Using ICT in mathematics case study 5 - 'Symbolically, numerically, orally, graphically'
Headline
My students always find it difficult to find the nth term of a linear sequence and relate this to the equation of a straight line
A lesson using different representations of sequences in tabular and graphical form using a graphic calculator.
Context
Year 7 class set 2 (level 3/4 borderline) 32 children in the class, in a school in southern England.
Teaching and learning objectives
To be able to find, interpret and use the ‘n’th term of a linear sequence – Framework for teaching mathematics Year 7 objective.
ICT resources and context
Graphical Calculators for each child with an emulator displayed on the IWB. A spreadsheet was also used in the plenary to reinforce multiple representations. Some time was allowed for children to become familiar with the graphic calculators.
Explanation of the lessons (including materials used)
- Teacher used an analogy of window struts and joints to generate a sequence.
- Represented sequence as a table of numbers then represented this symbolically as 2n+1 etc.
- Handout with other sequences given out with sequences to represent symbolically.
- Graphical calculators distributed and explained using the IWB.
- Graphical representation explored and children used to check the functions 'answers' from the previous handout.
- Spreadsheet model used to 'predict' terms in the sequence and develop rules.
Evaluation of the impact of the ICT on the learning
The ICT allowed for far greater pace and progression within the lesson. Children's misconceptions were easier for children themselves to spot and the use of ICT meant that it was quick and easy to explore individual child misconceptions and questions.
- The connection with the 'n number' in the function being the nth term.
- Why if we were adding 2 each time, we multiplied by 2 in the equation.
- What is the graph showing on the calculator?
Children worked independently so if a child had a particular query, it was easy to display their individual graph using the software. Without ICT time would have been spent drawing graphs on the board – boring for children and teacher alike. Children spent time exploring functions and the graphs of them, not the majority of the lesson plotting points and joining them up to produce 1 or 2 graphs.
The use of the software at the end provided opportunities and a context for all to demonstrate the understanding and learning that had taken part in the lesson.
The ICT skills and techniques developed quickly, within 15 minutes children could explore the concept of Snogging in their Maths lesson!
S : represent a sequence symbolically
N: explore a sequence numerically
O: orally discuss the progression of a sequence
G: graphically represent the sequence
The Teacher said; 'The use of ICT made my teaching easier and I was able to cover substantially more that in a traditional lesson. The next lesson allowed children to explore the y = mx + c relationship and they were able to predict what a particular graph would look like and tell me what the effect of 'm' and 'c' have in the equation of a straight line.
This is beginning to work at level 7. Without ICT it would have been difficult for children to achieve this progression and also to see the connections between the nth term and the graph of a function.'
Children described their learning as 'new, different – so stuck in mind'; 'better than using brains'; 'easy because helped remember it in funny ways'; 'it was better than, say, using matchsticks or cubes because saves times getting everything out'; 'no hassle setting up the shapes'; 'get more out of it because doing more'.
Opportunities for further developments
- More complex linear sequences.
- Quadratic sequences.
Links to resources
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