### Teaching not telling

“learning is an active, contextualized process of constructing knowledge rather than acquiring it.”

If learning is an active process, what does that mean for me as the teacher and what is my role in the classroom? Most in-service teachers and pre-service teachers (at least in the primary context as this is my experience) believe that knowledge is constructed from students’ previous experiences and personal models and representations. This constructivist approach to learning therefore impacts how we teach, knowing that our role is not to ‘fill the students with knowledge’ but ‘fill the students with a sense of wonder’ so they can build knowledge connections for themselves by linking new knowledge to prior understanding.

“A constructivist view of learning suggests an approach to teaching that gives learners the opportunity for concrete, contextually meaningful experience through which they can search for patterns; raise questions; and model, interpret, and defend their strategies and ideas.”

Fosnot, C (2013)

### There’s modelling and then there’s modelling

Hopefully you are nodding as you read this blog (that this is information you already know) and this belief of how students learn impacts your planning, teaching and assessing of students’ knowledge and understanding. Even though we believe this, sometimes mathematics lesson plans and the way knowledge is shared in the classroom doesn’t match this belief. Sometimes mathematics lessons are more like telling than teaching. This is evident when the teacher explains how to ‘do the maths’ giving students recipe style step-by-step instructions to follow a procedure.

This way of presenting content to students may be due to a lack of confidence in how to break down mathematical concepts, a fear of ‘not getting through content’ so just teaching the rules, or may reflect how the teacher themselves learned mathematics at school. Although it may be tempting to simply show students what to do then have them repeat a few examples, this does not allow students to draw on their prior knowledge, make errors in trying to find the solutions or processes or procedures that lead to learning, or allow them an opportunity to show you what they already know.

I see some possible problems. Lots of research on the use of base ten blocks; glad you are reading. Purpose of models should not be to "show" math and have kids read answers off of manipulation. Models should affect cognitive reordering. Compare to Mystery of the Meter (dials). https://t.co/HXGU6Hv3ID

— cathy fosnot (@ctfosnot) December 18, 2018

This may seem like modelling, as part of modelled, guided, independent instruction. However in mathematics, the modelling is often better shared after the students have first explored the ideas and strategies for themselves. Students need to build their own representations of concepts and try to solve the tasks without too much assistance to begin with, this allows for productive struggle to occur. When students struggle, they learn important skills like perseverance, trial and error or different strategies and this creates a need for mathematics, a need for a more efficient way to solve a problem – this is where the modelling then comes in.

This is not to say that any teaching prior to providing problems for students to solve is not valid. In fact Russo and Hopkins (2017) describe this as a “highly focussed, efficient approach to learning that effectively activates prior knowledge and provides opportunities for students to be successful and to feel suitably supported”. Note however that the focus is not on showing or explaining procedures to students or telling them what strategy to use, but is on providing time in the lesson to explore ideas and make links to what students already know e.g. use of Number Talks, Quick Images, Number Strings or Open-Strategy Sharing discussions.

How some of my students saw the quick dot image.

— Simon Gregg (@Simon_Gregg) February 5, 2019

I was pleased AV shared a way using subtraction; he explained it really well too - that he'd counted four twice so needed to subtract them. pic.twitter.com/j5Eo9z9BJy

Maor (1999) proposed 5 key practices that define constructivist learning environments:

- personal constructions of reality
- simulated authentic learning environments
- multiple representations of data
- active learning
- collaboration

This research is 20 years old and yet these suggestions still hold true. These practices represent ways we can open our classrooms and our lessons to allow students opportunities to construct knowledge, like building blocks, on top of one another, beside one another, interconnected to one another.

### What does helping look like in maths?

Most of the time when teachers are telling students what to do or how to do it, it comes from a good place, a well intended place. Unfortunately it’s like teaching a child to ride a bike. No amount of me telling them what steps to do and in what order is going to teach them how to ride the bike, they need to get on the bike and see for themselves what happens! So if we shouldn’t explain everything to our students, what does it look like to help students come to understand processes and procedures? It looks like a question.

- What do you think the problem is about?
- What do you think you might try to work it out?
- What do you already know that could help you?
- Where might you start?
- What could you draw or write to help you as you are thinking?
- What strategy do you think might work? Why?
- What do you think a reasonable solution might be? why?
- Is there another way to solve it? Could you try another strategy?

### What does helping not look like in maths?

Teachers are great helpers, we like supporting students and want them to succeed and part of succeeding is feeling a sense of achievement. In mathematics this is often interpreted as ‘getting the answer right’. Sometimes we can be too helpful though, not allowing enough wait time, or not allowing students to just sit with their idea and try it work it out by themselves. We can be quick to say try this … or this is a good way … or maybe start by … As helpful as it sounds, learning is not occurring when we tell students what to do. The focus also needs to shift from the answer to the process. If you find your students are answer-driven give them the anser, then ask for at least two ways to get there. Also ask for an explanation of both the process they used and a justification as to why their solution is valid.

### Student pathways in learning are not drawn by you

Our curriculum documents guide us in what to teach and when, creating a ‘pathway for all’. But every student’s path is different and is a complex web of connecting concepts that are built up over time as their personal environment, experiences, and representations influence each building block of knowledge that is created. Although we are there to guide them, ultimately it is the students who create their learning pathway. The Oxford dictionary defines teach as: to cause (someone) to learn or understand something by example or experience. Learning through their (students’) examples and their experiences. Our job is to prepare the way, removing the stumbling blocks of misunderstanding or filling the pot holes of misconceptions. That’s what teaching is to me.

#### References

Cey, T. (2001). *Moving towards constructivist classrooms.* Saskatoon, Canada: University of Saskatchewan Saskatoon. Retrieved from http://sydney.edu.au/education_social_work/learning_teaching/ict/theory/constructivism.shtml on Sat 16 February 2019

Fosnot, C. T. (2013). *Constructivism: Theory, perspectives, and practice*. Teachers College Press.

Maor, D. (August 1999). Teachers-as-learners: the role of a multimedia professional development program in changing classroom practice. *Australian Science **Teachers Journal, 45* (3), 45- 51.

Russo, J., & Hopkins, S. (2017). Examining the Impact of Lesson Structure When Teaching with Cognitively Demanding Tasks in the Early Primary Years. *Mathematics Education Research Group of Australasia.*