Mindfully or Mindlessly?

 A key thing here is whether our focus is on finding answers to calculations OR becoming mindful of the reasoning underlying the mathematics.

Can we all agree on something... We still devote too much time to the former!

 Mindful Maths (more on that in a minute) will empower learners to own their mathematics and create meaning and understanding in authentic ways. 

HOWEVER...

 Since helping hundreds of learners become fluent with their maths facts in primary school we see FIRST HAND  the impact this has on their maths confidence, independence and success! An essential tool for overall mathematical achievements (Nunes et al., 2012)

 We understand exactly how numberness and automaticity of number facts develops — it opens the door for higher order fluency and comprehension. Cognitive science supports this:  

Becoming fluent with numbers reduces the cognitive load, thereby freeing resources for more advanced problem solving to occur (Sweller, 2005).

This is important for the development of deeper and more complex maths learning.

 Fluency is one of the three aims for the 2013 national curriculum. It is also one of NCETM’s ‘Five Big Ideas of Teaching for Mastery’ where it’s defined as “quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics”.

Here at FLUENCY HQ we believe you can help learners achieve fluency with numbers if learners understand the CONDITIONALITY of most ‘facts’. 

This will all make sense in a minute... I promise I'll explain but first a ⚠️DISCLAIMER ⚠️  This article is not about mindful meditation! (Wouldn't that be nice?) HOWEVER, it is to do with the process of actively noticing new things. When you do that, it puts you in the present. It makes you more sensitive to context and perspective.

“It’s the essence of ENGAGEMENT. And it’s energy-begetting, not energy-consuming,” says the the wonderous Ellen Langer author of ‘The Power of Mindful learning’ and professor of psychology at Harvard University. The first woman ever to be tenured in psychology at Harvard University.

If you haven’t come across her work, then I highly recommend it.

 One of the key findings from Prof Langer’s research of over 4 decades is that learning - Maths learning -   is more powerful if we are MINDFUL of the conditionality of most ‘facts’...

 Ah yes, I hear, but mathematics is not conditional, it is absolute! Children need to know that 2+2=4 and not think that it could be 5 or a banana. Well yes and no! Some simple arithmetical facts are not that 'open' to being conditional, but even then MOST mathematics is not that fixed.

More seriously, a lack of conditionality when it comes to different calculations can make a difference.   For example, typically, children meet multiplication predominately as repeated addition. 

Five times three could be five added three times but it could also be lots of other things! 5 groups of 3 is a conditional interpretation, but  children come to regard this as absolute. 

This absolute and limited view children then hold means they often get STUCK! 

So five bags of 3 apples can be represented as 3 + 3 + 3 + 3 + 3

 Notice that these particular images (above) invite learners  to attend to structure when making the comparison.

TRY THIS...

 Cathy Fosnot and her colleagues have some other examples of working with conditionality from her 'Young Mathematicians at work' project. 

And in their paper, Habits of Mind: An Organizing Principle for Mathematics Curricula, researchers Cuoco, Goldenberg and Mark call for mathematics curricula to have ways of thinking about mathematics at their core, rather than specific mathematical results. They believe that if we really want to empower our learners we have to help them develop genuinely mathematical ways of thinking. They also believe it is important to try to make the use of these habits of mind explicit to encourage learners abilities to make connections among mathematical ideas.

 With this in mind, we at FLUENCY WITH NUMBERS HQ, believe that children learn better when they are empowered to be actively involved in the 'meaning making' of maths. We believe that maths involves multiple ideas, voices, strategies and ways of seeing and thinking. I'm  excited to share these truly AWESOME (not to mention) IMPACTFUL ROUTINES. These will help children to develop a strong 'number feel' and develop EFFICIENT-calculation strategies. A range of visual representations are used. These are SIMPLE and ENJOYABLE to play!

 I have suggested that there are two ways to approach mathematics: mindfully and mindlessly. We need to adopt different styles of pedagogy for these learning outcomes. 

Too much of current practice raises mindless learning over the mindful. 
 

If you want to learn more about MINDFUL learning, Professor Ellen Langer shares her experience and insight of how we can learn about mathematics and any other discipline in a more mindful way so that we can have the freedom to make it our own:

What is your thinking on Mindful and Mindless Maths?  

I’d love to hear your thoughts. Have you evet thought about maths being mindful or mindless?  What mindful routines do you use? How do you use them? Which ideas resonate with you? What do you disagree with?  What questions do you still have? All views are welcome - post in the comments.  Or SMASH the REPLY button! I can't wait to hear from you!

Thank you for all you do to support your children's number journey. 

Love, Janey x

 To further inform your thinking here are some useful links to literature that support the research and the pedagogy:

The Power of Mindful Learning by Ellen J. Langer 

The Mindful Teacher by Elizabeth MacDonald and Dennis Shirley 

Values and variables: Mathematics education in high-performing countries by Mike Askew, Jeremy Hodgen, Sarmin Hossain and Nicola Bretscher.