Interdisciplinary Maths and Science Findings

(January 2019)

During 2018 the IMS team worked with three schools in Melbourne and Geelong, with 12 teachers spread over classes at grades 1, 2/3 and 4. At each cohort level we worked with all teachers who collaborative planned with the research team and monitored and discussed approaches to teaching as they went along. As a research team we also visited regularly, videotaping classes, collecting student work, and interviewing and discussing next steps with the teachers.

During the year we produced lesson sequences in three distinct topics, with versions for each of the cohort levels. The topics were:

Modeling motion: Measurement of constant motion; representing relationships between distance, speed and time; motion down a ramp. The mathematics was concerned with data measurement and variation, and graphical representation and relationships.

Ecology: Living things in the schoolground: Investigating and counting living things in different parts of the schoolground. Sampling using plots in different habitats. Representing and comparing data for different organisms. Investigating and explaining variation. Animal adaptation. In the grade 1 classes this unit was linked to the PC schoolyard safari module.

Astronomy: Tracking shadows over the day. Movement of the sun from an earth perspective. Day and night from a space perspective. Movement of shadows due to the earth’s rotation. The mathematics related to spatial reasoning; angle, rotation, length.

Working with teachers: publishing the units

For each unit sequence the team initially produced a draft, linked to the curriculum, and then drew on the expertise of the teachers to refine the approach, for each year level. Teachers provided advice on how best to structure the teaching, so that for grades 1 and 4 although the shape of lessons was similar, they were different in the detail of what was covered and the pace. As the lessons proceeded teachers adapted the approach to their particular styles and to students’ learning needs.

Each year we will be producing the refined units, with student work and teacher comment on teaching strategies, for the resources section of the website.


Findings

Teacher practice

Teachers were generally very enthusiastic about the units regarding both the engagement of students, and their learning. Detailed findings over the three years of the project will be published in a series of conference papers and journal articles, but here we summarise an overview of teacher responses, from interviews, regarding the units:

  • Teachers found that students looked forward to these lessons which involved active inquiry and creation and discussion of representations
  • The lessons often took longer than expected because the open questioning approach and scaffolding of discussion around students’ ideas and productions took time. This was considered a really valuable part of the approach but needed to be accommodated time-wise.
  • Teachers were also generally enthusiastic about the approach which involved targeted scaffolding and discussion of student productions – diagrams, maps, tallies, tables and graphs of different kinds, explanatory text – and they found that students (Grade 1 in particular) achieved an impressive level of competence in graphical representation in particular, during the motion and ecology units. They were impressed how in these comparative discussions of student work, children learnt from each other ‘more so than from me as a teacher’ – supported by careful guidance.
  • They felt that the enhanced performance of children in graphing was related to the fact that the graphical representation was of their own, real data and therefore had a purpose.
  • Teachers came to understand and appreciate the links between the units in that they were centrally concerned with student invention of representations /models, and understanding of the purposes of modeling including graphical work.

Student experience and learning

Modeling motion

Students developed their skills in understanding the nature of motion and how to represent motion in different ways. Grade 4 children developed graphical modeling skills tracking the ability of the class to walk a constant rate over 8m, and testing whether a probot travels at constant speed.

Ecology of the schoolground

During the ecology unit Grade 1 students developed graphical ways of representing the count of different living things in their plot, and then graphed each particular species across the different habitats. Children developed their graphical skills considerably.

They developed a class chart that mapped their habitats onto a map of the schoolground, and displayed living things counts in each and commentary on how animals were adapted to

  • Teachers at both schools noted that there were students, including EAL students and children with processing or learning difficulties, who achieved beyond their expectations within this unit.
  • Teachers felt that the unit had deep learning and understanding outcomes.
  • Year One students were increasingly confident with graphing at both schools.
  • Students requested to show their work, with a clear sense of pride and increasing efficacy. An example of student dialogue:
    “I wasn’t feeling good about what I was doing. I didn’t know what I was doing, now I do. I know how to do a clear graph; can I show you?” (see example of change for one student, below)

Grade 1 graphs

Astronomy

Students spent a day tracking their shadows on the asphalt using a chalk outline, linking this to the apparent movement of the sun in sky – rotation and angle, and linking the sun’s position with the position of the shadow. The changing length of shadows was tracked by a variety of means. A gnome was placed in the yard and it’s shadow traced on poster paper at regular intervals, giving a sense of the continuous change in length and directions. This could then be used in the classroom to model the change in the sun’s position using a torch, and to show how the same results could be had if the earth (poster paper) moved and the sun (torch) remained still.

A presentation of the earth’s rotation using video animation was shown and children played with globes and torches to model their shadow results.

  • Children achieved a confident sense of the spatial relation of their shadow movement to the sun’s movement in the sky
  • They were confident to describe night and day as being caused by the earth’s rotation. For the grade 1 children the link between shadows and the globe’s movement was difficult to comprehend. Grade 4 children were much more ready to apprehend these relations.
  • The pre-post test showed significant learning gains for the Grade 1 students. The Grade 4 students had strong pre-test results so the growth was not as clear.