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# Selecting tools and tasks for learning : Post 16 Level 2 : Mathematics-specific Pedagogy

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Post 16 Level 2
Selecting tools and tasks for learning
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# 1. How confident are you that you can draw on a range of tools to support learners in their mathematical development?

## Activity

The following are some uses of ICT in mathematics:

For each one say how effective you think they are.

1. Teacher asking learners to enter statistical data manually into a spreadsheet before performing calculations on the data.
2. Teacher asking learners to use an applet to simulate probability experiments.
3. Teacher posting lesson notes and exercises on the college VLE (Virtual Learning Environment).
4. Teacher asking learners to produce a PowerPoint presentation explaining how to solve quadratic equations that factorise.
5. Teacher using a PowerPoint presentation to explain how to solve quadratic equations and show their solutions on a graph.
6. Learners using dynamic geometry software to investigate straight line graphs and their equations.
7. Teacher using dynamic geometry software to demonstrate the circle theorems.
8. Teacher making a video of him/herself writing a model answer to a GCSE question which they then post online.
9. Teacher providing links to resources available for self-study online.
10. Teacher asking learners to investigate transformations using an interactive microworld.

Prompt 1.

Decisions about when and how ICT (or indeed any resource) should be used to help teach mathematical facts, skills or concepts should be based on whether or not the ICT supports effective learning of the lesson objectives. The use of ICT should allow the teacher or learners to do something that would be more difficult without it, or to learn something more effectively or efficiently.

## Commentary

Decisions about when and how ICT (or any resource) should be used to help teach mathematical facts, skills or concepts should be based on whether or not the ICT supports effective teaching of the lesson objectives. The use of ICT should allow the teacher or learners to do something that would be more difficult without it, or to learn something more effectively or efficiently.

1. Teacher asking learners to enter statistical data manually into a spreadsheet before performing calculations on the data.

It would not be an effective use of ICT to ask learners to input large amounts of data into a spreadsheet. If you want them to work with large data sets it would be better to provide them with a spreadsheet that already contains the data so that they can concentrate on the analysis. Statistics from small data sets may usually be more efficiently found using a calculator.

Spreadsheets can be powerful investigative tools. Here’s an example of their use with small data sets: Ask learners to input any 5 numbers into a spreadsheet and calculate the mean. Then ask them to investigate what happens to the mean when every value is doubled, trebled etc. What happens when every value is increased by 100? What happens when a new value is added that is very much larger than the original data?

2. Teacher asking learners to use an applet to simulate probability experiments.

This can be an effective use of ICT. For example, a simulation of tossing coins allows learners to do many trials in a short amount of time leaving time for them to analyse the results of those trials.

3. Teacher posting lesson notes and exercises on the college VLE (Virtual Learning Environment).

This can be very useful if learners miss a lesson for one reason or another and to support learners in following up lessons or revising.

4. Teacher asking learners to produce a PowerPoint presentation explaining how to solve quadratic equations and show their solutions on a graph.

Although some learners are motivated by tasks involving creating presentations, the time taken to do this particular task is likely to outweigh any benefits. A better task would be to ask them to create a poster by hand so that the focus is on the maths rather than the presentation of the maths.

5. Teacher using a PowerPoint presentation to explain how to solve quadratic equations and show their solutions on a graph.

Substituting “chalk and talk” with a PowerPoint presentation does not by itself make a particularly effective use of ICT. Disadvantages of using PowerPoint can be
• It reinforces a view of mathematics that it is a series of algorithms to be rote-learned
• It can reduce the amount of student-centred use of ICT in learning mathematics
• It is usually a static form of mathematics and there are many easy tools for creating equivalent dynamic forms of mathematics. (Tom Button, DigitalMathematicsBlogSpot)

However some of these disadvantages can be overcome by the use of embedded links to dynamic software and video, using the “hide and reveal” feature for whole class questioning and adding hyperlinks to slides to show connections between different representations of mathematics.

6. Learners using dynamic geometry software to investigate straight line graphs and their equations,

This can be a very effective use of ICT as the software allows the learners to change the values of a, b and c quickly in the equation ax + by + c=0 and then form and test conjectures based on what they notice. If the learners are already familiar with the software you can ask them to do this task independently. Otherwise you could produce (or download) a “microworld” where only the values of a, b and c can be modified by the learners.

7. Teacher using dynamic geometry software to demonstrate the circle theorems.

A great advantage of using dynamic geometry software is that you can create clear diagrams with a few clicks of the mouse buttons. This allows you, as the teacher, to concentrate on helping learners understand the concepts and language of the topic rather than on drawing unambiguous diagrams. Involve your learners in the demonstration by, for example, asking them to make predictions which can be quickly tested.

8. Teacher makes a video of his/herself writing a model answer to a GCSE question which they then post online

This use of ICT is similar to the teacher working through a model answer on the whiteboard – the learners get to see a procedure step by step and can hear the teacher’s thinking behind each step. The advantage of producing a video is that learners can access this outside the classroom and can pause and rewind to watch a step in the procedure as many times as they need.

A major disadvantage is that there is no opportunity for the learners to interact with the teacher through questioning unless the teacher is willing to include an email address at the end of the video.

9. Teacher provides links to resources available for self-study online.

An advantage of this is that in a Post-16 GCSE maths course, there is likely to be a wide range of ability and experience of mathematics in your group, with a restricted amount of contact time. Spending time in class helping your learners identify the areas where they need to do more work and then providing links for resources for self-study can help your learners to use time outside the classroom effectively.

10. Teacher asking learners to investigate transformations using an interactive microworld

A microworld is an interactive learning environment. You can create microworlds using software such as spreadsheets or dynamic graphing packages or use readymade microworlds such as those found in Bowland Maths. Using a microworld allows learners to investigate, make conjectures and then test them. Logo Turtle Geometry allows users to experiment with geometric concepts by manipulating a turtle that follows user commands. The turtle can be used to help learners understand coordinate diagrams or draw elaborate graphics using circles, rectangles, and squares. Students manipulate the turtle by giving it directions, changing its shape and position, and thinking about the objects they create and change. Interaction with the turtle produces feedback which encourages reflection and assists learners as they resolve the natural conflicts that arise as they interact in the Logo Environment. Using Microworlds in Teaching and Learning (PDF)

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