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

problem-solving skills.

## 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.

## Deep understanding

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.

## Continuum learning

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.