Example intro text. Teaching is tricky. Exploring different pedagogical ideas allows us to improve our educational practice but the pedagogy can often be unclear, so this article outlines the pedagogical practices Blutick draws on to support the teaching and learning of mathematics.
Example body copy. In a nutshell, pedagogy includes all the behaviours and methods that a teacher uses to teach.
Mathematics teaching is complex. Teachers teach mathematics in a variety of ways just as students learn in a way that makes sense to them. Blutick appeals to a large international audience and so it needs to be able to offer a way of teaching and learning that both students and teachers can relate to. For this reason Blutick does not subscribe to one pedagogical practice in favour of another. Instead, it focuses on students being able to engage with, understand and think about the mathematics but from a variety of starting points.
It is not just teachers who are thinking about pedagogy. School leaders too recognise the need for more understanding about professional learning systems to support teacher development.
To start with we outline some of the more general pedagogical practices that can be applied to mathematics (and other subjects) that are also prevalent in Blutick.
As with any pedagogical practice, how teachers apply the theory depends on how true they stay to the overarching principles. Similarly, students are free to access the site and may use it in many different ways.
This is the process that Jean Piaget described as schema development in which students assimilate new ideas alongside old ideas and then accommodate them into a new schema by adjustment and restructuring.
Example block quote – Blutick allows students to construct their knowledge one piece at a time by encouraging students to enter line-by-line working, thus allowing them to build up ideas at their pace. Both teachers and students can access the mathematical content in any order too, so it is not a one-way system but instead gives this choice and autonomy to the user.
In 2010 Barak Rosenshine published a set of 10 Principles of Instruction, based on evidence from cognitive science, classroom research and other cognitive supports. In its broadest meaning this could include any form of teaching that starts with a review of earlier learning, introduces tasks that have a specific mathematical goal in mind and gives feedback that synthesises and corrects the students’ path towards that goal. Tasks offered are usually heavily guided towards a given outcome by one reasoning pathway.
Blutick uses some of the Rosenshine 10 Principles:
Active learning is essentially about getting students to think, reason and problem solve, as opposed to passive learning where they are fed information with little cause for them to think. Active learning helps students to develop long-term memory. This is not only about storing what went into their memories in the same form as it went in rather, it is mainly about identifying and storing patterns, relationships, connections and generalities, all of which are the products of our active minds. These are key skills for mathematics and in particular, mathematics progress.
Blutick supports active learning through inviting students to show their working, as opposed to just their answer. In this way, it dissuades the student from simply guessing and instead, encourages them to think about the solution and the stages of thinking required to reach an answer.
The main idea being used here is that giving students too many things to think about at the same time can be confusing and obstruct learning the target knowledge. The suggestion is that teachers should therefore organise knowledge into small pieces of information that can be drip fed, well learnt and accumulated to make a bigger body of knowledge.
Both teachers and students can choose how much mathematical content to access so they can control the flow of information as required. Students can complete one question or 1000s of questions. Questions are supported with short videos and worked examples, thus helping to manage the flow of information in a systematic and logical way.
Although many have written about formative assessment, Dylan Wiliam is probably the most well known researcher to be associated with this practice. Formative assessment is the idea that teaching is adaptive to the student’s needs. As part of formative assessment, a teacher’s role is to engage in responsive teaching, so that their inputs and interactions with students allow them to adapt and respond, depending on how the learning is going.
Blutick is designed to allow teachers to watch how their students are responding to questions — in real time — so that teachers can be responsive to the needs of their students. Teachers can see their students’ answers to questions but also their line-by-line thinking which enables them to provide feedback that will enable them to move learners forward. The intelligent feedback offered also allows students to be owners of their own learning too, thus supporting self-assessment principles.