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Diversity and Differentiated Curriculum
Colleen Vale
Victoria University
Melbourne, Australia
In this paper I propose to discuss the student diversity in prior mathematics learning and achievement confronting teachers of junior secondary mathematics (students aged 12 to 15 years) and to describe and discuss the differentiated curriculum approach being used in some secondary schools in Victoria, Australia.
The majority of schools in the western suburbs of Melbourne have student populations with low socio-economic and diverse ethnic backgrounds including recent migrants and refugees. A combination of many factors means that students beginning secondary school have a diverse level of mathematics knowledge and skills, and in some schools the majority are well below the expected standard of knowledge for their grade. Significant numbers of junior secondary mathematics teachers are often not qualified to teach mathematics or are unprepared to teach a class of students with a range of skills and knowledge.
Some schools choose to respond to the diversity of students mathematical achievement by implementing a streaming policy, that is, sorting students into mathematics class groups according to mathematics achievement. (Different terms are used to describe such policies in other countries, for example, setting in the UK and tracking in the USA.) Rarely do these policies provide for and enable students to move between groups once the groups have been set. Often the sorting of students in their first year of secondary schooling is based on the results of a single written mathematics test. As a consequence some students will be inappropriately allocated to groups.
Furthermore, the practice of streaming has been shown to widen the achievement gap between students in the lowest and highest streams. This happens because teachers have different expectations, and therefore goals, for students in the high and low achieving groups, and consequently they offer intellectually demanding learning experiences to the higher stream students while tending to set routine computational tasks for students in the lower stream. Hence, streaming of students in this way is reinforcing, rather than removing, existing achievement differences between top and bottom streamed students.
Many schools appreciate these problems with streaming of students and so assign students to heterogenous classes for mathematics and other subjects. However teachers have still struggled to respond to the diverse needs of students in the group. Recently, some schools in the western region of Melbourne have begun to design and implement a differentiated curriculum for these heterogenous classes.
A differentiated curriculum has multiple learning programs and different approaches and activities for the students to meet their particular needs, interests, and preferred ways of learning. Differentiated curriculum may include various pathways, perhaps involving choice of activities for students, different tasks or levels of depth and engagement for students, various models and representations for working with mathematical ideas, various tools for aiding mathematical work and learning, or various media for recording and reporting mathematical learning.
In the remainder of this paper I describe an example of tiered curriculum, one of the models for differentiating the curriculum. In a tiered curriculum the teacher prepares a collection of activities that are appropriate for the diversity of student need and hierarchical in terms of level of complexity. As is shown in the example below, the use of digital resources is an important feature of such curricula as these resources may provide alternate learning approaches and various representations and models of mathematics.
Hands on/gamesPolygon mobile construction p.39
(3D shapes)
Taylors Lakes mapping
(co-ordinates/scale)
Batty Lizards
(Semi-regular tessellations)
Numeracy gameExercise 2.04 qn 1-10
(3D shapes)
Exercise 11.05 qn 1-4
Taylors Lakes mapping
(co-ordinates/scale)
Batty Lizards
(Semi-regular tessellations)
Numeracy gamePlatonic Solids rich task page 49
(polygons)
Orienteering Adventure
(Compass directions, coordinates, scale and distance)
Taylors Lakes mapping
(co-ordinates /scale)
Batty Lizard
(semi-regular tessellations)
ICTPlot plans and silhouettes
(2D and 3D structures)
Whats the point
(Coordinates)
Planet Hop 1
(Coordinates)
Building Houses
(3D shapes)
TangramsWhats the point
(Coordinates)
Planet Hop 2
(Coordinates)
Building Houses 4-7
(3D shapes)Whats the point
(Coordinates)
Planet Hop 3
(Coordinates)
Building Houses 8-10
(3D Shapes)
WorksheetDescribe that shape
(3D shapes)
Name that shape
(3D shapes)Welcome to Springfield (ratio/co-ordinates)
Ratio Problems
(Ratio)Ratio and Proportion Difficult ratio problem.
(Ratio)
Text tasksExercise 12.01 on 1-4
(Ratio)
Exercise 2.02 on 1
(2D shapes)
Exercise 12.01 on 5-7
(ratio)
Exercise 12.02 on 1-4
(proportion)
Exercise 12.06 1-3Review Chapter 2 on 11-13
Exercise 12.02 on 5-9
(proportion)
Page 367 on 7
ratio)
HomeworkSummarise notes p.40
Shape Riddle
Spelling Championship
Puzzling Pantry Problem
Who is Escher?
Vocab Challenge
Figure 1. A tiered curriculum (Source: Taylors Lakes Secondary College)
Figure 1 illustrates the tiered curriculum for grade 7 students at one secondary school for the topic shape and location, one of the five content areas of the mathematics curriculum for students in Victorian schools. In this program there are three tiers of challenge. This program also caters for the different learning preferences of students. It includes practice tasks and problems from paper-based resources including the textbook as well as practical hands on tasks or games, and online interactive activities. The underlined tasks are compulsory for all students. This program differs from a streamed program because the students choose a set of activities to complete based on the teachers advice and support.
The program of differentiated curriculum for each topic in the grade 7 mathematics curriculum was designed by a group of junior secondary mathematics teachers who were being coached by more experienced teachers at their school as part of a program of innovation and improvement. These teachers worked as team in an open plan teaching area large enough to accommodate their three grade 7 classes. This modern learning space included twenty PC computers with internet connection, an area with tables arranged so that students could work in groups on practical tasks, another area with student work desks organised in rows for instruction, and a conversation pit for group discussion. An interactive white board was also located in this open-plan classroom.
Each mathematics lesson included a 10-minute instruction segment in which attention was given to the explicit teaching of a skill or concept for all students. For the remainder of the lesson the students worked on their selected activities individually, in pairs or in small groups. Teachers also conducted 10-minute clinics for small groups of students to consolidate or teach skills. These clinics are designed for mathematical skills, individual and group learning skills and ICT information and communication technology skills. These clinics were shared among the teachers. The students accessed the digital online activities through the schools learning program software on the intranet site. Specific times for student reflection on individual and group learning were included in the structure of these lessons.
The teachers and students conducted on-going evaluation of the tiered curriculum throughout the year. They noted the benefit of providing students with choice as the students were engaged and enjoyed learning and they also supported each others learning through peer tutoring. The teachers thought that the range of activities generally catered appropriately for students needs though they recognised the need to change or add to the set of tasks to address more explicitly some learning outcomes specified in the mathematics curriculum, or to improve student learning. They believed that the clinics, that is the focussed explicit teaching with small groups of students, was successful. Specialising their teaching activities within each lesson enabled the teachers to address the diverse needs of their students more comprehensively than normally occurred in a classroom with a single teacher working on a common program for all students. The teachers at this school did however note that individual learning did not suit all students and that some students were reluctant to attend clinics. They also found that there was no time to do whole class activities on extended investigations, something that they wanted to include in their curriculum as they refined their work.
Acknowledgements: I would like to thank the mathematics staff at Taylors Lakes Secondary College, in particular Nicole Claxton, Josephine Postema and Graeme Taylor. This project was part of the Equity and Technology in Mathematics (EaTiM) project ( HYPERLINK "http://education.vu.edu.au/eatim/" http://education.vu.edu.au/eatim/) funded by the Commonwealth Government of Australia through the Australian Schools Innovation in Science Technology and Mathematics (ASISTM) program ( HYPERLINK "http://www.curriculum.edu.au/ccsite/cc_asistm,17919.html" http://www.curriculum.edu.au/ccsite/cc_asistm,17919.html).
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