First steps to ”The Exploration” in Y11 Mathematics SL

   by Paula Waldman & Estela Valcárcel    


St. Andrews´ students  study throughout Year 11 and Year 12 the International Baccalaureate Diploma Programme. It is a rigorous pre-university course that aims to encourage students to be knowledgeable and inquiring, among other important skills. There are six academic areas in the course; one of them being Mathematics.  One of the three mathematics´ subjects that students can choose at St. Andrews is Mathematics SL.

This project was born at the end of 2012 to accompany some significant syllabus´ changes that affected mainly the internal assessment of Mathematics SL. These changes have been implemented in 2013 and Y11 was the first cohort of students affected. As from this year the internal assessment will consist on writing an individual piece of work that requires investigating an area of Mathematics. This piece of work is called “The exploration”.


This project is strongly related to the IB philosophy on teaching and learning mathematics and particularly linked to “The exploration”. In this context the objectives are in line with those of the IB.

In order to achieve these objectives we have created a series of short investigations. An investigation is a sequence of activities focused on researching a particular mathematical topic supported by an appropriate technological resource.

Aim of the project

To appropriately introduce throughout the course the processes of mathematical inquirymathematical modelling and applications and the use of technology.

Objectives of the investigations

  •  To investigate unfamiliar situations, involving organizing and analysing information, making conjectures and drawing conclusions.
  • To encourage students, where appropriate, to discover, use and appreciate the power of technology as a mathematical tool.
  •  To encourage students to enhance mathematical communication by both choosing and using appropriate ICT tools such as graphic display calculators, screenshots, graphing, spreadsheets, databases, drawing and word-processing software, etc.
  • To be aware of the number of tools that the software Geogebra provides and to use them in different scenarios.

The investigations

The four investigations accomplished during 2013 with the Y11 Maths SL groups (90 students) are the following:


–  “Geogebra activity: functions”

–  “Transformations of graphs”

– “Modelling and Geogebra”

Through these investigations the students had the opportunity to

  •  communicate mathematics in a variety of contexts through the use of correct terminology and/or diagrammatic representations.
  •  develop an understanding of some mathematical principles.
  •  explore the use of the graphic display calculator.
  • work collaboratively to discover new features of the given software.
  • use Geogebra to model set of data points and compare models.
  • explore the software Geogebra and some of its applications.

The mural shown below summarises the process the students went through to achieve these objectives..

(Click the full screen button for a better view)

Students involved in this project

The four Y11 Maths SL groups were involved in this project, which means a total of 90 students.

Teachers involved in this project

The project was created and led by both Paula Waldman and Estela Valcárcel. It was implemented* by the four Y11 Maths SL teachers Lara Sanchez Peña, James Thomas, Paula Waldman and Estela Valcárcel.

Working collaboratively in this project has enriched this Maths SL teacher´s team not only as teachers but also as learners.

*Note: the last investigation “Modelling and Geogebra” was implemented only in two of the groups due to calendar constraints.

 Examples of students’ work

(Click on the images below to see the examples; the last two examples are interactive. Don’t miss the oportunity to see how the students achieved their conclusions!)

Functions                                                  Geogebra &Functions

image              image

Transformations                                         Transformations (interactive)

image                        image

Modelling (interactive)



At this stage of the project we are in the position to say that it has been a very positive experience. Through the different activities students have shown an increasing confidence to use technology and they have also started to understand the meaning of writing mathematics, inquiring and drawing conclusions. The final fruit of this project will be seen by the time the students  have finished writing their own explorations during their second year of the IB course.

Although we understand that this is a subject specific project, we felt that this contest was a good oportunity to show to the St. Andrew’s School Community some of the activities that students carry on in a Mathematics IB lesson.

Paula y Estela

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