Maths: the keystone for high school learning?
Thoughts on developing the "maths-genius-halo-effect"
Mathematics is an incredibly important subject, given its connectivity to virtually every discipline and future career: journalism (understanding statistics); plumbing (gradients); philosophy (probability) – to name a few.
In addition:
“One of the challenges with mathematics is that the concepts are hierarchical. That is, if children don’t develop a deep understanding of foundational topics such as place value, gaps in learning begin to occur”1
Mathematics is oft-depicted as the domain of “geniuses” – compare tropes in The Big Bang Theory, depictions of Albert Einstein or Stephen Hawking. These outliers are assumed to be born with special abilities; out of reach of the everyday person. This mythologising is a major hurdle, leading to feelings of shame if maths doesn’t come “naturally.”
Victoria Education highlights this with some common myths:
gene myth – you either have a maths gene or you don’t
gender myth – one gender is better than another at maths
speed myth – ability in mathematics can be measured by how quickly a problem is solved
memory myth – maths is only about memorising facts, rules and procedures
perfection myth – mathematicians never make mistakes
creativity myth – maths is not a creative pursuit as there is usually one right way and one right answer.
“When mathematics becomes more complex, children struggling with the foundations of mathematics cannot keep up with their peers and fall behind, often leading to negative attitudes, poor self-efficacy, and disengagement”.
This is mirrored in my own experience when checking-in with students, they express feelings of shame, confusion, and disengagement. When I emphasise that there are math tutorials multiple times per week, and homework club; students express a reluctance to attend.
That is not to say that teachers are unapproachable; rather, they are viewed as an extension of the “math genius myth” and avoided to circumvent feelings of shame.
If we accept that some students harbour feelings of shame around mathematics, then any impediment – no matter how small – can be enough to derail learning.
In trying to conceptualise these issues, I have borrowed from a chemical reaction graph (x-axis=time, y-axis=energy):
If mathematical learning requires activation energy (EA1), then we can substantially lower the energy required through various interventions:
Inverse Effort Obstacle
For example, printed copies of Cartesian planes and a table for coordinates when learning to plot linear equations, so students have one less impediment to learning or using a portable whiteboard to work through examples with students (repeating what the teacher has said).
I understand that some may view this step as discouraging student responsibility, but my thinking here is specifically for ADHD students who struggle with task initiation.
Inverse Shame
For example, a teacher aide who is honest with students when they don’t understand something or they’re confused. The hope is that, having an adult admit to their deficiencies will demonstrate that its okay not to know everything. In addition, feigning ignorance, and asking a teacher over to explain (within earshot of the student); again, this models asking for help.
I’m not sure that this strategy would work/is appropriate for teachers.
How else can we *possibly* improve student learning?
Asking for help
Consider lunch break mathematics tutorials as a playground duty for teacher aides to be assigned (under the direction of a teacher). Teacher aides are not as strictly associated with math genius mythologising – this may encourage higher student attendance and engagement (particularly with those who need it most).
Could attendance at these extra-curricular maths sessions count towards a student’s grade for effort?
Consider more peer learning – breaking the class into groups can lower shame, and encourage students to learn from each other. This also flips the emphasis from individual struggle, to collective problem solving.
An example of embedding Indigenous methodology for learning.
Undermine Mathematical Myths
Emphasise the everyday-ness of maths. Connect the mathematical concepts to relatable examples.
When linear graphs were posed as “which salary would you prefer?” - students were able to identify the graph with the steepest gradient that was positive.
Brain breaks! I’ve watched this integrated to great success. Mathematics can be a place where we laugh and have fun.
Emphasise that maths skill and knowledge is built. Dissolve and blur the binary of good at math vs. not.
High standards and expectations for everyone in the classroom.
Tell stories about maths in context – Sacred Geometry; differing base number systems Mayans (base 20), Babylonians (base 60), Egyptians (base 12); Google avoids hiring too many “top mark” students – persistence, curiosity, and innovation and intellectual humility are more important than results.
Correct answers are great but students will never get there, if they’re too scared to even try - highlight the importance of maths methodology, thinking, building knowledge, giving it a go.
This example uses yarning as an Indigenous learning methodology.
Revelation of “maths secrets” – for example, how to multiple any two-digit number by 11. These quick math tricks are great for engaging students in maths, and also fun for students to share with families and friends.
Some question the appropriateness of “tricks” because they discourage students from fully understanding the conceptual thinking behind the mathematics. However, my suggestion is in relation to students who are already disengaged and might need a “jump-start”.
Maths as a language
Frame maths as a language, with rules of “grammar” and varying levels of fluency, depending on study and practice.
There are multiple ways in which you can say the same thing and arrive at the same conclusion, however, communication and clarity is key; being able to build an “argument” and showing how you arrived at a conclusion.
Maths has its own “alphabet” and “script” which may require special understanding but can be decoded.
Maths is a skill that is built, refined and then reified.
For some students, conceptualising of maths as a language will garner greater “buy-in”. Language is associated with the arts; something creative, fun, everyday.
Parental messaging
Parents and carers may not be aware of the ways in which they reinforce “maths mythologising” - this is a huge impediment to student learning.
It’s not unusual to hear people says things like:
“I’m no good at maths”
“Maths is hard”
“You better ask your teacher about that one”
More subtly, the avoidance of maths in general is hugely impactful for reinforcing cues about the difficulty of maths. Consider immediately googling an answer, reaching for the calculator for basic addition or avoiding helping with maths homework entirely.
How might a student’s view of maths change if caregivers approached maths problems with enthusiasm and curiosity?
Incorporate movement and groups
Professor Peter Liljedahl advocates getting students to stand up to increase “thinking behaviours”. In addition, the student scribing should be writing the other student ideas.
Randomised groups were also determined to be better for lowering stigma and improving the chance of “thinking behaviours”.
I hypothesise that if a student who was previously disengaged from mathematics, significantly raises their achievement; this will have impact across the entirety of their subjects, through what I’m calling the “math genius halo effect”.
In addition, these skills are disseminated through to their family members, potentially uplifting communities in real and tangible ways (e.g. avoidance of loan sharks through knowledge about compound interest).
If I had my way, education would significantly invest in mathematical learning:
targeted training for teacher aides;
maths specialisations for teacher aides;
partnerships with universities for evidence-based research;
development of NHMRC/ARC grants for developing community maths mindfulness courses;
homework centres developed more broadly into community learning hubs, which also assist parents and carers (alongside their children).
If a student knows that they can do maths, this builds their academic confidence overall, and will contribute to better educational outcomes.
backoftheclassroom.substack.com
https://theconversation.com/saying-im-not-good-at-maths-is-not-cool-negative-attitudes-are-affecting-business-53298