Using ICT in mathematics case study 7 - 'Visual stimulation'

Headline

The students always seem to find it difficult to remember the difference between the term-to-term rule and position-to-term rule (nth term).  Also the misconception that the 10th term is twice the 5th term, etc.

Context

Lower ability group of students in Year 8 (set 4 of 5); and a middle ability class of students in Year 7 (set 3 of 5). The case study focuses on two lessons one which uses graphical calculators and a second that uses a spreadsheet.

Teaching and learning objectives

• To be able to generate the given linear sequences by finding the term-to-term rule.
• To be able to find the nth term for a linear sequence.
• To be able to generate the given linear sequences by finding the position-to-term rule.

ICT resources and context

The students were then introduced to the way of getting the graphics calculator to generate sequences using the term-to-term rule (ANS + 3, etc). In the subsequent lesson the students worked on generating the term-to-term rule in a spreadsheet. Then they used a custom-built spreadsheet that generated random linear sequences and work on finding the nth term. The class then had the opportunity to generate the nth term rule using formulae on the spreadsheet.

Explanation of the lessons (including materials used)

Lesson 1
The first teaching episode involved the use of a picture of the end grill of a hairdryer to provoke the students into thinking about how to work out what would come next in a sequence. (Questions being what times table is that like? – what do we have to do to the 3 times table to get the number of holes in the grill?) 

The students were then introduced to the way of getting the graphics calculator to generate sequences using the term-to-term rule (ANS + 3, etc) This was done via TI Smartview on the IWB and by students each with a graphical calculator. The students then had to fill in ''calculator screens'' to show how to generate the sequences shown. 

Lesson 2
Firstly the students work on generating the term-to-term rule in a spreadsheet.  Then they use a custom built spreadsheet that generates random linear sequences to practice finding the nth term. 

Evaluation of the impact of the ICT on the learning

Lesson 1
The students were able to check their own work to see if their term-to-term rule worked.  This helped to reduce the number of misconceptions through error. Some students went off task because they were using other options on the calculator that they had experienced before however most students were working fairly quickly as they were able to generate the sequences easily. The calculators appeared to increase the students’ confidence to discuss their work and ask each other for help. 
 
Lesson 2
The use of ICT allowed instant feedback for the pupils, and encouraged them to refine their answers.   The lesson had a good pace to it and despite allowing all pupils to work comfortably at their own pace. The pupils were already familiar with spreadsheets and this activity allowed them to see a mathematical application for their skills. Consequently the use of formulae in the spreadsheet removed any calculation errors and allowed pupils to work on the concepts. A parallel group who were not given access to the ICT did not seem to make as much progress as the ICT enabled group.

In particular, shy girls reported some enjoyment from the lesson, particularly as using individual machines allowed them to understand at their own pace.

Opportunities for further developments

In hindsight – the first spreadsheet was not really necessary – and may have confused the issue as more time was needed to explain how to use the spreadsheet. Over the course of two lessons the second spreadsheet has been modified to rearrange the layout and add some colour – see year 7/8 spreadsheets. The use of formulas to develop an understanding of the difference within a pattern i.e. 2,4,6,8, (2) may be counter productive as it will not be a rule to link the term to its position.

The use of drag handles (as suggested by a child) may be more appropriate as an introduction as it established a need for a rule because, for instance it is tricky to drag down to 10 000.


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