True north: Setting your bearings with surveying

By Bryan Morrison, Mathematics Teacher

This article explains the emergence and evolution of one of the Pymble Mathematics Department’s most iconic assessment tasks – the surveying task. This learning activity was designed by Bryan Morrison and Miriam Tenney more than 15 years ago and is still engaging our students in a very practical way in abstract mathematical concepts.

Many Pymble students and staff have witnessed Bryan and colleagues over the years as they have set up and conducted the task with students on Lang Lawn with clipboards, compasses, iPads and calculators in hand. In 2019, the Mathematics Department worked together in Reflect-ReviewRenew Professional Learning time on the topic of assessment and used the surveying task to look at ways to continue enhancing the learning experiences of our students.

THE SURVEYING ASSESSMENT

Miriam Tenney and I started forming the task in 2004 in anticipation of using it as a Year 12 assessment. The task comprised two parts; a rightangled Trigonometry problem (where students calculated the height of a flag on the flagpole, the drop of some blinds on the Colonnade Building or calculating the height of the Chapel spire), followed by a non-right-angled problem, involving a radial survey of an area set in probable scenarios (such as reto work and co-operate with

turfing a lawn, making a carpark or a helicopter pad). Following a Board of Studies (BOS) directive to develop different styles of assessment, our task was expanded to encompass the ideas of the curriculum and outdoor mathematics. We decided that instruction would take place in the outdoors environment where students would learn to use the theodolite, tape measures and compasses in order to make the necessary measurements to apply to trigonometric problems. The girls would be broken randomly into teams of four to make the measurements at two to three stations which would be recorded into a field book. Upon completion of the recording of the measurements, the students would proceed to the classroom where they would complete questions and problems based on the outdoor

The teamwork approached encouraged the girls of teamwork, practical application

different students and share their knowledge and acquired skills to get the correct measurements.”

stations. Miriam and I found that over the years, despite the simplicity of our equipment, students consistently attained a high degree of accuracy within the limits of error set for the task. USING THE COLLEGE ENVIRONMENT

We set the stations for this assessment within the confines of the College campus. Initially, we picked basic locations (the flagpole and the Marden Lawn) for our stations. Control of the process required that the stations were not too far apart which assisted with a smooth flow of students between each station and the examination room. Over the years, we developed more ideas for problems to solve and consequently moved to the Main Oval and used other sites such as the Chapel, Lang and Marden Lawns, the Colonnade Building and the Kate Mason Building.

Students working in teams using theodolites for the surveying task

We incorporated into the assessment mathematical tasks involving measuring and surveying carpark areas, designing a helicopter pad for the campus, re-turfing the various lawns, determining the height of the Chapel and the flagpole for repairs, and determining the dimensions of the exterior wall of the Kate Mason building for re-painting.

PHASES OF THE TASK

The task followed the following phases:

To start, there was a planning phase where we decided to either modify a previous task or integrate a new site to consider. A timeline was made to monitor the progress of the task and set waypoints to ensure a smooth transition to completion. Consultation with the teachers of the General/Standard Mathematics courses ensured the topic content would be complete and on time for the assessment. A time for outdoor instruction of the equipment was scheduled for each class or group of classes.

Once the relevant, theoretical content in class commenced, the outdoor instruction also began. It was found that a maximum of two classes at a time could engage in the outdoor teaching program. Alongside the instruction phase, a practice paper was introduced during the lesson to cement for the students the concepts of measuring and the application of Trigonometry. Once it was completed, the students were encouraged to meet with staff if they had concerns or needed further clarification.

Meanwhile, I would measure up the sites and mark up areas ready to install markers and pegs.” Concurrently, the question paper was developed, checked and worked through. A briefing of supporting staff followed and final preparations and checks were made two days prior to the assessments. On the day, the students were given a quick briefing of the proceedings and locations of the sites. The assessment then commenced with staff at the various sites, floating staff maintained flow and supervising staff oversaw calculations in the examination room. Before mobile phones, communications were maintained by walkie talkies (loaned to us by the PDHPE Department or Pymble Security team). As the amount of equipment we used increased, the assessment time gradually reduced in time. Finally, there was a pack up of the sites and marking of the students’ assessment papers.

SURVEYING TECHNOLOGY

Initially, we had only a few theodolites and measuring tapes and compasses but over the years we have acquired a dozen sets of each of the items above. As mentioned, we were able, over time, to reduce the time the task took to complete. Originally, it was not uncommon to take up to five hours to complete the assessment for all the students but now we rarely go past three hours to do the same.

Measurements, on average, take no more than 15 minutes to complete and the students have as much time as they need. Typically, most girls finish the full assessment after 90 minutes. This allows us to require no special provisions as we allow students as much time as they need.

The surveying assessment continues into 2020, marking our sixteenth year of teaching surveying in an outdoor environment to College students.”

However, we have reduced any damage to the theodolites by placing them on plywood triangular bases to steady them and to mark out pegs for the areas. The other key technologies are 30 metre tape measures which are also very robust and Silva compasses which place nicely upon the protractor base of the theodolite to orient it to North. A new means of measuring angles of elevation and depression and taking compass bearings comes with the use of the iPad. A friend of mine introduced a free surveying app. I loaded it onto one iPad with a camera tripod and found it worked quite well. Working with my colleague, Pamela Stott, we further trialled this technology and incorporated it into the assessment. The app worked reasonably well, and the College’s Conde Library team graciously allowed us to use their iPads and loaded the app for us. Issues with the app included an

impact from the external temperature and some interference with compass bearing due to wireless communications across the campus. After two assessments using the app, we decided to return to simpler technology until the interference could be further investigated.

ASSESSING THE TASK

The biggest innovation developed in the task was using an Excel spreadsheet to assist in marking students’ papers as we were quickly about to take into account the wide variation in calculations. A former colleague, Adam Antonio, created the spreadsheet which greatly eased the stress of marking. Since this time, I have modified Adam’s document to take account the variation in calculations of differing scenarios and we have further modified the task to include smaller parts that test the skills and knowledge and yet still utilise the spreadsheet.

CONCLUSION

The surveying assessment continues into 2020, marking our sixteenth year of teaching surveying in an outdoor environment to College students. In recent times, we have been increasingly at the mercy of inclement weather and have relied on a wet weather plan which involves using the master measurements without an outdoor experience. We are now working towards using the Jeanette Buckham Gymnasium and spots on the floor as markers. We continue to develop the task and may improve or re-introduce previous technology to further improve the experience that this task has provided other the years.