Here at Maths Pathway, five core beliefs shape everything we do.
Our five core beliefs are:
- Learning, then assessment, then reporting
- Multiple learning modes
- Relationships and feedback
- Deep understanding
- Continuum learning
Learning, then assessment, then reporting
We believe that courses should be structured around effective student learning first.
Assessments should be diagnostic and formative — they should reflect, measure and enhance
student learning. Reports should then draw on this assessment data to give an accurate picture of
how a student’s learning is going.
But the reality is that most maths courses are structured the other way around. Data will
be needed for reports, so assessments are designed to provide that data. These assessments
are not diagnostic or formative at all: students sit a maths test, their grade is recorded in a
spreadsheet, and nothing else happens with that data. Then, finally, it is down to the
teachers to work out how to make student learning effective in the lead-up to each
summative assessment. This is backwards, and puts effective student learning last.
Multiple learning modes
We believe that students should learn to recognise and use mathematical ideas in situations
outside the mathematics classroom, such as in other school subjects and employment. This
is part of why we believe that students need to learn in a variety of modes. They should
develop confidence with mathematical digital technology, and hand-written maths skills.
They should also have opportunity for hands-on learning, group work, and discourse.
But the reality is that most Australian schools, maths courses are textbook driven. The
course focuses on ticking off all of the curriculum dot points, and in doing so leaves no time
for meaningful projects, investigations, rich activities, and real-world applications. Students
graduate without knowing how to apply the maths they’ve learned, and without creative
Relationships and feedback
We believe that teachers’ impact on student learning is not limited to content delivery. The
relationship between teacher and learner is of critical importance to building mathematical
self-confidence. Teacher feedback can have a huge impact. Direct instruction can also have great
impact, but only if correctly targeted.
But the reality is that the teacher’s role is restricted by the structure of maths courses.
Most of the class time gets chewed up by content delivery to the whole class at once, which
is just incorrectly targeted direct instruction. Very little time is left for one-on-one
conversations with students in the class, deep feedback for students or relationship building.
The parts of teacher practice that have are the most enjoyable and have the greatest impact are squeezed into the background.
We believe that students should build a deep understanding of the mathematics they learn,
rather than just rote-learn procedures.
But the reality is that most students are just rote-learning maths. The evidence of this is all
around us: students forgetting things from year to year, being unable to transfer skills into
other subject areas, being unable to problem-solve, only feeling confident with ready-made
recipes, and calling maths one of the hardest subjects.
We believe that students have a diverse range of learning needs. We know that in a typical
mathematics class, students enter with a wide range of levels, and with different gaps and
competencies to their peers. We also know that mathematical understanding is built
cumulatively; to understand a new piece of mathematics, students must already have
understood the sub-concepts. We therefore believe that different students should be
learning different mathematics at any given time. Students should not be constrained to
work “at grade level”; rather, they should grow along a continuum from wherever they
happen to be.
But the reality is that most students are constrained to work “at grade level”. Most
Australian schools batch students into year groups, and put those batches through a
production line of learning outcomes. The learning outcomes that students are aiming for –
and being graded against – are one-size-fits-all. That is, they are pre-determined by their
age, and by the time of year. Some differentiation happens, but only as a way to get students
to meet that same one-size-fits-all outcome in different ways. The outcome itself is never
questioned. This is not tailored to each student’s need, and students are not learning
different mathematics at the same time.