Approaches to teaching

There are many common approaches to teaching and they tend to develop as teachers gain experience.  

When teachers start out, especially in Maths, a text is your best friend.  It helps with sequencing, pacing, depth and the hidden elements/assumed knowledge of a syllabus.  There is a lot to do. By reading a few texts treatment of a topic, the main elements can be drawn out and students are given sufficient practice to get by.  Link it together with some worksheets and the occassional activity that is broadly linked to the topic (Kahoots are the current tool of choice) and a class won't get too bored with the approach.  Teaching is predominantly aimed bottom/middle with some end of chapter extension work.  Teachers are generally time poor, trying to cope with a variety of demands on their time whilst trying to demonstrate their enthusiasm and confidence.

As time passes, dependence on the text becomes less, the teacher evaluates where the class is at the start of a topic via some form of formative assessment, teaches the content that the syllabus indicates and provides practice to the class, balanced by the capacity of the class - developing its work ethic, revision strategies, collaborative skills and appreciation for learning.  The focus is reasonably narrow to ensure that the main ideas are cemented in for the next topic, making teaching a bit stop/start.  The difficulty level may shift from topic to topic based on the strength of students but the content taught is basically the same across the class.  Teachers are still time poor, but time spent is more effectively on the tasks chosen, the ability to collaborate is significantly higher and the search for efficient partnerships with other teachers begin, typically for resource sharing and assessment writing.

Ultimately the teacher can teach each topic without the text, gains a feel for where the class is at (usually based on time to complete initial tasks) and a lesson becomes a journey through the topics bridging from one idea to the next, creating a picture in the mind of the student of mathematics and establishing the elegance and wonder of mathematical process and solutions.  The text is used only as an example of how increasingly abstract concepts taught can be applied widely, providing opportunities to explore and journey in ever wider circles bridging between different branches of mathematics.  Focus is given to the individual needs of each student and the method of teaching is adapted as required. The skill of the teacher is ensuring that main concepts are well understood, changing the order of learning if required, but ensuring flow/engagement is maintained during learning.  Collaboration becomes more effective, reflecting on effectiveness of learning in different contexts, not just looking at resource sharing.

Many times when a student complains about a teacher, it is that they are familiar with a particular style of teaching, have adapted to it, were doing better and are finding it difficult to evolve to a new style.  All three styles above can support high and low achieving students within acceptable parameters, but the responses of students will be different.

Understanding where a teacher is in their own learning journey assists with setting fair expectations and areas for reflection.  Judgement by others should be suspended with understanding taking its place, being patient as each teacher moves through their current level of learning towards teaching competency.