Over the last year, my school has set up to run the PGCEi course (an international version of the theoretical part of the PGCE) alongside its own ITT system. We are the first school to set something like this up in South America, and it has provided a great opportunity to many existing teachers (to get a UK based teaching qualification) and also as a way to train new teachers. Teacher training is an area that I looked at before moving abroad, and I ran some sessions on using Autograph in the classroom, both for the mathematics PGCE trainees at Oxford Brookes and also for several local mathematics departments. But this new endeavour at my school has allowed me to take this one step further, and I am now acting as a mentor to a teacher doing the PGCEi. This course is very different to the PGCE offered in the UK. Firstly, it is only the theoretical elements of the course, and as such, does not actually qualify teachers to teach in the state system in the UK. As mentioned above, my school is suplementing this theoretical part with its own ITT program, which assigns a mentor to each trainee, and also puts on some workshops for them. I have been mentoring a new teacher in maths teaching, and have found the experience to be very interesting, and a great way to develop my own practice further as well. Another major difference to the PGCE course in the UK, is that she is teaching a full timetable of her own classes. I am observing twice a week, and finding time to sit down to discuss both these observations and how the week has gone more generally. In these observations and discussions, although the focus has clearly been on developing her own teaching methods and reflecting on her practice, I have found that in doing so I am also reflecting on my teaching practice more than I used to. This is both because of things I have seen her do, and also ideas that I am giving her (which I remember from when I did my training, but never really got around to implementing). I am really enjoying this new aspect of my job, and it is definitely something I would like to continue to work on at the moment.
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This year my school got a subsciption to www.mathster.com, and I have been using it over the last couple of months, mainly in support of the flipped classroom that I am using. Introduction Mathster advertises itself as a total solution for delivering the UK Curriculum Mathematics. I should state that I do NOT teach the UK curriculum as I am currently in teaching in a school in Lima, Peru. We teach the Cambridge IGCSE and IB. For this reason, I cannot really comment on its matching to the new UK curriculum, but I will give a general overview of this amazing resource. The Question Bank There are several sections to the site, but the main area of interest is the Question Bank. This is where you choose the types of questions you would like ot include in the current assessment. You choose the age range that you are teaching, the area of mathematics within this key stage, the topic and finally the subtopic that you want a question for. Now you get the choice of the different question types available for this subtopic. By clicking on the question a popup appears with that type of question. You can click the "Regenerate Question" button to create a new question with new numbers. This will give you an idea of the random element to the questions (which I will discuss further below). You can then add up to 10 of this type of question to the current assessment, by choosing the number to add, and pressing the "Add to Assessment" button. If you particularly like the shown example (the numbers work particularly well), then you also have the choice to lock those numbers in place. In my opinion, one of the main strengths of the system of Mathster is that the questions are all randomly generated (obviously this is something that I like, as most of my website is based on this premise). This means that every time the assessment in regenerated, the questions will be the same but with different numbers involved. We shall see how this effects each of the main options as we go through them. Once the questions are added they appear in the right hand part of the screen, and you have the option to reorder them, and adjust the number of points available for each question. You then have to choose how you want to use these questions. IWB Mode The first option is to use them directly on the IWB. You then have three options: Timer; Slideshow; Display all. The timer option sets a time limit to the questions, the slideshow allows you to move through the questions at your own pace, and the display all is great for a differentiated task, where different students can focus on different questions. In all of these modes, you have the option to regenerate the question at anypoint, so if the class has not fully understood, you can just display another question of the same type with a different set of numbers. This is perfect if you want to use the questions with the whole class as examples, or a quick starter/plenary. Video/Online Assessment The second option is the one that I have been making the most use out of in the flipped classroom. You can set the questions as an online assessment. To do this, you have to set up a class first, and give students their login details (this is a breeze to do), and then assign the assessment to that class. You have several options, such as the dates that it will be available, and how many attempts you want to allow per question. With the assessment set, student log in and it appears in their homepage user interface. They then type their answers into the relevent answer boxes, and submit their answers as they go. There is a working out pad built into the system, which records all their working, and also a calculator available (if you choose to allow it). The power of the random questions comes into effect here as well, as every student is given different numbers (so copying is impossible). After they answer each question, they are given immediate feedback as to whether they are correct or not, and if you allowed multiple attempts, they can try and correct any mistakes. This system as I have described it is a fantastic resource for homework, but it gets even better. As students answer questions, they are recorded in real time in your Grade Book. You can click on each individual assessment for each student to see there answers (and any working out that they did on the working pad). You can then award points for their answer as appropriate, and use the built in messaging system to give feedback to the students within the Mathster interface. You can also leave general feedback on the assessment, and this and the final mark are both recorded in your online gradebook. You can also add external grades to the gradebook with a single click, and download the whole gradebook as an Excel file (with or without your feedback). The real benefit for me in using the flipped classroom is that I can also attach a video to this online assessment. So when students open the assessment, the first thing they see is the video, and then when it finishes the questions appear. Alternatively, even better, you can set the video to stop at a certain time to show the first set of questions, and then restart when these have been completed before stopping again for the next set. It also has a system to record your own videos (though I have not used it as I use another program to make my videos available on YouTube). One other nice feature is what is called thee Secret Code. This allows you to set a code, which students can choose to use once during an assessment to be taken to a mathematical game to play for 5 minutes before being taken back to the assesssment. This is a nice way to give students the opportunity to have a small break and allow their brains to relax for a moment before continuing. Worksheet The final option is to turn it into a printed assessment. This is easily done, and you can add options such as the title, a box for students name, a smiley face selfassessment box, show the points available or not, add clip art to the worksheet, and borders and backgounds. You can regenerate each question individually until you get ones that suit your needs, and then export either as a PDF (not editable but much faster) or a Microsoft Word .docx file (which is fully editable, but has fewer options). Obviously, the answer sheet is also created. This is a great way to create a worksheet for practice, but also for creating tests and exams. You can have a set assessment, and each year, simply regenerate it with different numbers. And all this in a matter of minutes! Other Areas of Mathster There are many other great features in Mathster. There is a set of stock assessments that have been put together for a large number of topics across all age ranges. You can also share all your assessments with the other members of your department so you can all use them with your classes. Another nice feature is the Report Wizard, which I have not used yet, but has a variety of stock phrases to help build reports quickly and easily. Within each class that you set up you also have the ability to view your gradebook (as discussed above), send messages to students, add or remove students throughout the year, and also set a seating plan (either manually or by using the random option). Overall Review
Mathster is a fantastic resource for all Maths teachers. The question bank allows you to utilise random mathematical questions in a variety of setting which will suit every teacher in some form. The printed worksheets are invaluable, and so easy to generate, and the online assessments provide a fantastic way to keep track of student progress through the automatically updated gradebook. I would not look back, and know that I will be using Mathster for many years to come. An A* product! I had a really great lesson today. I am teaching IB Standard Level, and they need to know the effects of changing the original data by a linear transformation, and what this does to the mean and the standard deviation of the data. I started with the simple question shown below from Autograph, where I used the raw data function to create a random sample with a normal distribution, and then plotted this as a histogram. I then asked students to calculate the mean, median, mode, IQR and standard deviation of the data. We also discussed the fact that this was an estimate as the data was grouped, and compared these statistics with the statistics of the raw data using Autographs statistics box. After this we got into the main part of the lesson, and I have made a brief video explaining how to use Autograph to investigate what happens to the statistics of data as you perform a linear transformation on the original data. If you would like the Excel file I showed briefly at the end of the video, it can be downloaded here. Just press F9 to generate new questions.

Dan RodriguezClark
I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice. Categories
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December 2018
