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I need to produce at least 30 test/exam papers a year, plus a few assignments and investigations. I have good source material but need to change numbers and contexts and output original papers that meet our curricula/student requirements.

How do you, as a high school mathematics teacher, produce mathematics test papers? I’m interested in methods from screenshot-crop-n-paste hacks to use of advanced typesetting programs.

Most importantly, how do you get consistent-looking graphs and figures? If it were just equations and mathematical statements, Microsoft Word would be sufficient. But figures and graphs are essential.

There are so many programs and packages for mathematics and publishing but what works for producing day-to-day high school test papers quickly?

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  • $\begingroup$ In following up some suggestions below, I also stumbled across Ipe (ipe.otfried.org) which looks useful. $\endgroup$ – lukejanicke Oct 9 '16 at 20:42
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Really great question, I will first start with a general overview of my test-generation workflow and then go into more detail on the specifics below that.

General Workflow For Generating Tests

The first thing that I do when I start to create a test is I go through all of the notes/slides/worksheets/homework from the chapter or unit that I am testing. From these things, I make a list of what specific skills and types of problems that I think students should be able to complete after learning the chapter (I do this before I start teaching a chapter as well, but I always like to redo the list at the end just incase there was something extra that I got into or something that we skipped, for whatever reason). Once I have my list of topics/problem types, I start to search for them. Now, at this point, I do have a pretty large stockpile of worksheets, images, problems, and other assessments all stored digitally so I will usually start digging through them first. If there is something that I would like to have on the test but don't currently have a copy of, rather than trying to make it all from scratch I will do some Googling to see if I can find something that has already been made or at least partially made. Once I find a problem I am looking for, I quickly screenshot it and paste it into a Google Doc. At this point, I am not worried about organization, I am more just trying to collect all of the problems that I would like to use in one place, which I will organize and structure later. Once I have compiled my "collage" of problems, I start to refine them and organize them in Google Docs. Now this part really depends on the specific types of problems and the quality of the screenshots. I try to use the raw screenshots as much as possible, but more often than not, they will either be to low quality to withstand photocopying or they will need to be reworded, so I will usually end up using my screenshots as models for problems and then end up retyping/formatting them. At this point my test is pretty much done. The last step is inserting graphics/charts/etc, which I will go more into below. I find that this general workflow is very efficient for me (usually takes no more than an hour to make a test completely from scratch) and always ends up with an organized and fair assessment.

Finding Problems

Like I said above, I already have a pretty large collection of worksheets/images/problems/etc to pull from. My biggest suggestion for finding problems is to do Google/Google Image searches and just horde anything you can find that is at all relevant on Google Drive. I really like Google Drive for this because it makes it so all of my resources are accessible from anywhere so if I need to make a test over the weekend, I don't have to lug my work laptop home on the train, I can just use my home desktop. It also integrates really nicely with Google Docs, which I prefer over Word for the same "anywhere-accessiblilty". The key to collecting these resources is to keep them very organized, otherwise all the time you save by collecting them will be wasted when you go to try to find a specific problem. I like to make a main folder for each chapter and then subfolders for each specific type of problems/worksheets. It does take some time to find these resources, but once you have them saved and organized you should never need to go hunting for them again. One last thing on collecting problems, it is probably worth a look in your school's basement/textbook storage closet to see if there are any old workbooks or textbooks lying around that you could scan and use. I have found a lot of my best resources digging through the piles and piles of books in the basement.

Working With Images

My main technique for compiling the individual problems into one Google Doc is to use screenshots from worksheets. For Mac, use Command Option Shift 4 and click and drag over the problem and it will automatically get copied to your clipboard which you can paste directly into a Google Doc (you won't have 500 screenshots saved to your desktop this way!). For Windows, I use the Snipping Tool. Just save as image and then drag into Google Docs. If the problem you found was already an image then even better, just drag into Google Docs! Once in Google Docs, I will further manipulate the images to try to get them to work for the test without having to retype the whole problem. Your best friends will be Crop (right click the image and select Crop Image) Image Options (right click the image and select Image Options). Cropping is super-useful to get rid of the numbering of problems on worksheets, or to reduce the whitespace around an image so that it will fit better in with the rest of the problems. I use the Image Options to adjust the brightness and contrast of images to make them more readable. This doesn't always work, depending on how low-quality the original image was, but it usually is enough to make an almost-readable problem, into a totally-readable problem. The last trick for working with images in Google Docs is to take advantage of the different image modes: Inline, Wrap, and Break (appear in Google Docs when you click on the image). I use the Wrap Text mode for all of my images, because this allows me to manually position them wherever I want on the page and not have to worry about dealing with tons of spaces and returns.

Graphics and Diagrams

For the most part, I try to recycle diagrams and graphics from problems that I have saved in my collection. Just Crop out any of the text, leave the diagram, and reuse for a different problem. For instance, if the test is on parallel lines cut by a transversal, no need to make my own diagram. Just find one already made and tailor whatever problem you want on the test to fit to the numbering/labelling/etc on the diagram. If I really have to create my own diagram for a test I use one of two applications: either Geogebra or Geometer's Sketchpad. They both have a slight learning curve but with about half an hour of practice you should be off and making whatever diagrams you would like. I have recently been using Geometer's Sketchpad, only because my district has a bunch of licenses, but Geogebra is great as well and I have made a ton of diagrams with it. What I will usually do is screenshot directly from Geometer's Sketchpad/Geogebra into the test and then save the actual file later just incase I want to tweak the diagram in the future. If I want to make a graph, I will use Desmos and just screenshot. You can do graphs in Geogebra but it is a bit annoying. To organize my custom diagrams, I will usually make a Google Doc for each category of diagram (triangles, quadrilaterals, graphs, etc) and just copy and paste the screenshots into there without worrying about formatting. This way, I don't have to find and open the original file if I want to reuse the diagram, I just go to the Doc and Copy Paste.

Reusing Tests

Generally, after I have made a test and have students take it, I will make notes of bad questions or confusing directions and then immediately update my file with the changes. Then, the next year when I go to administer the same test it will already have the improved language and I won't have to try to remember what didn't work about it. For the most part I will reuse tests and just change the specific numbers in problems and the order of the problems from year to year. I have never had an issue with students from a previous year giving current students old tests because even if they do do this, the updated numbers and different order of questions is typically enough to negate having access to the previous versions.

I hope this helps, I will update this answer if I can think of anymore tricks/hacks/techniques that I use. But for the most part screenshot, crop, and reuse are the words I live by when generating tests.

Also side note, Kuta software is an amazing application and I highly suggest trying to get your hands on a copy. I rarely use it to make chapter or unit tests but I almost always use Kuta for larger cumulative exams like midterms and finals because it is just so fast and is completely customizable and can totally randomize and easily generate many different versions of the same test. I do use Kuta heavily to generate homework and classwork handouts too, again because of its amazing ease use.

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  • $\begingroup$ I don’t have a collection yet but I appreciate the other aspects of your workflow you describe. I have GeoGebra and just need to use it more. $\endgroup$ – lukejanicke Oct 9 '16 at 20:40
  • $\begingroup$ "screenshot, crop, and reuse" I'm not sure this an appropriate description, unless you actually mean to advocate producing exams like a robot. $\endgroup$ – Buffer Over Read Oct 9 '16 at 23:38
  • $\begingroup$ @TheBitByte I understand your concern and the actual decisions on which questions to use should be anything but robotic, but I tried to answer the question as directly as possibly by strictly sticking to describing my method of production for tests, which should be as efficient as possible, especially for a high school educator. As for the content of the test, that is an entirely different matter and a separate question. $\endgroup$ – celeriko Oct 10 '16 at 2:03
  • $\begingroup$ Is your method optimized for quality, speed, or both? $\endgroup$ – Buffer Over Read Oct 10 '16 at 21:37
  • $\begingroup$ @TheBitByte both, the part that I outline here is mostly for the speed aspects, but the part that I didn't really get into which is researching new problems and stockpiling a collection of them is where the quality comes in. I guess it wouldn't be streamlined for quality per say, as it does take some time to do the research and collect the problems, but once i have them, i have them forever. $\endgroup$ – celeriko Oct 11 '16 at 18:48
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Disclaimer: I do not teach high school, and this isn't the easiest startup option.

But if you don't mind a bit of a learning curve, I would suggest using LaTeX, which is very customizable and (key) will allow for easy reuse and renumbering and re-everything. Some college instructors use SageTeX with it for creating graphs or randomization, though one can also use TikZ for that; on nice feature is that you could change some numbers on a harder problem and have it compute the answer key for you as well.

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  • $\begingroup$ Also: there are packages that let you write the answers along with the questions, then set easy switches to print an answer sheet or display them or not. The learning curve is steep, but you can get lots of help at tex.stackexchange.com $\endgroup$ – Ethan Bolker Oct 9 '16 at 14:40
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    $\begingroup$ I think I can handle the learning curve. Time to start. $\endgroup$ – lukejanicke Oct 9 '16 at 20:29
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    $\begingroup$ It’s been a year but I am now proficient with most LaTeX mathematics, and I use a Markdown editor that live renders it. I installed BasicTeX and can input LaTeX in Ipe (ipe.otfried.org) for figures and graphs. On the web, I’ve experimented with MathJax and KaTeX for rendering on my own webpages. Thanks for your suggestion. It’s gone a long long way! $\endgroup$ – lukejanicke Jan 7 '18 at 5:59
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As a community-college math lecturer, my primary course-preparation tool is the Pearson TestGen program. Pearson provides pre-made testbanks to accompany all of their textbooks; so you can begin by drag-and-dropping selected questions into a test of your construction. Thereafter you've got a single push-button functionality to randomize values within questions, scramble the order of multiple-choice options, etc. Math formula editing is straightforward. You can even export a test to the Blackboard learning management system, if desired (which is how I make tests and quizzes on Blackboard; easier than BB's own interface).

TestGen is free but requires an instructor account with Pearson; contact a representative and hopefully you can get one.

enter image description here

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    $\begingroup$ Never knew about this, my school uses Pearson, I need to see if we have access to this, thank you! $\endgroup$ – celeriko Oct 8 '16 at 17:49
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    $\begingroup$ That program seems to provide a complete solution. And it’s free. Great. $\endgroup$ – lukejanicke Oct 9 '16 at 20:27
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For creating graphs, I almost always use Desmos.com to plot the graph and then I screenshot it to paste into Word. Desmos let's you graph pretty much anything you'd want.

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  • $\begingroup$ Desmos + screenshot = Simple and fast workflow. +1 $\endgroup$ – lukejanicke Oct 9 '16 at 20:30
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I teach elementary school and also create tests for middle school students. I suspect some of my techniques could be used in high school. I have Smart Notebook software on my computer. This is free because I have Smart Notebook in the classroom. I have found it is terrific for diagrams, particularly geometric ones. I also use Microsoft Word with MathType by design science which I found sufficient for all equations and easier (for me) than LaTex which is also popular. For graphs, I have used TI Connect software (from Texas Instruments) to take screenshots of my graphing calculator. If you google screenshots of TI 83, you can find different methods and products. Good Luck.

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  • $\begingroup$ TI software + screenshot = simple/fast. Great. We also use a TI calculator and I think our school has licenses for software. $\endgroup$ – lukejanicke Oct 9 '16 at 20:31
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Maybe my LaTeX template will be helpful to someone. It's a relatively short LaTeX code producing 24 different versions for 4 tutorial slots where students sit by 6 at each table. It's a bit tricky to auto-generate solutions, especially for the first question, but let me know if you're interested - I'll figure it out.

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  • $\begingroup$ Nevermind auto-generating solutions. How did you auto-generate variations in the questions? Or are those numbers manually changed? (New to LaTeX.) $\endgroup$ – lukejanicke Oct 13 '16 at 9:17
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I used Word for most questions, and for formatting. For graphs (in Algebra I and II) I would insert a grid and then draw on the grid with Word's tools or by hand. I think LaTeX is very promising despite its relatively steep learning curve. Other images that I needed were typically drawn or cropped from other sources.

However, I would like to persuade you to work with your local colleagues. Especially important if you are not the only math teacher in your school, but worth cultivating relationships with neighboring schools if you are on your own. You should use a format that is compatible with the people you are most likely to share materials with. Being able to share resources conveniently with other teachers will be more valuable than any particular workflow or format. Furthermore you may find that some of your colleagues may have some great ideas.

Working with others will help you refine materials to create better resources as you will have more time and more sets of eyes on each piece. I like using shared resources because they tend to have a more diverse style of questioning than I would write by myself. The process of refining materials is much easier to do if you don't have to create so many of the resources you need.

You may have to deal with some inefficiency if some of your colleagues are stuck in their ways, but I have found that to be minor compared to the time saved by being able to share resources. Introducing new programs has had some success, and I think it is more likely to be successful if you're willing to learn your colleagues way of doing it before you ask them to learn yours.

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  • $\begingroup$ Yes. We are a small international school. But there is a network I can go to. $\endgroup$ – lukejanicke Oct 13 '16 at 9:12

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