Most of the GeoGebra articles on this site demonstrate the power of GeoGebra for junior high school mathematics. The articles aim to encourage those mathematics teachers who are not utilizing GeoGebra (or similar dynamic geometry software) as a regular demonstration tool, to start doing so. I have reason to suspect the portion of mathematics teachers not yet regularly utilizing GeoGebra (or similar) to be significant. The common reason for this, I summize, is a lack of awareness. It is logical to assume that the following misconceptions are held by these teachers:
For many teachers the reason will be simpler – they simply do not yet realize how powerful GeoGebra is, even when used as a simple demonstration tool. In the article Let GeoGebra transform your math teaching I show how using GeoGebra as a demonstration tool can revolutionize the impact a teacher has on their students’ engagement and understanding. Importantly, this can be achieved simply by employing the pluginthedataprojectorandshowthefile method. It is the one opportunity a math teacher has to make an immediate and significant impact on the engagement of and understanding by his students without having to make wholesale pedagogical changes. In this article, we look beyond the pluginthedataprojectorandshowthefile method into an even more powerful use of GeoGebra, that of studentled GeoGebra investigations. Unlike simple, teacherdirected demonstrations, studentled GeoGebra investigations do require a different pedagogy to the traditional procedural approach in addition to considerable planning for the uninitiated teacher. Five tips for studentled GeoGebra tasks:
Let’s consider two categories of studentled investigations:Category 1) Beginner investigations: for students who are new to investigations and/or less likely to stay ontask. Category 2) Advanced investigations: for students who are selfstarters and enjoy investigating mathematical systems in a selfdirected manner. NOTE: When introducing such an activity (i.e. an activity requiring a departure from tradition), the potential positives are high as is the chance for glorious, dismal failure!! Many factors, therefore, need consideration, the first of which is the students. Engagement.Generally speaking, how engaged are your students? Are they familiar with studentcentered activities? How do they respond to them? Do some students tend to veer off task at the first opportunity? Is the class difficult to manage? If yes, are you hoping that a student centered GeoGebra investigation might help win them to your cause? Where disengagement is the norm it is important to understand that introducing technology per se won’t fix the problem. Disengagement can be turned into engagement using a range of strategies. My point is that the information in regard to how to turn disengagement into engagement is way too extensive for a short article. I will say this though – teachers with classes where students are not particularly engaged but where the situation is manageable are encouraged to trial a GeoGebra investigation as long as steps are followed to maximize the chance of the activity being a success, as suggested below. For those who teach functional, generally motivated students who are prepared to explore mathematical systems, you are clearly ready to proceed. Teach basic skills first, using selfdirected notes or videos.First things first. You will need to teach students some GeoGebra skills before expecting any fullscale investigation. In other words, don’t plan for or expect any structured investigations at the same time as students are learning the skills. Allow the initial investigation to be ‘play time’. Students will naturally want to play anyway so why cause an unnecessary war. Rather, make their play match your cause. Teach the basics and ask them to play (explore, investigate) but don’t cloak this in mathematical investigation language. As an example, after teaching students how to create lines, segments, perpendiculars, circles and arcs you might ask them to create an ‘award winning’ design. Or set them a challenge, for example, “Using these 5 objects in a total of 20 ways, see how many closed spaces you can make.” In regard to the skill instructions, deliver them via student centered printed handouts or videos. Stress to students that they must READ (or WATCH) the instructions and follow them. Don’t allow students to ask you or anyone else any questions relating to the instructions unless they have read / watched the instructions twice. When they do ask you, get them to read the instructions back to you. Lead them to finding the answer. Be aware that many students will want you to spoon feed them, because that’s all they know. Your task is to wean them off the spoon feeding. It won’t happen overnight! Make the investigations openended.Beware of the temptation to make the investigations highly prescriptive, that is to overtly steer students into discovering what it is that you want them to discover. Prescriptive and complex instructions detract from the investigative experience. However, prescriptive investigations have their place – they are appropriate as beginning (Category 1) investigations. Scaffold the investigation.The number one reason for student investigations failing, especially with students who are unfamiliar with such tasks, is a lack of scaffolding. The form the scaffolding takes is up to you. One option, ideal for Category 1 investigations, is to build ‘construct files’. A construct file is a GeoGebra file with the instructions written inside the file. Assuming students know how to execute the specific skills, construct files are excellent because they guide students into creating a file without requiring them to refer to another instruction source. To see construct files in action spend a minute observing the two dynamic images displayed in this article. They both feature construct files which deliberately steer students into a particular understanding. Now I realize we just established above, that investigations need to be openended. However, as category 1 investigations, the files on display here could be ideal. But once you move beyond Category 1 into more advanced investigations the suggestion is to make the investigations as open ended as possible. Construct files could also be used for this purpose. Another reason to scaffold an investigation is to reduce the amount of time the investigation will take. An example of such a scaffold would be to deliver a partly built file to students. Rather than expecting each student to spend 20+ minutes building the same file, construct the basis for the file yourself and allow students to explore. Using a similar figures investigation as an example, the initial file could contain similar figures which move in tandem. The investigation could then be for students to explore the ratios of side lengths, areas and volumes of the similar figures. Obviously students will need to first learn how to create dynamic formulas. Encourage collaboration.Ideally, investigations are collaborative. Therefore encourage and/or engineer collaboration to occur, especially for the advanced (Category 2) investigations. If you’d like to become proficient with GeoGebra, an ideal way is via the course Geometry – Become a proficient, inspired practitioner. Note also that the course is set up so that multiple teachers from the one department can participate as a Team. Here’s what one participant wrote after competing the course: GeoGebra is a tool which I use to improve student engagement and understanding. It is very rewarding to see students independently exploring a topic in order to Other articles containing dynamic demonstrations of quality GeoGebra files:
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AuthorRichard Andrew likes to write about stuff that matters in education. That boils down to 'anything that helps teachers to betterengage their students'. His view? "Not much else really matters  engaged students learn. Disengaged students do not." ArchivesCategories
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