Studying Mathematics with a computer is just like learning in any other way. A variety of types of activity is essential to best serve the learner for three reasons. Firstly everyone has their own preferred learning style and experiencing a variety of activities is likely to include opportunities for learning in that style. Secondly, and strangely opposite to the first reason, students should not be content with only learning Mathematics using their preferred learning style but should be introduced to different ways of learning which may support their understanding of a topic. Finally variety is the spice of life and prevents us from becoming bored!
This area of the Transum website is designed to provide some ideas for different ways to use laptops in Mathematics lessons. Each of the ideas presented below have been used very successfully with Secondary school aged children. Each of the types of activity suggested here has seen students really engaged in their mathematics. It is important however to make sure the learning accomplished with the technology could not be replicated without it. If the technology becomes superfluous maybe the traditional exercise book would be sufficient.
Being organised and never loosing sight of the 'big picture' is an important aspect of learning Mathematics. Traditionally students have had an exercise book or a ring binder in which they keep their notes and their solutions to problems. In moving to a laptop computer the student will need to develop different ways to organise their work and their time. This may include a logical system of folders for their stored files or the use of a particular piece of software.
Microsoft's OneNote may be used as an electronic mathematics notebook to keep a record of work completed on a computer. OneNote assists in:
OneNote operates just like a paper exercise book or folder of notes. It can be divided into sections (Maths strands or topics) with pages. It is easy to organise and has the added feature over an exercise book of being searchable so information can be found again. OneNote saves all your notes automatically.
In addition to being a great place to store all of your notes and other content, OneNote also serves as a calculator with its Napkin Maths feature. Just type the equation anywhere on OneNote's page surface, followed by an equals sign "=" and as soon as you press the <Spacebar> or <Enter>, OneNote performs the calculation.
You can use programs such as Geometers' Sketchpad or GeoGebra (free) to draw shapes which can move. This makes teaching dynamic geometry so much more meaningful compared to the static way textbooks are limited to. However students may prefer to use software they are familiar with, such as Powerpoint which allows animations to be created very quickly.
Could your students produce a PowerPoint slide show to demonstrate rotations, translations, reflections, enlargements and mixed transformations?
Our ultimate aim for mathematics students it to enable them to operate independently and solve 'new' problems. Investigations are excellent for developing the inquisitive mind and laptops are the perfect tools to support investigative work.
We have become so familiar with spreadsheets that we forget what a great tool they can be for investigating number patterns and relationship. Our favourite example is to use a spreadsheet to recreate the Lemon Law starter.
Four one digit numbers are typed in the cells B1,B2, C1 and C2.
In cell D1 the formula is =10*B1+C1
Similar formulas are entered into cells D2, B3 and C3.
In cell D3 the formula is =D1+D2+B3+C3
The challenge is to change the numbers in B1,B2, C1 and C2 so that the D3 total is 88.
Investigate further to see what numbers are and are not possible to get in D3 by changing the numbers in the yellow cells.
The power of technology is not being fully utilised if we only use computers to access scanned copies of traditional textbooks. My Maths is an online alternative to the text book. Students can interact with the system which provides them with instant feedback about their mathematics.
Of course this (Transum) site provides lots of resources too. Here is an example about how the content can be more than just 'textbooks online'.... Hi-Lo Prediction, a version of the 'Play Your Cards Right' TV show. There is a lot written about games for learning and how much better they are than doing 'exercises'. This activity proves the point. Students will have the experience of working out a lot of simple probabilities while at the same time figuring out what that probability means when it comes to betting.
Here is an example of paired work in Mathematics called Pattern Clues. Even though the world has been working towards a one to one ratio of students to computers it is sometimes a better learning experience if the students work in small groups sharing a computer.
A set of clues produces a given pattern in a five by five grid. The clues are available on cards which are randomly distributed between the two (or more) students sharing one computer. Each student can read out a clue but they can't show their cards to anyone else.
Students might find using laptops very useful for coursework assignments in Mathematics and other subjects. When they have mastered the finer points of the available software they clear obstacles away from their ability to be creative. Laptops facilitate many ways to store, analyse and present data that the creative student can use to wonderful effect.
Here's a way to use a very familiar tool in a Mathematics lesson. It can be used to provide pace and speedy feedback for the teacher. The activity we will model is called Smallest Number. It is a competition with a winner. In the first minute of the activity each person is to send an email to the teacher. The subject of the email must be "Number" and in the body of the email there must be a positive whole number (Natural Number). The winner is the person who emails the smallest number which nobody else has chosen.
Other lesson starter activities using email include asking students to type in the most:
If your lesson starts at 9:00am you could add that the time stamp on their emails to you must ne less than 9:07am.
"To work out the probability of a drawing pin landing point up students conduct an experiment in which a drawing pin is dropped many times. If the pin lands point up on x occasions out of a total number of N trials, the relative frequency of landing point up is x/N. When an experiment is repeated many times we can use the relative frequency as an estimate of the probability of the event occurring. That's Pin Probability!"
We included this example here to show an example of collaboration between students. They can collaborate to gather the data in the first instance then collaborate to produce a report or extend this activity to more complex probability situations.
Students are never too old to learn their times tables. Fast Factors and Tablesmaster allow students to time themselves answering times tables questions. They can record their scores in a spreadsheet and work to achieve their personal best. These two programs also allow you to have a class competition and the system produces a table of scores.
A new feature in Excel 2010 called Sparklines is great for showing progress or otherwise.
Unlike other school subjects, Mathematics presents problems for the laptop user when writing out mathematical expressions. Some mathematical exercises really are best done using pen and paper but tools do exist to help the computer user.
Math Input Panel is a great little application introduced with Windows 7. Its purpose is to use input devices such as touchscreens, external digitizers or even a mouse to write mathematical formulas which are easily recognized and inserted into different types of documents. The formulas you write in Math Input Panel are inserted into documents in a completely editable form so that you can edit the output as you would edit any type of text. This can seriously improve your productivity when you need to create documents or presentations with lots of mathematical formulas.
When writing a formula, don't hesitate to use the tools available on the right side of the application. If you made a mistake, you can easily fix it using the Erase tool. Click on it and erase the mistake completely.
There are scenarios when Math Input Panel doesn't recognize very well what you write. You can correct the way it interprets your writing by clicking on 'Select and Correct'. Then click/select the character you want to correct and a drop-down menu with possible options will appear. From that menu select the correct interpretation and resume your writing by clicking on Write.
Note: Math Input Panel can only insert math into programs that support Mathematical Markup Language (MathML).
Do you have any tips for using laptops (or other portable computers) in Mathematics lessons? Click here to enter your ideas.