New findings regarding the relationship between beliefs and adult engagement in mathematics/numeracy

One primary aim of my research has been to identify how beliefs may act as constraints or affordances to learning. Affordances are things that help us to achieve things.  For example, door handles help us to open doors and therefore are affordances to opening doors. It's a word that doesn't see much sunlight outside of acadamia.

The term 'constraints' on the other hand is pretty easy to grasp. Constraints can also mean items designed to reduce movement and behaviour, and my use of the word is much the same but related to mental and physical behaviour.

My research now clearly demonstrates that a wide range of beliefs operate to constrain adult engagement in mathematics. These include epistemic beliefs and beliefs about mathematics, oneself, and one's relationship with mathematics.

New findings
My most recent finding identify that many (almost all) lower-achieving NZ learners dichotimise 'understanding'. That is they view understanding as an either/or state, a bit like a switch.  Either something is understood, or it is not.  Secondly, they believe that understanding is something that will happen in a single instant.  This is often expressed by them as 'getting it'.

"Sometimes I just get it, but when I don't get it I stop trying".

By 'getting' it, they mean sudden understanding.  They don't necessarily mean they will understand something on the first exposure but they do expect the content to just 'click' at some point.

Thirdly,  lower-achieving learners believe understanding is transferred to them by an expert, in a 'content packet'.  If they don't understand the first time, then repeated explanations of the content are needed. My participants only had one responses to this question -"What should someone do if they haven't understood what is being taught?"

Answer:  Ask the teacher to repeat it.

Classic non-agentic responses. Contrast it with higher achieving learners answers, "Oh, go and study it at home, go on Youtube, hit the teachers up, work through the problems till you start to see patterns".

The harm...
How might these beliefs hurt low achieving learners?  First let's quickly discuss how understanding really develops.  There are multiple theories, but they all basically say that understanding is created by the individual as they struggle to make sense of and incorporate new information into existing understandings.  New understandings are also thought to result from receiving information you do not understand, that challenges your existing understanding, causing you to have to reconfigure your existing ideas to accommodate the new ones (long sentence!).

In other words, new understandings require you to 'make sense' of information that you do not understand. It requires that you struggle and ultimately reconfigure your existing understandings.  This takes time and effort.  It is an entirely different process to hearing something and understanding it.

Do you see the problem?
This set of beliefs leads students to expect to understand information when they hear it.  If they don't understand they think there is something wrong.  Then they think they are dumb, and that others think they are dumb, so they disengage.  If they are persistent and motivated they ask the teacher for help.  By 'help', they mean repeating the information, again and again.  If they still don't understand then they are out of options (often blaming the teacher or themselves for not being smart enough).

By expecting understanding to occur in response to an explanation learners take a very passive role in their education, expecting the packet of content to match their existing understandings.

The truth is that understanding is a process, not a state.  It takes time, and it is constantly evolving.  There is no 'either I understand' or 'I don't understand', there is only coming to a further understanding.

Summary

You are in trouble if you believe any of the following:

• Learning is about understanding what you hear at the time, and then applying it.
• Not understanding what you hear, might mean you are not as smart as others who can.
• If you don't understand the content you must get the teacher to explain it to you again so that you can understand. 

If you answered yes to more than one, then you have either been very lucky, or have some issues around education and learning.  Yes, the first one is what our 'training' sector is based on but has quite different goals than developing understanding. 

All of my low-achieving participants believe these three, and all my high-achieving participants don't.  That should get people thinking.

Beliefs are the foundation of the mind.  They determine how you interpret the world and what you deem important, and as such are the most essential factor in all education.