In this post, we are going to continue with the latest chapter of How I Wish I’d Taught Maths, by Craig Barton, about evidence-based education. Today we will discover a type of activity that can be tailored to both novice and expert learners: purposeful practice.
As we have seen in a previous post, deliberate practice is an optimal model for the presentation of new content. Once that phase is achieved, purposeful practice allows students to develop procedural fluency and create opportunities to establish deeper knowledge. Purposeful practice is perfect for remembering and summarizing concepts that have already been worked on.
According to Nuthall (2007), ”students already know 40-50% of whatever we are trying to teach them. The problem is that 50-60% of the things they don’t know is likely different for every student.” Reviewing concepts has clear advantages such as filling in knowledge gaps that may have been leftover or gaining deeper knowledge.
Once new content is introduced to students, that is when the divergences begin to appear. Some absorb the concepts more quickly while others need more practice. This is why methodologies that adapt in real-time to each student, like Smartick, are essential to respect different learning rhythms.
The fundamental element of purposeful practice is the goal beyond the practice. It is based on five principles:
1. Students need to experience early success.
Students’ success and the perception that they can progress are critical to their motivation. It’s necessary that students feel that they can progress early on.
2. There must be plenty of opportunities to practice the key procedure.
As we have seen before, practicing key procedures is very important. Practice respecting the different rhythms and opportunities for self-explanation helps make learning happen. Furthermore, an essential element is the intention for them to practice a specific procedure.
3. The practice must feel different.
Students already have previous experience with the topics and content that they are working on. Those who found it difficult may think it won’t be any different this time and those who find it easy may think, ”Why are we doing this again?” Therefore, adding a goal that goes beyond just practice helps to motivate students.
4. Opportunities must exist for students to make connections, solve problems, and think deeper.
Students need to be able to transfer their acquired knowledge to new situations, make connections, solve problems, and think creatively. Once they reach a certain level of experience, the activities that allow them to reach it will be the ones that take them to the next level.
5. The focus is always on the practice.
Students need to have procedural knowledge stored, available, and automated in their long-term memory. This way cognitive ability is free to perform the processes described in the principle mentioned before, and they will learn from experience. All of this needs to happen in the way that we intend and therefore, procedures must be a fundamental part of the process.
The Educational Power of Purposeful Practice
- Every student is working on the same task. Differentiation occurs through the connections students make.
- Students who are not experts are able to practice the key procedures. There is a greater goal in mind than just practice and it feels different.
- The more experienced students have the opportunity to develop a deeper knowledge and understanding.
- Most importantly, all students benefit from purposeful practice.
If you would like to acquire procedural fluency and develop a deeper understanding of math, log in to Smartick and try it for free.
- Barton, Craig. 2018. How I Wish I’d Taught Maths : Lessons Learned from Research, Conversations with Experts, and 12 Years of Mistakes. Melton, Woodbridge: John Catt Educational Ltd.
- Nuthall, Graham, and New. 2007. The Hidden Lives of Learners. Wellington, N.Z.: New Zealand Council For Educational Research.
- Worked Examples and Metacognition
- Interleaving vs Blocked Practice to Learn Math
- Teaching Principles and Learning Phases of Singapore Math
- Practice and Repetition as the Base of Learning
- Singapore: Experiences in Learning