Transcript of integrating digital technology in Stage 5 mathematics
Speaker 1: So, I'd like to kick off this session today just by revisiting 10 key points from Session number 3 last week.
Number 1, excuse me, research supports the view that integrating ICTs in the mathematics classroom motivates students and leads to improved performance. I think we probably all agree with that, or else we wouldn't be here listening to this presentation.
Information and Communication Technology Capability is one of the general capabilities in the new syllabus.
The new syllabus makes specific mention of these digital technologies: calculators; spreadsheets; dynamic geometry software; and computer algebra and graphing software.
The importance of these digital technologies to mathematics education is in their inherent 'interactivity'. That function of ICT, which I described as enabling rapid and dynamic feedback and response.
Students use ICT effectively and appropriately when investigating, creating and communicating ideas and information, including in representing mathematics in a variety of ways to aid understanding. I think from this statement alone, I think you will all see the obvious synergy between effective use of ICTs and working mathematically, remembering that working mathematically relates to the syllabus objective. Students develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning.
Information and communication technologies should always be thought of as being in the service of pedagogy. Remember the words of [Johnston and Still 00:01:52] "Pedagogical foundations must be solid because the tool will achieve no heights that the underlying pedagogy will not support."
For the bulk of Information and Communication Technology Capability content, say that ten times fast, identified in the new syllabus, a scientific calculator, MS Excel and GeoGebra are invaluable tools. The ICT capability content should not be looked upon as a definitive list. I'm sure you're all being very imaginative teachers, you will be able to identify many more opportunities to use ICT-based tools to aid student understanding in the new syllabus.
The new syllabus makes no mention of Web 2.0 technologies. However, the value of these tolls in developing collaboration and communication skills in students should not be overlooked.
And we finished the session last week with a brief look at pivot tables, and said that they enable easy organisation and analysis of authentic data sets.
Okay, so that's where we're at. Last week we also mentioned a number of sites, websites for professional support and for access to teaching and learning resources. Remember, Tools+ on TaLe, and you access that by the little link there at the [headering tale 00:03:23] indicated by the red arrow on the screen. This is where you can get access, support software applications provided under the digital education revolution of New South Wales, connect to classrooms programme and technology for learning. So visit Tools+ for the tools for you and you create [suites 00:03:46]. And of course TaLe for resources relevant to the new syllabus. The majority of these including the syllabus [Bytes 00:03:56] are rich in technology-related activities. If you click on the link shown there on the screen, that will give you access to a search, or you can enter the same criteria shown there on the screen.
Okay, the GeoGebra Institute of Australia website of course has teaching and learning resources produced by the DDC. A livery of applets contributed by our users, and links to resources from the international community.
Intel Teach Elements, we mentioned that last week, particularly for those teachers are comfortable with the mathematics focused tools, but I'm looking to broaden their applications of ICT in the classroom. These course are all institute-registered and they provide deep exploration of 21st century learning concepts and strategies for ICT integration. And if you click on that link there's further information, and I've also included the flyer in the file download pod on the final screen of the session today.
Okay, last week I showed you how to organise large and complex data sets with the aid of a pivot table, and there was at least one request for more of the same. Unfortunately, we won't have time today to do this, but if there is a demand it could fall in the basis of a future session. Later I'll let you know how you can feed into the design of future sessions.
In the intro, I suggest that, once again, you work your way through the random sampler activity that we looked at last week, which is again available for download from the fileshare prompt today. Also of course going onto the web, there are literally thousands of tutorials available on this topic. I've included a link at the bottom of this page to one set which I think does a pretty good job of explaining the basics of using pivot tables.
Okay, as mentioned last week, a great advance with the online syllabuses is the facility to philtre syllabuses for learning across the curriculum areas, and you can philtre by syllabus, by stage, or by the learning across the curriculum area, and you can preview it in context, or click through to the syllabus content. I hope you've all done your homework and had a look at that since last session.
This was the tag cloud I generated for the Stage 4 content, and we discussed that last week, and we can see by the size of those terms, of course indicating the relative frequency of them in the document, that calculators, graphing dynamic geometry and statistics all feature pretty heavily.
I've done the same thing for the content for Stage 5.1, there were 15 results returned, and of course the word 'graph' is one that stands out there, to give you an indication of what the focus is of 5.1.
5.2, the results, there were 12 results returned. Again the word 'graph' stands out along with 'angle', 'equations', 'polygons' and 'data', and the operative term is 'investigate'.
And finally, for 5.3, 18 results returned. The high frequency terms such as 'data' and 'dynamic geometry' give an indication of what you can find in a closer look at the content for this stage. And speaking of which, let's just do that.
Okay, this is a download, and you won't be able to see it very clearly I wouldn't think on that screen. But this is a download of those ICT capability content statements, and I've just gone through and I've highlighted them, or aligned them to, or mapped them to the most appropriate tool that we'd use to teach that content. This document, incidentally, is also available on the file share pod on the final screen.
Okay, so, what you can see there, in Stage 5.1 there's aside from the obvious uses of scientific calculators, their opportunities integrate the use of spreadsheets, computer algebra and graphic software, and of course dynamic geometry software. Down near to 5.2, a similar sort of spread of tools, and the in Stage 5.3 there are many opportunities to use spreadsheets, computer algebra and graphic software and dynamic geometry software. So as I said, that's available for download in the final pod, and I urge you to have a look at it.
I think one thing you will pick up from my highlighting, is that for some content it is possible to use more than one tool, especially given the tools that we have at our disposal. For example, GeoGebra does a whole lot of functions that other tools also do.
Okay, once again, that the ICT capability content should not be looked upon as the definitive list. I keep harping this point, I know, but it's really important I think that you take that one away. There are, as I said, lots of opportunities to use these tools right throughout the syllabus, and once again, once you're confident with these I'd recommend that you'd start to look at some of the advantages of using Web 2.0 technologies to develop collaboration and communication skills with your students.
Okay, we're gonna have a closer look now at GeoGebra, I think it's no secret that I'm a bit of a fan of the software. I first started using it back in 2008, and I like many other people, have enjoyed watching the development of the software from a what began as a very good dynamic geometry package, but has since morphed into a tool for all occasions. On the website, it describes itself as an interactive geometry, algebra and calculus application, and the latest version, version 4 and later, it combines a dynamic geometry environment with a computer algebra system, and the functionality of spreadsheets is the most recent addition.
Okay, in the domain of the dynamic geometry environment and computer algebra capabilities of GeoGebra, in this capacity the instructions can be made with points, with vectors, segments, lines, polygons, conic sections, inequalities, polynomials and functions. All of them can be changed dynamically afterwards Elements can be entered and modified directly on screen or through an input bar. GeoGebra also has the ability to use variables for numbers, vectors and points, to find derivatives, integrals of functions, and has a comprehensive complement of commands.
As I said, GeoGebra version 4 later incorporates spreadsheet functionality, and a basic, but more than adequate, statistics package as well which we'll be having a look at later on in this session. The link at the bottom of the page is to PDF 'Introduction to GeoGebra 4.2', so I recommend that you have a look at that one as well.
Okay, Geogebra licences are free. Geogebra desktop is available for common operating systems including Windows and MacOSX. GeoGebra tablet apps are now available from the Windows Store, from the App Store and from Google Play. As we've mentioned before, this latest advance is very timely, given that the digital education programme is drawing to a close, and we are all now transitioning to a brand new [OS 00:13:02] environment. So to download a copy of GeoGebra, follow the link at the bottom of the page.
Okay, I made this collection of how-to videos at the Centre for Learning Innovation, a few years and at least two [restructures 00:13:17] ago. These were produced for an earlier version of GeoGebra, but the concepts around the dynamic geometry and the tools that you use are the same in the latest version of the software. So each of those videos there are very short, but they open in any browser and so I recommend them to you.
Okay, in Stage 5.3 single variable analysis, students compare the relative merits of the range, interquartile range and standard deviation, bi variate data analysis, which is of course new to the New South Wales K-10 syllabus. It involves students in investigating relationships between two statistical variables, including their relationship by the time. In Stage 5.3, students investigate the relationship using lines of best fit, and in the [audits 00:14:26] of ICT capability content that I showed you a little while ago, if you'd see it you'd notice that most of the content aligned in this area is to a spreadsheet. Now, most, perhaps all the content mentioned here, could be taught with the use of a spreadsheet application such MS Excel, but reinforcing a point I made earlier, this can now also be covered with GeoGebra.
[Shaking 00:14:55] statistics in Stage 5 is one of the so-called building capacity resources we've produced at the end of last year. In this resource you will find a step-by-step professional learning activity which includes sample data sets, to familiarise yourself with the capability of GeoGebra spreadsheet view and the statistical functions. You will also find sample lesson plans and their related assets, comparing measures of spread, which is on the topic of single-variable analysis, and wealth vs. health on the topic of bi variate data analysis. There is a direct link to this resource shown at the bottom of the page, or you can find this and other resources on the New South Wales syllabuses for the Australian Curriculum implementation support website, and that's on the DET intranet under the 'curriculum resources' tab.
GeoGebra Institute of Australia website, as I've mentioned earlier is a stack of resources produced by the [DDC 00:16:13], which you'll find here, you'll find lesson plans, you'll find applets for teaching various mathematical concepts from Stage 3 right up to Stage 6. You'll also find some professional learning resources. In the GeoGebra community resources website, here you'll find links to all of the stuff in the international community which will be of use to you. If you're just starting out with GeoGebra, GeoGebra channel here is a growing collection of how-to video tutorials and there's also a whole lot of sites where you can find ready-made applets, including of course GeoGebra 2. So there's more than enough resources there to keep you occupied for a very long [career 00:17:11].
We also have now a facility in which you can submit your own resource, and once again I urge you to do that. If you've produced something which you've found of value in the classroom, please do consider sharing it with the wider GeoGebra community, and I'll just show you also the library of applets that have been submitted, and there is now a keyword search here which you can now have it filled. I might say I have a big backlog of these things which I'm gradually uploading, but when you find what you want it's just a matter of clicking on the screen there, and you can either click right through to the resource or right-click on it and download a local copy.
This is obviously a Stage 6 resource, but you'll find ... This is the standard of resource which is available to you, and of course this is I guess reflects a pretty common HSC style question where the students have to find the chicken run of the maximum area, and I can see here graphically that somewhere around here are the dimensions of a chicken run which will give that maximum area, and if they're completely stumped, they can click on that and it will show the calculation of the stationary point. There are some questions to lead them through that process and that's typical of what you could see in the library of resources.
We're back to the ... [inaudible 00:18:59] view, so I'm just going to click that and I'm going to close the graphics and algebra views. I've also opened an Excel document which has some data, so I'm just going to highlight that, and I'm going to paste that there. All right, and now of course you can enter that data.
Just a couple things, we're running short of time, but I can just ... If you highlight, for example, that column, come here, get the sum down here. All right, or if we highlight it again, you can get the main highlighter stuff, so it's very user-friendly and I think your students in particular will find that particularly easy to use, certainly in comparison to some of the spreadsheets which are around.
Okay, look, have a look at the bi variate analysis here. So we're going to use the two variable regression analysis tool, just by clicking there, there are the two data sets, click 'analyse'. The great thing is it immediately draws a very nice scatter plot. You can click on here to change the axes around. What else can we do, we can open this button, and we can remove certain data points, and it automatically redraws the graphs. And come down here, click on 'linear regression', and you can see as I put those back, it's recalculating the line of best fit each time. Of course, we can use this field down here, 'evaluate', I enter for example '185', you remember if you'd had a quick look ... If I remove the original data sets, the height in cm. vs. the arm span in cm. of [inaudible 00:21:01] students.
That incidentally came from the [inaudible 00:21:04] school website, a random sample downloaded from there. So you enter '185' in there and hit 'return', and you can see it returns a value for, is that the arm span? Yes, the arm span in centimetres. So in Stage 5.3, students use lines of best fit to estimate what might happen between known data values, and predict what happens beyond known data values, so that's just a very, very quick look at the spreadsheet view, and if I click here you can see some very nice stacked box plots for that same data set.
So, if you haven't already had a look at it, I would suggest that it's a good idea to do so.
Okay. All right, we're getting close to finishing up now, just working our way through the final few screens. No doubt in the weeks and months ahead, the tasks of programming will occupy a great deal of your time. Before we end this session today, just another plug, a reminder that the latest addition to the implementing new curriculum suite of online professional learning programmes "A Process for programming a unit of learning: Mathematics K-10" is now live, and the course provides a guided approach to curriculum planning and programming for the new syllabus. It's obviously preferable that teachers who participate in the course collaborate with a small team of colleagues, if not the entire faculty, an experienced teacher or supervisor may lead a group of teachers through the course as a presenter, and if the opportunity for collaboration is not available, teachers can complete the course individually and then confer with a supervisor to have their course completion verified on MyPL. So ask your principal to schedule an event at your school with the course currently showed on screen.
Okay, and finally, an e-newsletter out of the United States, eSchool News, is essential reading I think for educators using technology to advanced learning, registration is free. This will give you full access to the eSchool News online website, and you will receive the eSchool News digital [inaudible 00:23:35] via email.
Okay, well that concludes the session for today, and the SyllabusPLUS series for 2013. Please remember to complete your evaluation on MyPL. To do this, the steps are you log onto MyPL, you click on the 'My Professional Learning History' tab, you'll find there a link to this event, scroll to the bottom of the page and then click on 'Post Event Evaluation' and then that's where you enter the required information at the next screen, and enter the post evaluation questions and click 'Submit', so that's the process. There's a selection of files available as I've said throughout the presentation for download now from the files pod in the bottom right corner of your screen. These may also be downloaded from the recording of this session, and the URL of the recording will be e-mailed to all participants probably tomorrow or Monday.
SyllabusPLUS will be back in 2014, we would like to enlist your help in designing a programme of events for the next year, so keep an eye out for an e-mail before the end of the year in which you'll be invited to complete a very brief, I promise, online survey.
Nagla and I would like to wish you all well for what remains of this very busy year, and we hope that you'll find plenty of time in the Christmas break when that eventually comes around to recharge your batteries. Thank you for attending these events, we hope to see as many of you as possible back in 2014, so it's goodbye for now.