Maths Mentor Program
Russell Feben and Garry Chapman
Ivanhoe Grammar School, Victoria
Abstract
The Maths Mentor program was initiated to provide an engaging and challenging enrichment program for upper
primary students with mathematical ability in a technology-rich school setting. Extended units of work aim to build
students’ understandings about real-life subject matter before they undertake authentic mathematical investigations.
The use of rubrics for assessment enhances the program. Senior secondary student mentors assist with tutoring.
Each of the mathematical investigations involves structured, yet open-ended problem solving. A wide range of uses
of software applications is an integral part of the program. We will demonstrate aspects of the program through the
use of several units of work. Work samples will be used to illustrate how students respond to the program.
Background
Buckley House is a co-educational primary school campus of Ivanhoe Grammar School. Students are
required to have their own notebook computers from the beginning of Year 5.
In our upper primary classes, we have a fairly typical spread of student ability. While the majority are
working at or slightly above the expected level, some are yet to achieve this level and receive special
support aimed at boosting their mathematical competencies. We also have a number of students who
display special talents in this subject. They are working well beyond the expected level, and display
aptitude in mathematical thinking and problem solving.
We felt that our regular classroom mathematics programs did not go far enough in catering for these
students. We wanted to develop a mathematics enrichment program which could extend and challenge
these children.
Parameters
We established some parameters for the program.
It had to have relevance for our students, based on authentic tasks. The content of the units had to also be
of interest to young adolescents. We wanted them to understand ways in which they might engage with
real life mathematics problems.
We wanted to plan extended units of work, based on constructivist pedagogy. We believed that in order to
fully understand and engage with the mathematics investigations, students would need to undertake some
preliminary learning which may not necessarily be mathematics-based.
We thought the program should promote risk taking and problem solving behaviour and should allow for
open ended outcomes. Activities should be of interest to both boys and girls and, where possible, choice
should allow students to pursue different interests and learning styles.
We wanted to ensure our lessons catered not only for the mathematics discipline, but also aspects of the
personal learning and interdisciplinary strands of the Victorian Essential Learning Standards, covering
aspects of design and creativity, thinking and communication.
As our students all have their own notebook computers and our classrooms are equipped with wireless
networking, ceiling mounted projectors and screens, we believed it was essential that our program utilised
this technology in effective and engaging ways.
We were determined to provide an assessment model which covered not only the mathematical learning of
the project, but also provided feedback on other aspects such as engagement with the topic, presentation
and creativity. It had to assess both process and product.
And, of course, we were keen to develop units of work which our students would enjoy. These units had
to engender a love of learning as much as they had to challenge mathematical minds.
Mentors
As we belong to a P-12 school, we have access to assistance from secondary students who perform
community service when our enrichment classes were scheduled. We arranged for the support of a small
number of mentors who would visit our class each week and help our students with their tasks. We
believed that our students would benefit from the assistance of senior mentors who were skilled
mathematicians themselves.
Composition of the Group
The student group comprises between 20 and 25 students from Years 5 and 6. They are selected from a
group of students who have been identified by their class teachers as being capable mathematics students.
They must then demonstrate an ability to take risks and tackle challenging problems through their
performance in a pre-test. Regular monitoring of students both within the enrichment group and in
classrooms leads to occasional changes in group composition during the school year.
Units of Work
We vary the topics of every unit so that each is quite different from the previous one in terms of the
subject matter, the mathematics used and the software applications used. Last year our topics included
pattern, statistics, planning a dinner party and mobile phones. We began this year with the mathematics of
the human body and followed this with a kitchen design unit.
We aim to build understandings through a carefully structured sequence of activities as each unit
progresses. We plan a sequence of lessons together, then create a document which details the weekly
activities and contains links to relevant websites and documents. It also contains the assessment rubric.
This is placed on a public drive where all students and mentors can have easy access to it.
The first session of each unit aims to tune the students in to the unit and provide some background
information. In the first session of the mobile phone unit, we wanted our students to understand what
mobile phone capabilities were and ways in which people use them. Students were offered choice – they
could use Inspiration to show the many different ways people used mobile phones, use a publishing or
word processing program to compile a glossary of mobile phone terminology, or use an appropriate
program to label the different working parts of a mobile phone and identify their uses. Each student then
completed a survey on personal mobile phone use and emailed it back to us.
The second week of most units is working with data. In the mobile phone unit, we gave students the
compiled data from the previous week’s survey. They were asked to find some statistics of interest,
represent them in a spreadsheet, graph them, then write explanations of what they observed and what
implications this might have for mobile phone use.
In this unit, it was also necessary to develop an understanding of user profiles, so we asked the students to
investigate the difference between the needs of teenage and adult phone users. We also asked them to find
out the difference between pre-paid and fixed term plans and to complete graphic organisers listing the
advantages and disadvantages of each.
The mathematics investigation usually takes place over two weeks. The mobile phone unit’s major task
was to find the best plan for a teenage user and the best plan for an adult user. They were asked to base
their decisions on the user profiles they had developed and to compare three different providers’ plans.
They had to create comparison tables and rank each plan as 1, 2 or 3 against a range of criteria. The
senior mentors help our students to find better ways to organise data, to sort out what is important from
what is not, and to set up tables and spreadsheets to best represent this data.
Following the investigation, we usually allow a week for completing unfinished work. This allows time to
tidy up presentations, finish time-consuming tasks, seek feedback from mentors and share ideas with
others. It also allows us to check that all students will be ready to submit their finished work one week
later.
The final week of each unit is for presentation, allowing students an opportunity to display their finished
work onto the screen and present it to their peers. We use this time to highlight problem solving strategies
used, creativity and presentation, ideas which others might find useful, etc.
Our students submit their finished work via email. We assess it, using the rubric, and provide feedback
prior to commencing the next unit. We spend time with each student discussing their work and explaining
how we rated their work against the rubric.
Assessment
We developed a rubric which provided feedback on many different elements of the students’ performance,
including ability to gather and interpret data and ability to develop mathematical understanding, but also
dealt with important aspects such as engagement, spelling and punctuation, presentation, creativity, and
ability to meet work requirements. It assesses both process and product. Additional points are gained by
exceeding the basic work requirements.
We have been quite astounded by the results the rubric has helped us to achieve. Because our students
understand that the process and the product are both assessed, their levels of engagement and achievement
have risen considerably. The feedback from earlier projects has motivated them to work harder in areas
requiring improvement. Many students also use the rubrics for self-assessment.
Issues
A number of issues have arisen throughout this project, but we have overcome most of them.
Perhaps the biggest problem was getting the composition of the group right. Our first group comprised of
students identified by classroom teachers as being capable mathematics students. Some of these students,
however, did not handle problem solving well. The introduction of a problem solving pre-test has since
helped us to identify the students best suited to a problem solving enrichment program.
The opportunity to use senior students as mentors was appealing. We believed our talented
mathematicians would benefit from working with like minded senior students. Unfortunately, not all
student mentors have been as keen to participate or as skilled mathematicians or communicators as we
would have hoped. We aim to improve the methods in which our program requirements are
communicated to senior students in future, so that we are able to recruit skilled mathematicians who will
become willing participants in the program.
Another issue was the feedback we received from some students who felt that there wasn’t enough
mathematics in the program. They expected to do little more than solve algorithms every week. They
didn’t appreciate the importance of developing related understandings, and often lacked confidence in
solving open ended problems. The feedback provided by rubrics and an improved selection process have
since resolved this issue.
The units are quite complex and require considerable effort. The final products students must submit
reflect six weeks of learning. Initially we had problems with incomplete submission of work. We
resolved this issue with the introduction of a rubric which made explicit the importance of engaging with
the topic throughout the unit, completing all work requirements, going beyond the minimum expectations,
etc.
Interruptions to the program are frustrating and break the flow of the units. Swimming programs, class
excursions, school productions and other events led to one or more year levels being unavailable on a
number of occasions in the first semester of this year. This caused units to drag on too long and students
lose a degree of focus. Rescheduling of some classes and some events was helpful, but the long term
success of the program depends on us being able to find a slot in the weekly timetable which is likely to be
left alone in future. We are working on it.
The Future
The future looks promising for this program. We feel we have established something which will become
a permanent feature of our upper primary curriculum. We believe it engages and challenges our talented
mathematicians and allows them to immerse themselves in extended mathematical investigations.
We feel that elements of these units of work could be adapted for classroom mathematics programs, which
would allow all students in the upper primary to also participate in extended investigations. The units
allow multiple entry and exit points, making it possible for less able students to also enjoy them and
achieve success.
We have shared our ideas, planning and resources with our colleagues who teach mathematics at lower
secondary level. They are interested in the possibility of running a similar program for talented
mathematics students at Years 7 and 8. There are timetabling and staffing issues to overcome, but the
entire transition process is currently under review and programs such as this are viewed as ways in which
we might help to bridge the gap for students moving from primary to secondary school.
We would be happy to share aspects of our units of work with teachers in other schools. Please contact us
if you would like to see some of the units.
Russell Feben (Curriculum Coordinator, Buckley House, Ivanhoe Grammar School)
russell.feben@igs.vic.edu.au
Garry Chapman (Assistant Director of Curriculum, Ivanhoe Grammar School)
garry.chapman@igs.vic.edu.au