This conference was held in Nelspruit from 27th June to 1st July.

We will present a number of workshops:

#### Grade 9 revision: introducing a new approach

*This workshop is about a lesson designed by researchers and teachers to help Grade 9 learners prepare for their end of year examinations. The idea behind the lesson was that it should motivate and involve learners as active participants and at the same time should provide the teacher with information about which areas of mathematics provided the greatest challenge for the learners (so that in future lessons he or she can target these areas).*

*The lesson is designed around the idea of ‘here is the answer, what is the question?’ In this case there are three answers, and the lesson requires learners to work in pairs to work out which questions fit with each of the three answers. *

*The workshop will present the activity to the participants, who will begin by working through it in small groups. They will reflect on their experience and discuss how the activity would provide them, as teachers, with information about their learners’ current levels of understanding in a range of mathematical areas. They will consider how they might use this information to decide what to do next, both within the lesson and in future lessons. *

*To conclude, we will report on how some teachers taking part in our research (FaSMEd) used the lesson and how the learners responded. The whole group will discuss how the lesson can be improved or adapted for different classes.*

#### A formative assessment lesson on multiple representations of algebraic relationships: equations, graphs, tables and rules

*This workshop begins with a brief discussion on formative assessment, also known as assessment for learning. Participants then work in pairs on a lesson that was designed as a ‘formative assessment’ lesson. The lesson requires learners to work in pairs to link the various representations of functions and non-functions: the equation, the rule in words, the graph and a table of values.*

*Participants then discuss the lesson in their pairs, noting the strengths and weaknesses of the lesson both in terms of the mathematics and the teaching approach. Importantly, they also discuss the ways in which the lesson can be seen as a ‘formative assessment’ lesson. *

*As a group, we discuss the participants’ responses and consider in detail how the lesson can be used to promote effective formative assessment. To conclude, we share with participants some experiences of teachers who have already taught the lesson (first-hand reporting from one of the presenters and some video of other classrooms). We also report on the learners’ responses to the lesson.*

*The workshop introduces participants to an innovative approach to teaching graphs and functions, which involves learners in constructing their own knowledge through their discussion and activity.*

#### Linking algebraic equations to real life situations: a card matching activity

*Many learners struggle to make sense of variables when they are introduced in the senior phase. Some never understand why ‘letters are used with numbers’ or why variables are useful in ‘real life’. In this workshop participants will be introduced to a card matching activity that aims to give learners an experiences of using variables to describe ‘real life’ situations and through this, to develop their understanding of variables. The learners work in pairs or small groups to match equation cards with the real life situations; their discussion and the use of cards provide an opportunity for the teacher do formative assessment by giving them insights into their learners’ thinking. The activity has been carefully designed to highlight common misconceptions, for example, the difference between the number of apples and the price per apple. Although it was originally designed for use in American schools, it has subsequently been adapted for and trialled in South African schools where it has been successfully used in both senior phase and mathematical literacy classes in a range of schools. Participants will receive a hard copy of the template to make the cards for this activity.*

#### Geogebra as a tool to introduce and extend the theorem of Pythagoras

*Do your learners know the rule for Pythagoras’ theorem off-by-heart but still fail to apply it correctly? In this workshop we will explore how GeoGebra can be used to introduce the theorem of Pythagoras and to begin to embed an understanding of when and how it can be used. The interactive and dynamic nature of GeoGebra provides learners with the opportunity to explore the relationship between the areas of squares on the sides of many different triangles and therefore to come up with their own conjecture before formally being introduced to the theorem.*

#### Egg boxes and folded paper: low cost materials for introducing fractions and operations with fractions

*This workshop will show you how you can use low cost materials such as egg boxes and paper to help your learners understand fractions and operations with fractions. We will begin by using paper folding to introduce the concept of equal parts of a whole. These folded papers will then be used to introduce addition and subtraction of fractions and the idea that it is possible to have a fraction equal to more than a whole. We will then explore multiplication and subtraction of fractions – first using paper folding and then using egg boxes. Intermediate phase teachers can use ideas from this workshop to introduce fractions and to lay the foundation for work done in the senior phase. Senior phase teachers can use the ideas to help their learners who do not yet have a good understanding of what fractions are and to explain the algorithms used for multiplication and, particularly, division of fractions.*