Mobiles phones and patterns: Teresa Gadaleta provides an excellent example of using technology to create relevance for students and promote mathematical learning.
What is technology?
Today we live in a world that has been created in large part using mathematics--a world of computers, of information technology, and of rapid communications, around the world. The creation of that world has presented mathematicians with a new challenge: understand that new world--find its hidden patterns--and help us to live in it (Devlin, 1998, p. 179).
Like mathematics, technology is a tool: calculators, rulers, computers, the Internet and intranets, software programs, databases, projectors, interactive whiteboards, televisions, DVDs, Palm pilots, pagers, phones, wireless technologies, Boolean operatosr, megabytes, signals, waves, patterns, images, data, lines, angles, formulas, algebra, volume, pixels, URLs, graphics, MP3s, etc. are all forms of technology.
Technology is an agent of change. There is a constant emergence of new hardware, interactive software and an online environment which has rapidly grown in recent years (Bitter & Pierson, 2005). The World Wide Web is the largest, fastest and quickest resource and is readily available at most people's fingertips. In this technological day it is almost assumed that a person has access to a computer and the internet, has an email address and a mobile number. The way we research information has changed, with the Internet providing access to masses of online information. With the push of a button broadband will connect you to the Internet, giving an almost immediate response. There are also search engines designed for student use, making searching and sifting through information easier and more efficient.
The Internet is a key tool in finding out about and doing mathematics. The majority of students probably know how to access the Internet, yet may not have the skills, knowledge and terminology for successful and proficient searching. For example, when searching for a topic or specific information for example, "mathematics patterns" students will probably access a popular search engine, do a basic search and receive around 10 500 000 results very quickly. Now what? Already, there are a lot of questions, searching options and mathematics to be explored: What is a search engine is and how does it work? How do I narrow down the results? What types of words should I use? How can I make my search better? Where does mathematics fit into all of this? There are mathematical ideas behind all of these questions.
Integrating technology into mathematics
When integrating information and communication technology (ICT) into mathematics and other learning areas, it should be used as facilitator and a tool, with the goal of improving and enriching learning. The use of technology for the sake of technology is not nearly as worthwhile as using it as a tool to support learning (Bitter & Pierson, 2005).
Computers and related technologies are useful tools to use for mathematical experiences in learning and teaching. In a computer alone there are easily accessible tools such as the calculator, spreadsheets, graphing tools and various other stimuli that would promote mathematical discussion and exploration of ideas. For example, researching data on a specific topic such as the weather to recognise and predict patterns for the future. This would include collating and representing data using computer software such as a spreadsheet program in order to get precise and diverse representations of the data to be analysed (Bobis, Lowrie, Mulligan & Taplin, 1999). Other software programs and Internet resources such as 3D drawing programs like LOGO and DesignCAD can be used to explore shapes, angles, lines, symmetry, repetition, dimension, etc.
Mathematics and technology activity
An example of an activity I have explored in workshop involved the use of a mobile phone as a stimulus in mathematics activity related to time, patterning and the use of technology. The activity fits into the Measurement (time) and Number strands and could be easily modified for the early years to the middle years.
We started with a collection of mobile phones and asked the group to explore the features and functions of their mobile phones to see what "mathematics" they could find in them.
Responses from a brainstorm included:
* the keypad, numbers on the keypad and pattern of numbers on the keypad;
* the clock, alarm clock and timer (time);
* the calendar, days, weeks, months, years, the find a date function (time and cycles);
* numbers on the screen, phone numbers and other data;
* the camera, pixilation;
* symbols available in the message menu and options, e.g., dollar sign, percentage sign, fraction line, equals sign, the Franc sign, brackets, less than and greater than signs;
* GPRS data counter and connection timers which count the amount of data being sent;
* Web connections;
* PocketNews--finance, weather, sports, surf reports and horoscopes.
The group looked more closely at the time features; the clock, timer and calendar. We asked:
* How are they useful?
* How do they relate to mathematics?
In smaller groups, we focussed specifically on the calendar and set the task of investigating patterns in the calendar; e.g., patterns of days, patterns in a year, in ten years, etc. We specifically asked the groups to investigate the patterns in their own birthdays.
* What patterns can you find?
The groups used the calendars in their phones to find out what day of the week their birthday fell on in the present year and for a few years into the future. Students could also use electronic calendars on the computer, the internet or electronic organisers, printed calendars or personal calendars they have created.
We looked at the data we had recorded and presented for the first few years and asked questions such as:
* Do you notice a pattern so far?
* What day will your birthday fall on in the next year?
Once we reached 2008, a leap year, the regular pattern in the data changed, causing the pattern to skip a day.
* What do you notice about the pattern now?
* What differences do you notice in other patterns?
* Why could this be happening? This activity is just a starting point and could be extended in many ways, including investigating the patterns in leap years, how they affect our records of time and why we need them. Other forms of technology could be used to represent, collate and display data. We experimented with the graphing tools in Microsoft Excel and with a few clicks of a button created different visual representations of the data of a birthday over a ten year period. We recorded the data for our birthday patterns and other significant dates in the year on paper first and then used computers to record the data on a spreadsheet format.
The data was entered into a table as shown in Table 1. We then wanted to experiment with graphing the data using different forms of charts available on the program. For the computer to recognise and use the data we had recorded to form graphs for us it needed numerical data. We realised we had to code the days of the week in numerical form, so we labelled each day a number from 1-7 and re-entered the new data into the table (Table 2).
We then used the graph functions in the program to experiment with different visual representations of the data. The program produced the different forms of graphs below, which each promoted interesting discussion.
Examples of graphs
Examples of the graphs generated are shown in figure 1-4.
[FIGURES 1-4 OMITTED]
The spiral representations of the data reminded us of the Fibonacci sequence and the logarithmic spiral, mathematical forms which can be found throughout nature in objects such as pinecones, pineapples, petals and branches from plant stems (Britannica, 2002). From these ideas, even more mathematical discussion is promoted explored through the use of ICT.
Integration, motivation, relevance and the real world
Learning the skills to use ICT is a process of learning skills for life. The use of technology is an important tool in the interest of exploring real, relevant and interesting maths. It can be used to learn specific skills, as a stimulus for learning, as a tool for learning and investigating. If used in a well planned program, the benefits definitely outweigh the restrictions. Technology is relevant to mathematics and to the real world. It can motivational and interesting and can be naturally integrated into the learning areas, especially mathematics.
Bitter, G. & Pierson, M. (2005). Using Technology in the Classroom (6th Ed.). Boston: Pearson Education.
Bobis, J., Lowrie, M., Mulligan, J. & Taplin, M. (1999). Mathematics for Children: Challenging Children to Think Mathematically. Sydney: Pearson Education Australia.
Britannica (2002). Encyclopedia Britannica [CD/DVD].
Devlin, K. (1998). Life by the Numbers. Canada: John Wiley & Sons.
Department of Education & Children's Services (2001). South Australian Curriculum Standards and Accountability. Accessed at http://www.sacsa.edu.au.
Teresa Gadaleta is a teacher education student at the University of Adelaide.
Table 1 15 July 1 January 28 February 29 February 2005 Friday Saturday Monday -- 2006 Saturday Sunday Tuesday -- 2007 Sunday Monday Wednesday -- L 2008 Tuesday Tuesday Thursday Friday 2009 Wednesday Thursday Saturday -- 2010 Thursday Friday Sunday -- 2011 Friday Saturday Monday -- L 2012 Sunday Sunday Tuesday Wednesday 2013 Monday Tuesday Thursday -- 2014 Tuesday Wednesday Friday -- 2015 Wednesday Thursday Saturday -- Table 2 15 July 1 Jan 28 Feb 29 Feb 2005 5 6 1 -- 2006 6 7 2 -- 2007 7 1 3 -- 2008 2 2 4 5 2009 3 4 6 -- 2010 4 5 7 -- 2011 5 6 1 -- 2012 7 7 2 3 2013 1 2 4 -- 2014 2 3 5 -- 2015 3 4 6 --
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|Title Annotation:||new VOICES|
|Publication:||Australian Primary Mathematics Classroom|
|Date:||Jun 22, 2006|
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