Southern Cross University (SCU) educators and local teachers have developed a fivelesson instructional sequence built around fluke identification as a way of resolving the question: How fast do humpback whales travel up the east coast of Australia?

Introduction

Every year, humpback whales move up and down the east coast of Australia from their feeding grounds in the Antarctic to their breeding grounds in tropical waters of eastern Australia, near Hervey Bay in Queensland. Peta Beeman, a research student at Southern Cross University (SCU), is recording the patterns of whale flukes, the powerful swimming fin or tail of a whale. (Figure 1 shows a breaching humpback whale.) The pattern of each fluke is distinctive for each whale and, when people send images to Peta, she is able to process them using pattern recognition software called Fluke Matcher. This allows Peta and her team to recognise where each whale is at a particular time.

In 2014 SCU initiated a team project that developed resources for teachers and school students designed to involve them in real-world investigations being undertaken by some of our scientists. Peta worked with a team of university educators and local teachers to develop a five-lesson instructional sequence built around fluke identification as a way of resolving the question: "How fast do humpback whales travel up the east coast of Australia?" (1) The idea was for students to go through similar processes to a scientist who was trying to answer this question, to see how they would respond to being involved in a real-world scientific inquiry.

Why tail flukes

There were several reasons for presenting students with this problem. One was that there was a lot of information already available about humpback whales. A team led by Daniel Burns at the Marine Ecology Research Centre, a SCU centre with researchers based at Coffs Harbour and Lismore NSW, had already documented the migration of humpback whales and their behaviours during their journey up and down the migratory corridor off the east coast of Australia (Burns et al., 2014). It was this team that developed the Fluke Matcher software, using it to identify whales from their fluke patterns--scars and pimentation patterns which act like fingerprints due to their uniqueness for each individual (Figure 2) (2).

Humpback whales had been part of a once-flourishing industry based at whaling stations along the migration route, including near the modern-day observation point at Byron Bay, which is as far east as the Australian coastline extends. Humpback whale numbers were estimated to be as low as 100 when whaling ended in the 1970s, but numbers had increased to 10,000 in 2015 (Bejder et al., 2016) and Peta has reported that numbers are expected to be more than 30,000 in 2018. Whale watching is now a major tourist attraction and people flock to various places along the east coast to observe them in the wild, particularly at Hervey Bay (Queensland), where the whales stay for up to two months, mating and giving birth to young calves before their return to the Antarctic.

Peta's question was designed to find out how fast the whales travelled on their migration. This included considering the questions: Do they travel at a constant speed?, Do they vary their speed at night?, Do they all leave Antarctic waters at the same time?. Knowing that fluke identification could be used to log the whales' journey, Peta invited contributions of fluke images from whale watchers all along the east coast of Australia for the East Coast Whale Watch Catalogue, a citizen science project. Since images uploaded also note a date and location, identification in Fluke Matcher allows her to create a catalogue that shows an individual whale at particular times during its journey up and down the coast.

Analysis of photographs of flukes, such as those contributed by people on whalewatching boats, enable researchers to identify individual whales in repeated sightings from year to year along their migration path (Figure 3). The catalogue has been used to analyse data on over 1000 humpback whales (between 2005 and 2014) enabling researchers to obtain valuable information about life histories, population size, migration timing, travel speeds, movement and association patterns (who swims with whom, and when).

Whale tail lessons

The topical issue of whale migration was included as part of the Regional Universities Network's (RUN) (3) Digital Classroom project conducted from 2013 to 2015. The aim of this project was to bring scientific and mathematical research into the secondary classroom, using collaborations within each of the six universities of RUN, and with teachers and secondary school students within each university's educational footprint. Peta's research question was considered a good example of how science and mathematics (4) could be integrated across a real-world problem, using appropriate levels of knowledge, skills and experiences from each subject. The five-lesson whale migration sequence is shown in Table 1, although it can easily be reconfigured to take up more or less time in a school program.

Each lesson plan provided an opportunity for an instructional practice based on student-centred inquiry around a central goal statement, rather than an expositional or didactic framework (teacher explaining and students listening). In this way student participation can be optimised verbally and through interaction with peers as well as with the teacher. The lesson materials provided opportunities for students to develop their own conclusions individually and in groups, and compare them with those of their peers and their teacher.

A focus on spatial reasoning

Although real-world problem solving was the central focus of the five-lesson whale sequence, several of the study components (lesson plans and resources) in the first two lessons incorporated spatial reasoning. A number of studies have focused on the importance of spatial reasoning (or spatial thinking) in secondary schools, as well as its importance in STEM (Wai, Lubinski, & Benbow, 2009). Importantly, Uttal et al. (2013) have shown that spatial skills are malleable, that is, they can be taught. Although the use of spatial skills is integral with human-lived experience and spatial negotiation in a 3D world, school curricula have only recently begun to recognise the value of teaching that encompasses these skills (Bruce et al., 2017).

The first two lessons in the sequence have a strong spatial skill component: lesson one is dedicated to students finding a way to identify whales from patterns on their tail flukes; and lesson two is dedicated to using spatial information to document the whales' journey and their speed of travel. The two lessons involve categories of spatial skills in teaching tasks described by Uttal et al. (2013) as either intrinsic or extrinsic, and as involving either static or dynamic tasks (see Figure 4).

'Intrinsic' specifies the parts of an object and their relations whereas 'extrinsic' refers to the relations among objects in a group. 'Static' refers to fixed information and 'dynamic' refers to objects that are moving or moved, or viewed from a moving reference point. The classroom identification process required that students synthesise and differentiate the patterns represented in a set of given whale fluke images, as well as visualise the identification patterns. In other words, students combine elements from several sources to identify a commonality in pattern, but also separate elements according to difference to determine which fluke patterns are different. The second lesson, to do with the whales' speed of travel, required that students use identification data as well as annotated maps of travel pathways.

How did this work in the classroom?

The lesson sequences, along with the associated resources, were trialled successfully in several schools in the SCU region. The researcher acted as a passive observer in each lesson of the sequence, but took extensive notes during the lessons. At the end of each lesson the researcher interviewed the teacher, engaging them in discussion of how the lesson was received. A summary of the first two lesson outlines in the sequence is provided in Table 2.

Lesson observations

Lesson one: Fluke matching

Classes were not accustomed to this type of real-world inquiry (even though an expectation of the curriculum) but teachers were interested in seeing how students handled an issue clearly relevant for them through their familiarity with, and interest in, whales and whale migration. In the first two parts of the lesson, teachers employed the lesson format as recommended, with the introductory video followed by Whale Fluke Bingo done in competing groups: some of the flukes shown by the teacher have images matching those in the image set provided to each group. Teachers asked students how they identified similar whale flukes in the game and provided information from university scientists to confirm student responses.

The third part of the lesson, also conducted in small groups, engaged students in using the images and an acetate grid (unit squares) to find percentages of dark or light pigmentation (Figure 5). Teachers used the fourth part of the lesson, as recommended, for a guided discussion around the similarities and differences in fluke patterns that could be used for identification.

Lesson two: Whale travel

Each teacher used the given lesson materials to develop this part of the investigation in different ways. Despite having a narrative context for the whale journey, students experienced particular difficulty in interpretation of the visual material on the maps provided. Students also had difficulty in trying to provide reasons for changes in whale speed and how this related to latitude markings (see Figure 4 right-hand images). The teachers used a diagram from Burns et al. (2014) showing a map of the migration as well as locations and times (summarised in Figure 4). The materials provided were designed to assist in interpretation of a diagram representing the entire journey of Migaloo (an albino whale with a dedicated fan base and website, migaloo.com.au) and an 'average' whale, through use of partially completed interpretative tables.

What does this say about spatial reasoning?

In this section, we are looking to examine what spatial reasoning skills were integral to each lesson. Clearly the scientists working on this problem had an excellent command of the skills required to answer their real-world research questions. In observing student activities in lessons one and two, we were able to see what spatial reasoning skills students already had and what skills they were yet to obtain, at least in this problemsolving context. The spatial reasoning skills indicated in Figure 4 can be organised into four categories as outlined in Table 3. In observing student behaviour we focused on the four combinations of: intrinsic-static; intrinsic-dynamic; extrinsic-static; and, extrinsic-dynamic.

Lesson one: Fluke matching

In the whale problem context of lesson one, intrinsic refers to spatial activities that involved describing objects, such as pigment markings or scars, tail or fin shape and edge markings on the whale flukes. The patterns on the fluke did not change with respect to each other and hence were considered static. There was almost no requirement in lesson one for students to consider objects that were dynamic, for example, in predicting what the fluke might look like if it was seen from another angle. Extrinsic here refers to spatial activities where the students determined relations; in lesson one these were the relations between the flukes, fluke shapes and markings.

In the trials, students were able to refer to intrinsic-static features, such as overall shape, the colour and shape of distinctive markings from fluke images provided, as well as edge patterns, including scarring. In the exercise with acetate grids (Table 2 and Figure 5), many students were also able to calculate relative percentages of coverage of black or white patches, and some students were also able to recognise symmetry in the fluke markings. Extrinsic-static features recognised included patterns of configurations of shapes and colours within the fluke. Some students were able to additionally recognise these in the same fluke in a different position. Although there was little opportunity for observing dynamic spatial reasoning skills in lesson one, a few students (three or less) were able to model an identity pattern for a whale fluke and use this to identify whales from twisted or rotated fluke images. These students were also able to predict the distance of the same fluke viewed from a greater distance, by comparing the sizes of the grid of black or white areas on current images.

Lesson two: Whale travel

In lesson two the exercise was essentially dynamic, developed around graphing spatial positions and predicting time of travel and spatial position against a pattern of differing sets of information that served as a distraction. The static object was the map of eastern Australia showing degrees of latitude in only some parts of the journey, with lines showing the migratory path of the humpback whales, and duration markers (directional arrows) showing travel times, north and south, between the given latitude lines. For example, for the breeding range of the whales (latitudes 21[degrees]S to 15[degrees]S), the duration markers indicated travel times up and back as 2.5 weeks for the average whale, but 1.1 weeks for Migaloo.

Most students were able to interpret that the intrinsic-static features of latitude lines (degrees) and duration markers (weeks) on the resource sheet (annotated map) were members of a spatial category, such as static-extrinsic (although they did not need to know the names of such categories). The difficulty arose from the irregular spacing of the latitude lines and duration markings (Figure 1, top right image). The intrinsic-dynamic skills were less often observed where the skill needed was to transform the spatial codings of latitude and duration to predict whale positions for either the average humpback or for Migaloo. Most students had difficulty in interpreting the latitude lines in relation to time travelled and, hence, did not generally demonstrate this skill.

In lesson two, extrinsic refers to spatial activities where the students determined relations between a whale's location relative to other whales, or to the latitude and time markings, or places labelled on the map. Demonstration of extrinsic-static features required that students relate latitude of whale sighting to travel time, which was not in equal increments (e.g., a relatively long time in the breeding area). Few students were able to estimate distances between locations of the map by spatial partitioning, or to convert degrees to kilometres as required in this activity, even when the teacher provided exemplars for this context (for Migaloo). When provided with a completion table (Table 4) over the route taken, students fared better and were able to convert the information to a distance/time graph. The extrinsic-dynamic category was even more difficult. Students needed to predict the position of a whale based on the slope of a distance time graph derived from the sighting data and only three students were observed to do this.

How did teachers overcome the difficulties in lesson two?

Teachers reported that, although they had conceived this lesson as having a group activity component, the difficulty of the interpretation of these kinds of largely extrinsic spatial skills was best dealt with as a teacher-guided activity. One teacher, for example, prepared additional graphs and projected these from her laptop for the whole class to view. These graphs related to translating the distance travelled in given time periods and using this to compare parts of Migaloo's journey with that of an average whale.

One of the issues apparent from the lesson observations was that most students did not appear to have sufficient prior knowledge related to the map context and were consequently unable to engage completely with potential solutions to the problem. As the teachers indicated, prior knowledge of both spatial and non-spatial skills in such contexts may have assisted students in identifying and using latitude measurements to calculate distances. The lessons also required an overlap of cognitive functions, for example, integration of spatial skills with calculation or reading skills. Students, however, seemed to understand the nature and context of the problem, even where they were not always able to use the data provided for its resolution.

Conclusion

Overall, the project was successful in engaging world-class researchers, specialist educators, teachers and students in co-creation of digital teaching resources based on real-world problems and up-to-date solutions. The 'tail of a whale' lesson sequence is of particular interest to mathematics teachers since it is one of the few resources that aligns elements of the Australian Curriculum in both science and mathematics for Years 9 and 10. Some of our teachers have shown, however, that the whale lesson sequence can be separated as lessons for Years 7 to 10. The financial mathematics required for Lessons four and five are best suited to Years 9 and 10, as is the analysis of sound graphs in Lesson three.

Our trials of Lessons one and two indicated that our students may need a stronger background in spatial reasoning skills, albeit in a context of particular problems. A broader view of spatial reasoning skills across the curriculum may benefit from the overarching view, at least from the viewpoint of school learning, that all students may have skills that are based in their lived experiences in the 3D world, but which need to be adapted to the contexts required in school subjects. The approach taken in developing this lesson sequence suggests that spatial reasoning skills can be built into classroom problem solving, with motivational aspects provided by use of real-world contexts that are familiar to the students.

Acknowledgement

The Australian Government funded project, Regional Universities Network (RUN) maths and science digital classroom: A connected model for all of Australia (the RUN Digital Classroom), involved participants from the Regional Universities Network (RUN) and three associated organisations working with community-based educators and secondary school students within the educational footprint of each RUN institution. RUN is based in eastern Australia and comprises Southern Cross University and the University of New England in New South Wales, Central Queensland University, the University of Southern Queensland and the University of the Sunshine Coast in Queensland, and Federation University Australia in Victoria. The organisations involved in the collaboration were the Commonwealth Scientific and Industrial Research Organisation (CSIRO), the Australian Mathematical Sciences Institute (AMSI) and the Primary Industry Centre for Science Education (PICSE). These lesson sequences are available, along with the other educational resources developed for the Virtual Centre, on http://www.usq.edu.au/research/ research-at-usq/institutes-centres/adfi/digital-classroom.

References

Bejder, M., Johnston, D. W., Smith, J., Friedlaender, A., & Bejder, L. (2016). Embracing conservation success of recovering humpback whale populations: Evaluating the case for downlisting their conservation status in Australia. Marine Policy, 66, 137-141.

Bruce, C., Davis, B., Sinclair, N., McGarvey, L., Hallowell, D., Drefs, M., Francis, K., Hawes, Z., Moss, J., Mulligan, J., Okamoto, Y., Whitely, W., & Woolcott, G. (2017). Understanding gaps in research networks: using spatial reasoning as a window into the importance of networked educational research. Educational Studies in Mathematics, 95(2), 143-161.

Burns, D., Brooks, L., Harrison, P., Franklin, T., Franklin, W., Paton, D., & Clapham, P. (2014). Migratory movements of individual humpback whales photographed off the eastern coast of Australia. Marine Mammal Science, 30, 562-578.

Newcombe, N. S., & Shipley, T. F. (2015). Thinking about spatial thinking: New typology, new assessments. In J. S. Gero (Ed.), Studying visual and spatial reasoning for design creativity (pp. 179-192). Netherlands: Springer.

Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological bulletin, 139(2), 352-402.

Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817-835.

What makes a good fluke photo?

* Photo must show the underside surface of the fluke.

* Focus and contrast should be sharp enough that the markings can be clearly seen.

* The angle of the fluke should not be so sharp that the markings are obscured.

* At least 50% of the fluke should be showing above the waterline.

* Photos should be high resolution, saved as digital files (e.g., .jpeg or .tiff files).

To contribute photos to the East Coast Whale Watch Catalogue, please use the online form at www.eastcoastwhales. com.au

Geoff Woolcott

Southern Cross University, NSW

<geoff.woolcott@scu.edu.au>

(1.) Although travel speed was an important part of Peta's study, its overall focus was looking at patterns of migration timing, such as year-to-year consistency, and residence time in the northern and southern termini of the migration.

(2.) Similar software can also be seen at https://happywhale.com/.

(3.) The Regional Universities Network (www.run.edu.au/) is based in eastern Australia and comprises Southern Cross University (SCU) and the University of New England (UNE) in New South Wales, Central Queensland University (CQU), the University of Southern Queensland (USQ) and the University of the Sunshine Coast (USC) in Queensland, and Federation University Australia (FedU) in Victoria.

(4.) This paper focuses on mathematics and science but recognises that this focus may lie within the overall framework of Science, Technology, Engineering and Mathematics (STEM).

Caption: Figure 1. A breaching humpback whale on its migration north, seen off the coast of New South Wales.

Caption: Figure 2. Peta used Fluke Matcher to identify a humpback whale from the pattern on its tail fluke.

Caption: Figure 3. What makes a good fluke photo?

The photos to the right, are of the same whale travelling south near Ballina in 2004 (left) and then again in Byron Bay in 2009 (right).

Caption: Figure 4. Illustrations of the four categories that combine the intrinsic/extrinsic and static/dynamic categories of Uttal et al (2013).

Caption: Figure 5. A whale fluke image being examined for patterns using an acetate grid of unit squares.

Caption: Over 50% of fluke submerged.

Caption: Oblique angle, low contrast.

Caption: Markings clearly visible.

Table 1. The lesson sequence for the whale migration research
question.

Lesson one     How are whales identified? Whale fluke
                 patterns as identification criteria.
Lesson two     How can we identify how fast individual
                 whales are travelling? Using
                 rate/ratio, latitude and longitude.
Lesson three   Whale-song graph analysis.
Lessons four   Tourist Operator Analysis--investigating
  and five       the tourism industry surrounding
                 whale sightings.

Table 2. A summary of the four parts of each of the first
two lessons in the Whale Fluke sequence.

Lesson 1: How are whales            Lesson 2: How can we identify
identified? Whale tail Bingo.       how fast  individual whales are
                                    travelling?

Part 1. Presentation and            Part 1. This lesson involves
  introduction of the                 looking at how fast whales
  question.                           travel up and down the east
Research background in the            coast.
  form of a five-minute video,      The teacher introduces using
  presented by the project            diagrams outlining the
  scientist, on humpback              movements of whales from
  migration and identification.       their Antarctic feeding
                                      grounds to their breeding
                                      grounds near the Great
                                      Barrier Reef off
                                      Queensland.

Part 2. Identification of           Part 2. Calculating distance and
  matching and non-matching           time of travel. Students, in
  tail flukes.                        pairs, interpret the resource
Whale fluke bingo using a set         sheet information to obtain
  of 50 printed  whale fluke          distance and time data and use
  images. The teacher displays        it to complete a table
  ten images on a                     provided. Table to be completed
  projector/screen and students       for both Migaloo and for the
  work to match their group's         average whale'.
  images with those displayed.      The sheet shows the east coast of
  Played as a game with three         Australia and extends to the
  correct matches of flukes           Antarctic waters. The latitude
  being a win for a team.             lines, labeled with degrees,
Teacher then encourages               are included for significant
  students to note how the            locations on the map. The
  identified image was the            teacher presents the key
  same:  What markings,               question:
  shapes, etc did they use?         What assumptions/approximations
                                      about time must we make about
                                      residence times to get travel
                                      times for both the feeding
                                      range and the breeding range?

Part 3. Calculating the             Part 3. Constructing travel
  estimated area of a fluke.          graphs.
  Teacher/students overlay          Students, in pairs, interpret
  fluke images with an                Figure 3 in the resource sheet
  acetate grid. Teacher               to obtain distance and time
  demonstrates how to                 data and use it to complete
  calculate the area with a           the travel graphs for both
  grid. Teacher presents              Migaloo and for the 'average
  key questions:                      whale'.
How can we calculate the
  percentage of dark
  pigmentation using the
  grids acetate? What area
  of the whale fluke was
  black? White? What
  percentage was white or
  black?

Part 4. Teacher-guided group        Part 4. A teacher-led discussion
  discussion around two main          Using the graphs, interpret
  questions.                          the slopes and identify the
How can we use the information        fastest segment and slowest
  collected to build a model          segment of the whale's journey.
  for identifying whale flukes?       Students examine and interpret
  Can we generate a rule,             their graphs to determine the
  pattern, or set of guidelines       fastest and slowest segments of
  for identifying whale flukes?       the trip. The teacher presents
                                      the key question:
                                    What factors could influence the
                                      speeds at which whales travel?

Table 3. The four categories of spatial reasoning skills adapted
from Newcombe and Shipley (2015).

                    Category of spatial skill

Intrinsic-static    Coding the spatial features of objects,
                      including their size and the arrangement
                      of their parts i.e., their configuration
                      (e.g., to identify objects as members of
                      categories).
Intrinsic-dynamic   Transforming the spatial codings of objects,
                      including rotation, cross-sectioning,
                      folding, plastic deformations (e.g., to
                      imagine some future state of affairs).
Extrinsic-static    Coding the spatial location of objects relative
                      to other objects or to a reference frame
                      (e.g., to represent configurations of objects
                      that constitute the environment and to
                      combine continuous and categorical
                      information).
Extrinsic-dynamic   Transforming the inter-relations of objects as
                      one or more of them moves, including the
                      viewer (e.g., to maintain a stable
                      representation of the world during navigation
                      and to enable perspective taking).

Table 4. Migaloo's journey compared with an average humpback
provided as part of lesson two.

              'Average' humpback whale migration patterns

                            Distance    Degree      Time        Time
Location                     from      latitude    between      since
                             origin                 points      start

Feeding range                             70       25 weeks    0 weeks
Top of feeding range                      60
Feeding range to Ballina    3500 km       29       9 weeks
Ballina to Hervey Bay       1000 km       21      2.5 weeks
Breeding grounds                          15       4 weeks

                         Migaloo's migration patterns

                            Distance    Degree      Time        Time
Location                     from      latitude    between      since
                             origin                 points      start

Feeding range                             70      28.6 weeks   0 weeks
Top of feeding range                      60
Feeding range to Ballina    3500 km       29       4 weeks
Ballina to Hervey Bay       1000 km       21      1.1 weeks
Breeding grounds                          15      11.7 weeks

Note: 1 degree latitude represents approximately 112 km