MEGAN HALE, FHARIA LOBA and ELIZABETH SIMPSON
This paper discusses:
• How practice can engage Stage 1 students to acquire speed at recalling basic addition facts to 10 (e.g. 6+4=10, 1+3=4, 5+2=7 et cetera)
What are schedules of practice and how they can be used effectively?
This article provides teachers with a practical framework for using schedules of practice in their classrooms to help develop the specific needs of students with learning difficulties. Most teachers are familiar with how using practice can improve basic skills of their students over time, especially by scheduling practice to incorporate it into everyday work then moving it into a more intermittent role. The term ‘schedules of practice’ refers to a concept that allows teacher to set up effective scaffolding for students to practice a specific skill or master some required knowledge. The following steps are involved:
– Teachers break down the task into its component parts then provide opportunities for students to practice the task at regular intervals building up their knowledge in the area.
– Students practice at less regular periods to allow the student to develop their internal support structures instead of relying on the teacher.
– Timing of schedules of practice is important as students move through the various stages of learning acquisition, proficiency, generalization, and maintenance. Teachers need to provide appropriate levels of practice at each stage to maximize learning opportunities for their students.
– Feedback and assessment also need to be integrated into those steps to complete the teaching and learning cycle.
Prior knowledge and assessment
Before beginning any new unit of work teachers should establish the prior knowledge of their students and this is also recommended before implementing any of the ideas presented in this paper. Stage 1 children who are beginning to learn their number facts to ten should already have mastered several key skills. These are as follows:
– Number order
– Cardinal numbers
– Groups of 1’s, 10’s, 100’s and 1000’s
– Numeral values
– One-to-one correspondence
– One-to-many correspondence
– Terminology and notation
– Mathematical symbols
– Multi-digit numbers
To assess for these skills teachers can use a variety of tests, including the Schedule for Early Number Assessment (SENA) put out by the Department of Education and Training. This test will give a clear indication to teachers about the mathematical knowledge of each student in their class and where they may need extra support before attempting any new mathematical concepts. Once these skills and knowledge is in place students are then ready to begin learning their addition facts to ten.
Students who have difficulties with maths
Some students may consistently perform below average in all curriculum areas. Others have learning disabilities affecting maths: language processing problems, visuo-spatial confusion, memory and sequencing difficulties. A very small number – about 3% – have developmental dyscalculia. The largest group is students with learned difficulties who have difficulties learning maths because of past learning experiences with particular teachers.
The sequence for instruction in problem solving of students with learning difficulties … follows a logical sequence beginning with direct teaching, followed by guided practice and ending with student-centred control and independence. (Westwood, P. 2008, p. 69)
The NSW K-6 mathematics syllabus: Addition facts to10 (NB in syllabus taught concurrently with subtraction)
In early stage 1 (NES 1.2) a student combines, separates and compares collections of objects, describes using everyday language and records using informal methods. In Stage 1 (NS1.2) the student uses range of mental strategies and informal recording methods for addition and subtraction involving one- and two digit numbers.
Concrete to abstract
In maths, concepts must be grasped by concrete methods before moving to the more abstract, particularly for children with difficulties. Students must learn to understand why they are doing certain steps rather than performing by rote otherwise they will not be able to generalise. Sometimes students face extensive problem in relating the instructional language with the symbols or pictures, because gaps between children’s relatively concrete informal mathematics and their relatively abstract formal instruction preclude understanding and are a key reason for learning difficulties.
Pushing through the maths curriculum at a rate faster than students can move is the reason there is the large group of otherwise capable students who feel they are “no good at maths.”
Diagram 1 (below) shows an example of the sequence of instruction at the beginning stages of teaching addition.
Example of a sequence of activities for teaching addition – moving from concrete to abstract
The amount of material covered in one class would depend on the group.
After this sequence there would be progression to:
– Using nubers eg: 3+5=8
– Flash cards with the combinations of addition facts to 10 : 1+9, 2+8, 3+7,4+6,5+5,6+4,7+3,8+2,9+1. Start lesson with 5 minutes of these
– Introduction of posters for remembering how to count on
– Teach touch adding – in 5+3 the children touch the numeral 3 on three different sections to add on – rather than putting down their pencil to use fingers
– Move to word problems eg: The teacher had three books, a students handed in five more. How many does the teacher have now?
Role of computer programs
Practice >> First grade >> Addition: Addition with pictures – sums to 10
If computer laboratories are available, software to teach maths and programs freely available on line such as the example above can be invaluable in the schedule of practice for teaching maths facts for the following reasons:
– Programs are aimed at specific ages and skills
– Computers make maths more attractive and fun for some children
– The child can submit answers and get immediate feedback, which is not publicly seen by other classmates
– Pictures of objects and numbers ease the transition to abstraction
– Repeated practice is possible at the child’s own pace
MEGAN HALE: Senior instructor (Literacy/numeracy) at TAFE, NSW, Australia; FHARIA TILAT LOBA: Deputy Manager (Education), ActionAid Bangladesh; ELIZABETH SIMPSON: Secondary School Teacher (Math), Sydney, NSW, Australia.
Note: It was a group assignment to fulfil partial requirement Master of Education (Special Education) degree of Literacy and numeracy Instruction course, University of Sydney, Australia in 2010. Hope it will help the primary school teachers as well as curriculum developers to have an idea how the teachers in developed countries like Australia think about teaching addition to students with learning difficulties.