http://www.adrianoldknow.org.uk/

1.2 Changes in teaching approaches



It is quite possible to use ICT in mathematics lessons in a way which does
not throw into question your own teaching approaches. However the power of
the medium is such that to restrict its use in this way is to deprive the
students of access to a resource which could revolutionise their learning.
It was to address this issue that the DfES' mathematics curriculum IT
support group produced its `Mathematics and IT - a pupil's entitlement'
leaflet in 1995, now republished on the Becta ICT Advice website:
http://www.ictadvice.org.uk/downloads/entitlement_doc/entitle_maths_sec.pdf
. It lists six major ways in which ICT can provide opportunities for
students learning mathematics:



Learning from feedback: The computer often provides fast and reliable
feedback which is non-judgemental and impartial. This can encourage
students to make their own conjectures and to test out and modify their
ideas.

Observing patterns: The speed of computers and calculators enables students
to produce many examples when exploring mathematical problems. This
supports their observation of patterns and the making and justifying of
generalisations.

Seeing connections: The computer enables formulae, tables of numbers and
graphs to be linked readily. Changing one representation and seeing changes
in the others helps students to understand connections between them.

Working with dynamic images: Students can use computers to manipulate
diagrams dynamically. This encourages them to visualise the geometry as
they generate their own mental images.

Exploring data: Computers enable students to work with real data which can
be represented in a variety of ways. This supports interpretation and
analysis.

`Teaching' the computer: When students design an algorithm (a set of
instructions) to make a computer achieve a particular result, they are
compelled to express their commands unambiguously and in the correct order;
they make their thinking explicit as they refine their ideas.



These opportunities are equally valid now, but we have more widely available
tools to help us provide them for our students. QCA have established the
National Curriculum in Action web-site
http://www.ncaction.org.uk/subects/maths/ to help teachers map these
opportunities onto the main types of ICT resources such as graph-plotters,
spreadsheets, dynamic geometry software, computer algebra, small software,
Logo, statistics packages, graphical calculators, data-loggers and web-based
resources. The DfES have refocused their overall ICT strategy for 2003-6 to
aim to see ICT embedded in the teaching of all subjects. They are currently
funding groups, such as the Mathematical Association, to produce a variety
of lesson plans, resource materials, case studies and guidance as part of
what will be known as the DfES Key Stage 3 ICT Offer to schools to be
launched at BETT 2005.





1.6 Evaluating the impact of the use of ICT



Evaluation occurs at many levels - e.g. of the use of some ICT as part of a
lesson, or of the lesson as a whole, or maybe of your own, or the
department's, facility with ICT. You will also need to be able to evaluate
particular ICT tools in considering their usefulness for mathematics
teaching. Let's start with how you might evaluate a lesson which used ICT.




Evaluating a lesson using ICT



Useful references here might be the `Review and Evaluation' questions on
page 210 and the `Planning a lesson' on page 238 of Oldknow & Taylor's
`Teaching Mathematics using ICT' . Also the list of bullet points on page
9 of the TTA's `Identification of Training Needs - Secondary Mathematics'.



In order to set the context we will need to know:



* What are you trying to do?
* How are you trying to do it?
* Who are you going to work with?



Then we will need to pose appropriate questions such as:



* Did you meet the learning objectives?
* Were the students actively engaged and were all abilities catered
for?
* Were the students confident?
* Did the plenary work - could they transfer knowledge to other
scenarios?
* What mathematics did they use?
* What progress did they make?
* Can it be extended further?





The Oldknow & Taylor book includes a sample activity review sheet. Below is
a reproduction of a teacher's evaluation of a lesson exploring number
sequences with graphical calculators:





1. What did you expect to get from the task, i.e. purpose and learning
intentions?

These are defined in the Teaching/learning objectives in the lesson plan.



2. What additional knowledge and skills did you need :


about the technology


Using the data handling facilities associated with the "stat" key and the
calculator's ability to manipulate "lists". For the follow up lesson: how to
plot data and superimpose functions.



about the mathematics

Fairly confident with the mathematics, but talked to mentor about the
expectations and level of challenge appropriate for this Year 9 group.



about teaching strategies and approaches?

How to engage all pupils in the whole class interaction, use of the growing
design and matchsticks as an initial task accessible to all pupils. The use
of more open-ended questioning at the start of the lesson to establish what
pupils already know. Getting the pupils to discuss in pairs to ensure
everyone is involved was a good idea. I like collaborative work and often
use this approach in my lessons. Pupils learn so much when they have to
explain their thinking to others. It also improves their listening skills.



3. What additional knowledge and skills did the pupils need:


about the technology


How to enter, edit and manipulate data in lists.



about the mathematics

An ability to analyse growing patterns and convert observations in words
into conventional mathematical symbols



about learning strategies and approaches?

Be prepared to explore, look for patterns and try things out, develop their
use of visual imagery to explain their thinking. Work and co-operate with
other pupils in their group. Explain and communicate ideas to other pupils
in the class



4. Was the focus of your teaching on developing skills or
understanding?

Both; I wanted pupils to develop pupils reasoning and communication skills
through an accessible context. I also wanted to develop pupils understanding
of equivalent algebraic expressions and introduce them to algebraic
manipulation and give purpose for further work on this topic. Although I
think it is much more important that pupils can use algebra to
formulate/model situations.



5. Did the pupils focus on understanding or pressing buttons?

At the beginning of the first lesson some time was spent getting used to the
data handling facilities on the GC. However, pupils were quick to come to
terms with these and after an initial hiatus were able to use the GC with
confidence to explore, check and validate their algebraic rules.



6. In what ways were your answers to questions 4 and 5 affected by the
use of the technology for the topic?

The technology acted as an extra "teacher". Pupils were able to try out
their ideas on the calculator and it provided them with instant feedback on
the validity of their conjectures and formulae.



7. Would the use of the technology for this topic change the order in
which concepts were taught?

Might try to introduce simple modelling and formal algebraic conventions
earlier. Pupils coped well with the symbolism in the context of growing
geometric patterns and had little difficulty using the GC.



8. What were the benefits/disadvantages of using the technology?

Benefits; see 5,6 and 7. Disadvantages; some initial problems getting to
know the GC. I had considered using "mouseplotter" and/or a spreadsheet in
the school's computer room but chose the GC because of its easy use in the
classroom and the similarity of the GC's notation with the standard
algebraic convention.



9. What would you do differently next time?

As pupils become familiar with the GC I will get the pupils to plot the
results and link the graphs to the rules such as the kind of "rule that
produces a straight line and the connection with the gradient and the
intercept.







Number of teachers who have developed specific ICT skills e.g.:

Data-handling used database or statistical software:
[ ]

Dynamic geometry used DGS for constructions and transformations:
[ ]

                                    extended their use e.g. for coordinates,
measures etc.: [ ]

Graph-plotters used graph-plotting software in their teaching:
[ ]

Graphical calculators used numeric and graphing aspects of graphical
calculators: [ ]

                                    used data-handling and other aspects of
graphical calculators: [ ]

                                    used graphical calculators with
data-loggers: [ ]

Logo used Logo to manipulate a screen turtle and
write procedures: [ ]

                                    extended their use of Logo e.g.
recursion, microworlds...: [ ]

Small software used curriculum focused software e.g. Smile, Maths Alive..
[ ]

Spreadsheets set up a basic spreadsheet e.g. entered and
replicated formulae: [ ]

                                    used extended facilities of a
spreadsheet e.g. statistical graphing: [ ]

Symbol manipulation used computer algebra software:
[ ]

Web-sites explored web-sites relevant to mathematics
teaching: [ ]

Whiteboards used electronic whiteboards for whole-class
work: [ ]



3. Curriculum resources

This section establishes whether there are appropriate mathematical
activities and other support materials (published, or produced within
school) for the different categories of ICT:

Departmental resources/starting points for working with:



Data-handling



Data-loggers



Dynamic geometry



Graph-plotters



Graphical calculators



Logo



Small software



Spreadsheets



Symbol manipulation



Web-sites



Whiteboards



Other relevant ICT skills:





4. ICT resources

This section is about the hardware available in the school. How many
machines (desktop PCs, laptops, palmtops, graphical calculators etc.) are
available in mathematics classrooms? Comment on suitability, sufficiency,
accessibility and reliability.





How many purpose equipped computer suites are there; how many are bookable
for maths?



Comment on the adequacy, or otherwise, of the bookable resources:



Time available for maths classes:



Availability and suitability of generic software (e.g. spreadsheets):



Availability and suitability of mathematics software:

5. Entitlement opportunities:

`Mathematics and IT - a Pupil's Entitlement' highlights six major
opportunities for exploiting the power of the computer. This section
establishes which opportunities are offered in your school. Indicate on a
scale from 1 (minimal) to 5 (extensive) the extent to which pupils in your
school have access to the following opportunities:



Learning from feedback:



Observing patterns:



Seeing connections:



Working with dynamic images:



Exploring data:



Teaching the computer:



What do you believe are the most important benefits which using ICT brings
to mathematics teaching?





6. ICT development

This section establishes how you arrived at your current stage of
development.

Can you identify helpful factors? Have you had contact with other schools
through an LEA group, subject association, project etc.? Are ICT resources
available for teachers to take home? Can you identify helpful sources of
ICT support and advice inside the department, school or elsewhere?











7. Action plan

Completing the previous sections may have suggested directions for
development. Your action plan could be written under the following
headings, giving some indication of time scales.

Embedding ICT (entitlement opportunities and curriculum objectives):





Staff development, both within and outside school:





Updating and improving ICT resources:





What is needed in order to achieve this plan within the stated times?