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“You don’t start out writing good stuff. You start out writing crap and thinking it’s good stuff, and then gradually you get better at it. That’s why I say one of the most valuable traits is persistence.”
— Octavia E. Butler
There is definitely some truth on what writer Butler says about writing. Writing good stuff is hard! This is no different when it comes to writing high quality educational content for mathematics where abstract concepts need to be digested and nicely explained. Writing something simple and appealing can take many weeks and many many drafts.
In what follows, we will dive into the process of writing educational math content using our platform. We will get insights from our most experienced authors and answer questions such as: What goes inside the heads of our authors when designing an exercise in the platform? How they need to anticipate the mistakes that students might do when solving an exercise and how this is used in designing useful feedback. We’ll also share a step-by-step guide our authors use when creating theory pages and exercises.
Imagine you are an author at SOWISO and you need to create an exercise for a specific topic in mathematics, for example differentiation of polynomials. Since you are an experienced mathematician you don’t need to fear about not understanding the topic, you got this. Now, how to communicate it? This is where the challenge begins.
First of all, it is good to know your audience and their expectations on the content. Who are they? What is their perspective towards math? What do they want to get from your content? How would the content be used?
The answers of these questions will help you shape the content, narrative approach and level of difficulty of the theory and the exercises. Once you get clear answers, you are ready to start designing your material.
To grab inspiration, it is always important to have some good and well established references at hand. These could be well known math textbooks or other online trustworthy resources. Still, the key ingredient for designing a nice math exercise is creativity. This is one of the fundamental skills of an author.
Creativity plays a crucial role in designing interesting exercises, in creating interactive figures illustrating the theory, as well as in explaining the solution of an exercise so that it is easy to follow. A nicely explained solution is one that can be taken by the student and be reused for similar math problems. Moreover, you need to be creative on how to use the programming tools used for designing open exercises in SOWISO. So, as an author, you not only are proficient in mathematics but also in basic programming. Having this ability will make things easier when designing more challenging math exercises and feedback that helps the student with their mistakes.
Creativity is not only important when designing the questions or solutions of an exercise. It is necessary for imagining what are the possible errors that students might make in their process of solving it.
Every student is different and there are infinite possibilities for errors, so anticipating all of them is of course an impossible task. Still, not everything is lost. The reasoning patterns of a human mind at the schooling stage are somehow not so different from other minds when it comes to learning mathematics. In simple words, the errors students can make in a certain exercise often can be identified as having a similar nature or being of the same type. This way, our authors can identify the most common types of errors which will cover the most recurrent cases.
Here is a step-by-step guide that our in-house authors use for the creation of theory pages.
Books, syllabuses, online sources like videos or well established mathematical/educational forums will help you decide on the concepts, ideas, and results that you want to address in your theory pages.
We, as educational writers, can sometimes overdo our explanations which might be counterproductive and create confusion. It is important to know how much information we want to give to the student. Our motto is ``less is more”, but of course this is not so easy to achieve. Identifying core ideas among an ocean of information is crucial for creating simple but informative theory pages.
Accompanying the theory with intuitive and interactive graphics is a must for capturing the attention of the learners. You can plug in Geogebra applets or images directly in the pages.
Providing many examples will help the learners to connect the dots between the abstract concepts presented and the way to implement them. For this, it is enough to write two or three examples and make use of the power of randomized variables.
Something useful for the student is to add a SOWISO’s subject specific glossary. This contains the core concepts used in the topic the author is writing about. So when the student places the mouse pointer on a term belonging to the glossary, a tiny window with the definition of the term will appear. It works as having your math-dictionary next to you at all times.
Here is a step-by-step guide that our in-house authors use for the creation of theory pages.
By having this clear, you can know what level of difficulty you will require from your exercises.
It is always better to start designing simple exercises where the main intuitions are tested and, exercise by exercise, transition into questions that increase the level of analytical reasoning.
These are what we call Sets in SOWISO and are our students’ favourites. It is a very useful way to break down complex mathematical problems into simpler exercises.
Hints really make a difference for those that are struggling with math. You can think of hints as breadcrumbs leading the students to a mental place for understanding the problem and the strategy for solving it.
Useful feedback allows the learners to learn from their mistakes. Authors can write feedback rules for the most common mistakes made by learners. We will elaborate more on this in the following section.
Your feedback rules should be triggered in the right way and for the right mistakes. To check this, you can make use of the functionality test scenarios present in many exercise types (open and open free). Here, you can write possible common mistakes that you want to link to the feedback rules you have created and test that the right feedback will be presented to the learner.
For each type of error, you can create a feedback rule that will be triggered in the platform when a student makes precisely that mistake. The feedback should be able to guide the student back in the right direction for solving the exercise.
Something important to have in mind when creating feedback is to give information that helps the student to re-think their reasoning steps but without giving away the correct answer. Part of the learning process is to learn from one’s mistakes, so you as an author should give enough room for that. Another important aspect when creating feedback is to put yourself in the shoes of the student. This way you can have a better understanding of what kind of details to write in your feedback. You want to avoid being too general, so writing things like “Your answer is wrong, check your calculations again” is a no-go.
Something to have in mind is that, with SOWISO, you can distinguish between positive feedback and negative feedback. Authors should use the power of such distinction! Positive feedback gets triggered when the student’s answer is correct but it does not correspond to the required forms. SOWISO’s intelligent system can still allow for multiple correct answers and discard the ones that we want to avoid. Think of an exercise asking to calculate $6+2$ and express it in the form of a fraction. We don’t want the student to answer $6+2$ which indeed is equal to $6+2$ or to answer $4+4$. We want the student to answer things like $\frac{8}{1}$ or $\frac{16}{2}$. SOWISO will identify all of these answers as correct, but by means of positive feedback, the author can let the student know that $6+2$ or $4+4$ are not in the desired form.
How does the platform “knows” which feedback to present to the student? For this, you as an author need to tell the platform about the type of errors expected for each particular exercise by using a bit of programming. There are various layers of programming code acting in this respect. The good thing is that, for the most part, SOWISO’s team of developers has taken care of that. Still, an author needs to identify the type of code that will correspond to the type of error in mind.
Coming back to the wise words of Octavia E. Butler shared at the beginning, there is one inevitable process that every writer needs to go through. That is constantly revising their work.
Only by the process of change and transformation of content that comes with rereading, rethinking and rewriting is that solid and clear ideas can be communicated. In the context of writing for STEM education, authors have noticed that this process of revising is, without a doubt, necessary for connecting thoughts, concepts, and results across multiple topics addressed in a digital math course.
The authors at SOWISO are not alone in this task. Our team of editors are key commentators and information architects for shaping the final version of the content. They work hand to hand with authors on making the theory and exercises of the best quality possible.
It is known that the best textbooks in mathematics have been written in approximately 8 or 10 years. Patience is essential for accomplishing a great final result. However, a final printed book is no longer subject for continuous improvement. It can take many years until a new improved edition comes in!
Improving the content directly on the go is an important aspect of the high quality standards we have in SOWISO. Most of the improvements come from the direct feedback we receive from the users: professors, educators, and teachers who, by using the material with their students, can pinpoint the ways in which we can make things better. Who better than them to evaluate and improve our content.
Our team of authors hopes that you find these tips useful!
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