief about the importance of teaching before testing. By emphasizing the need for a strong knowledge base and providing students with explicit instruction, educators can empower students to transfer their learning effectively. Teaching before testing ensures that students have the necessary understanding and skills to approach assessments with confidence. By incorporating Haskell's insights into our teaching practices, we can create a solid foundation for students' academic success and foster their ability to apply their knowledge in real-world contexts.

Literature review #1 - Visible Learning by J. Hattie

John Hattie is a Professor of Education and Director of the Visible Learning Labs, University of Auckland, New Zealand and we all know his famous work "Visible Learning. A Synthesis of Over 800 Meta-Analyses Relating to Achievement" first published in 2009. 

I decided to reread his book, especially some parts that I found important for my teaching inquiry this year. According to J Hattie, "The effect size of 0.40 sets a level where the effects of innovation enhance achievement in such a way that we can notice real-world differences, and this should be a benchmark of such real-world change." 

This is a great reminder to all of us that our inquiry into improving our teaching practice, commitment to numerous PLDs, and our aim to develop student agency are vital components in fostering positive student outcomes in mathematics. By focusing on refining the curriculum and our instructional skills as teachers, and prioritizing student engagement and empowerment, we have the potential to make a profound impact on students' mathematical understanding and achievement. 

This research also provides valuable insights into instructional strategies that yield positive results for student learning. When it comes to teaching math, a well-structured program and direct teacher instruction have been found highly effective factors (Hiebert & Grouws, 2007).  Explicit teaching, clear explanations, and demonstrations have a significant impact on student understanding and achievement.

Manipulatives play a crucial role in the early years of mathematics education and show a great effect when working with low-achieving middle school students. They provide concrete experiences that help students build a solid foundation and develop a deep understanding of mathematical concepts (Mitchell, 1987). By engaging students in hands-on activities, manipulatives foster conceptual understanding and lay the groundwork for later abstract thinking.

When it comes to effective teaching strategies, certain approaches have shown particularly promising outcomes. Strategy-based methods, guided practice, peer tutoring, teacher modeling, specific forms of feedback, mastery criteria, sequencing examples, and instruction responsive to feedback have demonstrated high effect sizes (Hattie, 2009). These strategies actively engage students, provide guidance, and create opportunities for practice and feedback, leading to significant improvements in mathematics achievement.

On the other hand, research suggests that peer group strategies and independent practice with technology have relatively lower effect sizes (Hattie, 2009). While they still have some value, working within a peer group and relying heavily on technology for independent practice may not yield as substantial improvements in mathematics learning compared to other approaches.  (I have personally observed similar situations where students collaborate on their independent activities, and despite my reminders that they should only help by explaining rather than telling, it can be challenging to monitor.)

Reading "Visible Learning" by J. Hattie confirmed my hunch and hypotheses about the most important and effective components of teaching mathematics:

• Structured mathematics programs: Comprehensive and organized curricula that provide a framework for effective instruction and learning in mathematics.
• Direct Teacher instruction and modelling: Engaging students through clear explanations, demonstrations, and guidance from the teacher to deepen their understanding of mathematical concepts.
• Strategy-based methods: Teaching students specific problem-solving strategies and approaches to empower them in tackling mathematical tasks effectively.
• Guided practice and feedback: Providing students with opportunities to apply their knowledge through practice activities while receiving targeted feedback to enhance their learning and mastery of mathematical skills.

Citations:

Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students' learning. In F. K. Lester Jr. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (Vol. 2, pp. 371-404). Information Age Publishing.

Mitchell, M. M. (1987). The effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 18(6), 449-457.

Hattie, J. (2009). Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement. Routledge.

Formulating my Hypothesis

Based on my previous TAI steps, I identified the following most important hunches for my inquiry:

I believe that 

- updating the maths programme to include all areas tested in the PAT, 

- sharing and unpacking Term 1 testing results with our learners, 

- teaching students how to use self-assessment (matrices) to support their own learning, and

- collaborating with other teachers and sharing best practices 

will improve students' learning outcomes and enhance their learning experiences.

Taking a more data-driven approach by updating the maths programme to align with the areas covered in the PAT can help to ensure that students are receiving instructions that are relevant to the assessment tool used to evaluate their learning. 

By unpacking the term 1 results with students, educators can help them understand their strengths and weaknesses and take ownership of their learning.

Teaching students how to use Maths Matrices should also help them identify areas where they need additional support and extra practice. By providing students with the tools they need to support their own learning, educators can help to foster a sense of agency and responsibility in their students.

Teacher collaboration and data sharing are essential in Maths education. By working together and sharing data, educators can identify areas for improvement, set goals, create and share resources, and adjust their teaching practices to improve student outcomes.