Hello all, I’m struggling to find a way to effectively assess learning and inverse functions. In order to do this, students must switch the x and y variables and solve. Multiple choice questions become obvious, while show your work questions would be too tedious to grade all at once. Do you have any suggestions on question types or alternate forms of assessment I could use? So far I have one resequence, a couple of theoretical questions that are multiple selection and multiple choice and a graphing question.
Thanks in advance!
I haven’t taught Inverse Functions before but would love to help if I can. Do you have a list of objectives that you would like students to be able to meet? If you share that list, I’d be happy to give you some suggestions of how they might work with Formative. I’d love to hear other suggestions that @Math_Educators have.
Thanks for the quick reply, I’m looking for a basic understanding of how to calculate an inverse function. Like so:
Given y = x³ - 1 find the inverse function.
The answer would be y = ³√(x +1)
Like I mentioned, there is a process to get there which lends itself great to show your work type questions. However to give 5 show your work type questions makes for a lot of grading. And to give 5 multiple choice questions, would almost be too easy and not a true assessment. I thought about doing more resequencing but feel that would give away the answer also.
Could you somehow embed Desmos to help you?
What about an error analysis question. Show the process but make mistakes, students have to figure out the mistakes. It can be s multiple choice or short response.
Or could you do a fix the mistake question? Give a solution that has one or more errors and they have to circle the errors and explain how to fix it.
I love the idea that @2007236 & @Dawn_Frier1 brought up! It’s a nice balance of having students see the process without having them write out each step. You could create them using a Show Your Work question and drawing out the steps. Then as Dawn mentions, you can have them circle the mistakes and as Yelena mentions, they can “confirm” them in answers to proceeding multiple choice, multiple selection, or short answer questions that may be auto-scored.
Thanks @Dawn_Frier1 and @david for the responses! I’ve got just enough time to build that in. Even though this is off-topic, I wanted you all to know that Formative show your work questions work VERY well with the Apple Pencil and iPad pro. I will probably use that or the canvas to draw the question out in handwriting.
Thank you, @albertbryant for that
I didn’t know.
That’s great to know Albert! I will definitely be sharing that with educators who need recommendations for using the Show Your Work tool!
I just saw this. I like the sequencing… it helps set the ‘pattern’ for working through inverse functions. I also like the graphing the function and it’s inverse to see how they are related. (It’s also a great way for students to see how they are related… .and to check to see if their inverse is correct.)
In addition to the ‘mistake’ problems that were suggested, you could add scaffolded problems… show part of the work and have students type in the ‘next step’ as a short answer. Of course, some problems would be harder to type in as SA. As a work around, students can show their steps in a Desmos graphing tool. As long as they are typing an equivalent equation, the ‘steps’ would all be graphed on top of one another.