J is for Jumping forward too fast
A difficult balancing act for teachers is to balance the need to get through the national curriculum and to ensure a deep level of understanding for their students. With the pressures related to the national curriculum and the various assessments through a child’s mathematical journey, teachers are being increasingly pushed to move students on through topics without allowing them the time to fully understand a subject.
What is the impact of this? Children are only learning something at shallow level leading to poor application and the development of misconceptions.
So what do we need to do? We need to stop jumping forward too fast and assuming quick rote recall of maths means that a child understands a concept. Instead we need to push the agenda of “Maths Mastery” so students at all levels develop an enduring, confident, and flexible comprehension of the subject.
How do we achieve this? Let’s delve into four essential pillars for mastery: Number Sense, Metacognition, Visualisation, and Generalisation.
Number Sense: The Foundation of Mathematical Fluency
Number sense is more than just the ability to manipulate numbers; it's an intuitive understanding of how numbers relate to one another and the real world. It involves grasping numerical magnitude, recognising patterns, and understanding the properties of numbers. A strong number sense enables learners to estimate, reason, and problem-solve with confidence.
To develop number sense, students benefit from exposure to various representations of numbers, such as number lines, manipulatives, and real-life contexts. Activities that encourage mental math, like number talks and math games, foster flexibility and efficiency in calculations. By building a solid foundation in number sense, learners gain the confidence to tackle more complex mathematical concepts.
Metacognition: Thinking About Thinking in Maths
Metacognition refers to the awareness and understanding of one's own thought processes. In the context of maths, metacognitive skills involve monitoring, planning, and evaluating one's problem-solving strategies. Students who engage in metacognitive practices reflect on their approaches, identify errors, and adjust their methods accordingly.
Encouraging metacognition in the maths classroom involves promoting a growth mindset, where mistakes are viewed as opportunities for learning. Teachers can scaffold metacognitive skills by asking probing questions, prompting self-explanation, and modelling their own problem-solving processes. By fostering metacognition, learners become more autonomous and strategic mathematicians.
Visualisation: Seeing the Maths to Understand the Maths
A step that can often be forgotten about when developing learning through concrete, pictorial and abstract is visualisation. Visualisation plays a crucial role as it helps to progress from concrete to abstract. A learner needs to learn how to visualise the concept and how to represent this is their mind. By encouraging visualisation, educators empower students to develop a deeper understanding of mathematical concepts and their applications.
Generalisation: Making Connections and Finding Patterns
Generalisation involves identifying overarching principles, recognising patterns, and making connections across mathematical concepts. It allows learners to extend their understanding beyond specific instances to more abstract principles. Generalising in maths involves recognising similarities, formulating conjectures, and applying principles across different contexts.
To foster generalisation, educators can provide opportunities for exploration, inquiry, and problem posing. Tasks that encourage experimentation, such as open-ended projects and investigations, stimulate curiosity and promote deeper mathematical reasoning.
I appreciate that in the current climate this can be a difficult idea to follow and concerns about falling behind in the curriculum and not allowing a student full exposure to the curriculum. Here’s my challenging thought, if we don’t spend enough time initially on mastery for the basic concepts, how much time will you waste later on down the line when you’re having to re-visit multiplication to be able to find the area of a square or having to re-teach a misconception for fractions where they will add the top numbers and the bottom numbers with no real understanding of why this is wrong.
