Education research is constantly developing what we know about teaching and learning. Often, it confirms existing practices, or expands them further, and sometimes it gives us completely new strategies to try. With so much information out there, it got us thinking — what is the ultimate maths class according to education research?
We’ve read and researched (and read some more!) to put together the top 10 strategies and practices that every maths class should include.
When students know where they’re going they have the opportunity to practice so they can get there. According to this study by Marzano (2006), students who have a clear understanding of their learning targets significantly outperform those who don’t. By outlining the learning outcomes before commencing a new focus area, in a clear way that your students understand, students will have a specific goal that they can work towards. This provides the focus and structure students need to work on a concept giving them more opportunities to perform well in assessments.
Students learn best in classrooms that support both independent and collaborative learning. There is no shortage of research on the benefits of collaborative learning. This literature review groups the benefits of collaborative learning across many studies into three key areas; social, psychological and academic. Some notable benefits include improved classroom results, the promotion of critical thinking and active learning, increased self-esteem and reduced anxiety. By structuring lessons to incorporate individual, partner, group and whole-class activities we give students the opportunity to learn from others, to experience different ways of thinking and to clarify their own thinking.
Ask any teacher and they’re likely to tell you that students learn best when they’re taught what they’re ready to learn. And research supports this. In fact, personalised learning can have dramatic results on student progress.
When students experience this type of teaching they often don’t just progress in their learning, they become more engaged. When they’re learning the maths that they’re ready to learn, students can experience success and become more confident in their mathematical abilities, leading to more interest in the subject. This idea was first introduced by psychologist Lev Vygotsky decades ago and made its way into mainstream educational theory in the 1970s. Today, it’s widely accepted that teachers should target their teaching to meet each students’ Zone of Proximal Development. This ‘goldilocks’ point — not too hard, but not too easy — is a vital part of personalised learning. Students should be challenged and engaged by a problem, but they must also have the foundation knowledge to be capable of solving it.
Explicit teaching is widely known as one of the most effective ways to teach. Decades of research has examined its benefits in the classroom, with consistently successful results. When teachers adopt this approach, they show students exactly what they need to do and how to do it. It is a totally unambiguous approach and involves a high level of teacher-student interaction. Teachers need to check understanding regularly and provide individual support and feedback to ensure students are fully grasping concepts. This can be difficult to do, particularly if students have gaps in their learning. A targeted explicit approach can give teachers the information they need to use this method more effectively.
A challenge many teachers face and much research explores is engaging students in learning. We know that engaged students are more actively involved in the learning process, but we also know that when our students walk into the classroom some are more willing to participate than others. The beginning of class is a great time for teachers to employ strategies that bring students together and get them ready to learn. One strategy to try is energisers. Research shows that energisers are a great way to connect students, build rapport and create a safe learning environment. These 8-10 minute teacher-led activities that involve the whole class and are proven to improve student participation and focus and ultimately improve learning.
Check out these great energisers to try with your class.
Spaced repetition is a learning technique that involves reviewing learned information at increasing intervals of time. This technique takes advantage of the psychological phenomenon known as the spacing effect, which was first researched over 100 years ago by German psychologist Hermann Eddinghaus. This approach to learning is highly effective as it commits the information to long term memory, assisting quick recall.
Creating lessons that are engaging is key to maths learning. In a 2003 report by Lokan, McRae and Hollingsworth, it was found that students benefit from working on problems that require discussions of alternative solutions and give them the opportunity to explain their thinking. This paper by Malcolm Swan, also states that students need challenges to learn and that these challenges should exist in a classroom environment that encourages questioning of student thinking.
One way to incorporate these sorts of challenges in the classroom is through Rich Learning. Rich Learning involves the whole class coming together for thought-provoking, teacher-led group activities where mathematical concepts are explored using open-ended questions with multiple entry and exit points. It has roots in situational and social learning. The concept first came to light in 1987 in Afzal Ahmed’s work that explored the importance of rich mathematical tasks in education. Further research, including this Queensland report on productive pedagogies and Jo Boaler’s Railside study, solidified Rich Learning as an evidence-based teaching practice. To learn more about Rich Learning, and for Rich Tasks you can run with your class, click here.
When students learn, they draw upon existing knowledge, linking the new concept to the network of what they already know. This means that when a student is introduced to a new concept that they have little related knowledge of, it can be difficult for them to learn it. That’s why before starting a new concept in the classroom, we must first assess students to understand what they already know. Formative assessments will help us uncover this, allowing us to look back, before we move forward. After all, assessments should only exist so learning can take place.
Summative assessments will then give us the additional information to determine whether students are learning the new content or to identify gaps forming in their learning. This continuous use of evidence to support the next steps in student instruction are recommended as a part of an effective assessment learning cycle.
Feedback is extremely powerful in the classroom. Its impact is ultimately defined by how effective the feedback is. If limited to just the grade (whether a letter grade or number), students will not get the information they need to understand their strengths or how they can improve.
So what is effective feedback? According to this 2020 study, the more information feedback includes, the more effective it is, especially if it contains information about the students’ accuracy and procedural appropriateness. Occasional feedback on self-regulatory skills like emotion, attention or motivation during a task also contribute to effectiveness. In a review of 71 formative assessments studies, Lane et al (2019) also found that effective feedback should be individualised, timely and aligned with the curriculum; and detailed and provide actionable steps for students. Assessments can only do their job if they are accompanied by effective feedback, so it’s vital to ensure feedback is included as part of the assessment process.
Encouraging students to self-assess gives them the opportunity to take ownership of their learning. Research has found reflection can encourage self efficacy and metacognitive prompting, which in turn improves problem-solving and efficiency. Teachers can help students develop self-assessment skills and habits by building reflection time into the assessment process. According to this study, a 5-point scale for reflection on the learning process is a great model for self-assessment. This scale could include statements like the following:
Clear goals set before assessment, coupled with feedback from the teacher creates a foundation for students to evaluate their own performance. Often over time, student and teacher evaluations begin to align, and students are able to set realistic goals for future learning.